Effective Hamiltonian Crystal Field: Present Status and Applications


A.L. Tchougreeff


MSU, MCCME, IAC RWTH



Abstract:

We review the fundamental basics of the Effective Hamiltonian Crystal Field (EHCF) method originally targeted for calculations of the intra-shell excitations in the d-shells of coordination compounds of the first row transition metals. The formalism of effective operators is applied to derive the explicit form of the effective operator for the dipole moment in the d-shell electronic subspace. This allows to calculate the oscillator strengths of optical d-d transitions which are otherwise forbidden when treated in the standard framework of EHCF. We also extend the EHCF methodology to describe magnetic interactions of the effective spins residing in several open d-shells of the polynuclear coordination compounds. This is a challenging task of improving the precision of ca. 1000 cm-1 (that of describing the excitation energies of single d-shells by the already well successful EHCF method) to that of ca. 100 cm-1 characteristic for the energies required to reorient the spins, i.e. eventually by an order of magnitude. This is performed within the same paradigm as in the EHCF method: the concerted usage of the McWeeny's group-function approximation and the Löwdin partition technique. These are applied to develop the effective description of the d-system. This approach is implemented and tested on a series of binuclear complexes [{(NH3)5M}2O]4+ of trivalent cations featuring μ-oxygen super-exchange paths in order to confirm the reproducibility of the trends in the series of values of exchange constants for the compounds differing by the nature of the metal ion. The results of calculations are in a reasonable agreement with available experimental data and other theoretical methods. The Effective Hamiltonian Crystal Field (EHCF) method has originally been designed to reproduce the excitations in the d-shells of coordination compounds of the first transition row, and this approach has been extended in the MagAîxTic package to magnetic interactions of the effective spins in multiple open d-shells. It is now tested on a series of binuclear Fe(III) complexes featuring μ-oxygen superexchange pathways. Good agreement with experimental values is reached either for linear or bent bridge geometries as well as for protonated bridges.