Theoretical calculation of the pure electronic spectrum of ${\mathrm{MnF}}_6$${\mathrm{}}^{4\mathrm{-}}$ in vacuo and in ${\mathrm{RbMnF}}_3$

The pure electronic d-d spectrum of the ${\mathrm{MnF}}_6$ ${\mathrm{}}^{4\mathrm{-}}$ complex ion has been computed at different values of the ${\mathrm{Mn}}^{2+}$-${\mathrm{F}}^{\mathrm{-}}$ 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 ${\mathrm{MnF}}_6$ ${\mathrm{}}^{4\mathrm{-}}$, a variation of the 10Dq with R as $R^{\mathrm{-}3.6}$ (1.7≤R≤2.3 Å), 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.