The electron density of the environment (ρB) generates the orbital-free embedding potential [Wesolowski and Warshel, J. Phys. Chem., 97 (1993) 8050]. The analytic form of this potential is not known. In practical calculations it is approximated using explicit explicit density-dependent functionals for its exchange-correlation and non-additive kinetic energy components. Currently, we use the approximation for the kinetic energy component chosen based on our dedicated analyses of different approximations [Wesolowski, J. Chem. Phys. , 107 (1997) 8616].
In the calculations, embedded orbitals were used to construct ρA (the electron density of the lanthanide cation), whereas the ligands (six Cl- anions) are represented as frozen electron density (ρB).
Orbital-free embedding potential (LDA level) calculated for a spherical trial density ρA in the cage formed by six Cl- ligands (shown in the plane of four Cl- atoms).
Splitting between the t2u and a2u levels for lanthanide cations in cristal (octahedral) environment. Calculated values were obtained using the orbital-free embedding potential approximated using gradient-dependent functionals.