Theoretical calculation of the pure electronic spectrum of MnF6 4- in vacuo and in RbMnF3.

Abstract

The pure electronic d-d spectrum of the ${\mathrm{MnF}}_{6}$${\mathrm{}}^{4\mathrm{\ensuremath{-}}}$ complex ion has been computed at different values of the ${\mathrm{Mn}}^{2+}$-${\mathrm{F}}^{\mathrm{\ensuremath{-}}}$ distance R along the ${a}_{1g}$ vibration mode, following an open-shell self-consistent-field--molecular-orbital (SCF-MO) methodology. Both cluster--in-vacuo and cluster--in-the-lattice (${\mathrm{RbMnF}}_{3}$) calculations have been performed in terms of rigid-lattice and partially-relaxed-lattice models. Theoretical spectral parameters have been obtained from the SCF results, and the evolution of the 3d splitting and the d-d repulsion with R has been examined. The lattice effects on the computed spectrum turned out to be very small in the present calculation. The overall description of the pure electronic single- and double-excitation transitions is rather good: sixteen transition energies are calculated with an rms deviation smaller than 1.9 kilokaysers (kK). This energy calculation partially supports the assignment of the peaks at (42--44) kK to double excitations. The energy splitting of the $^{4}\mathrm{A}_{1\mathrm{g}}$, $^{4}\mathrm{E}_{\mathrm{g}}^{\mathrm{a}}$ states and its relationship with the electronic delocalization of the 3d MO's have been analyzed. The present calculation predicts, for ${\mathrm{MnF}}_{6}$${\mathrm{}}^{4\mathrm{\ensuremath{-}}}$, a variation of the 10Dq with R as ${R}^{\mathrm{\ensuremath{-}}3.6}$ (1.7\ensuremath{\le}R\ensuremath{\le}2.3 A\r{}), in agreement with the thermal expansion of the ${\mathrm{RbMnF}}_{3}$ lattice, the red shifts shown by the lower quartets upon cooling, and the results of other theoretical calculations. Conversely, the Racah parameters B and C show a very slight and opposite variation with R.