Effective Hamiltonian crystal fields: Present status and applicability to magnetic interactions in polynuclear transition metal complexes

The fundamentals of the Effective Hamiltonian Crystal Field (EHCF) method, used originally to calculate intra-shell excitations in the d-shells of coordination compounds of the first row transition metals, are reviewed. The formalism of effective operators is applied to derive an explicit form of the effective operator for a dipole moment in d-shell electronic subspace, allowing us to calculate the oscillator strengths of optical d-d transitions, which are otherwise forbidden when treated in the standard EHCF approach. EHCF methodology is also extended to describing magnetic interactions of the effective spin in several open d-shells of polynuclear coordination compounds. The challenging task of improving a precision of ∼1000 cm^-1 (describing the excitation energies of single d-shells by EHCF) to one of ∼100 cm^-1 for the energies required to reorient spins by an order of magnitude is considered within the same paradigm as EHCF: the targeted use of McWeeny's group function approximation and the Löwdin partition technique. These are applied to develop an effective description of a d-system. This approach is tested on a series of binuclear complexes [{(NH₃)₅M}₂O]⁴⁺ of trivalent cations featuring oxygen super-exchange paths in order to confirm the reproducibility of the trends in the series of exchange constants values for compounds that differ in the nature of their metal ions. The results from calculations are in reasonable agreement with the available experimental data and other theoretical methods.