Wavefunction methods

The electronic problem  -  The N-electron wavefunction

Within all cluster models described in this work, multiconfigurational wavefunctions are constructed for the state of interest. The Molecular orbitals are expressed in terms of a linear combination of basis functions (ANO basis set):

A single determinant of these MOs which will then correspond to a monodeterinantal description of the wavefunction can be written :

If we now look for the determinant that minimize the energy with respect to the coefficients of these basis functions we obtain the monodeterminental Hartree-Fock solution. For many cases it is not possible to approximate the electronic wavefunction by a single configuration because some configurations are almost degenerate and need to be included from the beginning. Moreover in most cases we need to treat transition metal ions which are open shell system with unpaired electrons. More than one of these determinants should be considered and all the possible excitations or configurations should be taken into account. Since the number of these determinants is increasing enourmously with the number of electrons, we separate the space in 3 parts. Inacive space where the orbitals stay doubly occupied, active space where all excitations are considered and virtual space which contains unoccupied orbitals. From there we obtain the CASSCF wavefunction as it is shown in the following equation :

The CASSCF wavefunction is obtained by minimizing the energy with the respect of both coefficients : the CI coefficients in our multiconfigurational wavefunction but also the coefficient of the basis functions :