The subject of this thesis lies in the field of many-body theory. This field emerged from the aim to understand the behavior and characterize the properties of many-body systems. When the systems considered are large, the interactions between the elementary constituents of these systems can construct phenomena which may be very different from the behavior of the constituents considered as separated. In an attempt to describe these large systems, these very interactions complicate the description far beyond the computational possibilities. In order to study the collective behavior of the interacting elementary constituents, the complexity of the interaction between them calls for simplifications. All physical approximations made in order to advance in understanding the behavior of many-body systems constitute the field of many-body physics. Within the field of many-body physics, the Green Function Theory describes the behavior and the properties of a system with the aid of an object called the Green function. The Green function is the probability amplitude of finding a particle that has been inserted in the system at (r', t') and removed at (r, t). Since between addition and removal the particle propagated through the system interacting with all other particles, the Green function contains information about its properties. In the Green Function Theory, the interactions of an electronic system i.e. the effects of exchange and correlation, are incorporated into the so called self-energy operator. There are different possible approximations of the self-energy and they completely determine the properties of the system. One of the most widely used approximations of the self-energy is the GW approximation. In this approximation, the self-energy operator is the product of the Green function that describes the propagation of particles and holes in the system, and the dynamically screened interaction which describes how the bare interaction between electrons is modified due to the presence of the other electrons.

We have developed a time propagation scheme for the Kadanoff-Baym equations for general inhomogeneous systems. These equations describe the time evolution of the nonequilibrium Green function for interacting many-body systems in the presence of time-dependent external fields. The external fields are treated nonperturbatively whereas the many-body interactions are incorporated perturbatively using Φ-derivable self-energy approximations that guarantee the satisfaction of the macroscopic conservation laws of the system. These approximations are discussed in detail for the time-dependent Hartree-Fock, the second Born and the GW approximation.

We perform GW calculations on atoms and diatomic molecules at different levels of selfconsistency and investigate the effects of self-consistency on total energies, ionization potentials and on particle number conservation. We further propose a partially self-consistent GW scheme in which we keep the correlation part of the self-energy fixed within the self-consistency cycle. This approximation is compared to the fully self-consistent GW results and to the GW₀ and the G₀W₀ approximations. Total energies, ionization potentials and two-electron removal energies obtained with our partially self-consistent GW approximation are in excellent agreement with fully selfconsistent GW results while requiring only a fraction of the computational effort. We also find that self-consistent and partially self-consistent schemes provide ionization energies of similar quality as the G₀W₀ values but yield better total energies and energy differences.

Multiconfigurational wave functions are calculated for a series of Fe complexes. We find a linear correlation between the experimental ⁵⁷Fe Mossbauer isomer shift and the calculated electron density at the Fe nucleus. However, the analysis of the wave function in valence bond terms shows that there is no straightforward relation between the density at the nucleus and the Fe charge. The analysis of the CASSCF wave function expressed in localized orbitals shows that the isomer shift is very sensitive to the weight of charge transfer con- figurations and hence to the covalency, rather than to the absolute charge.

In this thesis we developed the time-dependent version of the multicomponent density functional approach to treat time-dependent electron-nuclear systems. The method enables to describe the electron-nuclear coupling fully quantum mechanically. No Born-Oppenheimer approximation is involved in the approach. The multicomponent density functional theory is formulated for an electron-nuclear system in the body-fixed coordinate frame attached to the nuclei. It allows us to describe properly the internal properties of the system. The nuclei in the system are described by the diagonal of many-body density matrix which depends on all nuclear coordinates. In the Kohn-Sham picture this density matrix is calculated from an equation with a time-dependent potential that depends on all nuclear coordinates. For the diatomic molecule in the stationary case this potential turns out to be very close to the familiar Born-Oppenheimer potential. However, the Kohn-Sham scheme goes much beyond the Born-Oppenheimer picture in allowing an exact quantum description of the motion of the nuclei. As a consequence of the body-fixed frame transformation the external potential acting on the electrons, which is a one-body potential in the laboratory frame, becomes a many-body potential u with respect to the nuclear coordinates in the body-fixed frame.

This dissertation presents the results of theoretical investigations of the electron distribution in crystals. Electronic and magnetic properties can be investigated using the theory of quantum mechanics developed at the beginning of the 20th century. The increased power of computational tools enables nowadays the treatment of more and more accurate models to simulate electron motion in crystals or molecules and complement experimental observations and interpretations. Crystals containing transition metal elements are studied in many laboratories for the complex behavior of electrons leading in some cases to intriguing properties like superconductivity or magnetoresistance. These properties are often intimately connected to the open shell character of the transition metal ions, which are susceptible to adopt different electronic configurations and oxidation states depending on their environment. This dissertation focuses on the distribution of electrons between transition metal and ligands and discusses various definitions of oxidation state and charges for the transition metal ions and compares with estimates on the basis of different experimental techniques.

We present here the discrete reaction field (DRF) approach, which is an accurate and efficient model for studying solvent effects on spectra, chemical reactions, solute properties, etc. The DRF approach uses a polarizable force field, which is (apart from the short-range repulsion) based entirely on second-order perturbation theory, and therefore ensures the correct analytical form of model potentials. The individual interaction components are modeled independently from each other, in a rigorous and straightforward way. The required force field parameters result as much as possible from quantum-chemical calculations and on monomer properties, thereby avoiding undesired fitting of these parameters to empirical data. Because the physical description is correct and consistent, the method allows for arbitrary division of a system into different subsystems, which may be described either on the quantum-mechanical (QM) or the molecular mechanics (MM) level, without significant loss of accuracy. This allows for performing fully MM molecular simulations (Monte Carlo, molecular dynamics), which can subsequently be followed by performing QM/MM calculations on a selected number of representative snapshots from these simulations. These QM/MM calculations then give directly the solvent effects on emission or absorption spectra, molecular properties, organic reactions, etc.

In a previous study of the 3s X-ray photoelectron spectra, XPS, of Mn, we identified a new intraatomic many-body effect that lead to an ~50% increase in the predicted exchange splitting of the main high spin and low spin XPS peaks. The new many-body effect involved the promotion of one electron from the M shell, 3s, 3p, and 3d, into a 4f orbital and a redistribution of the remaining electrons over the M shell orbitals; of particular importance were frustrated Auger configurations. FAC's where the 3s shell was filled. In the present work, we demonstrate the general importance of these 4f FAC's by showing that they are of comparable importance for increasing the 3s exchange splitting in Ni as they were in Mn.

Novel mononuclear, trinuclear, and hetero-trinuclear supermolecular complexes, [Co(phen)₂(H₂O)(HTST)].2H₂O (1), [Co₃(phen)₆(H₂O)₂(TST)₂].7H₂O (2), and [Co₂Cu(phen)₆(H₂O)₂(TST)₂].10H₂O (3), have been synthesized by the reactions of a new tri-sulfonate ligand (2,4,6-tris(4-sulfophenylamino)-1,3,5-triazine, H₃TST) with the M²⁺ (M=Co, Cu) and the second ligand 1,10-phenanthroline (phen). Complex 1 contains a cis-Co(II)(phen)₂ building block and an HTST as monodentate ligand; complex 2 consists of two TST as bidentate ligands connecting one trans- and two cis-Co(II)(phen)2 building blocks; complex 3 is formed by replacing the trans-Co(II)(phen)₂ in 2 with a trans-Cu(II)(phen)₂, which is the first reported hetero-trinuclear supramolecular complex containing both the Co(II)(phen)₂ and Cu(II)(phen)₂ as building blocks. The study shows the flexible multifunctional self-assembly capability of the H₃TST ligands presenting in these supramolecular complexes through coordinative, H-bonding and even π–π stacking interactions. The photoluminescent optical properties of these complexes are also investigated and discussed as well as the second-order nonlinear optical properties of 1

In this report, we will give an overview of Density Matrix Functional Theory (DMFT). In the first part we will discuss the extended Hohenberg-Kohn theorem for non-local potentials, which claims a one-one mapping between the groundstate wavefunction and the reduced density one-matrix. The eigenequations for the natural orbitals are derived, which provide a means to apply DMFT in practice. The main part of the report consists of the discussion of several functionals which have been proposed to include electron correlation. Of the 5 discussed functionals (BB, GU, BBC1, BBC2 and BBC3), BBC3 performs best for the potential energy curves of small molecules. It is however not applicable to infinite systems, such as the homogeneous electron gas. A universal functional remains to be found.

The hydrothermal reaction of Co(NO₃)₂.6H₂O and a newly designed ligand H₂DCNT yields a three-dimensional polymer [Co(DCNT)(H₂O)]_n (1), H₂DCNT=2,4-bis(4-carboxyphenylamino)-6-diethylamino-1,3,5-triazine. In the structure of 1, each DCNT_2- has three coordination sites, one nitrogen atom in the triazine ring coordinating to Co(II) and two carboxylates adopting _{_2}-bridging mode, which make the infinite Co(II) chains array uniformly and evenly towards the crystallographic c axis. Luminescent and magnetic properties of 1 were also studied.

The novel supramolecular silver(I) compound with formula [Ag₆(TST)₂(bipy)₆(H₂O)₂]_n . 3nH₂O (1) based on assembly of Ag(I) and mixed ligand bipy/TST³⁻, bipy = 2,2′-bipyridine, H₃TST = 2,4,6-tris(4-sulfophenylamino)-1,3,5-triazine, has been prepared by hydrothermal method. In the solid-state structure of 1, two-dimensional layered polymeric structures extended with subunits [Ag₆(TST)₂(bipy)₆(H₂O)₂] interact each other in the form of π–π attractions between bipy, forming a three-dimensional supramolecular architecture. Compound 1 represents a Ag-containing polymeric compound possessing room-temperature luminescence.

A simple scheme is proposed to analyze the N-electron wave function obtained in embedded cluster calculations in valence bond terms such as ligand-to-metal charge transfer and non charge transfer determinants. The analysis is based on a unitary transformation of pairs of natural orbitals to optimal atomic-like orbitals. The procedure is applied to compare the degree of ionicity in NiO and MnO, and to explain the existence or absence of Jahn-Teller distortions in LaMnO₃, CaMnO₃ and CaFeO₃. We find that the ground state of LaMnO₃ is dominated by non charge transfer configurations, whereas the charge transfer configurations dominate the ground state wave function in the other two perovskites.

We report the calculated visible spectrum of [Fe^III(PyPepS)₂]^- in aqueous solution. From all-classical molecular dynamics simulations on the solute and 200 water molecules with a polarizable force field, 25 solute/solvent configurations were chosen at random from a 50 ps production run and subjected the systems to calculations using time-dependent density functional theory TD-DFT for the solute, combined with a solvation model in which the water molecules carry charges and polarizabilities. In each calculation the first 60 excited states were collected in order to span the experimental spectrum. Since the solute has a doublet ground state several excitations to states are of type three electrons in three orbitals, each of which gives rise to a manifold of a quartet and two doublet states which cannot properly be represented by single Slater determinants. We applied a tentative scheme to analyze this type of spin contamination in terms of Δ and Δ transitions between the same orbital pairs. Assuming the associated states as pure single determinants obtained from restricted calculations, we construct conformation state functions CFSs , i.e., eigenfunctions of the Hamiltonian S_z and S₂, for the two doublets and the quartet for each Δ,Δ pair, the necessary parameters coming from regular and spin-flip calculations. It appears that the lower final states remain where they were originally calculated, while the higher states move up by some tenths of an eV. In this case filtering out these higher states gives a spectrum that compares very well with experiment, but nevertheless we suggest investigating a possible re formulation of TD-DFT in terms of CFSs rather than determinants.

In this paper we derive the relativistic two-component formulation of time-dependent current-density-functional theory. To arrive at a two-component current-density formulation we apply a Foldy-Wouthuysen-type transformation to the time-dependent four-component Dirac-Kohn-Sham equations of relativistic density-functional theory. The two-component Hamiltonian is obtained as a regular expansion which is gauge invariant at each order of approximation, and to zeroth order it represents the time-dependent version of the relativistic zeroth order regular Hamiltonian obtained by van Lenthe et al., for the ground state J. Chem. Phys. 99, 4597 1993 . The corresponding zeroth order regular expression for the density is unchanged, whereas the current-density operator now comprises a paramagnetic, a diamagnetic, and a spin contribution, similar to the Gordon decomposition of the Dirac four current. The zeroth order current density is directly related to the mean velocity corresponding to the zeroth order Hamiltonian. These density and current density operators satisfy the continuity equation. This zeroth order approximation is therefore consistent and physically realistic. By combining this formalism with the formulation of the linear response of solids within time-dependent current-density functional theory Romaniello and de Boeij, Phys. Rev. B 71, 155108 2005 , we derive a method that can treat orbital and spin contributions to the response in a unified way. The effect of spin-orbit coupling can now be taken into account. As first test we apply the method to calculate the relativistic effects in the linear response of several metals and nonmetals to a macroscopic electric field. Treatment of spin-orbit coupling yields visible changes in the spectra: a smooth onset of the interband transitions in the absorption spectrum of Au, a sharp onset with peak at about 0.46 eV in the absorption spectrum of W, and a low-frequency doublet structure in the absorption spectra of ZnTe, CdTe, and HgTe in agreement with experimental results.

DFT was used to investigate molecular structure and metal affinity of the systems CH₃CO₂M (1), CH₃-O-SO₃M (2), CH₃-NH-SO₃M (3), (CH₃-O-PO₃M)^- (4), CH₃-O-PO₃M₂ (5), CH₃-O-(CH₃)PO₂M (6), and 1,4-DiOMe IdoA-2SM₂ (7; ²S_o conformation) (M = Li⁺ and Na⁺), respectively. Interaction enthalpies, entropies and Gibbs energies of the metal-coordinated systems were determined on the B3LYP/6-311+G(d,p) level. The computed Gibbs energies, ΔG^o, of the isolated systems 1-7 are negative and span a rather broad energy interval (from 500 to 1500 kJ mol^-1). The lithium and sodium binding enthalpies and Gibbs energies of a series of phosphate, carboxylate, N-, and O-sulfate anions indicate that multidentate chelation plays an important role in the binding. In particular, the glycosaminoglycan structural unit of heparin 1,4-DiOMe IdoA-2SM2 (M = Li⁺ and Na⁺) with coordinating groups in the hexopyranose ring exhibits enhanced metal ion binding energies. Computations that include the effect of solvation showed that in water the relative stability of Li⁺... Ligand and Na⁺... Ligand ionic bonds is rapidly diminished. The computed interaction Gibbs energy in water is small, slightly negative and/or positive, i.e. destabilizing. Thus in water, both contact ion pairs and solvent-separated ion pairs may coexist.

Analytic energy gradients with respect to atomic coordinates for systems with translational invariance are formulated within the framework of Kohn-Sham Density Functional Theory. The energy gradients are implemented in the BAND program for periodic DFT calculations which directly employs Bloch basis set made up of Slater-type (STOs) and numeric atomic orbitals (NAOs). The details of our implementation are described including the use of symmetry in the reciprocal and direct spaces, as well as the application of the frozen core approximation.

In this work, we investigate the Vignale-Kohn current functional when applied to the calculation of optical spectra of semiconductors. We discuss our results for silicon. We found qualitatively similar results for other semiconductors. These results show that there are serious limitations to the general applicability of the Vignale-Kohn functional. We show that the constraints on the degree of nonuniformity of the ground-state density and on the degree of the spatial variation of the external potential under which the Vignale-Kohn functional was derived are almost all violated. We argue that the Vignale-Kohn functional is not suited to use in the calculation of optical spectra of semiconductors since the functional was derived for a weakly inhomogeneous electron gas in the region above the particle-hole continuum, whereas the systems we study are strongly inhomogeneous and the absorption spectrum is closely related to the particle-hole continuum.

Ab initio calculations have been performed to clarify the character of the ground state of the high temperature phase of CaFeO₃ at different external pressures. The analysis of the correlated N-electron wave function of properly embedded FeO₆ clusters in terms of optimal atomic orbitals clearly establishes the character of the ground state as being dominated by charge transfer configurations. For all pressures, the number of Fe 3d electrons is around 5 and iron should be considered as a Fe³⁺ ion. We find a S=2 to S=1 transition around 25 GPa in the CaFeO₃ crystal.

The sequence of phase transitions and the symmetry of in particular the low temperature incommensurate and spin-Peierls phases of the quasi one-dimensional inorganic spin-Peierls system TiOX (X=Br and Cl) have been studied using inelastic light scattering experiments. The anomalous first-order character of the transition to the spin-Peierls phase is found to be a consequence of the different symmetries of the incommensurate and spin-Peierls (P2₁/m) phases. The pressure dependence of the lowest transition temperature strongly suggests that magnetic interchain interactions play an important role in the formation of the spin-Peierls and the incommensurate phases. Finally, a comparison of Raman data on VOCl to the TiOX spectra shows that the high energy scattering observed previously has a phononic origin.

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na₅ and Na₉⁺, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.

We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried out in order to achieve an electron density that reflects the internal symmetry of the system. We discuss the implications of this body-fixed frame transformation and establish a Runge-Gross type theorem and derive Kohn-Sham equations for the electrons and nuclei. We illustrate the formalism by performing calculations on a one-dimensional diatomic molecule for which the many-body Schroedinger equation can be solved numerically. These benchmark results are then compared to the solution of the time-dependent Kohn-Sham equations in the Hartree approximation. Furthermore, we analyze the excitation energies obtained from the linear response formalism in the single pole approximation. We find that there is a clear need for improved functionals that go beyond the simple Hartree approximation.

A crystalline sample of TiOBr is probed at room temperature by a combination of electron spectroscopies and the results are compared to theoretical embedded-cluster calculations. Resonant photoemission of the valence band confirms that the lowest binding energy feature arises from the singly occupied Ti 3d orbital. The polarization dependence of this orbital in nonresonant photoemission is consistent with the expected dominant d(y)(2)-z(2) character. The analysis of the Ti L-2,L-3 x-ray absorption spectra confirms the complete splitting of the Ti 3d shell. X-ray absorption and resonant photoemission at the O 1s edge provide direct evidence for hybridization between the transition metal orbitals and the O 2p levels, which leads to superexchange interactions between the Ti ions. The existence of a mixing of O and Ti states and of strong superexchange interactions is supported by calculations of the ground-state electronic and magnetic properties. The calculated superexchange interchain interaction is one fifth in strength of the total magnetic coupling along the chain, and is antiferromagnetic in character. This O-mediated interchain interaction is frustrated in the room temperature phase of TiOBr and thus couples strongly to distortions of the soft lattice. The competition between the interchain magnetoelastic coupling and the spin-Peierls interaction might be at the origin of the complex TiOX phase diagram.

The center-of-mass (c.m.) oscillation of a many-body system in a harmonic trap is known to be independent of the interparticle interaction. However, this is not necessarily the case if the interactions are treated approximately. Here, we prove a simple general criterion for preservation of the c.m. mode: the approximation has to preserve density and momentum. The result equally applies to zero and finite temperatures, as well as to nonequilibrium situations, and to the linear and nonlinear response regimes.

We implement time propagation of the nonequilibrium Green function for atoms and molecules by solving the Kadanoff-Baym equations within a conserving self-energy approximation. We here demonstrate the usefulness of time propagation for calculating spectral functions and for describing the correlated electron dynamics in a nonperturbative electric field. We also demonstrate the use of time propagation as a method for calculating charge-neutral excitation energies, equivalent to highly advanced solutions of the Bethe-Salpeter equation.

The origin of the features in the Ni 3s X-ray photoelectron spectrum of NiO is investigated using a non-orthogonal configuration interaction approach for an embedded [NiO₆] cluster. We study the interplay of inter-atomic screening with the metal core hole and intra-atomic exchange and electron correlation effects. We show that the spectrum can be described in terms of only few key configurations, provided that orbital relaxation effects are explicitly taken into account for the excited charge transfer configurations. The strength of this approach has been demonstrated earlier for those final states that have a high-spin coupling. In the present contribution the analysis is extended to include low-spin coupled 3s-hole states. The effects of enlarging the embedded cluster and of an improved representation of the nearest cluster surroundings were studied for the high-spin final states. We found only minor effects on the computed peak separations.

This Letter addresses a long-standing problem related to non-dynamical electron correlation effects. The origin of the large differential electronic correlation energy among the neutral 1S ground state, the lowest, 2P, ionic state and the first excited, 2S, ionic state of the Ne and Ar atoms is explained in terms of the near degeneracy of low-lying excited configurations. There is an anomalous correlation for the 2S state that is shown to be due to non-dynamical correlation involving a low-lying excited configuration. The conceptual framework used here is also appropriate to be used for other atomic and molecular systems.

The synthesis and detailed characterization of a few samples of the compound Rb_xMn[Fe(CN)₆]_y^.zH₂O are described. The composition of the materials significantly depends on the applied preparative conditions. Analysis of spectroscopic results (FTIR, Raman, ⁵⁷Fe Mössbauer, XPS) and X-ray powder diffraction data yielded a further assessment of the difference in structural features in terms of the amount of Fe(CN)₆ vacancies and the associated number of water molecules. The characteristic individual magnetic behavior, as well as the metal-to-metal charge transfer capabilities of the various samples could be related to significant changes within the structures which appear to be associated with the synthetic method used.

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We solve the Dyson equation for atoms and diatomic molecules within the GW approximation, in order to elucidate the effects of self-consistency on the total energies and ionization potentials. We find GW to produce accurate energy differences although the selfconsistent total energies differ significantly from the exact values. Total energies obtained from the Luttinger-Ward functional E_LW[G] with simple, approximate Green functions as input, are shown to be in excellent agreement with the self-consistent results. This demonstrates that the Luttinger-Ward functional is a reliable method for testing the merits of different self-energy approximations without the need to solve the Dyson equation self-consistently. Self-consistent GW ionization potentials are calculated from the Extended Koopmans Theorem, and shown to be in good agreement with the experimental results. We also find the self-consistent ionization potentials to be often better than the non-self-consistent G₀W₀ values. We conclude that GW calculations should be done self-consistently in order to obtain physically meaningful and unambiguous energy differences.

n.a.

In this work we investigate the circular dichroism (CD) spectrum of [Co(en)3]3+ in water, using the discrete solvent reaction field (DRF) model. The DRF model is a polarizable quantum mechanics/molecular mechanics (QM/MM) model. The implementation of the DRF model for CD spectra calculations based on time-dependent density functional theory (TDDFT) is presented. The combination of DRF with TDDFT allows for a computationally attractive solution for calculating chirooptical properties of molecules in solution when explicit solvent structures are of interest. Using a mixed coarse/fine-grained parallel computation, we show that average CD spectra from snapshots of the solvent structure can be obtained routinely. Classical polarizable molecular dynamics (MD) simulations have been used to obtain the solvent structure around the [Co(en)3]3+ (en=ethyldiamine) solute.We show that the final spectrum converges quickly with respect to the number of configurations. The DRF results were compared with results obtained from the much simpler conductor-like screening model (COSMO). Both models predicted similar blue shifts of the CD bands, but none of the models is in perfect agreement with the experiments. For instance, the calculated intensities are larger than what is found experimentally if reasonable empirical line width parameters are applied. From the DRF computations, we further show that almost all the solvent effects arise from ground-state solvation. Thus, ignoring the dynamic solvent response is a good approximation for a system like [Co(en)3]3+, where the solute is highly charged and the solvent is very polar.

We recently developed a scheme for first-principles calculations of hopping matrix elements between localized states in extended systems. We apply the scheme to the determination of double exchange (DE) parameters in lightly hole-doped LaMnO3 and electron-doped CaMnO3. DE is one of the important factors for understanding the properties of doped manganites. The calculations are based on the construction of wave functions for localized hole states or localized electron states for large embedded clusters. The wave functions of these clusters are expressed in terms of localized orbitals, obtained from calculations on smaller units, or "fragments", centered around a transition metal ion. The starting point of electronic states expressed in terms of localized orbital sets is conceptually attractive. It also allows for a rigorous treatment of local electron correlation and electronic relaxation effects. In the present study, the fragments are embedded [MnO6] units. The large clusters contain either two or four Mn ions and all neighboring oxygen ligands. The results are compared with conventional embedded cluster calculations. In both compounds, the effective hopping matrix elements, or "double exchange" (DE) parameters, in the ab planes (in the Pbnm space group) are larger than along the c axes. We found nearly perfect agreement with the Anderson-Hasegawa model for the spin dependence of the DE parameters. Nearest-neighbor parameters are more than one order of magnitude larger than next nearest-neighbor parameters. In LaMnO3 the DE in the ab planes is about -0.26 eV. If there were no Jahn-Teller distortion present in the material, it would have been twice as large. In CaMnO3, the corresponding nearest-neighbor DE parameter for hopping of a doped electron in the ab planes is only about -0.17 eV, due to the antiparallel spin coupling. However, since this interaction is much larger than the exchange coupling, we suggest that it induces local ferromagnetic clusters around the doped electrons.

In this work we present calculated absorption and emission spectra in acetonitrile (MeCN) solution of N-acetyl- 1-aminopyrene (PAAc, a spectroscopic model compound) and N-(1-pyrenyl)-1-methyluracil-5-carboxamide (PAUMe, a computational model for 5-(N-carboxyl-1-aminopyrenyl)-2'-deoxyuridine (PAdU)). The computational method used-the discrete reaction field approach (DRF)-combines a quantum mechanical (QM) description of the solute (here DFT and INDOs/CIS, i.e., the INDO parametrization for spectroscopy) with a classical, molecular mechanics (MM) description of the solvent molecules. The latter are modeled with point charges representing the permanent charge distribution and polarizabilities to account for many-body interactions among the solute and other solvent molecules. Molecular dynamics is used to sample the degrees of freedom of the solution around several solute conformations each in two electronic excited states. This leads to a large number of solute/solvent configurations from which 800 are selected for each excited state and collected into a single ensemble by means of proper Boltzmann averaging. DRF INDOs/CIS applied to the selected solute/solvent configurations give simulated absorption and emission band spectra-each based on 15200 calculated transitions-that compare well with experimental results. For example, the much broader absorption and emission bands in PAdU compared with PAAc are reproduced, and the simulated emission spectra of PAUMe agree well with broad (380-550 nm) charge transfer (CT) emission seen for PAdU in MeCN. The observed multiexponential fluorescence decay profiles for PAdU in different polar solvents are interpreted in terms of solute/solvent conformational heterogeneity here generated in the MD simulations for PAUMe in MeCN. Additionally, the simulations demonstrate the mixing of the forbidden Py+/dU- CT states with allowed pyrenyl 1(¹,¹*) states.

In this work we discuss the application of nonequilibrium Green functions theory to atomic and molecular systems with the aim to study charge and energy transport in these systems. We apply the Kadanoff-Baym equations to atoms and diatomic molecules initially in the ground state. The results obtained for the correlated initial states are used to analyze variational energy functionals of the Green function which are shown to perform very well. We further show an application of the Kadanoff-Baym equations to a molecule exposed to an external laser field. Finally we discuss the connection between nonequilibrium Green function theory and time-dependent density-functional theory with the aim to develop better density functionals in order to treat larger systems than those attainable with the nonequilibrium Green function method.

While the use of Green's function techniques has a long tradition in quantum chemistry, the possibility of propagating the Kadanoff-Baym equations has remained largely unexplored. We have implemented the time-propagation for atoms and diatomic molecules, starting from a system in the groundstate. The initial stage of the calculation requires solving the Dyson equation self-consistently for the equilibrium Green's function. This Green's function contains a huge amount of information, and we have found it particularly interesting to compare the self-consistent total energies to the results of variational energy functionals of the Green's function. We also use time-propagation for calculating linear response functions, as a means for obtaining the excitation energies of the system. We have presently implemented the propagation for the second Born approximation, while the GW approximation has now been implemented for the ground state calculations.

The coupling between electronic and nuclear motion plays an essential role in a wide range of physical phenomena. A few important research fields in which this is the case are superconductivity in solids, quantum transport where one needs to take into account couplings between electrons and phonons, the polaronic motion in polymer chains, and the ionization-dissociation dynamics of molecules in strong laser fields. Our goal is to set up a time-dependent multicomponent density-functional theory (TDMCDFT) to provide a general framework to describe these diverse phenomena. In TDMCDFT the electrons and nuclei are treated completely quantum mechanically from the outset. The basic variables of the theory are the electron density n, which will be defined in a body-fixed frame attached to the nuclear framework, and the diagonal of the nuclear N-body density matrix I', which will depend on all the nuclear coordinates. The chapter is organized as follows: We start out by defining the coordinate transformations to obtain a suitable Hamiltonian for defining our densities to be used as basic variables in the theory. We then discuss the basic one-to-one correspondence between TD potentials and TD densities, and subsequently, the resulting TD Kohn-Sham equations, the action functional, and linear response theory. As an example we discuss a diatomic molecule in a strong laser field.

The nomenclature quantum transport has been coined for the phenomenon of electron motion through constrictions of transverse dimensions smaller than the electron wavelength, e.g., quantum-point contacts, quantum wires, molecules, etc. To describe transport properties on such a small scale, a quantum theory of transport is required. In this Chapter we focus on quantum transport problems whose experimental setup is schematically displayed in Fig. 32.1a. A central region of meso- or nanoscopic size is coupled to two metallic electrodes which play the role of charge reservoirs. The whole system is initially in a well defined equilibrium configuration, described by a unique temperature and chemical potential (thermodynamic consistency). No current flows through the junction, the charge density of the electrodes being perfectly balanced. In the previous Chapter, Gebauer et al. proposed to join the left and right remote parts of the system so to obtain a ring geometry, see Fig. 30.1. In their approach the electromotive force is generated by piercing the ring with a magnetic field that increases linearly in time. Here, we consider the longitudinal geometry of Fig. 32.1a and describe an alternative approach. As originally proposed by Cini [Cini 1980], we may drive the system out of equilibrium by exposing the electrons to an external time-dependent potential which is local in time and space. For instance, we may switch on an electric field by putting the system between two capacitor plates far away from the system boundaries, see Fig. 32.1b. The dynamical formation of dipole layers screens the potential drop along the electrodes and the total potential turns out to be uniform in the left and right bulks. Accordingly, the potential drop is entirely limited to the central region. As the system size increases, the remote parts are less disturbed by the junction, and the density inside the electrodes approaches the equilibrium bulk density.

The Runge-Gross theorem [Runge 1984] states that for a given initial state the time-dependent density is a unique functional of the external potential. Let us elaborate a bit further on this point. Suppose we could solve the timedependent Schrodinger equation (TDSE) for a given many-body system, i.e., we specify an initial state |0 at t = t0 and evolve the wave function in time using the Hamiltonian H (t). Then, from the wave function, we can calculate the time-dependent density n(r, t). We can then ask the question whether exactly the same density n(r, t) can be reproduced by an external potential v ext(r, t) in a system with a different given initial state and a different two-particle interaction, and if so, whether this potential is unique (modulo a purely time-dependent function). The answer to this question is obviously of great importance for the construction of the time-dependent Kohn-Sham equations. The Kohn-Sham system has no two-particle interaction and differs in this respect from the fully interacting system. It has, in general, also a different initial state. This state is usually a Slater determinant rather than a fully interacting initial state. A time-dependent Kohn-Sham system therefore only exists if the question posed above is answered affirmatively. Note that this is a v-representability question: Is a density belonging to an interacting system also noninteracting v-representable? We will show in this chapter that, with some restrictions on the initial states and potentials, this question can indeed be answered affirmatively [van Leeuwen 1999, van Leeuwen 2001, Giuliani 2005]. We stress that we demonstrate here that the interacting-v-representable densities are also noninteracting-v-representable rather than aiming at characterizing the set of v-representable densities. The latter question has inspired much work in ground state density functional theory (for extensive discussion see [van Leeuwen 2003]) and has only been answered satisfactorily for quantum lattice systems [Chayes 1985].

In this chapter we give an introduction to the Keldysh formalism, which is an extremely useful tool for first-principles studies of nonequilibrium manyparticle systems. Of particular interest for TDDFT is the relation to nonequilibrium Green functions (NEGF), which allows us to construct exchangecorrelation potentials with memory by using diagrammatic techniques. For many problems, such as quantum transport or atoms in intense laser pulses, one needs exchange-correlation functionals with memory, and Green function techniques offer a systematic method for developing these. The Keldysh formalism is also necessary for defining response functions in TDDFT and for defining an action functional needed for deriving TDDFT from a variational principle. In this chapter, we give an introduction to the nonequilibrium Green function formalism, intended to illustrate the usefulness of the theory. The formalism does not differ much from ordinary equilibrum theory, the main difference being that all time-dependent functions are defined for time-arguments on a contour, known as the Keldysh contour.

In general, finite field DFT and TDDFT calculations yield accurate values for the response properties of molecular systems when standard approximations for the exchange-correlation functionals are used [Gross 1996]. In combination with their high efficiency, this makes these theoretical approaches ideal candidates for the calculation of physical properties of large molecular systems of technological interest. For an important class of materials, however, this potential is not yet realized.

The description of the ground state of crystalline systems within density functional theory, and of their response to external fields within the timedependent version of this theory, relies heavily on the use of periodic boundary conditions. As a model for the bulk part of the system one considers a large region containing N elementary unit cells. Then, while imposing constraints that ensure the single-valuedness and periodicity of the wave function at the boundary, one considers the limit of infinite N to derive properties for the macroscopic samples. In this treatment, one implicitly assumes that the Hohenberg-Kohn theorem [Hohenberg 1964] and the Kohn-Sham approach [Kohn 1965], and their time-dependent equivalents derived by Runge and Gross [Runge 1984], apply separately to the bulk part of the system. This implies that effects caused by density changes at the outer surface, which are artificially removed in this periodic boundary approach, can be neglected. However, this can not be justified as these effects are real.

The induced density can be obtained within a linear response calculation by solving a coupled set of equations, in which the first order change in the density follows from the first order change in the self-consistent potential and vice versa.

The geometry of a molecule or solid determines many of its physical and chemical properties. The ground state geometry of any system can be found by a geometry optimization. This procedure can also be used for e.g. transition state searches, reactions at surfaces etc. In the Born-Oppenheimer (BO) approximation, the total ground state energy of a system is a function of the coordinates of all nuclei (E0 = E0({R})). The minimum of the energy corresponds to the ground state geometry, whereas a first order saddlepoint on the BO-surface gives the transition state geometry. In solids we can vary two kinds of parameters; the nuclear coordinates of the atoms in the unit cell and the unit cell parameters. In this report, we will only consider the nuclear coordinates in a fixed unit cell. In order to find the stationary point of interest, we need the gradients of the energy with respect to the nuclear coordinates. These could be calculated by a numerical interpolation, but this is computationally not feasible, even for small systems. In this report, we give an analytical expression for the gradient of the total Kohn-Sham energy with respect to the nuclear coordinates.

The Direct Reaction Field (DRF) approach has proven to be a useful tool to investigate the influence of solvents on the quantum/classical behaviour of solute molecules. In this paper, we report the latest extension of this DRF approach, which consists of the gradient of the completely classical energy expressions of this otherwise QM/MM method. They can be used in (completely classical) Molecular Dynamics simulations and geometry optimizations, that can be followed by a number of single point QM/MM calculations on configurations obtained in these simulations/optimizations. We report all energy and gradient expressions, and results for a number of interesting (model) systems. They include geometry optimization of the benzene dimer as well as Molecular Dynamics simulations of some solvents. The most stable configuration for the benzene dimer is shown to be the parallel-displaced form, which is slightly more stable (0.3 kcal/mol) than the T-shaped dimer.

Recently the linear response of metallic solids has been formulated within the time-dependent current-density-functional approach [Romaniello and de Boeij, Phys. Rev. B 71, 155108 (2005)]. The implementation, which originally used only the adiabatic local density approximation for the exchange-correlation kernel is extended in order to include also the Vignale-Kohn current functional. Within this approximation the exchange-correlation kernel is frequency dependent, thus relaxation effects due to electron-electron scattering can now be taken into account and some deficiencies of the adiabatic local density approximation (ALDA), as the absence of the low-frequency Drude-like tail in absorption spectra, can be cured. We strictly follow the previous formulation of the linear response of semiconductors by using the Vignale-Kohn functional [Berger, de Boeij, and van Leeuwen, Phys. Rev. B 71, 155104 (2005)]. The self-consistent equations for the interband and intraband contributions to the induced density and current density, which are completely decoupled within the ALDA and in the long-wavelength limit, now remain coupled. We present our results calculated for the optical properties of the noble metals Cu, Ag, and Au and we compare them with measurements found in literature. In the case of Au we treat the dominant scalar relativistic effects using the zeroth-order regular approximation in the ground-state density-functional-theory calculations, as well as in the time-dependent response calculations.

A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.

We have calculated total energies of atoms and diatomic molecules from the Luttinger-Ward functional, using self-energy approximations to second order as well as the GW approximation. In order to assess the variational quality of this functional, we have also solved the Dyson equation self-consistently. The Luttinger- Ward functional is compared to the variational functional due to Klein, and we demonstrate that the variational property of the latter functional is inferior to that of the Luttinger-Ward functional. We also show how to obtain variational density functionals from the functionals of the Green function. These orbital functional schemes are important for systems where density-functional theory using local functionals of the density necessarily fails. We derive an optimized effective potential OEP scheme that is based on the Luttinger-Ward functional and, unlike the conventional OEP schemes, produces energies in good agreement with the values obtained from the self-consistent Green function. Our calculations show that, when applied to molecules, the Luttinger-Ward functional is more sensitive to the quality of the input Green function than when applied to atoms, but the energies are remarkably close to the self-consistent values when the Hartree-Fock Green function is used as input. This Luttinger-Ward functional is therefore a simple and efficient method for studying the merits of various self-energy approximations while avoiding the computationally demanding task of solving the Dyson equation self-consistently.

We present a systematic analysis of the optical properties of bcc transition metals in the groups VB: V, Nb and Ta, and VIB: paramagnetic Cr, Mo and W. For this we use our formulation of time-dependent current-density-functional theory for the linear response of metals. The calculated dielectric and electron energy loss functions are compared with new ellipsometry measurements and with data reported in literature, showing an overall good agreement. The experimental data of the dielectric functions presented by Nestell and Christy and by Weaver et al. differ mostly in the low-frequency region. However we found that their reflectivity data are in very good agreement up to about 3 eV. We attribute this apparent discrepancy to the Drude-like extrapolation model used by Weaver et al. in the Kramers-Kronig procedure to extract the optical constants from their reflectivity data. Our experiments are in good agreement with Nestell and Christy's data. The calculated absorption spectra show some deviations from the experiments, in particular in the 3d metals. We assign the spectra in terms of transitions between pairs of bands and we analyze which parts of the Brillouin zone are mainly involved in the absorption. Our results suggest that the blue-shift of some spectral features in our calculations can be attributed mainly to the incorrect description of the virtual d-bands by the approximations used for the ground state exchange-correlation functional. These virtual bands are too weakly bound by the local density and generalized gradient approximations, in particular in the 3d metals. We calculate separately the inter- and intraband contributions to the absorption and we show using a k⋅p analysis that, within the scalar-relativistic approximation, interband transitions contribute to the absorption already at frequencies well below 0.5 eV. This finding makes questionable the Drude-like behavior normally assumed in the experimental analysis of the linear response. We find that the combination of the Drude model in which we use the calculated plasma frequency and an optimized relaxation time, and the calculated interband response can well describe the experimental spectra. The electron energy loss spectra are very well reproduced by our calculations showing in each metal a dominant plasmon peak at about 22-24 eV, well above the corresponding Drude-like free-electron plasma frequency, and additional features in the range 10-15 eV. We show that the renormalization of the plasma frequency is due to the interplay between inter- and intraband processes, and that the additional features arise from the rich structure in the dielectric function caused by interband transitions.

We derive variational expressions for the grand potential or action in terms of the many-body Green function G which describes the propagation of particles and the renormalized four-point vertex which describes the scattering of two particles in many-body systems. The main ingredient of the variational functionals is a term we denote as the Ξ-functional which plays a role analogously to the usual Φ-functional studied by Baym (G.Baym, Phys.Rev. 127, 1391 (1962)) in connection with the conservation laws in many-body systems. We show that any Ξ-derivable theory is also Φ-derivable and therefore respects the conservation laws. We further set up a computational scheme to obtain accurate total energies from our variational functionals without having to solve computationally expensive sets of self-consistent equations. The input of the functional is an approximate Green function \tilde {G} and an approximate four-point vertex \tilde {Γ} obtained at a relatively low computational cost. The variational property of the functional guarantees that the error in the total energy is only of second order in deviations of the input Green function and vertex from the self-consistent ones that make the functional stationary. The functionals that we will consider for practical applications correspond to infinite order summations of ladder and exchange diagrams and are therefore particularly suited for applications to highly correlated systems. Their practical evaluation is discussed in detail.

Polymers were known to be good insulators for a long time. Almost three decades ago another type of polymers was discovered, the conducting polymers. The first conducting polymer found was polyacetylene which was doped with iodine[1]. The electrical conductivity found for this sample was found to be in the order of metallic conductivity, which is about fifteen orders of magnitude larger than for insulators. H. Shirakawa, A.J. Heeger and A.G. MacDiarmid even received the Nobel Prize for their discovery. It did not take long after this discovery before new polymers were found to be good conductors. An essential property of the conducting polymers is the fact that they are all conjugated polymers. Because of the fact that electrons are being delocalized makes the polymer suitable to transport charge through the polymer chains. If one is able to control the conducting properties in a good way many possible applications can be thought of. Polymeric electronic wires may substitute the inorganic ones used nowadays in the chip industry. The thickness of the wire, lying in the order of 1 molecule, is a good progress. Other applications are Light Emitting Diodes (LEDs), photovoltaic cells, photodetectors and optocouplers are some applications that have already been fabricated. These applications are possible due to the fact that a bandgap is present in conjugated polymers. The theoretical description of the conducting properties has been subject of a lot of discussion. Especially the relation between electron-electron interactions and electron-phonon interactions is still being investigated. Lots of properties have been explained by focusing on the electron-phonon interactions. This essay also shows the advantage of focusing on electron-electron interactions. At last I will give my point of view on the current state of discussions.

Azurin from Pseudomonas aeruginosa is a small 128-residue, copper-containing protein. Its redox potential can be modified by mutating the protein. Free-energy calculations based on classical molecular-dynamics simulations of the protein and from mutants in aqueous solution at different pH values were used to compute relative redox potentials. The precision of the free-energy calculations with the λ coupling-parameter approach is evaluated as function of the number and sequence of λ values, the sampling time and initial conditions. It is found that the precision is critically dependent on the relaxation of hydrogen-bonding networks when changing the atomic-charge distribution due to a change of redox state or pH value. The errors in the free energies range from 1 to 10 kBT, depending on the type of process. Only qualitative estimates of the change in redox potential by protein mutation can be obtained.

No abstract available

We have calculated the frequency-dependent refractive index and the third-order nonlinear susceptibility for C60 in the condensed phase, which is related to third-harmonic generation (THG) and degenerate four-wave mixing (DFWM) experiments. This was done using the recently developed discrete solvent reaction field (DRF) model, which combines a time-dependent density functional theory (TD-DFT) description of the central C60 molecule with a classical polarizable MM model for the rest of the fullerene cluster. Using this model, effective microscopic properties can be calculated that, combined with calculated local field factors, give macroscopic susceptibilities. The largest calculation was for a cluster of 63 C60 molecules in which the central molecule was treated with TD-DFT. For this molecule, the effective polarizability was increased with about 15% and the effective second hyperpolarizability with about 60% compared with the gas phase. The calculated refractive index was found to be in good agreement with experiments and other theoretical results. The agreement with THG experiments was within a factor of two, whereas for DFWM the agreement was less good due to the neglect of vibrational contributions in the calculations. It was found that it is more important to account for the dispersion in the third-order susceptibilities than in the corresponding second hyperpolarizability.

It was recently proposed to use variational functionals based on many-body perturbation theory for the calculation of the total energies of many-electron systems. The accuracy of such functionals depends on the degree of sophistication of the underlying perturbation expansions. The energy functionals are variational in the sense that they can be evaluated at rather crude approximations to their independent variables, which are the one-electron Green function, or the one-electron Green function and the dynamically screened electron interaction. The functionals were previously applied to the electron gas and shown to be extraordinarily accurate already at the level of the so-called GW approximation (GWA). In the present work we have tested the functional due to Luttinger and Ward, which is a functional of the Green function. Using DFT and Hartree-Fock Green functions as input variables, we have calculated total energies of diatomic molecules at the level of the GWA as well as with second-order exchange effects included.We will also discuss various other variational energy functionals, including DFT orbital functionals based on many-body perturbation theory.

A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By seperating the discrete local field into two distinct contribution we define two different microscopic properties, the so-called solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, third-harmonic generation (THG), and electric field induced second-harmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described.

In this paper the role of the solvent in the formation of the charge-separated excited state of 9,9'-bianthryl (BA) is examined by means of mixed molecular mechanical/quantum mechanical (QM/MM) calculations. It is shown that in weakly polar solvents a relaxed excited state is formed with an interunit angle that is significantly smaller than 90°. This relaxed excited state has a considerable dipole moment even in weakly polar solvents; for benzene and dioxane dipole moments of ca. 6 D were calculated, which is close to experimental data. These dipoles are induced by the solvent in the highly polarizable relaxed excited state of BA, and the dipole relaxation time is governed by solvent reorganizations. In polar solvent the charge separation is driven to completion by the stronger dipoles in the solvent and a fully charged separated excited state is formed with an interunit angle of 90°.

We have calculated the self-consistent Green's function for a number of atoms and diatomic molecules. This Green's function is obtained from a conserving self-energy approximation, which implies that the observables calculated from the Green's functions agree with the macroscopic conservation laws for particle number, momentum, and energy. As a further consequence, the kinetic and potential energies agree with the virial theorem, and the many possible methods for calculating the total energy all give the same result. In these calculations we use the finite temperature formalism and calculate the Green's function on the imaginary time axis. This allows for a simple extension to nonequilibrium systems. We have compared the energies from self-consistent Green's functions to those of nonselfconsistent schemes and also calculated ionization potentials from the Green's functions by using the extended Koopmans' theorem.

We included relativistic effects in the formulation of the time-dependent current-density-functional theory for the calculation of linear response properties of metals [P. Romaniello and P. L. de Boeij, Phys. Rev. B (to be published)]. We treat the dominant scalar-relativistic effects using the zeroth-order regular approximation in the ground-state density-functional theory calculations, as well as in the time-dependent response calculations. The results for the dielectric function of gold calculated in the spectral range of 0-10 eV are compared with experimental data reported in literature and recent ellipsometric measurements. As well known, relativistic effects strongly influence the color of gold. We find that the onset of interband transitions is shifted from around 3.5 eV, obtained in a nonrelativistic calculation, to around 1.9 eV when relativity is included. With the inclusion of the scalar-relativistic effects there is an overall improvement of both real and imaginary parts of the dielectric function over the nonrelativistic ones. Nevertheless some important features in the absorption spectrum are not well reproduced, but can be explained in terms of spin-orbit coupling effects. The remaining deviations are attributed to the underestimation of the interband gap (5d-6sp band gap) in the local-density approximation and to the use of the adiabatic local-density approximation in the response calculation.

In this work we have investigated the first hyperpolarizability of pNA in 1,4-dioxane solution using a quantum mechanics/molecular mechanics QM/MM model. The particular model adopted is the recently developed discrete solvent reaction field DRF model. The DRF model is a polarizable QM/MM model in which the QM part is treated using time-dependent density-functional theory and local-field effects are incorporated. This allows for direct computation of molecular effective properties which can be compared with experimental results. The solvation shift for the first hyperpolarizability is calculated to be 30% which is in good agreement with the experimental results. However, the calculated values, both in the gas phase and in solution, are by a factor of 2 larger than the experimental ones. This is in contrast to the calculation of the first hyperpolarizability for several small molecules in the gas phase where fair agreement is found with experimental. The inclusion of local-field effects in the calculations was found to be crucial and neglecting them led to results which are significantly larger. To test the DRF model the refractive index of liquid 1,4-dioxane was also calculated and found to be in good agreement with experiment.

A simple modification of the zeroth-order regular approximation (ZORA) in relativistic theory is suggested to suppress its erroneous gauge dependence to a high level of approximation. The method, coined gauge-independent ZORA (ZORA-GI), can be easily installed in any existing nonrelativistic quantum chemical package by programming simple one-electron matrix elements for the quasirelativistic Hamiltonian. Results of benchmark calculations obtained with ZORA-GI at the Hartree-Fock (HF) and second-order M¿ller-Plesset perturbation theory (MP2) level for dihalogens X₂ (X=F,Cl,Br,I,At) are in good agreement with the results of four-component relativistic calculations (HF level) and experimental data (MP2 level). ZORA-GI calculations based on MP2 or coupled-cluster theory with single and double perturbations and a perturbative inclusion of triple excitations [CCSD(T)] lead to accurate atomization energies and molecular geometries for the tetroxides of group VIII elements. With ZORA-GI/CCSD(T), an improved estimate for the atomization energy of hassium (Z=108) tetroxide is obtained.

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated sidentical to the number of the two-electron integrals of a full DiracHartreeFock calculationd was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5x10^-9 hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.

It is demonstrated that the LYP correlation functional is not suited to be used for the calculation of electron spin resonance hyperfine structure (HFS) constants, nuclear magnetic resonance spin-spin coupling constants, magnetic, shieldings and other properties that require a balanced account of opposite- and equal-spin correlation, especially in the core region. In the case of the HFS constants of alkali atoms, LYP exaggerates opposite-spin correlation effects thus invoking too strong in-out correlation effects, an exaggerated spin-polarization pattern in the core shells of the atoms, and, consequently, too large HFS constants. Any correlation functional that provides a balanced account of opposite- and equal-spin correlation leads to improved HFS constants, which is proven by comparing results obtained with the LYP and the PW91 correlation functional. It is suggested that specific response properties are calculated with the PW91 rather than the LYP correlation functional.

We show the results of ab initio embedded cluster calculations of the ground state and lowlying excited states of the (001) surface and bulk of NiO including the spin-orbit coupling effects. The calculations are performed by the Columbus package using the combination of the relativistic effective core potentials and the spin-orbit operators. These effects result in the splitting of the d-d excited states. The fine structure of the 3d⁸; levels of the Ni²⁺ ion in NiO bulk and its (001) surface is resolved yielding good agreement with experimentally observed second-harmonic and optical absorption spectra. In addition, we discuss the transition electric-dipole moments, which can be used for a quantitative comparison with the experimentally determined optical intensities as well as for the exploration of various ultrafast all-optical spin-switching scenario.

In this work we employ the Vignale-Kohn sVKd current functional in the calculation of the linear response properties of polyacetylene for both the one-dimensional infinite chain and the infinite three-dimensional crystal. We test the two existing parametrizations of the longitudinal and transverse exchange-correlation kernels of the homogeneous electron gas that enter the VK functional and show that they lead to very different results. We argue that this is mainly caused by the different values of these kernels in the zero-frequency limit in the two parametrizations. In this limit knowledge of the exchange correlation part of the shear modulus of the homogeneous electron gas becomes very important. It is exactly this quantity that is not known accurately. Furthermore, we show that our results are in good qualitative agreement with results obtained earlier using the Vignale-Kohn functional for polyacetylene oligomers.

We extend the formulation of time-dependent current-density-functional theory for the linear response properties of dielectric and semi-metallic solids [Kootstra, J. Chem. Phys. 112, 6517 (2000)] to treat metals as well. To achieve this, the Kohn-Sham response functions have to include both interband and intraband transitions with an accurate treatment of the Fermi surface in the Brillouin-zone integrations. The intraband contributions in particular have to be evaluated using a wave-vector-dependent description. To test the method we calculate the optical properties of the two noble metals Cu and Ag. The dielectric and energy loss functions are compared with experiments and with the classical Drude theory. In general we find a good agreement with the experiments for the calculated results obtained within the adiabatic local density approximation. In order to describe the Drude-like absorption below the interband onset and the sharp plasma feature in silver exchange-correlation, effects beyond the adiabatic local density approximation are needed, which may be included in a natural way in the present current-density-functional approach.

In the present work, we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory MBPT as developed during the sixties and later expanded by us in the mid-nineties. Due to this feature, the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nanoscale systems.

The aim of this work is to provide a physical model to relate the polarizability per unit cell of oligomers to that of their corresponding infinite polymer chains. For this we propose an extrapolation method for the polarizability per unit cell of oligomers by fitting them to a physical model describing the dielectric properties of polymer chains. This physical model is based on the concept of a dielectric needle in which we assume a polymer chain to be well described by a cylindrically shaped nonconducting rod with a radius much smaller than its length. With this model we study in which way the polarizability per unit cell approaches the limit of the infinite chain. We show that within this model the macroscopic contribution of the induced electric field to the macroscopic electric field vanishes in the limit of an infinite polymer chain, i.e., there is no macroscopic screening. The macroscopic electric field becomes equal to the external electric field in this limit. We show that this identification leads to a relation between the polarizability per unit cell and the electric susceptibility of the infinite polymer chain. We test our dielectric needle model on the polarizability per unit cell of oligomers of the hydrogen chain and polyacetylene obtained earlier using time-dependent current-density-functional theory in the adiabatic local-density approximation and with the Vignale-Kohn functional. We also perform calculations using the same theory on truly infinite polymer chains by employing periodic boundary conditions. We show that by extrapolating the oligomer results according to our dielectric needle model we get good agreement with our results from calculations on the corresponding infinite polymer chains. 2005 American Institute of Physics.

A previously neglected intra-atomic many-body effect has important consequences for the X-ray photoelectron spectra (XPS) of transition metal atoms and cations. This effect involves configurations where one elctron is promoted to a 4f orbital and another is dropped to fill the XPS hole; this can be viewed as a frustrated Auger configuration (FAC). The identification of this FAC is a major advance in the understanding of many-body effects in XPS. Its use affects the multiplet splitting and the absolute binding energy; it can also lead to new satallite structure. Furthermore, it is expected to be generally important.

We present a study of the static polarizability for the tubular fullerenes C(60+10i), where i=0-5, and the closely related [5,5] carbon nanotube, using time-dependent (current)-density-functional theory. Comparing the results obtained within the conventional adiabatic local-density approximation with those obtained using the Vignale-Kohn current-dependent exchange-correlation functional it is found that the extra long-range exchange-correlation effects described by the current-density functional are important to consider, especially for the longest fullerenes. The largest reductions upon inclusion of the resulting counteracting field were found for the longitudinal component of the polarizability, amounting to 18% for the total value of C(110) and about 32% for the value per unit cell in the infinite [5,5] carbon nanotube. For all systems studied the current-density functional results are in good agreeement with experiment, and the agreement with available ab initio self-consistent-field results and results from a point-dipole interaction model is much better than when using the adiabatic local-density functional.

Density functional theory (DFT) predicts that bicyclo[3.1.0]hexatriene (2) is more stable than its isomer m-benzyne (1). Hess [Eur. J. Org. Chem. (2001) 2185] has argued that experimental findings suggesting 1 can equally or even better be associated with 2. However, high level ab initio calculations (CCSD(T), CASPT2) show that 2 does not exist and that the previously measured infrared spectrum is correctly assigned to 1. Bond stretch isomers are possible for p-benzynes but not for m-benzynes. The electrophilic character of m-benzynes is in line with 1 but not with 2.

We study the dynamics of the electronic and nuclear degrees of freedom for molecules in strong laser fields using an ansatz for the wavefunction that explicitly incorporates the electron-nuclear correlation. Equations of motion for this wavefunction are derived on the basis of the stationary action principle. The method is tested on a one-dimensional model of the H2+ molecule that can be solved essentially exactly by numerical integration of the time-dependent Schrödinger equation. By comparison with this exact solution we find that the correlated approach improves significantly on a mean-field treatment, especially for laser fields strong enough to cause substantial dissociation. These results are very promising since our method has a simple orbital structure and can hence be applied to realistic many-electron molecules.

Mercury chalcogenides HgE (E=O, S, Se, etc.) are described in the literature to possess rather stable bonds with bond dissociation energies between 53 and 30 kcal mol^-1, which is actually difficult to understand in view of the closed-shell electron configuration of the Hg atom in its ground state (...4f¹⁴5d¹⁰6s²). Based on relativistically corrected many body perturbation theory and coupled-cluster theory [IORAmm/MP4, Feenberg-scaled IORAmm/ MP4, IORAmm/CCSD(T)] in connection with IORAmm/B3LYP theory and a [17s14p9d5f]/aug-cc-pVTZ basis set, it is shown that the covalent HgE bond is rather weak (27 kcal mol^-1), the ground state of HgE is a triplet rather than a singlet state, and that the experimental bond dissociation energies have been obtained for dimers (or mixtures of monomers, dimers, and even trimers) Hg₂E₂ rather than true monomers. The dimers possess association energies of more than 100 kcalmol^-1 due to electrostatic forces between the monomer units. The covalent bond between Hg and E is in so far peculiar as it requires a charge transfer from Hg to E (depending on the electronegativity of E) for the creation of a single bond, which is supported by electrostatic forces. However, σ bonding between Hg and E is reduced by strong lone pairlone pair repulsion to a couple of kcalmol^-1. Since a triplet configuration possesses somewhat lower destabilizing lone pair energies, the triplet state is more stable. In the dimer, there is a Hg-Hg π bond of bond order 0.66 without any s support. Weak covalent Hg-O interactions are supported by electrostatic bonding. The results for the mercury chalcogenides suggests that all experimental dissociation energies for group-12 chalcogenides have to be revised because of erroneous measurements.

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no abstract available

We give a brief overview of nonequilibrium Green function theory and some connections with time-dependent density functional theory (TDDFT). We will focus on how to obtain approximations that satisfy the conservation laws. The account given here is not meant to be comprehensive but tries to put in logical order the main arguments and results that are sometimes found scattered in the literature.

In recent years there have been some rather successful applications of a new variational technique for calculating the total energies of electronic systems. The new method is based on many-body perturbation theory and uses the one-electron Green function as the basic "variable" rather than the wave function of traditional variational calculations. It is the purpose of the present work to promote the new methods within the realm of traditional theoretical chemistry by demonstrating their utility for calculating the correlation energies of a number of atoms at a level corresponding to second-order Møller-Plesset perturbation theory. The generalization to any desired order of perturbation theory is not hard to accomplish.

Magnetic interactions in ladder vanadates are determined with quantum chemical computational schemes using the embedded cluster model approach to represent the material. The available experimental data for calcium vanadate is accurately reproduced and the nature of the interladder interaction is established to be ferromagnetic. An analysis of the main contributions to the magnetic couplings is presented and the role of the covalently bonded apex oxygen is elucidated. In the sodium vanadate, the ground state configuration of the rungs is V 3d¹ - O 2p⁵ - V 3d¹. We show that with this configuration good coupling constants are obtained for the hightemperature phase. The inter-chain coupling in NaV₂O₅ is predicted to be ≈34 K, ferromagnetic in nature.

Erratum: "Excitation energies for a benchmark set of molecules obtained within time-dependent current-density functional theory using the Vignale-Kohn functional" [J. Chem. Phys. 120, 8353 (004)]

In this article we explain how the existing linear response theory of time-dependent density-functional theory can be extended to obtain excitation energies in the framework of time-dependent current-density-functional theory. We use the Vignale-Kohn current-functional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)] which has proven to be successful for describing ultranonlocal exchange-correlation effects in the case of the axial polarizability of molecular chains [M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, Phys. Rev. Lett. 88, 186401 (2002); J. Chem. Phys. 118, 1044 (2003)]. We study a variety of singlet excitations for a benchmark set of molecules. The ¹* ¹ transitions obtained with the Vignale-Kohn functional are in good agreement with experimental and other theoretical results and they are in general an improvement upon the adiabatic local density approximation. In case of the ¹* n transitions the Vignale-Kohn functional fails, giving results that strongly overestimate the experimental and other theoretical results. The benchmark set also contains some other types of excitations for which no clear failures or improvements are observed.

Molecular dynamics (MD) simulations have been performed on quercetin 2,3 dioxygenase (2,3QD) to study the mobility and flexibility of the substrate cavity. 2,3QD is the only firmly established Cu-containing dioxygenase known so far. It catalyses the breakage of the O-heterocycle of flavonols. The substrates occupy a shallow and overall hydrophobic cavity proximal to the metal centre of the homo-dimeric enzyme. The linker connecting the C-terminal and N-terminal domains in the monomer is partly disordered in the crystal structure and part of it forms a flexible lid at the entrance of the substrate cavity. This loop has been tentatively assigned a role in the enzyme mechanism: it helps lock the substrate into place. The dynamics of this loop has been investigated by MD simulation. The initial coordinates were taken from the crystal structure of 2,3QD in the presence of the substrate kaempferol (KMP). After equilibration and simulation over 7.2 ns the substrate was removed and another equilibration and simulation of 7.2 ns was performed. The results show that the structures of the free enzyme as well as of the enzyme-substrate complex are stable in MD simulation. The linker shows strongly enhanced mobility in the loop region that is close to the entrance to the substrate cavity (residues 154-169). Movement of the loop takes place on a timescale of 5-10 ns. To confirm the conclusions about the loop dynamics drawn fromthe 7.2 ns simulation, the simulation was extended with another 8 ns. When substrate binds into the cavity the loop orders remarkably, although mobility is retained by residues 155-158. Some regions of the loop (residues 154-160 and 164-176) move over a considerable distance and approach the substrate closely, reinforcing the idea that they lock the substrate in the substrate cavity. The enthalpic component of the interaction of the loop with the protein and the KMP appears to favour the locking of the substrate. Two water molecules were found immobilised in the cavity, one of which exhibited rotation on the picosecond timescale. When the substrate is removed, the empty cavity fills up with water within 200 ps.

Active site modeling in molecular dynamics simulations is investigated for the reduced state of copper azurin. Five simulation runs (5 ns each) were performed at room temperature to study the consequences of a mixed electrostatic/constrained modeling for the coordination between the metal and the polypeptide chain, using for the ligand residues a set of charges that is modified with respect to the apo form of the protein by the presence of the copper ion. The results show that the different charge values do not lead to relevant effect on the geometry of the active site of the protein, as long as bond distance constraints are used for all the five ligand atoms. The distance constraint on the O atom of Gly45 can be removed without altering the active site geometry. The coordination between Cu and the other axial ligand Met121 is outlined as being flexible. Differences are found between the bonds of the copper ion with the two apparently equivalent N(d1) atoms of His46 and His117.The overall findings are discussed in connection with the issue of determining a model for the active site of azurin suitable to be used in molecular dynamics simulations under unfolding conditions.

Utilizing a point-dipole interaction model, we present an investigation of the static polarizability and second hyperpolarizability of fullerenes and carbon nanotubes by varying their structure. The following effects are investigated: (1) the length dependence of the components of the static polarizability, (2) the static second hyperpolarizabilities of C₆₀ and C₇₀, (3) the symmetry effects on the static second hyperpolarizability, (4) the length dependence of the components of the static second hyperpolarizability, and (5) the diameter dependence of the static second hyperpolarizability. It is demonstrated that the carbon nanotubes exhibit significantly larger second hyperpolarizabilities compared to a fullerene containing the same number of carbon atoms. Furthermore, the calculations show that the carbon nanotubes have a much larger directionality of the static second hyperpolarizability than the fullerenes.

The dipole-dipole polarizability, α, and the second hyperpolarizability, γ, as well as the corresponding linear and third-order susceptibilities, χ⁽¹⁾ and χ⁽³⁾, have been calculated for C₆₀ fullerene clusters by a point-dipole interaction (PDI) model. The size dependences of a linear chain, a mono-layer film, and a face-centered cubic crystal cluster have been investigated. It is found that the effects of the surrounding molecules on the molecular α and γ are large, in particular for the chain and the film because of the anisotropic surroundings, and that large clusters are required to obtain converged results. A localized PDI model gives the opportunity to divide α and γ into fragment contributions, and it is found that α and γ of molecules in the middle of the chain converge slower than the properties for the end molecules with respect to the length of the chain. Similar results are found for the mono-layer film. Finally, χ⁽¹⁾ and χ⁽³⁾ have been calculated using a modified local-field theory including the induced dipole moments of the surrounding molecules explicitly. The corresponding refractive index and dielectric constant compare well with experiments. On the other hand, the comparison of χ⁽³⁾ with experiments is complicated by dispersion and vibrational contributions. Nonetheless, our value of χ⁽³⁾ is in good agreement with a recent quantum chemical calculation adopting a self-consistent reaction-field model.

Over the last couple of years, it has been shown that Time Dependent Density Functional Theory (TDDFT) is able to predict accurately and efficiently the polarizability of molecules, when using appropriate exchange-correlation potentials and (large) basis sets. In a previous paper, we compared the accuracy of the predicted mean polarizabilities of 15 organic molecules with experiment, and with two other computational methods: the Restricted Hartree-Fock (RHF) method and the Direct Reaction Field (DRF) approach, the first of which is ignored in this paper. The (empirical) DRF approach however was shown to give comparable accuracies to TD-DFT with the values computed in just a few seconds. In this paper, we use TD-DFT for computing the molecular polarizabilities of the twenty amino acid residues, and compare them with the results obtained with the DRF approach. Although the mean absolute deviation of the DRF values from the TD-DFT values is reasonable (7 %), it is more than two times the accuracy normally found with the DRF approach. Therefore we decided to optimize the atomic parameters for these systems, and found after optimization, a good agreement with the TDDFT values (mean absolute deviation 1.0 %). As the TD-DFT calculations were necessarily obtained with two additional hydrogens to saturate the backbone bonds, the molecular value of the polarizability of the amino acid residues is overestimated by the TD-DFT calculations. Therefore, the DRF approach (with the newly optimized atomic parameters) has been used to get the actual polarizabilities of the amino acid residues.

A new method for calculating the indirect nuclear spinspin coupling constant within the regular approximation to the exact relativistic Hamiltonian is presented. The method is completely analytic in the sense that it does not employ numeric integration for the evaluation of relativistic corrections to the molecular Hamiltonian. It can be applied at the level of conventional wave function theory or density functional theory. In the latter case, both pure and hybrid density functionals can be used for the calculation of the quasirelativistic spinspin coupling constants. The new method is used in connection with the infinite-order regular approximation with modified metric (IORAmm) to calculate the spin-spin coupling constants for molecules containing heavy elements. The importance of including exact exchange into the density functional calculations is demonstrated.

We study the π*←π singlet excitations of the π-conjugated oligomers of polyacetylene, polydiacetylene, polybutatriene, polythiophene, poly(para-phenylene vinylene) and the lowest singlet excitations of the hydrogen chain. For this we used time-dependent current-density functional theory within the Vignale-Kohn and adiabatic local density approximations. By studying the dependence of the excitation spectrum on the chain length we conclude that the reduction of the static polarizability when using the Vignale-Kohn functional has two origins. First, the excitation energies of transitions with a large transition dipole are shifted upward. Second, the HOMO-LUMO character and oscillator strength of the lowest transition within the adiabatic local density approximation is transferred to higher transitions. The lowest transitions that have a considerable oscillator strength obtained with the Vignale-Kohn functional have excitation energies that are in most cases in better agreement with available reference data then the adiabatic local density approximation.

The infinite-order regular approximation ~IORA! and IORA with modified metric (IORAmm) is used to develop an algorithm for calculating relativistically corrected isotropic hyperfine structure (HFS) constants. The new method is applied to the calculation of alkali atoms LiÐFr, coinage metal atoms Cu, Ag, and Au, the Hg⁺ radical ion, and the mercury containing radicals HgH, HgCH₃, HgCN, and HgF. By stepwise improvement of the level of theory from HartreeÐFock to second-order M¿llerÐPlesset theory and to quadratic configuration interaction theory with single and double excitations, isotropic HFS constants of high accuracy were obtained for atoms and for molecular radicals. The importance of relativistic corrections is demonstrated.

Combining optical control theory with ab initio quantum chemistry and electronic crystal field theory we explore the laser induced femtosecond spin dynamics. We propose a scenario for ultrafast all-optical magnetic switching that results from the combination of spin-orbit coupling with appropriately shaped short laser pulses. We find that the application of the theory to the multiplet states within the gap of NiO(001) predicts for the first time the possibility of all-optical spin switching within 100 fs. The switching can be observed using any of the multiplets as the intermediate state.

We present a first-principles approach to the calculation of the electron-phonon interaction. This approachsolves some theoretical difficulties in the standard derivation of the electron-phonon interaction. We do notmake a Born-Oppenheimer approximation from the outset but transform the electronic coordinates to a frameattached to the nuclear framework. Subsequently coupled equations are derived which connect the nucleardensity-density correlation function to the electron Green function, the screened interaction, and the vertex.This set of equations is completely equivalent to the full problem and therefore higher-order effects aresystematically included. The derived equations are further compared to those obtained from the FröhlichHamiltonian. It is shown that careless use of this Hamiltonian leads to double counting but also insight is givenwhy use of this Hamiltonian has led to many useful results. Finally a simple method is presented that allowsfor the inclusion of electron-phonon coupling within a density-functional context.

It was recently proposed to use variational functionals based on many-body perturbation theory for the calculation of the total energies of many-electron systems. The accuracy of such functionals depends on the degree of sophistication of the underlying perturbation expansions. An older such functional and a recently constructed functional, both at the level of the GW approximation (GWA), were tested on the electron gas with indeed very encouraging results. In the present work we test the older of these functionals on atoms and find correlation energies much better than those of the random-phase approximation but still definitely worse ascompared to the case of the gas. Using the recent functional of two independent variables it becomes relatively easy to include second-order exchange effects not present in the GWA. In the atomic limit we find this to bevery important and the correlation energies improve to an accuracy of 10-20% when obtained from calculations much less demanding than those of, e.g., configuration-interaction expansions.

The character of the electronic ground state of La0.5Ca0.5MnO3 has been addressed with quantum chemical calculations on large embedded clusters. We find a charge ordered state for the crystal structure reported by Radaelli et al. [Phys. Rev. B 55, 3015 (1997)] and Zener polaron formation in the crystal structure with equivalent Mn-sites proposed by Daoud-Aladine et al. [Phys. Rev. Lett. 89, 097205 (2002)]. Important O to Mn charge transfer effects are observed for the Zener polaron.

Theor Chem Acc (2003) 110: 34-41 Due to an unfortunate misunderstanding, the BLAP3 values reported in the original paper were not computed correctly; LAP3 correlation was not included in these calculations, so in fact the values reported as BLAP3 correspond to Becke exchange-only.

We give an overview of the fundamental concepts of density functional theory. We give a careful discussion of the several density functionals and their differentiability properties. We show that for nondegenerate ground states we can calculate the necessary functional derivatives by means of linear response theory, but that there are some differentiability problems for degenerate ground states. These problems can be overcome by extending the domains of the functionals. We further show that for every interacting v-representable density we can find a noninteracting (i)v-representable density arbitrarily close and show that this is sufficient to set up a Kohn-Sham scheme. We finally describe two systematic approaches for the construction of density functionals.

In our previous work we developed the Finite Field method in order to calculate the fifth-order Raman response. The method was applied to calculate various polarization components of the two-dimensional response of liquid CS₂. So far, all calculations relied on the dipole-induced dipole. Accurate time-dependent density functional theory calculations have shown that this model has big discrepancies, when molecules are close together as in the liquid. We now report results of investigations on the importance of multipole and electron overlap effects on the polarizability and the fifth-order Raman response. It is shown that these collision effects, especially the induced multipoles, are crucial in the description of the fifth-order response. The impact is found to be especially pronounced for the mmzzzz response that is solely due to interaction induced effects. The calculated response will be compared with various experimental results.

Bonding, electric (hyper)polarizability and vibrational property of heterofullerene C₄₈B₁₂ are studied by first-principles calculations. Infrared- and Raman-active vibrational frequencies of C₄₈B₁₂ are assigned. In comparison to isolated carbon or boron atom, the static polarizability per atom in C₄₈B₁₂ is enhanced due to the delocalized pi electrons. The first-order hyperpolarizability in C₄₈B₁₂ is zero because of the inversion symmetry. The average second-order hyperpolarizability of C₄₈B₁₂ is about 180% larger than that of C₆₀. Our results suggest that C₄₈B₁₂ is an idea candidate for photonic and optical limiting applications because of the enhanced third-order optical nonlinearities.

For the quasi-relativistic normalized elimination of small component using an effective potential (NESC-EP) method, analytical energy gradients were developed, programmed, and implemented in a standard quantum chemical program package. NESC-EP with analytical gradients was applied to determine geometry, vibrational frequencies, and dissociation enthalpies of ferrocene, tungsten hexafluoride, and tungsten hexacarbonyle. Contrary to non-relativistic calculations and calculations carried out with RECPs for the same compounds, NESC-EP provided reliable molecular properties in good agreement with experiment. The computational power of NESC-EP results from the fact that reliable relativistic corrections are obtained at a cost level only slightly larger than that of a non-relativistic calculation.

All-electron CCSD(T), QCISD(T) and MP4(SDQ) calculations including relativistic effects via the use of the IORAmm Hamiltonian have been performed for PdCO. The optimized molecular geometry is in nice agreement with the recently obtained experimental data. The PdÐCO bond dissociation energy is estimated to be 38.8 kcal/mol. The vibrational spectrum of PdCO is calculated and a reassessment of the experimental datum for the frequency of bending mode is suggested.

This thesis is concerned with the investigation of the electronic structure of a number of insulating transition metal (TM) crystalline materials by using wave-function based embedded cluster calculations. Quantities and properties of interest studied in this work are related to the local ground-state electronic configuration, elementary, low-energy spin and charge excitations, and to core level excitation processes. Attempts to characterize and understand the electronic structure of solid TM compounds like oxides, halides, and silicides, began already in the 1940's. The main motivations at the time came from the issue of the Mott metal-insulator transition, the problem of magnetic ordering in insulators, and the problem of itinerant ferromagnetism. More recently, phenomena such as heavy fermion behavior, high-temperature superconductivity, colossal magnetoresistance, and spin-Peierls phase transitions have revived interest in these systems. Nevertheless, although considerable effort has been put into the field, many of the transition metal materials are poorly understood. The proper treatment of various competing physical effects, like electron localization as a result of strong electron-electron interactions and band-like behavior as a result of orbital overlap and translational symmetry, remains one of the most difficult problems in solid state physics. Within the quantum chemical approach the cluster method is directed to solving the Schrödinger equation for a small but relevant part of a larger system. Certain properties of crystalline solids, e. g. effects connected with the existence of isolated defects and impurities in an otherwise perfect infinite lattice, molecule-surface interactions, localized 3d or 4f electronic states in transition metal or rare earth compounds etc., are well suited to investigation by cluster methods. In the present work calculations were performed on clusters containing one or more TM sites plus the adjacent anions. The cluster is embedded in some effective potential that accounts for the crystal Madelung field and for short-range Pauli and exchange interactions due to the finite charge distribution of the nearest neighbors, respectively.

The third- and fifth-order time-domain Raman response can be calculated using a finite field method. This method will be described and compared to the time correlation function methods that can also be used. The advantages of the finite field method will be addressed and the calculated third- and fifth-order response will be presented for liquid carbon disulfide. The calculated third-order response is shown to agree very well with experiments. For the fifth-order response the problem of third-order cascaded response contaminating the experimental measurements will be addressed.

We give an overview of the underlying concepts of time-dependent current-densityfunctional theory (TDCDFT). We show how the basic equations of TDCDFT can be elegantly derived using the time contour method of nonequilibrium Green function theory. We further demonstrate how the formalism can be used to derive explicit equations for the exchange-correlation vector potentials and integral kernels for the Kohn-Sham equations and their linearized form.

In this work we demonstrate how to derive the Kohn-Sham equations of time-dependent current-density functional theory from a generating action functional defined on a Keldysh time contour. These Kohn-Sham equations contain an exchange-correlation contribution to the vector potential. For this quantity we derive an integral equation. We further derive an integral equation for its functional derivative, the exchange-correlation kernel, which plays an essential role in response theory. The exchange-only limits of the latter equation is studied in detail for the electron gas and future applications are discussed.

To describe the dynamical interplay of electronic and nuclear degrees of freedom in molecules exposed to strong laser pulses, we present two different variational approaches based on the statonary-action principle: A mean-field treatment of the electron-nuclear interaction and an explicitly correlated ansatz. The two methods are tested on a one-dimensional model of H₂⁺ which can be solved exactly. The correlated approach significantly improves upon the mean-field treatment, especially in the case of laser fields strong enough to cause substantial dissociation.

A series of tri-nuclear metal clusters MS₄(M'PPh₃)₂(M'PPh₃) (M=Mo,W; M' = Cu, Ag, Au) have been studied using density functional theory (DFT). The static polarizabilities and hyperpolarizabilities of the model clusters have been calculated using the finite-field (F-F) method. The model clusters, divided into two groups, are alike in that the structure of two fragments of rhombic units M-(m-S)2-M'(M=Mo,W; M'=Cu, Ag, Au), perpendicular to each other, are joined by sharing the node (bridge) metal M. It is the charge transfer from one of these moieties to the other in these characteristic sulfido-transitional metal cores that is responsible for the polarizabilities and hyperpolarizabilities. This kind of electronic de-localization, differentiated from that of planar p-system, is interesting and warrants further investigation. The structural effects on properties are important. In these models, considerable second-order nonlinearities are exhibited. The element substitution effect of Mo and W is weak, while that of Cu and Ag is relatively substantial. An overall order is, b_xxxx(Mo-Ag) > b_xxxx(W-Ag) > b_xxxx(Mo-Au) > b_xxxx(W-Au) > b_xxxx(Mo-Cu) > b_xxxx(W-Cu) and b_av(Mo-Ag) ~ b_av(W-Ag) > b_av(Mo-Au) ~ b_av(W-Au) ~ b_av(Mo-Cu) ~ b_av(W-Cu).

The division of a system under study in a quantummechanical and a classical system in QM/MM calculations is sometimes very natural, but a problem arises in the case of bonds crossing the QM/MM boundary. A new link model is presented that uses a capping (link) atom to satisfy the valences of the quantumchemical system, with the position of the capping atom depending on the positions of the real atoms involved in the link bond. This way no degrees of freedom for the capping atom are introduced. Moreover, the introduction of this artificial atom is corrected for by subtracting the classical molecular mechanics interactions with the real QM system it would have if it were a classical atom. That is, the capping atoms are Added and Removed. The new model has been tested on three amino acid residues, and shows a clear improvement over other link models (as represented by the IMOMM/ADF implementation). The average absolute deviation for the C_a-C_b bond distance as obtained when comparing the full QM and QM/MM results, is around 0.75 pm. The IMOMM model predicts distances for the C_a-C backbone and C_a-N backbone bonds with an average absolute deviation of 2.3-2.8 and 5.3-5.5 pm, respectively; this is an increase by a factor of 3.1-4.0 and 7.1-7.3 compared to the C_a-C_b bond. For the new AddRemove model, the average absolute deviations are 1.0-1.2 and 0.6-0.9 pm, respectively for the C_a-C backbone and C_a-N backbone bonds; compared to the C_a-C_b bond, this means only a slight change with a factor of 1.3-1.6 and 0.8-1.2 respectively. The new AddRemove model performs therefore much better, and is shown to be a substantial improvement over the IMOMM model.

1s ionization 1s->'4p' transition energies were determined by electronic structure calculations on embedded Mn ions and MnO₆ clusters to identify mechanisms which determine the chemical shift observed in X-ray photoelectron and X-ray-absorption near-edge spectroscopy of manganese oxide compounds. The effective atomic charge, expressed by the 3d occupation, of the Mn-ion and the Madelung potential were shown to be the two most important influences on the observed shifts, by systemically varying these in the embedded cluster models. The relatively small sensitivity of the 1s ionization energy to the material is explained by the compensating effects of the Madelung potential and the effective atomic charge of the Mn-ion. The chemical shift in the 1s->'4p' transition energies in different materials is explained by the effects of Madelung potential and 3d occupation no longer compensating each other. This expresses the difference in the spatial extent of the 1s and 4p orbitals. Agreement with experimental shifts is only obtained upon including the screening effects by explicit treatment of the first layer of O-atoms around the Mn-ion.

We provide a successful approach towards the solution of the longstanding problem of the large overestimation of the static polarizability of conjugated oligomers obtained using the local density approximation within density-functional theory. The local approximation is unable to describe the highly nonlocal exchange and correlation effects found in these quasi-one-dimensional systems. Time-dependent current-density-functional theory enables us to describe ultranonlocal exchange-correlation effects within a local current description. Recently a brief account was given of the application of the Vignale-Kohn current-functional [G. Vignale, W. Kohn, Phys. Rev. Lett. 77 2037 (1996)] to the axial polarizability of oligomer chains [M. van Faassen, P.L. de Boeij, R. van Leeuwen, J.A. Berger, and J.G. Snijders, Phys. Rev. Lett. 88 186401 (2002)]. With the exception of the model hydrogen chain, our results were in excellent agreement with best available wavefunction methods. In the present work we further outline the underlying theory and describe how the Vignale-Kohn functional was implemented. We elaborate on earlier results and present new results for the oligomers of polyethylene, polysilane, polysilene, polymethineimine, and polybutatriene. The adiabatic local density approximation gave already good results for polyethylene, which were slightly modified by the Vignale-Kohn functional. In all other cases the Vignale-Kohn functional gave large improvements upon the adiabatic local density approximation. The Vignale-Kohn results were in agreement with best available data from wavefunction methods. We further analyze the hydrogen chain model for different bond length alternations. In all these cases the Vignale-Kohn correction upon the adiabatic local density approximation was too small. Arguments are given that further improvements of the functional are needed.

In this work we present theory and implementation for a discrete reaction field model within Density Functional Theory (DFT) for studying solvent effects on molecules. The model combines a quantum mechanical (QM) description of the solute and a classical description of the solvent molecules (MM). The solvent molecules are modeled by point charges representing the permanent electronic charge distribution, and distributed polarizabilities for describing the solvent polarization arising from many-body interactions. The QM/MM interactions are introduced into the Kohn-Sham equations, thereby allowing for the solute to be polarized by the solvent and vice versa. Here we present some initial results for water in aqueous solution. It is found that the inclusion of solvent polarization is essential for an accurate description of dipole and quadrupole moments in the liquid phase. We find a very good agreement between the liquid phase dipole and quadrupole moments obtained using LDA and results obtained with a similar model at the Coupled Cluster Singles and Doubles (CCSD) level of theory using the same water cluster structure. The influence of basis set and exchange correlation functional on the liquid phase properties was investigated and indicates that for an accurate description of the liquid phase properties using DFT a good description of the gas phase dipole moment and molecular polarizability are also needed.

We perform first-principles calculations of the structural, electronic, vibrational and magnetic properties of a novel C₄₈N₁₂ aza-fullerene as well as C₆₀. Full geometrical optimization has shown that C₄₈N₁₂ is characterized by several distinguish features: only one nitrogen atom per pentagon, two nitrogen atoms preferentially sitting together in one hexagon, S₆ symmetry, six CN and nine CC bond lengths. The Mulliken analysis indicates that the doped nitrogen atoms in C₄₈N₁₂ exist as electron acceptors and three-fourths of carbon atoms as electron donors. Total energy calculations of C₄₈N₁₂ show that the highest occupied molecular orbital (HOMO) is a doubly degenerate level of a_g symmetry and the lowest unoccupied molecular orbital (LUMO) is a nondegenerate level with $a_{u}$ symmetry. The calculated binding and HOMO-LUMO energy gap of C₄₈N₁₂ are about 1 eV smaller than those of C₆₀. For both C₄₈N₁₂ and C₆₀, the total energies calculated with STO-3G, 3-21G and 6-31G basis sets differ from the 6-31G(d) basis set results by about 1.5%, 0.6% and 0.05%, respectively, and the HOMO-LUMO gap decreases about 5 eV and the binding energy increases about 2 eV due to electron correlations.
Vibrational frequency analysis predicts that C₄₈N₁₂ has totally 116 vibrational modes: 58 modes are infrared-active (29 doubly-degenerate and 29 non-degenerate modes) and 58 modes are Raman-active (29 doubly-degenerate unpolarized and 29 non-degenerate polarized). For C₄₈N₁₂, the Raman-active frequency (RAF) of the strongest Raman singal in the low- and high-frequency regions and the lowest and highest RAFs are almost the same as those of C₆₀. It is found that C₄₈N₁₂ exhibits 10 NMR (nuclear magnetic resonance) spectral signals. In comparison to isolated carbon or nitrogen atom, enhancement in the dipole polarizability is found due to the delocalized electrons in C₄₈N₁₂ and C₆₀. Meanwhile, the effects of basis sets are discussed in detail. The different methods for calculating nuclear magnetic shielding tensors are compared.
Our detailed study of C₆₀ reveals the importance of electron correlations and the choice of basis sets in the ab initio calculations. Our best calculated results for C₆₀ with the B3LYP hybrid density functional theory are in excellent agreement with experiment and demonstrate the desirable efficiency and accuracy of this theory for obtaining quantitative information on the structural, electronic and vibrational properties of these materials. Our first-principles results suggest that C₄₈N₁₂ could have potential applications as semiconductor components and possible building materials for nanometer electronics, photonic devices and good diamagnetic materials.

This paper discusses a time-dependent density functional theory (TDDFT) study of the effect of molecular structure on the excited state polarizability of conjugated molecules. A short phenylenevinylene oligomer containing three phenyl rings (PV2, distyryl benzene) is taken as a model system. Introduction of methyl side chain is shown to have only a small influence on the increase in polarizability upon excitation (the excess polarizability). Methoxy groups have a much larger effect but in this case the excess polarizability depends strongly on the dihedral angle between the side-chain and the backbone of the molecule. If the central phenyl ring of PV2 has a meta-configuration rather than para, both the optical absorption spectrum and the excess polarizability change considerably.

We present a Discrete Solvent Reaction Field (DRF) model for the calculation of frequency-dependent hyperpolarizabilities of molecules in solution. In this model the solute is described using Density functional Theory (DFT) and the discrete solvent molecules are described with a classical polarizable model. The first hyperpolarizability is obtained using Time-Dependent DFT in an efficient way by using the (2n+1) rule. The method was tested for liquid water represented as a water molecule embedded in a cluster of 127 classical water molecules. Frequency-dependent first and second hyperpolarizability related to the Electric Field Induced Second Hamonic Generation (EFISH) experiment was calculated both in the gas phase and in the liquid phase. For water in the gas phase, results in good agreement with correlated wavefunction methods and experiments are obtained by using the so-called shape-corrected exchange correlation (xc)-potentials. In the liquid phase the effect of using asymptotic correct functionals is discussed. Furthermore, it is shown that the first hyperpolarizability is more sensitive to damping of the interactions at short range than the second hyperpolarizability. The model reproduced the experimentally observed sign change in the first hyperpolarizaibility when going from the gas phase to the liquid phase.

A Discrete Solvent Reaction Field model for calculating frequency-dependent molecular linear response properties of molecule in solution is presented. The model combines a Time-Dependent Density Functional Theory (QM) description of the solute molecule with a classical (MM) description of the discrete solvent molecules. The classical solvent molecules are represented using distributed atomic charges and atomic polarizabilities. All the atomic parameters have been chosen so as to describe molecular gas phase properties of the solvent molecule, i.e. the atomic charges reproduce the molecular dipole moment and the atomic polarizabilities resproduce the molecular polarizability tensor using a modified dipole interaction model. The QM/MM interactions are introduced into the Kohn-Sham equations and all interactions are solved self-consistent, thereby allowing for the solute to be polarized by the solvent. Furthermore, the inclusion of polarizabilities in the MM part allows for the solvent molecules to be polarized by the solute and by interactions with other solvent molecules. Initial applications of the model to calculate the vertical electronic excitation energies and frequency-dependent molecular polarizability of a water molecule in a cluster of 127 classical water molecules are presented. The effect of using different exchange correlation (xc)-potentials is investigated and the results are compared with results from wavefunction methods combined with a similar solvent model both at the correlated and uncorrelated level of theory. It is shown that accurate results in agreement with correlated wavefunction results can be obtained using xc-potentials with the correct asymptotic behavior.

A dipole interaction model (IM) for calculating the molecular second hyperpolarizability, Gamma, of aliphatic and aromatic molecules has been investigated. The model has been parametrized from quantum chemical calculations of Gamma at the self-consistent field (SCF) level of theory for 72 molecules. The model consists of three parameters for each element p: an atomic polarizability, an atomic second hyperpolarizability, and an atomic parameter, Phi_p, describing the width of the atomic charge distribution. The Phi_p parameters are used for modeling the damping of the interatomic interactions.
Parameters for elements H, C, N, O, F and Cl were determined and typical differences between the molecular Gamma derived from quantum chemical calculations and from the IM are below 30% and on average around 10%.
As a preliminary test, the dipole interaction model was applied to the following molecular systems not included in the training set: the urea molecule, linear chains of urea molecules, and C₆₀. For these molecules deviations of the IM result for the molecular Gamma from the corresponding SCF value were at most around 30% for the individual components, which in all cases is a better performance than obtained with semi-empirical methods.

The geometries of various tautomers and isomers of 2-methylamino-2-imidazoline, 2-methylamino-2-oxazoline, 2-methylamino-2-thiazoline, 2-phenylamino-2-imidazoline, 2-phenylamino-2-oxazoline and 2-phenylamino-2-thiazoline have been studied using the Becke3LYP/6-31+G(d, p) DFT, ONIOM(Becke3LYP/6-31+G(d, p):HF/3-21G*) and ONIOM(Becke3LYP/6-31+G(d, p):AM1) methods. The optimised geometries indicate that these molecules show a distinctly nonplanar configuration of the cyclic moieties. In the gas phase the amino tautomers (with exception of 2-phenylamino-2-imidazoline) are computed to be more stable than the imino tautomers. Of the two possible (E and Z) isomers of methyl and phenyl derivatives of imino-oxazolidine and imino-thiooxazolidine species the (Z)-isomers have the lowest energy. The iminozation free energies in the gas phase were found to be 5 - 15 kJ/mole. Absolute values of KT depend strongly on the accuracy of the method used for calculation of free energy. Solvation (using the MD simulations) causes in most cases a shift in tautomeric preference towards the imino species.

Analytic expressions are derived for the evaluation of derivatives of the total molecular energy with respect to external parameters ~nuclear coordinates, external electric fields, etc.! within the relativistic regular approximation. The presented formalism employs the spectral resolution of the identity avoiding, however, the explicit use of an auxiliary basis set in the calculation of the matrix elements of the regular relativistic Hamiltonian. The final formulas for the total energy and energy derivatives are presented in matrix form suitable for implementation into standard quantum chemical packages. Results of benchmark calculations for gold containing diatomic molecules and for xenone hexafluoride performed at the HartreeÐFock and various correlation corrected levels of theory are presented and discussed.

A new method for relativistically corrected nuclear magnetic resonance (NMR) chemical shifts is developed by combining the individual gauge for the localized orbital approach for density functional theory with the normalized elimination of a small component using an effective potential. The new method is used for the calculation of the NMR chemical shifts of ⁹⁵Mo and ¹⁸³W in various molybdenum and tungsten compounds. It is shown that quasirelativistic corrections lead to an average improvement of calculated NMR chemical shift values by 300 and 120 ppm in the case of ⁹⁵Mo and ¹⁸³W, respectively, which is mainly due to improvements in the paramagnetic contributions. The relationship between electronic structure of a molecule and the relativistic paramagnetic corrections is discussed. Relativistic effects for the diamagnetic part of the magnetic shielding caused by a relativistic contraction of the s,p orbitals in the core region concern only the shielding values, however, have little consequence for the shift values because of the large independence from electronic structure and a cancellation of these effects in the shift values. It is shown that the relativistic corrections can be improved by level shift operators and a B3LYP hybrid functional, for which Hartree-Fock exchange is reduced to 15%.

The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c²⁰. Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations.

Analytic expressions for the derivatives of the total molecular energy with respect to external electric field are derived within the regular approximation to the full four-component relativistic Hamiltonian and presented in matrix form suitable for implementation in standard quantum-chemical codes. Results of benchmark calculations using the infinite-order regular approximation with modified metric method are presented and discussed. The static electric dipole polarizabilities of group VIII metal tetroxides MO₄ for M=Ru, Os, Hs (Z=108) are studied with the help of second-order Møller-Plesset perturbation theory using the infinite-order regular approximation with modified metric Hamiltonian. The polarizabilities obtained vary in the sequence RuO₄>OsO₄>HsO₄, which is different from those obtained in other studies. However, it is in line with calculated ¹T₂^←1A₁ excitation energies of the group VIII tetroxides, which provide a measure for the magnitude of their polarizabilities.

Early theoretical studies of magnetic interactions between paramagnetic centers in solids and molecules are briefly reviewed as an introduction to the main theme of this paper: non-orthogonal CI approaches for the prediction and interpretation of magnetic couplings. In a non-orthogonal CI approach, the wavefunctions are linear combinations of configuration state functions, which are each expressed in their own optimized orbital basis set. The NOCI approach allows for an adequate treatment of near-degeneracy correlation effects using a compact, transparent wavefunction. This facilitates straightforward analysis of the physical effects involved. A closely related method is State Interaction, where the final wavefunctions are linear combinations of multi-configuration functions. Comparisons are made with the use of conventional configuration interaction and perturbation theory methods. The compound La₂CuO₄ is selected as an illustrative example.

By expanding the Foldy-Wouthuysen representation of the Dirac equation near the free-particle solution it is shown that the Hamiltonian of the zeroth-order regular approximation (ZORA) leads to an infinite summation of the leading relativistic corrections to the free-particle, non-relativistic energy. The analysis of the perturbation expansion of the ZORA Hamiltonian reveals that the ZORA Hamiltonian recovers all terms of the Breit-Pauli theory to second order. This result is general and applies not only to hydrogen-like atomic ions (as was demonstrated before) but also to a wide variety of physical problems. ZORA is analogous to the random phase approximation in many-body theory in the sense that both methods include an infinite-order summation of the asymptotically non-vanishing terms. This highlights the difference between ZORA and the Douglas-Kroll method, with the latter being analogous to finite-order many-body perturbation theory. On the basis of this analysis the performance of ZORA when calculating various molecular properties is discussed.

An atomic dipole interaction model has been used for calculating the second hyperpolarizability of carbon nanotubes on the length scale up to 75~nm. It is demonstrated that an atomistic representation of mesoscale systems such as nanotubes can be used to obtain a cubic response property up to a size of the system where the property scales linearly with increasing size. In particular, it demonstrates that atomistic models are useful also for designing nonlinear molecular materials, where local modifications may give large macroscopic contributions. The saturation length has been calculated for carbon nanotubes. It is found that carbon nanotubes are comparable to conjugated polymers with respect to the magnitude of the second hyperpolarizability and are therfore very promising candidates for future nonlinear optical materials.

Radon hexafluoride is a bound species (bond length Rn-F: 2.008 Å) as demonstrated by correlation corrected relativistic ab initio calculations using IORAmm (infinite order regular approximation with modified metric) at the MP2 level of theory with a (24s20p13d8f)[15s13p8d4f]/aug-cc-pVDZ basis set. The calculated atomization energy is 226.9 kcal mol^-1 and the dissociation energy leading to Rn and 3F₂ is 126.6 kcal mol^-1. Results are in line with simple orbital-based predictions of possible relativistic effects. The relativistic effect for the atomization energy is 10.8 kcal mol^-1 rather than +27.7 kcal mol^-1 as predicted on the basis of Dirac-Hartree-Fock (DHF) calculations. The latter were flawed by the lack of correlation corrections and an erroneous polynomial fit of the potential energy surface in the vicinity of the global minimum.

An embedded cluster approach was applied to study the electronic excitations on the NiO(001) surface. Using a quantum chemical calculation, a small (NiO5)8- cluster was embedded in a set of point charges to model the NiO(001) surface. Starting from the unrestricted Hartree-Fock level of theory, we calculate the ground-state properties to provide some insight into electronic structure and excitation. We estimate the excitation energies and oscillator strengths using the single excitation configuration-interaction (CIS) technique. Our results show that the CIS method is reasonably accurate for estimating the low-lying d-d excitations below the gap. We then demonstrate the electron correlation effects on the d-d transitions at several levels of ab initio correlated theory [CID (with all double substitutions), CISD (with all single and double substitutions), (quadratic) QCISD, and (with all single, double, and triple substitutions) QCISD (T)]. The electron correlation tends to decrease the magnitude of d-electron excitation energies. Using the many-body wave functions and energies resulting from CID and QCISD(T) calculations, we compute the second harmonic generation (SHG) tensor for the NiO(001) surface. In contrast to bulk NiO, where the SHG response is forbidden within the electric-dipole approximation because of the inversion symmetry, the C4v symmetry of the surface leads to five nonzero tensor elements. From that, the intensity of the nonlinear optical response as a function of photon energy at different polarizations of the incident and outgoing photons is obtained. This quantity can be directly measured in experiment, and we suggest possible conditions in order to detect it.

Results of ab initio embedded cluster calculations indicate that the doublet ground state of the V-O_R-V rung originates from a V 3d_xy¹-O_R2p_y¹-V 3d_xy¹ configuration. In the high temperature undistorted geometry the unpaired electron on oxygen is low-spin coupled to the 3d electrons and spin density is equally distributed over the vanadium ions. Based on this picture of the electronic ground state we propose a mechanism for the phase transition at 34 K. We find that a symmetry-broken configuration, R(V_i-O_R) < R(V_j-O_R), leads to V_i 3d_xy- O_R 2p_y spin singlet formation and stronger V_i - O_R bonding. We suggest that the onset of the phase transition at 34 K is driven by the shift of the bridging rung oxygentowards one of the V neighbors. The calculations predict a reduction of the exchange coupling constant of about 25% when distorting the V-O_R-V rung. At the same time, structural distortions involving the O_L leg oxygens induce alternation of the coupling constant and therewith spin-gap behavior.

The fifth-order 2D Raman response of a liquid is calculated taking all possible interaction induced effects into account. Next to dipole-induced dipole interactions, close collision effects due to induced multipoles and electron overlap are found to give a significant contribution to the response of liquid carbon disulfide. A correct prediction of the spectrum is impossible, when these effects are not properly taken into account. The calculated response is found to be in good agreement with some of the most recent experiments.

The geometries of a set of small molecules were optimized using eight different exchangecorrelation potential in a few different basis sets of Slater type orbitals, ranging from a minimal basis (I) to a triple zeta valence basis plus double polarization functions (VI). This enables a comparison of the accuracy of the xc-potentials in a certain basis set, which can be related to the accuracies of wavefunction based methods like Hartree-Fock and Coupled Cluster. Four different checks are done on the accuracy by looking at the mean error, standard deviation, mean absolute error and maximum error. It is shown that the mean absolute error decreases with increasing basis set size, and reaches a basis set limit at basis VI. With this basis set, the mean absolute errors of the xc-potentials are of the order of 0.7-1.3 pm, which i s comparable to the accuracy obtained with CCSD and MP2/MP3 methods. In the second part of this paper, the geometry of five metallocenes is optimized with the same potentials and basis sets, either in a non-relativistic or a scalar relativistic calculation using the ZORA approach. For the first row transition metal complexes, the relativistic corrections have a negligible effect on the optimized structures, but for ruthenocene they improve the optimized Ru-ring distance by some 1.4-2.2 pm. In the largest basis set used, the absolute mean error is again of the order of 1.0 pm. As the wavefunction based methods either give a poor performance for metallocenes (Hartree-Fock, MP2), or the size of the system makes a treatment with accurate methods like CCSD(T) in a reasonable basis set cumbersome, the good performance of Density Functional Theory calculations for these molecules is very promising. Even more so as DFT is an efficient method that can be used without problems on system sizes of this kind, or larger.

A series of large molecular quadratic hyperpolarizabilities in donor/acceptor substituted trans-tetraammineruthenium(II) compelexes [Ru(NH₃)₄L^DL^A]ⁿ⁺ (n = 2, L^D = 4-(dimethylamino)pyridine, L^A = 4-pyridinecarboxaldehyde (1), 4-acetylpyridine (2), ethyl isonicotinate (3), or n = 3, L^A = N-methyl-4,4'-bipyridinium (4), N-(4-acetylphenyl)-4,4'-bipyridimium (4-AcPhQ⁺) (5), and n = 3, L^D = NH₃, L^A = (4-AcPhQ⁺) (6) has been studied using the TDDFT and ab initio HF method. It is found that the magnitude of the static hyperpolarizabilities b₀ increases as the donor/acceptor strength of L^D/L^A increases. The co-planes of the pyridine or benzene ring are not necessary to maintain the large non-linear optical properties. According to our study on Ru complexes, the TDDFT method is more reliable than the HF method in b-calculations.

In this work we have investigated the effects of substituting carbon atoms with B and N on the 2nd hyperpolarizability of C₆₀ using time-dependent density functional theory. We have calculated the 2nd hyperpolarizability of the double substitute-doped fullerenes C₅₈NN, C₅₈BB and C₅₈BN. For C₆₀ only small changes in the 2nd hyperpolarizability were found when doping with either 2 B or 2 N. However, by doping C₆₀ with both B and N, creating an donor-acceptor system, an increase in the 2nd hyperpolarizability with about 50% was found.

A recently developed variationally stable quasi-relativistic method, which is based on the low-order approximation to the method of normalized elimination of the small component, was incorporated into density functional theory (DFT). The new method was tested for diatomic molecules involving Ag, Cd, Au, and Hg by calculating equilibrium bond lengths, vibrational frequencies, and dissociation energies. The method is easy to implement into standard quantum chemical programs and leads to accurate results for the benchmark systems studied.

With the help of resolution of the identity (RI) a compact representation for the zeroth-order (ZORA) and infiniteorder (IORA) regular approximation Hamiltonians in matrix form is developed. The new representation does not require calculation of any additional molecular integrals, which involve an auxiliary basis set used in the RI. The IORA computational scheme is modified in such a way that the erroneous gauge dependence of the total energy is reduced by an order of magnitude. The new quasi-relativistic method, dubbed IORAmm, is tested along with the ZORA and IORA methods in atomic and molecular calculations performed at the SCF and MP2 level.

The static polarizabilities and the second-order hyperpolarizabilities of a series of tri-nuclear metal cluster models MS₄(M'PPh₃)₂(M'PPh₃) (M=Mo,W; M'=Cu, Ag, Au) have been calculated within the first-principle theoretical framework. The model clusters have two fragments of rhombic units and it is the charge transfer from one of these moieties to the other that is responsible for nonlinear optical property. This kind of electronic delocalization, differentiated from that of planar pi-system, is very interesting and is worthy for further investigation.

The objective of the work presented in this chapter has been to make a contribution to the development of quantum biology by carrying out the first density functional theoretical (DFT) investigation on larger segments of deoxyribonucleic acid (DNA). The challenges associated with this objective are twofold. In the first place, we wish to describe the structure and energetics of the DNA segments accurately and, in particular, we try to achieve a better understanding of the nature and behavior of this complex molecule of heredity on the basis of its electronic structure. Our analyses highlight the covalent character of hydrogen bonds in Watson-Crick pairs. Furthermore, they lead to the solution of a hitherto unresolved discrepancy between experimental (X-ray) and theoretical (ab initio and DFT) structures of AT (or AU) and GC base pairs. In the second place, the computational effort connected with first-principles quantum chemical studies on these biochemical systems is enormeous and, until recently, calculations on these systems have been out of reach. Thus, finding and implementing speed-up techniques that make our model systems computationally accessible constitutes the other challenge of this work that, in fact, had to be tackled first.

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Multi-reference effects can be covered by density functional theory (DFT) either implicitly via the exchange-correlation functional or explicitly via the form of the Kohn-Sham wave function. With the help of the exchange hole it is shown that the self-interaction error of the exchange functional will mimic long-range electron correlation effects if restricted Kohn-Sham theory is used. Functionals based on Slater or Becke exchange have a relatively large self-interaction error and, therefore, lead to a relatively large implicit coverage of long-range correlation, which, because of the possibility of doublecounting of electron correlation, has to be considered when using these functionals in connection with two- or multi-configurational descriptions based on ensemble DFT methods such as REKS (spin- Restricted Ensemble-referenced KS-DFT). Arguments are given that a REKS description of a multireference problem avoids a double-counting of long-range correlation effects, in particular as in this situation the self-interaction error of the exchange functional simulates more short- rather than longrange correlation effects. There is, however, no guarantee that the short-range effects are not doublecounted, namely once via the exchange and once via the correlation functional. Therefore, one should use hybrid functionals such as B3LYP in connection with multi-reference DFT methods because for hybrid functionals the self-interaction error and by this the implicit coverage of long(short)-range correlation effects is reduced due to the admixture of exact exchange. This rule applies also to broken-symmetry UDFT, which performs better with hybrid rather than GGA functionals. A way of avoiding the implicit coverage of multi-reference effects is given by the combination of wave function theory and DFT methods. The advantages and disadvantages of CAS-DFT are discussed and it is shown that an effective reduction of a double-counting of correlation effects is possible within this method.

The pulse-radiolysis time-resolved microwave conductivity technique was used to measure the mobility of charges along isolated chains of conjugated polymers. The mobility of holes along poly(phenylenevinylene) and polythiophene backbones were measured to be 0.43 cm²V^-1s^-1 and 0.02 cm²V^-1s^-1, respectively. The large difference between the mobility of holes on poly(phenylenevinylene) and polythiophene chains can be attributed to deviations from the coplanar alignment of structural units in the polymer backbone. The effect of such torsional disorder on intramolecular hole transport was theoretically investigated using a model based on the tight-binding approximation. The calculated ratio of hole mobilities along poly(phenylenevinylene) and polythiophene chains was found to be in agreement with experimental findings. For both polymers, estimated mobilities become consistent with the experimental values if polymerization defects and chain end effects are included in the calculations. This suggests that even higher mobilities than those reported here can be realized by improving the effective conjugation along the polymer chain.

A model of the polarizability of carbon disulfide dimers was constructed, using polarizabilities from accurate time-dependent density functional theory calculations as reference. This direct reaction field model takes dipole-induced dipole effects, induced multipole effects and effects due to the overlap of the electronic clouds into account in an approximate way. The importance of the induced multipole and the overlap effects is investigated. This polarizability model is subsequently used to calculate the third-order time-domain Raman response of liquid carbon disulfide. These results are compared to experimental data and earlier calculated response in which only dipole-induced dipole effects on the polarizability were included. The multipole effects are found to give a significant contribution to the subpico second part of the third-order Raman response.

Nonlocal interactions play a prominent role in the optics of inhomogeneous systems. Traditional discrete dipole descriptions take into account only electromagnetic nonlocality. This is insufficient to describe correctly the inhomogeneous optical response (reflectance anisotropy e.g.) for strongly bonded systems like semiconductor surfaces. For those systems exists also a prominent quantum mechanical nonlocality. In a cellular descripton this can be understood easily from the behavior of the wave function. For strongly bonded systems the wave function extends across cell boundaries and cells can only be polarized, when neigboring cells get polarized as well. This quantum induction introduces nonlocal polarizabilities in the description. The technical details how discrete dipole models have to be adapted to use nonlocal polarizabilities in finite systems and crystalline slabs and surfaces are given in this paper. The modified method is called discrete cellular method.

We have developed and investigated a dipole interaction model for calculating the polari zability of molecular clusters. The model has been parametrized from the frequency-dependent molecular polarizability as obtained from quantum chemical calculations for a series of 184 aliphatic, aromatic and hetero-cyclic molecules. A damping of the interatomic interaction at short distances is introduced in such a way as to retain a traceless interaction tensor and a good description of the damping over a wide range of interatomic distances. By adopting atomic polarizabilities in addition to atom-type parameters describing the damping and the frequency-dependence, respectively, the model is found to reproduce the molecular frequency-dependent polarizability tensor calculated with ab initio methods. A study of the polarizability of four dimers has been carried out: the hydrogen fluoride, methane, benzene and urea dimers. We find in general good agreement between the model and the quantum chemical results over a wide range of intermolecular distances. To demonstrate the power of the model, the polarizability has been calculated for a linear chain of urea molecules with up to 300 molecules and one- and two-dimensional clusters of C₆₀ with up to 25 molecules. Substantial intermolecular contributions are found for the polarizability anisotropy, whereas the effects are small on the mean polarizability. For the mean polarizability of C₆₀, we find good agreement between the model and experiments both in the case of an isolated molecule and in a comparison of a planar cluster of 25 C₆₀ molecules with experimental results on thin films.

The subpicosecond dynamics of binary mixtures of carbon disulfide and alkane have been studied using third-order time-resolved Raman techniques. Both the anisotropic and the isotropic responses were investigated. These depend differently on many-body contributions to the first-order susceptibility and probe different modes in the liquid. The anisotropic response is dominated by single molecule effects, whereas the isotropic response is completely determined by many-body contributions since the single molecule response vanishes. To interpret the experimental results, molecular dynamics simulations were performed on model mixtures. The effect of dilution on the subpicosecond response also cannot be explained by many-body effects in the first-order susceptibility alone. Explanations such as aggregation due to quadrupole moments on the carbon disulfide molecules and density changes cannot explain the observed dilution effects. Apparently the character of the many-body dynamics itself is modified by the change of the molecular force fields, when carbon disulfide molecules are replaced by alkanes.

In this paper a combined experimental and quantum chemical study of the geometry and opto-electronic properties of unsubstituted and dialkoxy-sustituted phenylene-vinylene oligomers (PV's) is presented. The optical absorption spectra for PV cations with different chain lengths and substitution patterns were measured using pulse radiolysis with time-resolved spectrophotometric detection from 1380 to 500 nm (0.9 to 2.5 eV). The geometries of the PV's studied were optimized using density functional theory (DFT) for both the neutral and singly charged molecule. The spectra for the PV radical cations were then calculated using singly excited configuration interaction with an intermediate neglect of differential overlap reference wave function method together with the DFT geometry. The agreement between experimental and theoretical absorption energies is excellent; most of the calculated radical cation absorption energies are within 0.15 eV of the experimental values. The pattern of dialkoxy-substitution is found to have a large effect on the optical absorption spectrum of the cation. Using the calculated charge distribution it is shown that the degree of delocalization of the charge correlates with the energy of the lowest absorption band. If alkoxy side chains are present on some of the rings the positive charge tends to localize at those sites.

The collision induced effects in the third-order Raman response of liquid xenon have been studied theoretically and experimentally. The effect of electron cloud overlap on the polarizability of xenon dimers have been studied using accurate time-dependent density functional theory calculations. The dimer polarizabilities have been modeled using a direct reaction field model that can be generalized to condensed systems. The polarizability model has been used in molecular dynamics simulations to calculate the third-order time-domain Raman response of liquid xenon. Excellent agreement is found between the shape of the calculated and the measured response. The shape of the calculated response depends little on whether the electron overlap effect is taken into account, but the intensity of the response is strongly affected by the electron overlap effect.

We have studied the medium effects on the frequency-dependent polarizability of water by separating the total polarizability of water clusters into polarizabilities of the individually water molecules. A classical frequency-dependent dipole-dipole interaction model based on classical electrostatic and an Unsöld dispersion formula has been used. It is shown that the model reproduces the polarizabilities of small water clusters calculated with time-dependent density functional theory. A comparison between supermolecular calculations and the localized interaction model illustrates the problems arising from using supermolecular calculations to predict the medium perturbation on the solute polarizability. It is also noted that the solute polarizability is more dependent on the local geometry of the cluster than on the size of the cluster.

A consistent derivation is given for local field factors to be used for correcting measured or calculated static (hyper-)polarizabilities in the condensed phases. We show how local fields should be used in the Coupled Perturbative Hartree Fock (CPHF) or Finite Field methods for calculating these properties, specifically for the Direct Reaction Field approach, in which a quantum chemically treated 'solute' is embedded in a classical 'solvent' mainly containing discrete molecules. The derivation of the local fields is based on strictly linear response of the classical parts and they are independent of any quantum mechanical method to be used.

Theoretical studies and simulation have been applied to explore novel nonlinear optical crystals in metal clusters. The structure-nonlinear optical property relationships of a series of the metal cluster molecules have been investigated theoretically within the density functional theory (DFT) framework. For example, the polarizability and hyperpolarizability of a set of three-nuclear metal cluster compounds of Mo(W)/Cu(Ag, Au) sulfur system are calculated to elucidate the influence of geometric configuration and the element substitution effect; a set of potential second harmonic generation (SHG) metal cluster crystals are studied and simulated such as, MoAg₂S₅(Py)(PPh₃)₂, MoS₄Cu₄I₂(Py)₆ cluster and more. The results indicate many of these crystals are promising SHG crystals that may be applied in infrared (IR) spectroscopic region. The studies are useful to the procedure of screening, simulations and design of novel nonlinear optical crystals in metal cluster compounds, especially those to be applied in medium/far-IR region.

The switching behaviour of 1,2-bis(5-phenyl-2-methyl-thien-3-yl)cyclopentene is studied by means of polarization selective nonlinear optical spectroscopy and time-dependent density functional theory. The combined information from the observed population and orientational dynamics together with the results of theoretical calculations show that on a subpicosecond time scale rapid mixing and relaxation of electronic states occur, before switching takes place. Such pre-switching dynamics was not studied in detail in these systems before. Then, the switching process itself occurs by the formation of a C-C bond in the central cyclopentane ring with a time constant of 4.2 ps. Driven by the ring closure, the side groups of the switch molecules rotate to a nearly coplanar conformation with a time constant of about 8 ps. The switching process is completed by relaxation of the vibrationally hot ground state of the closed form of the molecule to thermal equilibrium.

The oriented-gas model based on additivity hypothesis is widely used in predicting macroscopic the nonlinear optical susceptibility of a molecular crystal from molecular hyperpolarizability calculations. Here, we argue that the intermolecular hydrogen bond interactions will break the additivity relationship for the first hyperpolarizability of urea hydrogen-bonded clusters up to the nearest-neighbor configuration on the basis of our ab initio and time-dependent density functional theory (TDDFT) studies. The influences of basis sets, exchange-correlation potential and frequency dispersion on TDDFT calculation of (hyper)polarizability are discussed as well. We hope that the study will be helpful to the molecular design and simulations of novel nonlinear optical materials.

Ab initio theoretical results are reported to determine the role of inter-atomic screening of the metal core hole in Mn 3s X-ray photoelectron spectra, XPS, of MnO. We focus on the transitions to high spin 3s core-hole states. We have used configuration interaction wavefunctions within the framework of non-orthogonal orbitals for different configurations. This method allows for a balanced treatment of configurations that involve different degrees of screening of the core-hole. The differences between MnO and NiO are analyzed. In MnO inter-atomic screening of the core hole is found to play a minor role. This is in contrast with NiO, where, in previous work, the inclusion of inter-atomic screening of the metal core hole was shown to be crucial for a proper explanation of the Ni 3s XPS. The main reason for the difference is an essentially atomic effect, namely the larger electron affinity of Mn as compared to Ni. This difference is only partly compensated by the smaller crystal field in MnO.

We solve the longstanding problem of the large overestimation of the static polarizability of conjugated polymers obtained using the local density appro ximation within density functional theory. The local approximation is unable to describe the highly nonlocal exchange and correlation effects found in these quasi-onedimensional systems. Time-dependent current density functional theory enables us to describe ultra nonlocal exchange-correlation effects within a semi-local current description. For this we use the Vignale-Kohn functional [G. Vignale, W. Kohn, Phys. Rev. Lett. 77 2037 (1996)] and obtain the static polarizability of several polymers. The results are in excellent agreement with best available correlated wavefunction methods.

We provide evidence for a doublet ground state of the V-O-V rung of predominant V 3d_xy¹-O 2p_y¹-V 3d_xy¹ character in the HT phase of a-NaV₂O₅. By ab initio quantum chemical embedded cluster calculations, it is shown that such a model is able to explain the main features of the optical absorption spectrum, and the AFinteraction along the b axis. The unpaired electron on O is low-spincoupled to the V d electrons and spin density is predicted to be localized on vanadium. The optical absorption peak at 0.9 eV is assigned to a state with similar orbital occupations but a different spin coupling scheme, resulting in spin density localized on the oxygen of the V-O-V rung. Absorption peaks at higher energy are tentatively assigned to vanadium to rung oxygen and apex oxygen to vanadium charge transfer excitations. Our analysis suggests that the high temperature magnetic structure can still be described by a spin model with an effective S=1/2 spin on each V-O-V rung.

Molecular Dynamics simulation techniques together with Time-Dependent Density Functional Theory calculations have been used to investigate the effect of photon absorption by a 4-hydroxy-cinnamic acid chromophore on the structural properties of the Photoactive Yellow Protein (PYP) from Ectothiorodospira halophila. In this bacteria exposure to blue light leads to a negative phototactic response. The calculations suggest that the protein not only modifies the absorption spectrum of the chromophore, but also regulates the subsequent isomerization of the chromophore by stabilizing the isomerization transition state. Although signalling from PYP is thought to involve partial unfolding of the protein, the mechanical effects accompanying isomerization do not appear to directly destabilize the protein.

In this article we review time-dependent density functional theory for calculating the static and frequency-dependent dielectric function e(w) of nonmetallic crystals. We show that a real-space description becomes feasible for solids by using a combination of a lattice-periodic (microscopic) scalar potential with a uniform (macroscopic) electric field for the description of the effective one-electron system. We treat the time-dependent fields as perturbations in a periodic structure calculation. The induced density and microscopic potential can be obtained self-consistently for fixed macroscopic field by using linear response theory in which Coulomb interactions and exchange-correlation effects are included. The dielectric function can then be obtained from the induced current. We obtained e(w) for a wide variety of nonmetallic crystals within the adiabatic local density approximation (ALDA) in good agreement with experiment. In particular in the low-frequency range no adjustment of the band gap obtained within the local density approximation (LDA) seems to be necessary. Relativistic effects on the dielectric response have been found to be important for a few semimetals that have inverted bandstructures within the LDA. Exchange-correlation effects beyond the ALDA have been treated by a polarization-dependent functional for the effective electric field, with improved dielectric functions as result.

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We have calculated the reflectance anisotropy for the GaAs (110) surface using the discrete cellular method. This method extends the range of application of standard discrete dipole calculations by incorporating nonlocal polarizabilities. The method adds a second quantum mechanical channel of nonlocality, which turns out to be necessary and yields very good agreement between theory and experiment.

We give an overview of the underlying concepts of time-dependent density-functional theory. The basic relations between densities, potentials and initial states, for time-dependent many-body systems are discussed. We obtain some new results concerning the invertability of response functions. Some fundamental difficulties associated with the time-dependent action principle are discussed and we show how these difficulties can be resolved by means of the Keldysh formalism.

In this paper we treat the dominant relativistic effects in the optical response properties of mercury selenide using time-dependent density-functional theory. The scalar relativistic effects have been included within the zeroth-order regular approximation (ZORA) in both the ground-state DFT calculations, and in the time-dependent response calculations. Within this approximation the HgSe crystal is found to be a semimetal. In a previous study (J. Chem. Phys. 114, 1860 (2001)) we have shown that TDDFT/ZORA can be applied successfully to narrow-gap semiconductors, such as indium antimonide, that become semimetallic within the local density approximation when scalar relativistic effects are included. Results are given for the band structure, the static dielectric constantÊ and the dielectric function of HgSe, and these results are compared with the similar ones for InSb. We find considerably improved results for the dielectric function of HgSe when relativistic effects are included.

The third- and fifth-order time-domain Raman responses of liquid carbon disulfide have been calculated, taking local field effects into account through the dipole-induced dipole approximation to the polarizability. The third-order response is shown to be in excellent agreement with experimental data. The calculated two-dimensional shape of the fifth-order response is compared with recently reported experimental observations of what is claimed to be pure fifth-order response. Considerable discrepancies are observed which might be explained by contamination of the experimental results with sequential and especially parallel third-order cascaded Raman response. A new choice of polarization conditions is proposed, which increases the discrimination against these unwanted cascading effects, as compared to the previously discussed fully polarized and magic angle conditions.

In this paper we show how relativistic effects can be included in the time-dependent density-functional theory for the optical response properties of nonmetallic crystals. The dominant scalar relativistic effects have been included using the zeroth-order regular approximation (ZORA) in the ground-state DFT calculations, as well as in the time-dependent response calculations. We show that this theory can also be applied to indium antimonide in the zinc-blende structure, not withstanding the fact that it turns into a semi-metal when scalar relativistic effects are included. Results are given for the bandstructure, the static dielectric constant and the dielectric function, for the various levels on which relativity can be included, i.e. non-relativistic, only in the ground-state, or also in the response calculation. Comparisons of our calculated results are made with experiment and other theoretical investigations. With the inclusion of scalar relativistic effects, the bandstructure of InSb becomes semi-metallic within the local density approximation and we find a deviation of 5% from experiment for the static dielectric constant. Also the dielectric function is improved and the spectra are in good agreement with experiment, althought the spectral features are shifted to somewhat lower energies compared to experiment.

In this paper time dependent density functional theory (TDDFT) calculations of excited state polarizabilities of conjugated molecules are presented. The increase in polarizability upon excitation was obtained by evaluating the dependence of the excitation energy on an applied static electric field, the excitation energy was found to vary quadratically with the field strength. The excess polarizabilities obtained for singlet excited states are in excellent agreement with experimentally obtained values for short oligomers. For longer oligomers the excess polarizability is considerably overestimated, similar to DFT calculations of ground state polarizabilities. Excess polarizabilities of triplet states were found to be smaller than those for the corresponding singlet state. This also agrees with experimental results. Negative polarizabilities are observed for the lowest singlet A_g states which is caused by the quadratic Stark effect. All results are explained in terms of a sum-over-states description for the polarizability.

In this paper we present a new approach to calculate optical spectra, which for the first time uses a polarization dependent functional within current density functional theory (CDFT), which was proposed by Vignale and Kohn [Phys. Rev. Lett. 77, 2037 (1996)]. This polarization dependent functional includes exchange-correlation (xc) contributions in the effective macroscopic electric field. This functional is used to calculate the optical absorption spectrum of several common semiconductors. We achieved in all cases good agreement with experiment.

Time-resolved resonance Raman spectroscopy has been used to study the structure of the triplet excited state of bromanil. These experimental results were then simulated using parameters from density functional theoretical calculations and wave packet dynamics, in order to understand the structure and mode-specific displacements of the resonant excited state. The transition dipole moments and the energy separation of the T₁ and T_n states were obtained from time-dependent DFT calculations. We have demonstrated application of the technique to tetrabromo-p-benzoquinone. From our calculations, the observed T₁ >T_nabsorption spectrum has been assigned to the ³B_g > ³A_u transition. The geometry has been optimized for the resonant higher triplet state, T_n, and is found to be in good agreement with the predictions of the wave packet dynamical simulations. Mode-specific displacements of the triplet state geometry have been obtained from simulations and these have been rationalized with respect to the molecular orbital involved. Thus, we have demonstrated that from the simulations of the experimental TR3 spectral data, valuable additional information can be derived on the structure of the transient states that may then be used for elucidation of structure-reactivity correlation in the future.

A new charge analysis is presented that gives an accurate description of the charge distribution in molecules. The method is generally applicable to any method able to provide atomic multipole moments, but in this paper we take advantage of the way the Coulomb potential is calculated within the Density Functional Theory framework. We investigated a set of 31 molecules as well as all amino acids to test the quality of the method and found accurate results for the molecular multipole moments directly from the DFT calculations, as well as the values represented by the charges. The deviations from experimental values for the dipole/quadrupole moments are also small.

We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelisation, near order-N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper) polarisabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e. Kohn-Sham molecular orbital (MO) theory, and illustrate the power of the Kohn-Sham MO model in conjunction with the ADF-typical fragment approach to quantitatively understand and predict chemical phenomena. We review the "activation-strain transition state" (ATS) interaction model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled. Finally, we include a brief discussion of an application of time-dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena.

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In the present work, we have calculated the static and frequency-dependent polarizability tensors for a series of single-walled boron nitride nanotubes and compared with corresponding results for carbon nanotubes. The calculations have been performed by employing a dipole-dipole interaction model based on classical electrostatics and an Unsöaut;ld dispersion formula. In comparison, we have carried out ab intio calculations at the SCF level of the static polarizability of the smaller nanotubes with the STO-3G basis set. For the frequency-dependent polarizability of C₆₀ we found excellent agreement between the most accurate SCF calculations in the literature, the interaction model and experimental results. In particular, the frequency-dependence is modelled accurately indicating that the interaction model is a useful tool for studying the frequency-dependence of materials. For the nanotubes, we observe the same trends in the interaction model and in the SCF STO-3G results when the number of atoms is increased. However, the values obtained with the interaction model are about 100% larger than the corresponding SCF STO-3G results, due to the small size of the STO-3G basis set. We also find that the boron nitride nanotubes have smaller magnitudes of the polarizability tensor components than the corresponding components for the carbon nanotubes with the same geometry and number of atoms. Furthermore, we find that the geometry of the tube has a large influence on the anisotropy of the polarizability components, whereas the mean polarizability remains almost unaffected when the geometrical configuration is modified. Finally, we observe a relatively small frequency-dependence of the polarizability tensor of BN nanotubes.

The triplet excited state of tetrabromo-p-benzoquinone has been studied for the first time using time-resolved resonance Raman experiments. Density functional theoretical calculations have been carried out on the ground and triplet excited states. The molecular orbitals, geometries and vibrational frequencies have been analysed. Computed normal modes have been used to carry out normal mode analysis to obtain the potential energy distribution of all the vibational frequencies. Observed bands in the triplet state spectrum have been assigned using measured depolarization ratios, comparison with other quinones and calulated spectra. Changes in the geometry of the parent quinone on substitution with bromine has been correlated to the changes in the characters of the frontier molecular orbitals. Increased participation of the halogen lone pairs leads to significant changes in the geometry of the ground and excited states. It is found that the effect of halogen substitution is more pronounced on the excited state than on the ground state.

The polarization of the excited states of near-perpendicularly twisted ethylene in the condensed phase has been investigated by means of Direct Reaction Field (DRF) calculations. In these calculations, five organic solvents with variable polarity and polarizability were simulated by 50 discrete, classically described solvent molecules. The excited states of near-perpendicular ethylene were described using ab initio methods at the CISD level of theory using a DZV basis set.
It is demonstrated that there is a distinct correlation between the polarity of the solvent and the occurrence and stabilization of charge separated excited states of ethylene. Large dipole moments were observed for ethylene excited states in polar solvents, indicating that an asymmetric distribution of polar solvent molecules around the ethylene can introduce enough symmetry breaking to cause charge separation. This behaviour was not observed for (models of) non-polar solvents. This charge separation process can be designated as unbiased 'sudden polarization' since the solvent shells used were in equilibrium with the non-polarized ethylene solute.

In this thesis we present a new approach to calculate optical spectra, which uses a polarization dependent functional within current density functional theory (CDFT), which was proposed by Vignale and Kohn [Phys. Rev. Lett. 77, 2037 (1996)]. First we use a polarization dependentfunctional which includes exchange-correlation contributions in the effective macroscopic electric field. This functional is used to calculate the optical absorption spectrum of several common semiconductors. We achieved in all cases good agreement with experiment.
Building on these results we then use a functional which includes the full exchange-correlation contribution in the effective electric field. The outcome was that the microscopic contribution to the exchange-correlation field cannot be neglected. It is even found to be quite large compared to the macroscopic contribution. Further research is needed to evaluate this microscopic contribution to the exchange-correlation field.

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The dynamics of a two-electron system in a strong laser pulse is described by the time-dependent extended Hartree-Fock (TDEHF) scheme. Ionization yields for a one-dimensional helium model are calculated and compared with results of exact calculations (full correlation) and time-dependent Hartree-Fock calculations (no correlation). The knee-structure in the double ionization curve appears also for the TDEHF calculations, but the yields are more than an order of magnitude too low. The total ionization probability agrees well with the exact results and much improved results for the single ionization yields are obtained. Due to the reduced dimensionality of the model, the TDEHF ground state consists of a left and right orbital. While one of the orbitals easily transforms into a continuum state, the other remains localized and screens the nucleus. In this manner, even the one-dimensional orbitals can be considered to be inner and outer orbitals.

We present a density functional and time dependent density functional study of the ground, ionic and excited states of a series of oligomers of Thiophene. We show that, for the physical properties, the most relevant HOMO and LUMO molecular orbitals develop gradually from the monomer molecular orbitals into occupied and unoccupied broad bands in the large length limit. We show that the band gap and ionization potentials decrease with size as found experimentally and from empirical calculations. This gives credence to the simple tight binding model Hamiltonian approach for these systems. We demonstrate that the length dependence of the experimental excitation spectra for both the singlet and triplet excitations can be very well explained with an extended Hubbard like Hamiltonian with a monomer on site coulomb and exchange interaction and a nearest neighbor coulomb interaction. We also study the ground state and excited state electronic structure as function of the torsion angle between the units in a dimer and find almost equal stability for the transoid and cisoid isomers, with a transition energy barrier for isomerization of only 4.3 kcal/mol. Fluctuations in the torsion angle turn out to be very low in energy and therefore of great importance in describing even the room temperature properties. At a torsion angle of 90 degrees the hopping integral is switched off for the HOMO levels because of symmetry, allowing a first principles estimate of the on-site minus the next neighbor Coulomb interaction as it enters in a Hubbard like model Hamiltonian.

We present results of ab-initio electronic structure calculations of Mn core-valence and d-d transitions in LaMnO₃. The results are important for the analysis of recent X-ray absorption and anomalous X-ray scattering experiments at the Mn K-edge in LaMnO₃,. We compare on-site 1s to 3d excitations with excitations to the 3d shell of adjacent Mn ions and find that the first two peaks of the pre-edge region correspond respectively to majority-spin and minority-spin e_g (3d) states on neighboring Mn ions. For on-site 1s > 4p transitions we find an ordering of the p_x, p_y and p_zcomponents, due to Jahn-Teller distortion. In addition, our calculations indicate that energies associated, with 1s > 4p transitions are split due to 3d-4p exchange interactions.

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A subdivision of space into discrete cells underlies the traditional discrete dipole method. This model presumes that nonlocal electric interactions between cells only are sufficient to describe the electromagnetic response of a condensed matter system. This is realistic for simple dielectrics, but is not otherwise. Cells can also influence each other directly through the wave functions, if they extend across cell boundaries. In general such nonlocal quantum mechanical interaction results in the ocurrence of nonlocal polarizabilities. In this paper it is shown how existing discrete dipole descriptions of finite systems, slabs and (semi-)infinite systems have to be altered to incorporate the effects of nonlocal polarizabilities. The modified method is called the discrete cellular method.

The point-charge model for the nuclear quadrupole moment (PCNQM) was successfully applied to atoms and linear molecules for picture-change-error-free determination of electric field gradients (EFGs). From these EFGs accurate values for the nuclear quadrupole moment could be obtained in combination with spectroscopical data. In this work we will present an extension of this model to systems with low or absent symmetry. At the C₁ system of 1-fluoro-1-chloropropane we set up the formalism for the asymmetric PCNQM model. In cases where larger molecules with more than one heavy atom are considered, correlated Dirac-Fock calculations are still extremely expensive and methods which use approximate relativistic treatments or reduction to two components will find intensive use. Especially the Douglas-Kroll method is a very accurate approximation to the Dirac-Fock case and within the PCNQM formalism only operators of Coulomb-type are introduced allowing for a picture-change-error free description of EFGs for these molecules.

We discuss ways to obtain analytical gradients within the scalar Zeroth Order Regular Approximation to the Dirac-Fock equation within an ab inito context. Simply employing the relativistic density within the non-relativistic gradient package is in error by 10^-5. We introduce a new strictly atomic scheme which in addition to yielding exact gradients is also computationally inexpensive and avoids the gauge invariance problems that plague molecular ZORA approaches. We show that the total and orbital energies produced with the scaled version of this method are generally, i.e. except for very short interatomic distances, very close to the full molecular scaled ZORA results. Equilibrium geometries from full molecular scaled ZORA and strictly atomic ZORA are shown to be within 0.01 A from Dirac-Fock.

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Up till now, there has been a significant disagreement between theory and experiment regarding hydrogen bond lengths in Watson-Crick base pairs. To investigate the possible sources of this discrepancy, we have studied numerous model systems for adenine-thymine (AT) and guanine-cytosine (GC) base pairs at various levels (i.e., BP86, PW91 and BLYP) of nonlocal density functional theory (DFT) in combination with different Slater-type orbital (STO) basis sets. Best agreement with available gas-phase experimental A-T and G-C bond enthalpies (-12.1 and -21.0 kcal/mol) is obtained at the BP86/TZ2P level, which (for 298 K) yields -11.8 and -23.8 kcal/mol. However, the computed hydrogen bond lengths show again the notorious discrepancy with experimental values. The origin of this discrepancy is not the use of the plain nucleic bases as models for nucleotides: the disagreement with experiment remains no matter if we use hydrogen, methyl, deoxyribose or 5'-deoxyribose monophosphate as the substituents at N9 and N1 of the purine and pyrimidine bases, respectively. Even the BP86/DZP geometry of the Watson-Crick-type dimer of deoxyadenylyl-3',5'-deoxyuridine including one Na⁺ ion (with 123 atoms our largest model for sodium adenylyl-3',5'-uridine hexahydrate, the crystal of which had been studied experimentally with the use of X-ray diffraction) still shows this disagreement with experiment. The source of the divergence turns out to be the molecular environment (water, sugar hydroxyl groups, counterions) of the base pairs in the crystals studied experimentally. This has been missing, so far, in all theoretical models. After we had incorporated the major elements of this environment in our model systems, excellent agreement between our BP86/TZ2P geometries and the X-ray crystal structures was achieved.

The complexity of the electronic absorption spectrum of NO₂ can be attributed to a conical intersection of the potential energy surfaces of the two lowest electronic states, the electronic ground state of ²A₁ symmetry and the first electronically excited state of ²B₂ symmetry. In a previous paper we reported on the feasibility of using the hyperfine splittings, specifically the Fermi-contact interaction, to determine the electronic ground state character of the excited vibronic states in the region just above the conical intersection; 10,000 to 14,000 cm^-1 above the electronic ground state. High-resolution spectra of a number of vibronic bands in this region were measured by exciting a supersonically cooled beam of NO₂ molecules with a narrow-band Ti:Sapphire ring laser. The energy absorbed by the molecules was detected by the use of a bolometer. In the region of interest rovibronic interactions play no significant role, with the possible exception of the vibronic band at 12,658 cm^-1, so that the fine- and hyperfine structure of each rotational transition could be analyzed by using an effective Hamiltonian. In the previous paper we restricted ourselves to an analysis of transitions of the K_- = 0 stack. In the present paper we extend the analysis to transitions of the K_-=1 stack, from which, in addition to hyperfine coupling constants, values of the A rotational constants of the excited NO₂ molecules can be determined. Those rotational constants also contain information about the electronic composition of the vibronic states, and, moreover, about the geometry of the NO₂ molecule in the excited state of interest. The results of our analyses are compared with those obtained by other authors. The conclusion arrived at in our previous paper that determining Fermi-constants is useful to help characterize the vibronic bands, is corroborated. In addition, the A rotational constants correspond to geometries that are consistent with the electronic composition of the relevant excited states as expected from the Fermi-constants.

Time-dependent density functional theory has been used to calculate the static and frequency-dependent dielectric function of non-metallic crystals. We show that a real-space description becomes feasible for crystals by using a combination of a lattice-periodic (microscopic) scalar potential with a uniform (macroscopic) electric field as perturbation in a periodic structure calculation. The induced density and microscopic potential can be obtained self-consistently for fixed macroscopic field by using linear response theory in which Coulomb interactions and exchange-correlation effects are included. We use an iterative scheme, in which density and potential are updated in every cycle. The explicit evaluation of Kohn-Sham response kernels is avoided and their singular behaviour as function of the frequency is treated analytically. Coulomb integrals are evaluated efficiently using auxiliary fitfunctions and we apply a screening technique for the lattice sums. The dielectric function can then be obtained from the induced current. We obtained for C, Si and GaAs within the adiabatic local density approximation in good agreement with experiment. In particular in the low-frequency range no adjustment of the LDA band gap seems to be necessary.

We present here the measurement of the single-polymer entropic elasticity and the single covalent bond force profile, probed with two types of atomic force microscopes (AFM) on a synthetic polymer molecule: polymethacrylic acid in water. The conventional AFM allowed us to distinguish two types of interactions present in this system when doing force spectroscopic measurements: the first interaction is associated with adsorption sites of the polymer chains onto a bare gold surface, the second interaction is directly correlated to the rupture process of a single covalent bond. All these bridging interactions allowed us to stretch the single polymer chain and to determine the various factors playing a role in the elasticity of these molecules. To obtain a closer insight into the bond rupture process, we moved to a force sensor stable in position when measuring attractive forces. By optimizing the polymer length so as to fulfill the elastic stability conditions, we were able for the first time to map out the entire force profile associated with the cleavage of a single covalent bond. Experimental data coupled with molecular quantum mechanical calculations strongly suggest that the breaking bond is located at one end of the polymer chain.

A Finite Field MD method has been developed to calculate non-resonant Raman response. The method has been used to calculate the third- and fifth-order responses for liquid CS₂. From the third-order response the intensity of the third-order cascading processes, has been estimated. The calculated ratio between the true fifth-order intensity and the intensity of the third-order cascading processes supports experimental observations claiming the 2-dimensional Raman spectra to be dominated by the third-order cascading processes.

In this paper we present the implementation of the two component scaled ZORA method in the molecular electronic structure package GAMESS-UK. It is the first application of this method, which was earlier investigated in the context of Density Functional Theory, in molecular ab initio basis set calculations. The performance of the method is tested in atomic calculations, for which we can compare with numerical results, on Xenon and Radon and in molecular calculations on the molecules: AgH, HI, I₂, AuH, TlH and Bi₂. In calculations on the I₂ molecule we investigated the effect on the orbital energies of the different approaches regarding the internal Coulomb matrix used in the ZORA method. For the remaining molecules we computed harmonic frequencies and bondlengths. It is shown that the scaled ZORA approach is a cost effective alternative to the Dirac-Fock method.

The treatment of relativity and electron correlation on an equal footing is essential for the computation of systems containing heavy elements. Correlation treatments that are based on four-component Dirac-Hartree-Fock calculations provide presently the most accurate, albeit costly, way of taking relativity into account. The requirement of having two expansion basis sets for the molecular wave function puts a high demand on computer resources. The treatment of larger systems is thereby often prohibited by the very large runtimes and files that arise in a conventional Dirac-Hartree-Fock approach. A possible solution for this bottleneck is a parallel approach which not only reduces the turn-around time but also spreads out the large files over a number of local disks. Here we present a distributed-memory parallelization of the program package MOLFDIR for the integral generation, Dirac-Hartree-Fock and four-index MS transformation steps. This implementation scales best for large AO spaces and moderately sized active spaces.

The dielectric function of heavy nonmetallic crystals are studied within a relativistic framework using the ADF-BAND program package. The calculations are based on the work that has been done to calculate the dielectric response of nonmetallic crystals in article [7]. The starting point of the relativistic corrections is the Dirac equation in an quasi-static electric field. As the Dirac equation is a four-component equation it is first reduced to a two-component equation with the Foldy-Wouthuysen transformation. The then obtained two-component Dirac-Hamiltonian is then used to find (after some treatments of this Hamiltonian) an expression for the matrixelements required.
With these matrixelements the dielectric function can be evaluated, but now relativistically corrected. The obtained relativistic corrected dielectric function was finally evaluated for some light crystals; C,Si,GaAs and He and for heavier crystals asto see if the relativistic corrections indeed improve on the dielectric function of the studied crystals in article [7]. The heavy crystals with large errors as compared to experiment in article [7] were studied. The expectation is that for elements with an atomic number greater or equal to 50 ( Z ¥ 50) the relativistic corrections become important.

The aim of this project is to extend the NewSymmetry code of the Amsterdam Density Functional program package (ADF). The NewSymmetry routines are written in a modular style and will in the future replace the symmetry routines that ADF currently uses.
The NewSymmetry routines that are currently present in ADF (version 2.5 and up) were written by J.G. Snijders and tested by J.A. Groeneveld. These routines generate (general) point group symmetry information for all point groups and Clebsch-Gordan coefficients for point groups that consist of only real representations. The great advantage of these routines is their modular style and the fact that they handle point groups that are not yet implemented in ADF: the groups containing complex representations and the icosahedralgroups.
The routines that were added to the code use the symmetry information provided by the NewSymmetry routines to generate coefficients for symmetry adaptation of the basis functions. These coefficients are currently calculated in ADF, but as mentioned not all point groups are implemented. The information obtained by the new routines needs to be the same as the information that is generated by ADF.
Special care needs to be taken in case of complex representations. Because ADF does not handle complex information the complex representations are combined into real representations. This introduces complications because these representations can not be used like the other real representations. The theory of the complex representations is discussed in a separate chapter. The theory is not yet implemented but a section is added that discusses how the theory could be implemented.

The ab initio scalar ZORA/IORA approach, which was previously tested within the context of numerical and basis set SCF calculations, is generalised to include electron correlation. The technical details of the method are investigated in calculations on the systems: Ne₂, Ar₂, Kr₂, Xe₂ and AgH. For the weakly bonded rare gas dimers we calculated the bond lengths and well depths using the non-relativistic, ZORA, scaled ZORA and IORA MP2 method. The relativistic effect on the potential energy mininum, obtained with the most accurate method (scaled ZORA), is shown to account for the deviations between the best non-relativistic results and experiment.

Ab initio molecular orbital methods at the CBS-Q level of theory have been used to study the effect of substituent (F, Cl, NH₂, OH and CH₃) on the gas-phase acidities of formic acid, HCOOH its silicon and sulfur derivatives R- M(=X)XH(M = C, Si; X = O, S; R = F, Cl, OH, NH₂, and CH₃). For formic acid and its thio and dithio derivatives the acidity changes upon substitution are irregular and depend on both the type of substituent, possition and degree of replacement of oxygen atoms by sulfur atoms. For sila carboxylic acids and their thio and dithio derivatives the calculated acidities regularly increase in the order: R SiOOH < R Si(=S)OH << R Si(=O) SH < R SiSSH, (R = H, F, Cl, OH, NH₂, and CH₃). The chloro derivatives are the strongest among the sila acids studied. The highest gas phase acidity (1277.6 kJ mol-1) has been calculated for ClC(=S)OH.

We demonstrate that the description of the optical reflectance anisotropy of GaAs(110) requires a complete microscopic treatment of both surface and bulk, which is feasible in the discrete cellular method. This method is an extension of standard discrete dipole calculations and accounts for nonlocality in the electrodynamical local fields and ab-initio nonlocal polarizabilities. The results of our calculations are in excellent agreement with experiment and we show that the anisotropy is surface induced.

We present results of ab initio calculations for d-d transitions, which arise in the mid-infrared spectrum of undoped cuprate compounds. It has been suggested that these transitions arise at energies as low as 0.4 eV in La₂CuO₄ and Sr₂CuO₂Cl₂. We study the differences in d-d transition energies in a series of cuprates that contains compounds in which the Cu ions are sixfold, fivefold or fourfold coordinated. Furthermore, we analyze the dependence of theÊ 3d_x²-y² to Ê 3d_z² excitation energy on the ratio of theÊ in plane and apex copper-ligand distances in the model system CuO. Our cluster calculations do not support the assignment of the 0.4 - 1 eVÊ band to phonon and magnon sidebands of a d-d transition. On the other hand, we confirm the interpretation of the peak around 1.7 eV observed in CuGeO₃ as arising from d-d transitions.

The dielectric function of a range of non-metallic crystals of various lattice types is studied by means of a real-space and full-potential time-dependent density functional method within the adiabatic local density approximation. Results for the dielectric constant (at optical frequencies) are given for crystals in the sodium chloride, the fluorite, the wurtzite, the diamond and the zincblende lattice structure. The frequency-dependent dielectric function for the crystals in the diamond and zincblende lattice structure are also presented. We compare our calculated results with experimental data and other theoretical investigations. Our results for the dielectric constants are in good agreement with the experimental values. The accuracy of the results is comparible to the one which is commonly found for TDDFT calculations on molecular systems, typically with a deviation of 3-5% from experiment. The spectral features of the dielectric functions appear in the calculations at somewhat lower energies compared to experiment.

Ab initio theoretical results for the 2p and 3p hole states of an Mn²⁺ ion are reported in order to determine the importance of atomic contributions to the XPS spectra of bulk MnO. A combined treatment of relativity and electron correlation reveals important physical effects that have been neglected in virtually all previous work. The many body and relativistic effects included in the atomic model are able, without any ad hoc empirical parameters, to explain most of the features of the MnO XPS spectra. In particular, it is not necessary to invoke charge transfer to explain the complex p-level spectra

In this paper we present the first application of the ZORA (Zeroth Order Regular Approximation of the Dirac Fock equation) formalism in Ab Initio electronic structure calculations. The ZORA method, which has been tested previously in the context of Density Functional Theory, has been implemented in the GAMESS-UK package. As was shown earlier we can split off a scalar part from the two component ZORA Hamiltonian. In the present work only the one component part is considered. We introduce a separate internal basis to represent the extra matrix elements, needed for the ZORA corrections. This leads to different options for the computation of the Coulomb matrix in this internal basis. The performance of this Hamiltonian and the effect of the different Coulomb matrix alternatives is tested in calculations on the radon en xenon atoms and the AuH molecule. In the atomic cases we compare with numerical Dirac Fock and numerical ZORA methods and with non relativistic and full Dirac basis set calculations. It is shown that ZORA recovers the bulk of the relativistic effect and that ZORA and Dirac Fock perform equally well in medium size basis set calculations. For AuH we have calculated the equilibrium bond length with the non relativistic Hartree Fock and ZORA methods and compare with the Dirac Fock result and the experimental value. Again the ZORA and Dirac Fock errors are of the same order of magnitude.

In the Direct Reaction Field (DRF) approach to the description of events in the condensed phase, quantum parts (QM) are embedded in a (semi-)classical environment (MM). QM is described with any appropriate wavefunction, while MM is modeled with point charges and interacting polarizabilities and/or a dielectric continuum, which may have finite ionic strength. The static and response potentials are made part of QM's Hamiltonian (hence Direct RF), leading to one- and two-electron contributions. Hence we obtain also a good estimate of the dispersion. For QM/MM and MM/MM interactions point charges and polarizabilities are treated as belonging to (model) charge distributions. The rest of the short range repulsion is accounted for by a model atom pair potential borrowed from CHARMM. The same model - with a Saltier-Quirked dispersion expression, based on the same interacting polarizabilities - leads to a definition of a classical, polarizable force field used in QM/MM and MM-only Monte Carlo simulations. Here we present calculated static (hyper-)polarizabilities a, b and g for some molecules in various environments.

The view that the hydrogen bonds in the Watson-Crick adenine-thymine (AT) and guanine-cytosine (GC) base pairs are in essence electrostatic interactions with substantial resonance assistance from the p electrons is questioned. Our investigation is based on a state-of-the-art density functional theoretical (DFT) approach (BP86/TZ2P) which has been shown to properly reproduce experimental data. Through a quantitative decomposition of the hydrogen bond energy into its various physical terms, we show that, at variance with widespread belief, donor-acceptor orbital interactions (i.e. charge transfer) in s symmetry between N or O lone pairs of one base and N-H s* acceptor orbitals on the other base do provide a substantial bonding contribution which is, in fact, of the same order of magnitude as the electrostatic interaction term. The overall orbital interactions are reinforced by a small p component, stemming from polarization in the p-electron system of the individual bases. This p component is, however, one order of magnitude smaller than the s term. Furthermore, we have investigated the synergism in a base pair between charge-transfer from one base to the other through one hydrogen bond and in the opposite direction through another hydrogen bond, as well as the cooperative effect between the donor-acceptor interactions in the s- and polarization in the p-electron system. The possibility of C-H....O hydrogen bonding in AT is also examined. In the course of these analyses, we introduce an extension of the Voronoi deformation density (VDD) method which monitors the redistribution of the s- and p-electron densities individually out of (DQ > 0) or into (DQ > 0) the Voronoi cell of an atom upon formation of the base pair from the separate bases.

Direct Reaction Field (DRF) model was developed for calculations of electronic properties of molecules in the condensed phases. In the DRF approach the electrons of (part(s) of a system is described with wave functions, the larger parts classically with point charges and polarizabilities. Leaving out the quantum mechanical part(s) leads naturally to a polarizable force field. In this paper we demonstrate the usefulness of the Direct Reaction Field (DRF) model for the study of many body interactions in polar systems. We have calculated the many body interactions in clusters of HF, H₂O and urea in our classical polarization model and compared the results to ab initio calculations using large basis sets. We find that the results obtained using the classical model compare excellently to ab initio results.

Ab initio molecular orbital calculations at the CBS-Q level of theory have been used to study the rotational conformers and acidity of dithiosilanoic acid and several of its derivatives R-SiSSH (R=H, F, Cl, NH₂, OH and CH₃). Vibrational spectra were evaluated at the ab initio MP2(Full)/6-31G(d) level of theory. For all six acids studied the syn conformers are predicted to have the lowest energy. The syn - anti enthalpy difference is varying between 4 and 7 kJ mol^-1. Dithiosilanoic acid is about 60 and 96 kJ mol^-1 more acid than dithioformic and silanoic acid, respectively.

New experimental results are reported on state-dependent steric effects in NO-Ar inelastic scattering. The NO molecules are selected in theJ=1/2- Lambda-doublet state of the electronic ground state and oriented relative to the incident Ar-atoms. The steric asymmetry,S=(s_NO-s_ON)/(s_NO+s_ON) has been measured as a function of the final rotational state J'. In a previous study, quantum mechanical scattering calculations were found to predict strong oscillations in S, but experimental evidence for this behaviour was not conclusive. The results of recent experiments presented here provide clear evidence of the qualitative correctness of the theoretical calculations.

Time-dependent density functional theory provides a first principles method for the calculation of frequency-dependent polarizabilities, hyperpolarizabilities, excitation energies and many related response properties. In recent years, the molecular results obtained by several groups have shown that this approach is in general more accurate than the time-dependent Hartree-Fock approach, and is often competitive in accuracy with computationally more demanding conventional ab initio approaches. In this paper, our implementation of the relevant equations in the Amsterdam Density Functional program is described. We will focus on certain aspects of the implementation which are necessary for an efficient evaluation of the desired properties, enabling the treatment of large molecules. Such an efficient implementation is obtained by: using the full symmetry of the molecule, using a set of auxiliary functions for fitting the (zeroth- and first-order) electron density, using a highly vectorized and parallelized code, using linear scaling techniques, and, most importantly, by solving the response equations iteratively.

Starting from many-body perturbation theory we have constructed a new variational expression for the total energy of many-electron systems. This expression is a functional of two independent variables, the one-electron Green function and the screened Coulomb interaction. The new functional as well as a much older variational expression by Luttinger and Ward (LW) are tested on the interacting electron gas. Both functionals yield extraordinary accurate total energies although the new functional requires a much cruder input and is therefore easier to apply to more realistic systems.

In the present note we outline a simple scheme for generating the Configuration Interaction matrix elements for spin-orbit interactions in molecules. The procedure leads to a close parallelism with spin-free permutation group approaches. Unitary shift operators have been successfully used on the orbital space to generate the matching permutations necessary to evaluate the required matrix elements. The procedure has been adequately illustrated using examples.

We present the results of detailed studies of the potential energy surfaces of the iodine-benzene charge-transfer complex obtained from (fully counterpoise corrected) ab initio calculations at the MP2 level, and from (semi-)classical calculations . The most stable conformations found were the above bond and the above carbon conformations. The axial conformation was found to be somewhat less stable. The remarkable difference in intermolecular distance for different orientations of the iodine is explained in terms of the polarization anisotropy. This feature makes the construction of an accurate classical force field rather difficult because of the marked dependence of the repulsion parameter - usually the radius - for iodine on both orientation and polarization of the iodine. Investigation of the oscillator strengths of different complex geometries shows that there are many conformations in which the charge transfer excitation can take place.

Relativistic time dependent density functional calculations have been performed on the excited states of the M(CO)₆ (M = Cr, Mo, W) series. Our results, in agreement with previous DSCF [Pollak, 1997] and CASPT2 [Pierloot, 1996] calculations on Cr(CO)₆, indicate that in all members of the series the lowest excited states in the spectra do not correspond to ligand field (LF) excitations, as has been accepted in the past. Instead they correspond to charge transfer (CT) states. The LF excitations are calculated at much higher energy than suggested by the original assignment by Beach and Gray [Beach, 1968] and at different energy along the M(CO)₆ series, being much higher in the heavier carbonyls than in Cr(CO)₆.
These results lead to a definitive reassessment of the role of the LF states in the photochemical dissociation of the metal-CO bonds in the M(CO)₆ series, suggesting that the experimentally observed photodissociation of the M-CO bond upon irradiation into the lowest energy bands occurs in the heavier carbonyls, as it does in Cr(CO)₆, from CT and not from LF states. A comparison with the experimental data available and, in the case of Cr(CO)₆, also with high-level correlated ab initio calculations, [Pierloot, 1996] proves the reliability of the present TDDFT approach. The choice of the xc functional is found to have a large effect on the excitation energies, demonstrating that even for quite "normal", low-lying excitations the xc functional may play an important role. In the heavier carbonyls, mostly in W(CO)₆, relativistic effects are seen to be relevant for the LF states as well as for the CT states arising from the (2t_2g)⁵(3t_2g)¹ configuration.

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The electronic structure of NiO, with emphasis on the Ni 3s-hole ionic states, is studied using non-orthogonal configuration interaction, NOCI, wavefunctions for an NiO₆ model of the crystal. Orbital sets are relaxed, or optimized, separately for each configuration used in the NOCI and orbital symmetry breaking, or localization, is allowed. This localization is important for configurations that involve large amounts of charge transfer from O(2p) to the Ni(3d) shell. The NOCI method insures an unbiased treatment of the relative energies of configurations that involve different degrees of charge transfer from O(2p) to Ni(3d). The use of fully relaxed orbitals is shown to be necessary to obtain accurate energies and intensities for core level ionic states observed with X-ray photoelectron spectroscopy, XPS. The NOCI energies and intensities for the lowest and first excited, high spin coupled, 3s-hole states are in good agreement with XPS spectra. Both high spin 3s-hole states are found to have significant, but partial, charge transfer character.

The polarizabilities of 15 organic molecules are calculated using the Restricted Hartree Fock (RHF) method, Density Functional Theory (DFT) and the Direct Reaction Field (DRF) approach. The RHF method gives rather poor results, while the other two give average deviations comparable to the experimental uncertainty. The DRF approach is very fast (< 1s), but underestimates the anisotropy of molecules containing pi-bonds. Three DFT methods were used (Local Density Approximation, Becke-Perdew, model potential) which need more time (9 - 80 hours) but give a better overall accuracy, which increases towards the basis set limit. The model potential improves the Becke-Perdew potential, which in turn gives better results than the Local Density Approximation.

A brief overview is presented of some theoretical work on the symmetry breaking of electronic wavefunctions that followed the early work of Bagus and Schaefer who observed that a considerable lower SCF energy could be obtained for an ionized state of the O₂ molecule with a 1s hole if the symmetry restrictions were released, so that the core hole could localize on one of the two oxygens. In the present contribution some emphasis is put on the properties of symmetry adapted wavefunctions, which are obtained through a nonorthogonal CI amongst different symmetry broken wave functions. n-p* Excited states of para-benzoquinone and 3d-s ionized states of Cu₂ are used as illustrative examples.

Molecular properties of the uranyl ion ([UO₂]²⁺) are studied using both a non-relativistic and a relativistic method. Inclusion of relativity leads to a bond length expansion and makes the electric field gradient (EFG) at the uranium nucleus strongly dependent on the U-O bond distance. The non-relativistic EFG value is found to be much larger than the relativistic value. An analysis of the non-relativistic and relativistic wave functions is given and shows the presence of a so-called "U(6p) core-hole". A different ordering of the valence spinors is found compared to previous work. It is confirmed that the HOMO has su character and has a large U(5f) contribution.

A series of embedded cluster calculations have been performed to study the dependence of the calculated ionization and excitation energies in CuCl and NiO on the representation of the direct cluster surrounding. Different embedding schemes have been applied. First, a cluster of one TM ion plus its nearest counterions has been embedded in point charges only. Next, model potentials (AIEMPs) have been used to represent the first layer of ions around the basic cluster, and finally, we embedded the cluster in the charge distribution of frozen ions. The calculations show that the ionization and excitation energies change considerably when the Pauli repulsion of the cluster atoms with the direct surrounding is accounted for.

The Direct Reaction Field approach is briefly reviewed. Preliminary reports of the calculations on solvent induced shifts in the transition of acetone in various solvents, and the dissociation of ter-butyl chloride in water are given.

The minimum energy conformations and racemization barriers for the chiral sterically overcrowded helical alkenes, trans- and cis-1,1',2,2',3,3',4,4'- octahydro- 4,4'-biphenanthrylidenes (1 and 2), are reported. The trans-1 and cis-2 isomers can each adapt three different conformations, (P,P) and (M,M) (an enantiomeric pair) and an achiral (P,M) meso form, of which only the chiral isomers were obtained by synthesis. The conformations and heats of formation of (M,M)-(E)-1, (P,M)-(E)-1, (M,M)-(Z)-2, and (P,M)-(Z)-2 isomers were determined by MOPAC AM1 calculations. The racemization process for both the trans- and cis- isomers is postulated to occur via the (P,M) isomers by two successive inversions of the cyclohexenyl ring; (M,M) to and from (P,M) to and from (P,P). The (M,M) to (P,M) and reverse (P,M) to (M,M) isomerizations were simulated by reaction path calculations, providing the molecular structure and the activation energy of the transition state for each isomerization. For each racemization process, the activation enthalpy (DH±) was calculated as 23.9 and 19.9 kcal mol-1 for trans-olefin 1 and cis-olefin 2, respectively. These values reasonably agree with the experimental values obtained by temperature- dependent circular dichroism, optical rotation, and ¹H NMR magnetization transfer measurements: DH± = 24.6 and 20.8 kcal mol-1 for trans-olefin 1 and cisolefin 2, respectively. While the racemization of cis-isomer 2 is controlled by the steric interaction of H5 with C4'a and C4'b, the surprisingly high barrier for trans-olefin 1 is due to the severe steric interaction between H5 and H3'a and/or H3'b protons.

The first time-dependent density functional theory (TDDFT) calculations on the spectra of molecules containing transition metals are reported. Three prototype systems are considered, of which the assignments are controversial: MnO₄- , Ni(CO)₄, and Mn₂(CO)₁₀. The TDDFT results are shown to be comparable in accuracy to the most elaborate ab initio calculations and lead to new insights in the spectra of these molecules. In some cases, the presented TDDFT results differ substantially, in both the ordering and the values for the excitation energies, from the older DFT method for the calculation of excitation energies: the DSCF approach. For the Mn₂(CO)₁₀ molecule, the presented results are the highest-level theoretical results published so far. Over all, the results show that TDDFT can be a very useful tool in the calculation and interpretation of the spectra of transition metal compounds.

Proton-energy differences, ammonia adsorption, and D/H-exchange barriers for methane at selected isolated Brønsted sites in zeolites FAU, MFI, BEA, ERI, and CHA are studied by combined quantum-chemical-classical (QM/MM) calculations in an attempt to understand the factors that determine the reactivity at these Brønsted sites.
The barrier of the D/H-exchange reaction for methane was found to correlate well with the calculated ammonia chemisorption energy, but even better with the O-Al-O angle of the free zeolite Brønsted site the reaction is taking place on, provided the Si-O-Al-O-Si moiety over which the reaction takes place is more or less collinear. The barrier is considerably higher if this collinearity is weaker, which may be explained by the necessity of costly back-bone distortions to accommodate the geometrical requirements of the transition state. This is confirmed by similarly strong correlations with the O-Al-O angle change going from the free acid site to zeolite-ammonium-ion bidentate structures, which may be thought of as a measure of the back-bone distortion.
A new measurement of the D/H-exchange barrier in BEA is also reported. It was found to be 88 ± 18 kJ/mol, lower than the experimental barriers in both FAU and MFI.

A recently proposed spin-restricted open-shell KohnÐSham ~ROKS! method is applied to investigate various atomic and molecular multiplet states. A wide range of multiplets is considered: multiplet terms for which the spin-restricted open-shell theory of Roothaan applies, as well as state situations which cannot be described by RoothaanÕs theory ~e.g., states of square cyclobutadiene, etc.!. Problems associated with the use of approximate density functionals and possible perspectives of the ROKS method are discussed.

We show that a time-dependent particle density n(rt) obtained from a given many-particle system can, under mild restrictions on the initial state, always be reproduced by an external potential v(rt) in a many-particle system with different two-particle interactions. Given the initial state of this other many-particle system, the potential v(rt) is unique up to a purely time-dependent function. As a special case we obtain the well-known Runge-Gross theorem.

Density functional calculations on the (non)linear optical properties of conjugated molecular chains using currently popular exchange-correlation (xc) potentials give overestimations of several orders of magnitude. By analyzing exactand Krieger-Li-Iafrate xc potentials, the error is traced back to an incorrect electric field dependence of the response part of the xc potential in local and gradient-corrected density approximations, which lack a linear term counteracting the applied electric field.

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Local transitions at the NiO (100) surface have been studied with ab initio calculations by means of CASSCF/CASPT2. In addition to the well known surface specific d-d transition at 0.6 eV also the recently proposed surface d-d transition at 2.1 eV is confirmed. The broad peak at 1 eV is proposed to consist of transitions to the surface ³B₂, ³A₂, and b³E d⁸ states and the bulk ³T_2g state. Furthermore, the relative energies of the local ligand to metal charge-transfer excitations have been investigated. The lowest local CT state in NiO (100) has been calculated to be about 2 eV lower than in bulk NiO.

Many experiments that one would like to describe theoretically have a common (idealised) form: one starts by perturbing the system one wants to study by an external agent (such as a laserpulse) and after a certain time interval one probes the system by measuring one of its dynamical variables such as its polarisation (dipole moment). In other words the dynamical response of the system to an external perturbation is measured. Often the system of interest, such as a liquid, is macroscopic in nature and it becomes impossible to describe the motion of all its individual constituents in full detail and one has to resort to the methods of statistical (quantum)mechanics. In this case it is often profitable to divide the system into two parts, a small subsystem (hereafter simply called "the system") which is described in full detail (e.g. a molecule in a liquid) and the rest of the system (called "the environment" or "the bath") which is treated only statistically and which interacts with the system proper. At the start of the experiment one assumes that the system and the bath are in stationary equilibrium and can be described by equilibrium thermodynamics. The external perturbation then excites the system in various ways, taking it out of statistical equilibrium. Subsequently the system interacts with the bath and will tend to loose (dissipate) its excess energy to its environment and will eventually return (relax) back to thermodynamic equilibrium. One can now study this relaxation process by measuring the value of some observable of the system as function of the delay since the system was excited (the dynamic response function of this observable), thus obtaining information about the system bath interaction (the intermolecular forces in a liquid for example). If the delay is long enough one expects the system to have relaxed to equilibrium and one simply measures the equilibrium value of the response (which usually vanishes, e.g. the average dipole moment of a molecule in a liquid is zero, due to random orientations).
In this short course we will discuss the theoretical tools which are needed to describe the type of experiment discussed above. There are apparently three ingredients we will have to treat which are absent in the description of the groundstate properties of isolated molecules.
- We will have to decide how to describe a quantum system statistically rather than by specifying its wavefunction.
- We will have to describe the time dependent interaction with the external perturbing agent and the subsequent influence of this perturbation on the properties of the system as a function of time.
- Finally we will have to study the interaction of the system with its environment and decide on how to model the relaxation processes introduced above.
We will start with a brief summary of the quantum description of isolated systems and then we will address each of these three problems in turn and study how they come together in the description of quantum statistical response.

A theoretical investigation of the crystal field excitations in CoO is presented. Special attention is given to the excitation energy of the ⁴A_2g state. In recent experimental and theoretical studies an excitation energy around 3.1 eV was reported. This is in disagreement with the 2.1 eV deduced from optical spectroscopy data. After analyzing electron correlation effects, spin-orbit interactions and the material model to represent the CoO crystal we can confirm the interpretation of the optical data, not only for the ⁴A_2g state, but also for all other low-lying crystal field excitations. Electron correlation effects are found to have a significant differential effect on the excitation energies, ranging from +0.3 eV to -0.6 eV. Spin-orbit interactions are less important, affecting the excitation energies by at most 0.05 eV. Finally, we discuss the effect of the Pauli-repulsion between the cluster ions and the first shell of ions around the cluster. This affects the excitation energies by a small, but significant, amount.

If a polar molecule can be selected in a rotational state of definite parity, subsequent orientation of the molecule in an electric field mixes opposite parity states. The degree of mixing reflects the degree of orientation. Therefore, the intensity ratio of spectral lines that correspond to transitions starting from the two parity states being mixed, forms a sensitive and accurate probe of the molecular orientation. If saturation of the spectral lines of interest is avoided, the absolute degree of orientation can be determined, without recourse to other experimental data but line intensities. The method is illustrated for the case of the NO molecule.

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The effect of relativity on the properties of the interhalogens ClF, BrF, BrCl, IF, IBr and IBr is studied by comparing relativistic and non-relativistic calculations. Bond lengths, harmonic frequencies and dissociation energies show that the bond is weakened in the relativistic formalism. Relativity increases the electric dipole moment whereas the electric quadrupole moment and dipole polarizability display an irregular behaviour. The relativistic contributions to the electric dipole and quadrupole moment of the iodine containing molecules are 10-20% of the total value whereas the contributions in the other molecules cannot be neglected. The value of the electric quadrupole moment is dominated by the relativistic contributions.

DFT schemes based on conventional and less conventional exchange-correlation (XC) functionals have been employed to determine the polarizability and second hyperpolarizability of p-conjugated polyacetylene chains. These functionals fail in one or more of several ways:
i) the correlation correction to a is either much too small or in the wrong direction, leading to an overestimate;
ii) g is significantly overestimated;
iii) the chain length dependence is excessively large, particularly for g and for the more alternant system; and,
iv) the bond length alternation effects upon g are either underestimated or qualitatively incorrect. The poor results with the asymptotically correct van Leeuwen-Baerends XC potential show that the overestimations are not related to the asymptotic behaviour of the potential. These failures are described in terms of the separate effects of the exchange and the correlation parts of the XC functionals. They are related to the short-sightedness of the XC potentials which are relatively insensitive to the polarization charge induced by the external electric field at the chain ends.

An accurate determination of frequency-dependent molecular hyperpolarizabilities is at the same time of possible technological importance and theoretically challenging. For large molecules, Hartree--Fock theory was until recently the only available ab initio approach. However, correlation effects are usually very important for this property, which makes it desirable to have a computationally efficient approach in which those effects are (approximately) taken into account. We have recently shown that frequency-dependent hyperpolarizabilities can be efficiently obtained using time-dependent density functional theory. Here, we shall present the necessary theoretical framework and the details of our implementation in the Amsterdam Density Functional program. Special attention will be paid to the use of fit functions for the density and to numerical integration, which are typical of density functional codes. Numerical examples for He, CO, and para-nitroaniline are presented, as evidence for the correctness of the equations and the implementation.

In this paper we present time-dependent density functional calculations on frequency-dependent first (b) and second (g) hyperpolarizabilities for the set of small molecules, N₂O, CO₂, CS₂, C₂H₄, NH₃, CO, HF, H₂O, and CH₄, and compare them to Hartree--Fock and correlated ab initio calculations, as well as to experimental results. Both the static hyperpolarizabilities and the frequency dispersion are studied. Three approximations to the exchange-correlation (xc) potential are used: the widely used Local Density Approximation (LDA), the Becke--Lee--Yang--Parr (BLYP) Generalized Gradient Approximation (GGA), as well as the asymptotically correct Van Leeuwen--Baerends (LB94) potential. For the functional derivatives of the xc potential the Adiabatic Local Density Approximation (ALDA) is used. We have attempted to estimate the intrinsic quality of these methods by using large basis sets, augmented with several diffuse functions, yielding good agreement with recent numerical static LDA results. Contrary to claims which have appeared in the literature on the basis of smaller studies involving basis sets of lesser quality, we find that the static LDA results for b and g are severely overestimated, and do not improve upon the (underestimated) Hartree--Fock results. No improvement is provided by the BLYP potential which suffers from the same incorrect asymptotic behavior as the LDA potential. The results are however clearly improved upon by the LB94 potential, which leads to underestimated results, slightly improving the Hartree--Fock results. The LDA and BLYP potentials overestimate the frequency dependence as well, which is once again improved by the LB94 potential. Future improvements are expected to come from improved models for asymptotically correct exchange-correlation potentials. Apart from the LB94 potential used in this work, several other asymptotically correct potentials have recently been suggested in the literature and can also be expected to improve considerably upon the relatively poor LDA and GGA results, for both the static properties and their frequency dependence.

The visible absorption spectrum of NO₂ is very dense and irregular, and shows signs of a chaotic frequency and intensity distribution in the higher energy region. The complexity of the spectrum is related to a conical intersection of the potential energy surfaces of the two lowest electronic states. Above the conical intersection strong vibronic interactions lead to hybrid eigenstates, which can be viewed as mixtures of low vibrational levels of the electronically excited state and high vibrational levels of the electronic ground state. As a contribution to the elucidation of the nature of the vibronic bands of NO₂ we have measured high-resolution spectra of a number of vibronic bands in the region between 10,000 to 14,000 cm^-1, by exciting a supersonically cooled beam of NO₂ molecules with a narrow-band Ti:Sapphire ring laser. The energy absorbed by the molecules was detected by a bolometer, and in some cases, laser-induced fluorescence was detected. The hyperfine structure is dominated by the Fermi-contact interaction and the magnitude of this interaction is a direct measure of the (electronic) composition of the hybrid eigenstates. In the region studied, rovibronic interactions appear to be insignificant. The fine- and hyperfine structure of each rotational transition can be analyzed by using an effective Hamiltonian approach. In the present paper we have restricted our analysis to transitions of K_= 0 stacks. The composition of the hybrid eigenstates is compared with ab initio calculations reported in the literature, leading to the conclusion that measurements of the hyperfine structure are a helpful tool in characterizing vibronic bands.

The double-ionization yield of He is calculated with a one-dimensional fully correlated two-electron model for the low laser frequency of recent experiments. Results for a higher laser frequency also indicate a comparable very high double-ionization yield for sufficiently short pulses. It is shown that the Hartree - Fock approximation fails dramatically in describing the two-electron dynamics. Also, in a density functional theory approach, we demonstrate the need for an improved exchange correlation potential and for more accurate density functionals for the ionization probabilities.

Thole's modified dipole interaction model for constructing molecular polarizabilities from effective, isotropic atomic polarizabilities is reviewed and extended. We report effective atomic polarizabilities for H, C, N, O, S, and the halogen atoms, independent of their chemical environment. They are obtained by fitting the model both to experimental and calculated molecular polarizabilities, the latter to enable one to model ab initio polarizabilities for various basis sets.

The Direct Reaction Field model was used to calculate the solvent shift of the n to p* transition of acetone in eight different solvents. The computed shifts correspond excellently to experimental values. We found that dispersion interactions are an essential part of the model for correctly describing the shifts in both polar and apolar solvents. Improving the quality of the basis set generally improves the results, mainly due to an increase in electrostatic interactions.

Response calculations in the framework of time-dependent density functional theory (TDDFT) have by now been shown to surpass time-dependent Hartree--Fock (TDHF) calculations in both accuracy and efficiency. This makes TDDFT an important tool for the calculation of frequency-dependent (hyper-)polarizabilities, excitation energies and related properties of medium-sized and large molecules. Two separate approximations are made in the linear DFT response calculations. The first approximation concerns the exchange-correlation (xc) potential, which determines the form of the Kohn--Sham orbitals and their one-electron energies, while the second approximation involves the so-called xc kernel fxc, which determines the xc contribution to the frequency-dependent screening. By performing calculations on small systems with accurate xc potentials, constructed from {\it ab initio} densities, we can test the relative importance of the two approximations for different properties and systems, thus showing what kind of improvement can be expected from future, more refined, approximations to these xc functionals. We find that in most, but not all, cases, improvements to V_xc seem more desirable than improvements to f_xc.

We resolve an existing paradox regarding the causality and symmetry properties of response functions within time-dependent density-functional theory. We do this by defining a new action functional within the Keldysh formalism. By functional differentiation the new functional leads to response functions which are symmetric in the Keldysh time contour parameter, but which become causal when a transition to physical time is made. The new functional is further used to derive the equations of the time-dependent optimized potential method.

Reaction of pyridinyl-2-phosphonyl dichloride (6) with 1-phenyl-2,2-dimethylpropane-1,3-diol (9) leads to the two epimeric 2-oxo-2-(2-pyridinyl)- 4-phenyl-5,5-dimethyl- 1,3,2-dioxaphosphonnanes (10a,b). These can be separated and the stereochemistry assigned on the basis of 31P NMR spectroscopy. For 10a the pyridinyl substituent is arranged axially at phosphorus. Arguments derived from 2D NMR experiments indicated that the nitrogen of pyridine is locked in a conformation whereby the pyridinyl nitrogen points over the six-membered ring; in other words it is locked between the two ring oxygen substituents. This conclusion is substantiated by an X-ray crystal determination. Oxidation of 10a with hydrogen peroxide leads to the N-oxide (12). The crystal structure of 12 reveals that despite serious steric overcrowding the N-O bond is also oriented over the six-membered ring. Methylation of 10a with methyl trifluoromethanesulfonate affords the N-methyl pyridinium salt (13). NMR experiments indicate that in this case the methylated nitrogen has turned "outside" of the six-membered ring. The borane adduct of 10a appears on the basis of NMR data to have a conformation wherein the complexed borane is located just outside of the six-membered ring. Although crystal structures have not been obtained the pyridinyl-2-thiophosphonates (15a,b) obtained from treatment of 10a and 10b with [(4-MeOC₆H₄)₂PS]₂ appear to have the same conformational properties as 10a and 10b. Restricted Hartree-Fock geometry optimizations have been carried out to aid in clarifying this unexpected conformational behaviour. These calculational results are in excellent accord with the experimental observations, and provide insight into the reasons for the conformational behaviour.

One of the most important steps in a Kohn-Sham type DFT calculation is the construction of the matrix of the Kohn-Sham operator (the "Fock" matrix). It is desirable to develop an algorithm for this step that scales linearly with system size. We discuss attempts to achieve linear scaling for the calculation of the matrix elements of the exchange-correlation and Coulomb potentials within a particular implementation (the ADF code) of the KS method. In the ADF scheme the matrix elements are completely determined by a 3D numerical integration, the value of the potentials in each grid point being determined with the help of an auxiliary function representation of the electronic density. Nearly linear scaling for building the total Fock matrix is demonstrated for systems of intermediate size (in the order of 1000 atoms). For larger systems further development will be desirable for the treatment of the Coulomb potential.

The vibronic band at 13352 cm^-1 of NO₂ is measured up to the hyperfine structure by bolometric detection.The excited vibronic state involved is a hybrid state having a major contribution from the electronic ground state. This follows from the hyperfine splitting of the K- = 0 and K- = 1 stacks as well as from the value of the rotational constant A'. The anomalous intensity distribution induced by rovibrational interactions is not observed in the vibronic band analyzed here. Although the authors suggest the absence of rovibronic interactions of significant strength, the authors underline the presence of vibronic interactions in the vibronic band analyzed here.

The superexchange interaction, parameterized by J, of bulk NiO and the NiO[100] surface was investigated using ab initio quantum chemical techniques. J Is influenced by two opposing mechanisms; the reduced Madelung potential at the surface leads to a small increase, whereas the change in the nickel coordination from six to five oxygens gives a larger decrease. As a result J at the [100] surface is predicted to decrease by about 20% with respect to the bulk. This contradicts another recent prediction to the effect that J should increase by about 50%. Experimental data are not yet available.

In this letter a non-orthogonal configuration interaction study is presented for the high spin coupled final states involved in the Ni 3s X-ray photoelectron spectra of NiO. Charge transfer effects play an important role in the interpretation of this spectrum. These effects are incorporated in a conceptually attractive way by a non-orthogonal configuration interaction description, in which the wave functions are expressed as linear combinations of the reference configuration and relaxed charge transfer configurations. The energy separation and relative intensities of the high spin coupled final states were calculated in good agreement with experiment. Both final states have considerable charge transfer character.

The central subject of the research described in this thesis is the quantum theory of reflection of light at crystalline surfaces. This work comprises a description of concepts and mathematical techniques which have been developed to achieve a workable method of calculation, their implementation into a computer program and some results of model calculations.The first chapters contain much of the formalism required for the development of the computational schemes. It serves to establish notational conventions and provides a convenient summary of results and applications from the quantum theory of the solid state. I have tried to give a moderately comprehensive account of the ideas which were at the base of the implemented algorithms. The approach gradually changes from a general point of view towards a more specific treatment of the optical reflection problem, the subject of the middle chapters. The thesis concludes with a case study in which the machinery is applied to some model systems.

An approximation scheme was developed for the Kohn-Sham exchange-correlation potential v_xc, making use of a partitioning of v_xc into a long-range screening v_scr and a short-range response v_resp component. For the response part, a model v^mod_resp was used, which represents v_resp as weighted orbital density contributions, the weights being determined by the orbital energies. v^mod_resp possesses the proper short-range behavior and the atomic-shell stepped structure characteristic for v_resp. For the screening part, two model potentials v^mod_scr were used, one with the accurate Slater potential; the other one with the generalized gradient approximation (GGA) for the exchange part. Both use the GGA for the Coulomb correlation contribution to v_scr . The scheme provides an adequate approximation to v_xc in the outer-valence region with both the proper asymptotics and a rather accurate estimate of the ionization potential from the highest one-electron energy and a reasonable estimate of atomic E_xc and total energies E_tot.

A series of non singular two-component relativistic Hamiltonians is derived from the Dirac Hamiltonian by first performing the free-particle Foldy-Wouthuysen transformation and then a block-diagonalizing transformation. The latter is defined in terms of operators which can be determined iteratively through arbitrary order in c, leading to transformed Hamiltonians with the two-component block accurate through a^2k, k = 1, 2, 3, .... These Hamiltonians give relativistic energies which differ from Dirac's energies only in terms higher than a^2k. Their relation to other non singular methods of relativistic quantum chemistry (the Douglas-Kroll method, the regular Hamiltonian schemes) is discussed. By removing the spin-dependent operators, the derived Hamiltonians can be written in spin-free one-component form. The computational effort involved is essentially the same as in the case of the Douglas-Kroll scheme and amounts to relatively easy modification of the core Hamiltonian.

The results are reported of ab initio calculations on the magnetic ordering in NiO, a prototype of the antiferromagnetic insulator. By analyzing wave functions for different cluster models, information was obtained about the physical effects determining the sign and the magnitude of the magnetic coupling parameter J. The role of the edge oxygens, surrounding the essential unit (Ni₂O), is quantitatively important but purely environmental in contrast to the role of the bridging oxygen. Also, the importance of electron correlation and the usefulness of pseudopotentials in the calculations was studied. The final result of J compares reasonably with experiment (.apprx.50%), and possible sources for the remaining discrepancies are discussed.

The generalized gradient-approximated (GGA) energy functionals used in density functional theory (DFT) provide accurate results for many different properties. However, one of their weaknesses lies in the fact that Van der Waals forces are not described. In spite of this, it is possible to obtain reliable long-range potential energy surfaces within DFT. In this paper, we use time-dependent density functional response theory to obtain the Van der Waals dispersion coefficients C₆, C₇ and C₈ (both isotropic and anisotropic). They are calculated from the multipole polarizabilities at imaginary frequencies of the two interacting molecules. Alternatively, one might use one of the recently-proposed Van der Waals energy functionals for well-seperated systems, which provide fairly good approximations to our isotropic results. Results with the local density approximation (LDA), Becke-Perdew (BP) GGA and the Van Leeuwen-Baerends (LB94) exchange-correlation potentials are presented for the multipole polarizabilities and the dispersion coefficients of several rare gases, diatomics and the water molecule. The LB94 potential clearly performs best, due to its correct Coulombic asymptotic behavior, yielding results which are close to those obtained with many-body perturbation theory (MBPT). The LDA and BP results are systematically too high for the isotropic properties. This becomes progressively worse for the higher dispersion coefficients. The results for the relative anisotropies are quite satisfactory for all three potentials, however.

The character of the low-lying excited states of diatomic CuCl is studied primarily by means of the complete active space SCF (CASSCF) method and a second order perturbation approach with the CASSCF wave function as reference state [complete active space perturbation theory to second order (CASPT2)]. For comparison, the lower levels of the spectra of the Cu⁺ ion are also analyzed. A first order treatment of the scalar relativistic effects, the mass-velocity and Darwin terms, is included in the calculations. The importance of spin-orbit interactions is investigated by comparing our nonrelativistic valence shell CI (VCI) and relativistic results obtained with our four-component program suite MOLFDIR. The six lowest excited states of the CuCl molecule, which are related to the Cu⁺(3d⁹4s¹)Cl^-(3s²3p⁶) ionic configuration, are assigned. The assignments agree with earlier theoretical work. Where they can be compared, the calculated spectroscopic constants are in good agreement with the experimental data.

The electronic structure, spectroscopic and bonding properties of the ground, excited and ionized states of iodine are studied within a 4-component relativistic framework using the MOLFDIR program package. The properties of the ¹S_g+ ground state, calculated up to the CCSD(T) level of theory, are in good agreement with experiment. It is shown that relativistic effects and core-valence correlation need to be included in order to get results close to experiment and that the Breit interaction can be neglected. The lowest ionized states properties like the bond length, the dissociation energy and the harmonic frequency are studied at different levels of theory. The photoelectron spectrum and the potential energy curves of the ionized and excited states are calculated. The calculated properties of the excited states are in good agreement with experimental data and theoretical results of Teichteil and Pelissier [Chem. Phys. 180, 1 (1994)]. An alternative assignment of some recently measured, low lying, ionized states is proposed.

The gas-phase He(I) photoelectron spectra of the MF₄(M = Ti, Zr, Hf) molecules have been recorded for the first time. Assignment of the spectra was achieved with the aid of ab initio molecular orbital and density functional theory (DFT) calculations. The spectra are found to be similar for each molecule, with the exception that the A²T₂, ionic state in HfF₄ is split by spin-orbit interaction. The measured splitting (0.18 ± 0.03) eV, is in very good agreement with the value obtained from a relativistic DFT calculation, 0.16 eV, and arises from a small contribution from the Hf 5p orbital into the upper t₂, molecular orbital of HfF₄.

Theo Thole's Ph.D. work was the basis for the Direct Reaction Field method for incorporating a semi-classical "solvent" in quantum chemical calculations. The early stages of his work and later progress is reviewed, and a typical example of his analytical and programming skills-so far unpublished-is given.

Thole's interacting polarizability model to calculate molecular polarizabilities from interacting atomic polarizabilities is reviewed and its majorapplications in computational chemistry illustrated. The applications include prediction of molecular polarizabilities, use in classical expressions for intermolecular interactions for the computation of binding energies of molecular dimers and solvation (free) energies, and solvent effects in combined quantumchemical-classical (QM/MM) calculations. The examples demonstrate the wide applicability of the model, which is due to its firm foundation in the perturbation theory of intermolecular interactions, from which the polarizability emerges as one of the material properties determining the interaction between species. The true power of the model is its generality, rendering transferability to all sorts of chemical problems almost a non-issue.

After a word of welcome some personal remarks are made on Theo's start in theoretical chemistry, on his remarkable achievements thereafter and on his very special qualities as a friend and colleague.

The detailed reaction pathways for the hydration of carbon dioxide by water and water clusters containing two, three, and four water molecules (CO₂ + nH₂O -> H₂CO₃ + (n-1 )H₂O, n = l-4) have been investigated in both gas phase and aqueous solution using ab initio molecular orbital (MO) theory up to the quadratic configuration interaction QCISD(T)/6-31G(d,p)//MP2/6-31G(d,p) level, both SCRF and PCM models of continuum theory, and a mixed approach based on MO calculations in conjunction with Monte Carlo and reaction field simulations. It is confirmed that the CO₂ hydration constitutes a case of active solvent catalysis where solvent molecules actively participate as a catalyst in the chemical process. In aqueous solution the hydration mechanism is multimolecular, where geometric parameters of the solvent fully intervene in the reaction coordinate. The hydration reaction was found to proceed through an attack of a water oxygen to the CO₂ carbon in concert with a proton transfer to a CO₂ oxygen. The proton transfer is assisted by a chain of water molecules, which is necessary for a proton relay between different oxygens. Owing to a significantly larger charge separation in the transition structures, nonspecific electrostatic interactions between solute and solvent continuum also play a more important stabilizing role. Regarding the answer to the title question, our calculations suggest that although a water tetramer (n = 4) seems to be necessary for CO, hydration in the gaseous phase, a reaction channel involving formation of a bridge containing three water molecules (n = 3) is likely to be actively involved in the neutral hydration of CO₂ in aqueous solution.

Femtosecond pump-probe spectroscopy is used to explore the excited-state dynamics of TPE in polar and nonpolar solvents. Four excited states are shown to play an important role: the vertically excited S1 state, the Franck-Condon relaxed S1 state, a twisted charge-resonance state (in the literature often referred to as biradical), and a charge-separated state. The subpicosecond dynamics are dominated by a very large Stokes shift, which is primarily due to ultrafast elongation of the ethylenic C-C bond, and by wave packet motion of the phenyl-ring bending modes. On picosecond time scales, isomerization dynamics and charge separation by symmetry breaking occur. The latter process is made possible by an avoided crossing between the singly and doubly excited states of TPE, leading to a dramatic enhancement of the polarizability. The electron transfer across the C-C bond follows an adiabatic reaction path on the lower potential energy surface. In nonpolar solvents, an equilibrium is established with a symmetric charge resonance state, by thermally activated recrossing to the upper potential surface. In polar solvents this process is suppressed by solvent stabilization of the dipolar, zwitterionic form of TPE.

The spectral transitions and the character of the low-lying excited states of the copper halides, CuX (X= Cl, Br, I) are studied by means of two different relativistic computational approaches. One is based on the CASSCF/CASPT2 approach with operators accounting for scalar relativistic effects evaluated as a first order correction to the CASSCF energy. The other is a fully relativistic four component SCF-CI treatment based on the Dirac-Coulomb hamiltonian and hence accounts intrinsically for spin-orbit coupling as well as for scalar effects. The lowest excited states (^{1, 3}S⁺, ^{1, 3}P, ^{1, 3}D) are all closely related to the formal ionic configuration Cu⁺(3d⁹4s¹) X-(ns²np⁶). The agreement between calculated and measured transition energies and transition dipoles and their trends in the series strengthens recent assignments of the observed bands. Unobserved 'neutral' states, dominated by the configuration Cu(3d¹⁰4s¹) X(ns²np⁵), are situated mostly far above the 'ionic' states. Particular attention was given to the mixing of these states i.e. to the importance of charge transfer effects in the description of the observed states. These seem to be of significance only for the ¹S⁺ states, judging from the weights of the charge transfer configurations in the total wave functions and the character of the open shell orbitals. The calculated increase in charge transfer on going from Cl to I in the series goes together with an increase in the calculated transition dipoles for the ¹S⁺ states. This is consistent with the observed decrease of the lifetimes. The magnitudes of the spin-orbit splittings in the ionic states are governed by the splitting in Cu⁺ (2000 cm^-1) as expected.

Reaction of YCl₃.THF_3.5 with 2 equiv of [Me₂Si(NCMe₃)(OCMe₃)]Li produces [Me₂Si(NCMe₃)(OCMe₃)]₂Y-(µ-Cl)₂Li.THF₂ (1), which easily loses LiCl to give [Me₂Si(NCMe₃)(OMe₃)]₂-YCl.THF (2). Salt metathesis of 2 with LiBH₄, LiOAr (OAr = O-2,6-(CMe₃)₂C₆H₃), NaN(SiMe₃)₂, and LiCH(SiMe₃)₂ gives the corresponding yttrium bis((alkoxysilyl)amido) derivatives, [Me₂Si(NCMe₃)(OCMe₃)]₂YR (R = BH₄.THF (3), OAr (4), N(SiMe₃)₂ (5), CH(SiMe₃)₂ (6)). The alkyl compound 6 reacts with H₂ in THF to give an unstable hydride {[Me₂Si(NCMe₃)(OCMe₃)]₂Y(µ-H)}₂ (7), which was identified by 1H NMR as a symmetric dimer in solution. Isolation of the hydride 7 appeared not to be possible; the disproportionation product, [Me₂Si(NCMe₃)(OCMe₃)]₃Y (8), was obtained instead. With HC-CR, 6 undergoes protolysis of both the alkyl and the (alkoxysilyl)amido ligands to yield {Y(µC-CR)₃}_n for R = SiMe₃ (9) and CMe₃ (10). In contrast, polymerization to polyphenylacetylene was observed for R = Ph. Compound 6 reacts with N=CMe with metalation of the methyl group under proton transfer to the alkyl ligand to give CH₂(SiMe₃)₂. Insertion of another N=CMe into the new Y-C bond and 1,3-H shift produces {[Me₂Si(NCMe₃)(OCMe₃)]₂Y(µ(N,N')-NH-CMe=CH-C=N)}₂ (11). The molecular structures of 6 and 11 show that the bis(N,O-bis(tert- butyl)(alkoxydimethylsilyl)amido) ligand system is slightly more bulky than the bis(pentamethylcyclopentadienyl) ligand set in compounds Cp*₂YR. A ROHF INDO/1 semiempirical molecular orbital study on a stripped and symmetrized model of 6, [H₂Si(NH)(OH)]₂YCH₃, shows that the electronic properties of the bis((alkoxysilyl)amido) ligand system are quite different from those of [C₅H₅]₂YCH₃ but compare well with those of the bis(benzamidinato) anaiogue [HC(NH)₂]₂YCH₃. The (alkoxysilyl)amido ligand binds dominantly through a strong, ionic Y-N bond, while the ether function coordinates only weakly. Like in the bis(benzamidinato)yttrium system, the (alkoxysilyl)amido and the alkyl ligands accumulate negative charge, resulting in essentially ionic compounds. This high ionicity makes the compounds have little tendency to engage in d-bond metathesis reactions and (catalytic) insertion chemistry. Because of the absence of charge delocalization within the (alkoxysilyl)amido ligands, these behave as strong Brønsted bases and compete successfully with the Y-C bond in C-H bond activation reactions.

In this paper we first describe the implementation of the zeroth order regular approximation (ZORA) in our density functional program for extended systems. We have found an approximation that reduces the cost of the relativistic calculations. Secondly, we present the outcome of nonrelativistic, scalar relativistic, and spin- orbit calculations on the adsorption energy of CO on the (111) surfaces of Ni, Pd, and Pt. We have examined simultaneously the effect of different exchange-correlation (XC) functionals, i.e. the local-density approximation (LDA) versus the generalized gradient approximation (GGA) and spin-compensated versus spin- polarized variants of these functionals.

Existence of collective effects in magnetic coupling in ionic solids is studied by mapping spin eigenstates of the Heisenberg and exact nonrelativistic Hamiltonians on cluster models representing KNiF₃, K₂NiF₄, NiO, and La₂CuO₄. Ab initio techniques are used to estimate the Heisenberg constant J. For clusters with two magnetic centers, the values obtained are about the same for models having more magnetic centers. The absence of collective effects in J strongly suggests that magnetic interactions in this kind of ionic solids are genuinely local and entangle only the two magnetic centers involved.

Experimental as well as theoetical values for the frequency-dependent hyperpolarizability of C₆₀ differ by orders of magnitude. The authors present the first density functional calculation of a molecular frequency-dependent hyperpolarizability. Their implementation is very economical, enabling the treatment of molecules of this size in a potentially much more accurate way than can be obtained with alternative methods. Their results strongly support the recent results by L. Geng and J.C. Wright, who report much lower experimental values than previous authors.

1. Metoprolol, indoramine, codeine, tamoxifen and prodipine, compouds which are clinically used, and MDMA (ecstasy) were fitted in a small molecular model for substrates of human cytochrome P 4502D6.
2. For both the R- and S-enantiomer of metoprolol, the R- and S-enantiomer of MDMA, and for indoramine and codeine (all proven substrates of cytochrome P 4502D6) an acceptable fit in the substrate model was obtained.
3. For tamoxifen, for which the involvement of cytochrome P 4502D6 in the 4-hydroxylation is uncertain, no acceptable fit could be obtained in the substrate model.
4. For prodipine, a competitive inhibitor of P 4502D6, for which the involvement of P 4502D6 in the metabolism is uncertain, no acceptable fit in the substrate model could be obtained.
5. The substrate model was extended in a direction in which two large known substrates extend from the original substrate model. This extension did not change the flat hydrophobic region of the original substrate model.

The polarization behavior of the low lying excited states in the vicinity of perpendicularly twisted (D_2d) ethylene has been investigated in a quantum mechanical CISD approach, in which the quantum system was embedded in a polarized dielectric continuum modeling a non-symmetric distribution of the solvent around the solute. The results show a strong polarization in the two lowest lying excited states in the region where the two vacuum energy surfaces of those states intersect, which strongly suggests that the lowering of the symmetry of the solvent shell can provide the adiabatic coupling for the avoided crossing between both potential energy surfaces. All examined values of e, with the exception of the smallest investigated value (e = 2.0), showed that the polarization remains intact on progressive twisting towards the perpendicular geometry.

The partly filled 3d shell in solid transition metal compounds is quite localized on the transition metal ion and gives rise to large electron correlation effects. With the recently developed CASSCF/CASPT2 approach electron correlation effects can be accounted for efficiently. The CASSCF step accounts for the non-dynamical correlation and part of the dynamical correlation, the following CASPT2 step takes largely care of the remaining dynamical correlation in a perturbative way. This approach is applied to the d-d excitations in NiO for which both non-dynamical and dynamical electron correlation effects have substantial influence on the energy differences. Excitation energies that compare well to the experimental data are obtained and the importance of the different electron correlation effects can be assessed.

A two-parameter form of the Dirac Hamiltonian, which follows from the authors' earlier papers and can be treated in the framework of double perturbation theory, is derived. The usual 1/c² perturbation expansion is partitioned into a partial expansion in terms of 1/c² and additional expansion into a series of the metric perturbation parameter l². The block diagonalization of the two-parameter Dirac Hamiltonian corresponds to infinite summation with respect to the first of these parameters and leads to what is known as the 2-component Hamiltonian of the zeroth-order regular approxn. (ZORA, CPD). When corrected through first order in l² the ZORA Hamiltonian reproduces exactly all terms of the Pauli approximation. The block diagonalized Hamiltonian can be further modified to a form which has the non-relativistic energy operator as the leading term. However, this form has been found to possess several inconvenient features which are remedied by initializing the perturbation expansion with the ZORA Hamiltonian. This stresses the importance of the variation solution of the ZORA equation as the lowest order approximation for the expansion in the metric perturbation parameter l².

A new procedure for constructing double group symmetry functions is presented. Using this method integrals over Hermitian operators can become real quantities, even though the integrand and the functions themselves are complex. This is especially of interest to 4-component relativistic methods that use the Dirac-Coulomb Hamiltonian directly in electronic structure calculations.

The authors calculate the Heisenberg exchange J in the quasi-2D antiferromagnetic cuprates La₂CuO₄, YBa₂Cu₃O₆, Nd₂CuO₄ and Sr₂CuO₂Cl₂. The authors apply all-electron (MC)SCF and nonorthogonal CI calculations to [Cu₂O₁₁]^18-, [Cu₂O₉]^14-, [Cu₂O₇]^10- and [Cu₂O₇Cl₁₄]^14- clusters in a model charge embedding. The (MC)SCF triplet and singlet ground states are well characterized by Cu²⁺ (d_x²-y²) and O^2-. The antiferromagnetic exchange is strongly enhanced by admixing relaxed (MC)SCF triplet and singlet excited states, in which a single electron is transferred from the central O ion to Cu. The authors ascribe this effect to orbital relaxation in the charge transfer component of the wavefunction. Close agreement with experiment was obtained.

Recently, the 1st density functional theory (DFT) calculations of Raman intensities and depolarization ratios were published. Those calculations were done in the static approxn. Here, the authors use time-dependent DFT to include the dependence of those properties on the frequency of the exciting light wave. By analytically calculating the frequency-dependent polarizability at different nuclear positions, the approach is closer to a fully analytic one than the previous DFT studies. Results for five diatomics improve upon previous TDHF (time dependent Hartree-Fock) and SOPPA (second order polarization propagator approximation) ab initio results and show that the frequency dependence cannot be ignored in quantitative comparisons to experiment. Results for the important Q-branch differential Raman cross section of N₂ are closer to the experimental value than previous results. Inclusion of the frequency dependence has little effect on the depolarization ratios, but improves the results for the cross sections obtained in static DFT calculations. Results obtained with three different exchange-correlation potentials yield similar results.

The first direct experimental evidence is reported of large orientational (head-tail) effects in rotationally inelastic collisions, for the specific case of NO and Ar. NO is selected in the ²P_1/2 j = (1/2)^- state and oriented in an electric field. The steric effect, measured for collisions to three distinct final rotational states, appears to depend on the j' value and the parity of the final state. This behavior also follows from quantum-mechanical scattering calculations, but the calculated values do not coincide with the corresponding experimental ones.

No abstract available

The solvent shift of the n to p* transition of acetone in H₂O, MeCN, and tetrachloromethane was calculated in a combined quantum mechanical-classical mechanical approach, using both dielectric continuum and explicit, polarizable molecular solvent models. The explicit modeling of solvent polarizability allows for a seperate analysis of electrostatic, induction, and dispersion contributions to the shifts. The calculations confirm the qualitative theories about the mechanisms behind the blue shift in polar solvents and the red shift in nonpolar solvents, the solvation of the ground state in polar solvents and the red shift in nonpolar solvents, the solvation of the ground state due to electrostatic interactions being preferential in the former, and favorable dispersion interaction with the excited state, in the latter case. Good quantitative agreement for the solvent shift between experiment (+1,700, +400, and -350 cm^-1 in H₂O, MeCN, and tetrachloromethane, resp.) and the explicit solvent model (+1,821, +922, and -381 cm^-1) was reached through a modest Monte Carlo sampling of the solvent degrees of freedom. A consistent treatment of the solvent could only be realized in the molecular solvent model. The dielectric-only model needs reparameterization for each solvent.

An analysis of the structure of the optimized effective Kohn-Sham exchange potential v_x and its gradient approximations is presented. The potential is decomposed into the Slater potential v_s and the response of v_s to density variations, v_resp. The latter exhibits peaks that reflect the atomic shell structure. Kohn - Sham exchange potentials derived from current gradient approaches for the exchange energy are shown to be quite reasonable for the Slater potential, but they fail to approximate the response part, which leads to poor overall potentials. Improved potentials are constructed by a direct fit of v_x with a gradient-dependent PadŽ approximant form. The potentials obtained possess proper asymptotic and scaling properties and reproduce the shell structure of the exact v_x.

It is shown how the regularized two-component relativistic Hamiltonians of Heully et al. and Chang, Pelissier, and Durand can be viewed as arising from a perturbation expansion that unlike the Pauli expansion remains regular even for singular attractive Coulomb potentials. The performance of these approximate Hamiltonians is tested in the framework of the local density approximation and the relation of their spectrum to that of the Dirac Hamiltonian is discussed. The circumstances under which the current approximations are superior to the Pauli Hamiltonian are analyzed. Finally, it shown how the Hamiltonians could be used within the context of conventional Hartree-Fock theory.

The electronic structures and bonding of UF₆ and UF₆^- are studied within a relativistic framework using the MOLFDIR program package. A stronger bonding but more ionic molecule is found if one compares the relativistic with the nonrelativistic results. The first peak in the photoelectron spectrum of Karlsson, et al., is assigned to the 12g_8u component of the 4t_1u orbital, in agreement with other theoretical and experimental results. Good agreement is found between the experimental and theoretical 5f spectrum of UF₆^-. Some properties, like the dissociation energy and electron affinity, are calculated, and the necessity of a fully relativistic framework is shown. The Breit interaction has an effect on the core spinors and the spin-orbit splitting of these spinors but the influence on the valence spectrum is negligible.

The direct reaction field (DRF) force field gives a classical description of intermolecular interactions based on ab initio quantum-chemical descriptions of matter. The parameters of the DRF force field model molecular electrostatic and response properties, which are represented by distributed changes and dipole polarizabilities. The advantages of the DRF force field is that it can be combined transparently with quantum-chemical descriptions of a part of a large system, such as a molecule in solution or an active site in a protein. In this study, the theoretical basis for the deviation of the parameters is reviewed, paying special attention to the four interaction components: electrostatic, induction, dispersion, and repulsion. The ability of the force field to provide reliable intermolecular interactions is assessed, both in its mixed quantum-chemical-classical and fully classical usage. Specifically, the description of the water dimer and the solvation of water in water is scrutinized and seen to perform well. The force field is also applied to systems of a very different nature, viz. the benzene dimer and substituted-benzene dimers, as well as the acetonitrile and tetrachloromethane dimers. Finally, the solvation of a number of polar solutes in water is investigated. It is found that as far as the interaction energy is concerned, the DRF force field provides a reliable embedding scheme for molecular environments. The calculation of thermodynamic properties, such as solvation energy, requires better sampling of phase space than applied here.

The molecular Kohn-Sham exchange-correlation potential v_xc and the energy density e_xc have been constructed from ab initio first- and second-order density matrices for the series XH (X=Li, B, F). The way various effects of electronic structure and electron correlation manifest themselves in the shape of v_xc and e_xc has been analyzed by their decomposition into various components; the potential of the exchange-correlation hole, the kinetic component and (in the case of v_xc) the ``response'' component. The kinetic energy of noninteracting particles T_s, the kinetic part of the exchange-correlation energy T_c, and the energy of the highest occupied molecular orbital N have been obtained with reasonable accuracy and the effect of bond formation on these functionals has been studied.

A benchmark study of a number of relativistic correlation methods is presented. Bond lengths, harmonic frequencies, and dissociation energies of the molecules F₂, Cl₂, Br₂, I₂ and At₂ are calculated at various levels of theory, using both the Schrödinger and the Dirac-Coulomb-(Gaunt) Hamiltonian.

A benchmark study of a number of four-component relativistic correlation methods is presented. Bond lengths, harmonic frequencies, and dissociation energies of the molecules HF, HCl, HBr, HI, and HAt are calculated at various levels of theory, using both the Schrödinger and the Dirac-Coulomb-(Gaunt) Hamiltonian. The inclusion of relativity leads to a weakening of the bond, giving a decrease in the calculated harmonic frequencies and dissociation energies of the hydrogen halides. The effect on the bond length is small. These trends are explained by considering the relativistic change in hybridization induced by the spin-orbit coupling.

It is shown that it is possible to construct, within the framework of the basis set expansion method, the full Foldy-Wouthuysen transformation (i.e., to all orders in the inverse velocity of light) for an arbitrary potential once the Dirac equation has been solved. On this basic an iterative procedure to solve the Dirac equation is suggested that involves only the large component, obviating the time-consuming (at least in molecular calculations) introduction of large basis sets for a proper description of just the small components. The methods are used to compare the expectation value of radial distance operator in the Dirac picture and in the Shroedinger picture for the orbitals of the Uranium atom.

The exchange-correlation potentials .nu.xc which are currently fashionable in density functional theory (DFT), such as those obtained from the local density approximation (LDA) or generalized gradient approximations (GGAs), all suffer from incorrect asymptotic behavior. In atomic calculations, this leads to substantial overestimations of both the static polarizability and the frequency dependence of this property. In the present paper, it is shown that the errors in atomic static dipole and quadrupole polarizabilities are reduced by almost an order of magnitude, if a recently proposed model potential with correct Coulombic long-range behavior is used. The frequency dependence is improved similarly. The model potential also removes the overestimation in molecular polarizabilities, leading to slight improvements for average molecular polarizabilities and their frequency dependence. For the polarizability anisotropy, the authors find that the model potential results are not an improvement over the LDA and GGA results. The authors' method for calculating frequency-dependent molecules response properties within time-dependent DFT, which they described in more detail elsewhere, is summarized.

In this paper we will calculate the effect of spin-orbit coupling on properties of closed shell molecules, using the zero-order regular approximation to the Dirac equation. Results are obtained using density functionals including density gradient corrections. Close agreement with experiment is obtained for the calculated molecular properties of a number of heavy element diatomic molecules.

The formalism for a relativistic open-shell CCSD(T) method is presented and implemented in a computer program, RELCCSD. The code can be used for calculations with 2- or 4-component relativistic reference wave functions and allows a full inclusion of the spin-orbit coupling. The code is interfaced to the MOLFDIR program system. We illustrate its use with ab initio calculations of the fine structure splittings of Cl, FO, ClO, O₂⁺, and O₂-. The triples correction is found to make a large contribution to the Cl atom splitting, which is within 23 cm^-1, of the experimental value. The molecular results are within 4 cm^-1 of the experimental values where these are available. The value for FO is predicted to be -195 ± 4 cm^-1, in good agreement with experiment.

We report spin-restricted and symmetry-RHF cluster calculations on the lower excited states of a Cu+ impurity in NaF in order to investigate their dependence on cluster size. In contrast to previous work on smaller clusters, we found all states arising from the configurations e_g⁴ t_2g⁵ a_1g¹ and e_g³ t_2g⁶ a_1g¹ to be local. Delocalization can occur when an unbalanced choice of cluster and set of embedding point charges is made. These results confirm the local perspective from which previous spectroscopic assignments have been made. However, the inconsistency with the results from OD-EPR spectra remains.

The basis set superposition error (BSSE) for the Cr(CO)₅-CO and (CO)₅Mn-Mn(CO)₅ bonds is calculated for a large variety of STO basis sets. All investigated metal basis sets, being at least TZ for 3d and DZ for 4s are adequate. Ligand basis sets of TZD quality or better are required in order to have a low BSSE (6-8 kJ/mol or less) for both the metal-ligand and the metal-metal bond. When the ligand s, p basis set is of double-zeta quality, the BSSE is significant for the metal-ligand bond (16-22 kJ/mol depending on the polarization functions), but it is partly canceled by a basis set incompleteness error of opposite sign. For the metal-metal bond, the BSSE for DZ s, p ligand bases is unacceptably large (33-57 kJ/mol), leading to much too high bond energies if no correction for BSSE is applied. In general, the bond energies after correction for BSSE are rather stable. It is remarkable that for the metal-metal bond, but not for the metal-ligand bond, there is for all pure s, p ligand bases after correction for the BSSE a discernible basis set incompleteness error (ca. 15 kJ/mol), which only disappears after adding at least one polarization function. Agreement of the converged results for both geometries and bond energies with experiment is excellent. Cr(CO)₆.