Coupling with the Jahn-Teller mode for triplet states of MF(6) (M=Mn2+,Cr3+) complexes: Dependence on the M-F distance and influence on the Stokes shift

The microscopic origin of the V-E coupling constant with the Jahn-Teller mode E(g) for orbital triplet states corresponding to several excited states of MnF64- and the T-4(2g) State of CrF63- is explored by molecular orbital (MO) calculations. V-E is shown to be determined by the splittings Delta(c) and Delta(t) induced in the antibonding e(g)* and t(2g)* levels by a Q(theta)(similar to 3z(2) - r(2)) distortion and so V-E < 0 for the T-4(2g) state of CrF63- leading to a compressed octahedron as equilibrium geometry. V-E values have been derived from self-consistent charge extended Huckel and MSX alpha calculations performed al different Q(theta) values. The results for the T-4(1g)(G), T-4(2g)(G), T-4(2g)(D), and T-4(1g)(P) states of MnF64- are reasonably close to the experimental Figures. For the first excited state T-4(1g)(G) the value V-E approximate to 60 cm(-1)/pm found for a metal-ligand distance R equal to 213 pm leads to a Huang-Rhys factor S-E = 1.5 also close to experimental findings. On passing from this case to the T-4(2g), State of CrF63- \V-E\ increases by a factor of about two but S-E = 1.2 in agreement with experimental data for Rb2KGaF6: Cr3+. The latter figure implies a Stokes shift E(S)(0)(E) due to the E(g) mode equal to 1200 cm(-1) which is about 50% of the total Stokes shift. As a salient feature it is shown that for both MnF64- and CrF63- complexes V-E strongly depends upon R, as it also happens to the V-A coupling constant with the symmetric A(1g) mode. This reasonably explains the increase of the Stokes shift upon increasing R recently observed for Mn2+-doped fluoroperovskites. Although pure crystal field (CF) theory gives rise to V-E values much smaller than the experimental ones it is shown that the relation V-A/V-E = root 2 derived for the first excited state of MnF64- and CrF63- is not far from the results obtained through MO calculations.