## Modeling properties of molecules with open d-shells using density functional theory

### Atanasov, Mihail ; Daul, Claude A.

### In: Comptes Rendus Chimie, 2005, vol. 8(9-10), p. 1421-1433

An overview of the theory and applications of a recently proposed ligand-field density functional theory (LFDFT) is given. We describe a procedure based on DFT allowing to deduce the parameters of this non-empirical LF approach consisting of the following steps: (i) an average of configuration (AOC) DFT calculation, with equal occupancies of the d-orbitals is carried out (ii) with... Plus

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- An overview of the theory and applications of a recently proposed ligand-field density functional theory (LFDFT) is given. We describe a procedure based on DFT allowing to deduce the parameters of this non-empirical LF approach consisting of the following steps: (
*i*) an average of configuration (AOC) DFT calculation, with equal occupancies of the d-orbitals is carried out (*ii*) with these orbitals kept frozen, the energies of all single determinants (SD) within the whole LF-manifold are calculated and used as a data base in a further step to provide all the Racah- and LF-parameters needed in a conventional LF-calculation. A more rigorous analysis of this approach in terms of Löwdin's energy partitioning and effective Hamiltonians is used to provide explicit context for its applicability and to set more rigorous criteria for its limitations. The formalism has been extended to account for spin-orbit coupling as well. Selected applications cover tetrahedral CrX₄ (X = Cl, Br) and FeO₄²⁻ and octahedral CrX₆³⁻ (X = F⁻, Cl⁻, Br⁻) complexes. Transition energies are calculated with an accuracy of 2000 cm⁻¹, deviations being larger for spin-forbidden transitions and smaller for spin-allowed ones. Analysis show, that ligand field parameters deduced from experiment are well reproduced, while interelectronic repulsion parameters are calculated systematically to be by 30–50% of lower in energy. A generalization of the LFDFT theory to dimers of transition metals allows to calculate exchange coupling integrals in reasonable agreement with experiment and with comparable success to the broken symmetry approach; in addition they allow to judge ferromagnetic contributions to exchange coupling integral which have been ignored before.