Average of Configuration

The Wyboume crystal field parameters B (f, f), B (d, d), and Bjj(f, d), which describe the interaction due to the presence of the ligands onto the electrons of the lanthanide center. They are deduced from the ligand field energies and wave functions obtained from Kohn—Sham orbitals of restricted DFT calculations within the average of configuration (AOC) reference by placing evenly n — 1 electrons in the 4f orbitals and one electron in the 5d.33... 

Explicit account of the electron interaction within a self-consistent approach modifies the interpretation of the parameters. Slater s notion of the average of configurations and fractional occupation will be consistently applied in the grand canonical ensemble form. The one-particle reduced density matrix retains the symmetry of the crystal field and spin-orbit matrices, thus... 

Figure 19-11. MO energy diagram for complex I (Figure 19-10) calculated with LFDFT the energies of LFDFT orbitals are compared with those resulting from the average-of-configuration KS calculation. Orbital contours (pertaining to values of the density of 0.05 a.u.) are plotted, but atoms are omitted for clarity (see color plate section)...

Table 4.1 Comparison of central field calculations for Fe, Co, and Ni atoms. Energies in Hartrees. I Derived from Eq. (4.135). II Derived from Slater s average of configuration energy functional (from J. B. Mann)...

A simplified closed-shell expression for the Breit interaction can be derived as well [201]. For open-shell atoms, an average of configurations yields a similar total energy expression except for the intra-shell exchange energy [57, p. 164]. 

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