Jahn-Teller Effect in Crystal-Field Model

Jahn-Teller Effect in Crystal-Field Model 

The CF model is inappropriate for geometry optimization. The key parameters—the CF strengths Fm(L) rm)/Rm+1—are proportional to the elec- 

At a fixed geometry, however, the (harmonic) force field can be added by assuming the total Hamiltonian 

The force-field Hamiltonian appropriate to the e- and f2-type vibrations of an octahedron is 

Here the dimensionless normal coordinates of the tetragonal (e) vibrations are qu and qv those of the trigonal fa) vibrations are q, qn, and q. At this simple point several different nomenclatures exist. Hereafter, the (normal) vibrational coordinates Q relate to the dimensionless coordinates q by the formula q = Q(Mco/h)1/2, where M is the effective mass of the vibrator and co its frequency [88]. The force constant is K = a M. 

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