Embedded cluster approach

   The embedded cluster approach, which emerges from the ionic model, has a long standing tradition in the study the electronic structure of ionic compounds. Typically, a cluster containing one metal ion (M) and the nearest anions (L) is considered to represent the material. To introduce the effect of the rest of the crystal this MLn cluster is usually embedded in a set of point charges to account for long range electrostatic interactions, whereas the nearest ions around the cluster are represented by effective one-electron potentials [1]. Within this material model the electronic structure can be investigated by standard ab initio quantum chemical methods.

[1] C. de Graaf ,C. Sousa, R. Broer, Journal of molecular structure(theochem) 458, 53-60 (1999)


BC

Basic cluster (BC)

An all electron basis set is used to describe the motion of the electrons using ab initio wavefunction methods. In our case we used CASSCF wavefunction. The basis set employed in the present work is derived from a 21s15p10d6f primitive basis set for iron and 14s9p4d primitive basis set for oxygen. Following the ANO contraction of Widmark and co-workers [2,3], we use a 6s5p4d1f basis for Fe and a 4s3p1d basis for O.

[2] P. O. Widmark, P. A. Malmqvist, B. O. Roos, Theor. Chim. Acta, 77, 291 (1990)
[3] R. Pou-Amerigo, M. Merchan, I. Nebot-Gil, P. O. Widmark, B. O. Roos, Theor. Chim Acta, 92, 149 (1995)


BC+MP

Model Potentials (MP)

The ions that are directly linked with the basic cluster are represented with ab initio Embedded Model Potentials [5] (AIEMP). The AIEMPs for Ca, Fe and O in CaFeO3 are optimized following the procedure given in Ref. [4]. The theory of AIEMP is derived from the Theory of Electron Separability (TES)[5] [6] [7] which assumes a strong orthogonality between the different groups of electrons. For an ideal ionic system the strong orthogonality condition is fulfilled and bare AIEMPs give good representation of the external ions. However, when the cluster wavefunction has non-negligible amplitude outside the cluster region, the strong orthogonality condition can only be maintained by adding basis functions to the atoms represented by AIEMPs [pascual]. In the present work we add (1s,1p) valence basis functions to the oxygen and the iron (AIEMP-sp).

[4] L. Seijo, Z. Barandiaran, J. Chem. Phys., 94, 8158 (1991)
[5] Z. Barandiaran, L. Seijo, J. Chem. Phys., 89, 5739 (1998)
[6] S. Huzinaga, A. A. Cantu, J. Chem. Phys, 55, 5543 (1971)
[7] V. Luna, L. Pueyo, Phys. Rev. B, 39, 11093 (1989)


BC+MP+PC

Point charges (PC)

In addition the long-range electrostatic interactions were considered with a set of optimized point charges that reproduce the Madelung field in the cluster region arising from the rest of the crystal. This embedding scheme accounts for a finite size of the ions around the cluster and furthermore, exchange and so-called orthogonality interactions are partially included in the description of the electrostatic structure.