Vibronic reduction factor

Here = Kqq(0) is elastic constant of the tetragonal E vibrations in one octahedron. The coefficients q and p are well-known vibronic reduction factors [1,2,61]. As the vibronic coupling constant, V, increases, the reduction factors, q and p, approach their limiting values, q = and p = 0. Therefore, at strong vibronic coupling, the product qV in (38) increases linearly with V. Therefore, qV is known as the factor of vibronic amplification [1, 2, 61]. At the same time, the factor pV... 

Let us investigate the temperature dependence of the vibronic reduction factors C G3/2(I P) with the vibronic coupling with E and T2 vibrations taken into account [C 3/2 (e + t2) problem]. Within the basis set used for the construction of the pfy operators the density matrix for the linear Gm (e + t2) problem in the framework of the approximation, analogous to Eq. (13), is determined by the following relation (Ogurtsov and Kazantseva, 1983) ... 

Within the SH formalism the MPs (gx, gy, gz, D, E, /tip) are thought of as physical constants associated with each particular system. The electronic-magnetic theory beyond the SH formalism reveals that there are only the electronic-structure parameters (like B, C, ) associated with the electron configuration and the CF parameters [like F2(L) and F4(I)] for each ligand. A more realistic approach brings the orbital reduction factors k (which must be anisotropic) and in a particular case of the degenerate electronic states also the force-field and vibronic coupling parameters (like Kee, Xe, Xee, and eventually Ktt, Xt, Xtt, or even more parameters). 

The numerically calculated cos = (cos ( /2))-(sin ( /2)) is equal to the Ham reduction factor q for the ground vibronic state in the case of linear coupling and no strain [7]. The original suggestion that the zero point motion within a single potential minimum can result in a small admixture of an electronic state that can have a large effect on the g values of copper(II) complexes was made by O Brien [20]. 

In the basis of the ground vibronic wavefunctions i i=x,yadditional reduction factor is required to account for the reduced overlap between the vibrational wavefunctions ... 

It can easily be seen that in the absence of the vibronic coupling all the parameters 0G3/2(r, p), Q%n(T, /3), and Q n(T, P) are equal to one, and the Cotton-Mouton constant in this approximation is a quadratic function of the inverse temperature, similar to that inherent to molecules with nonzero magnetic moments and with anisotropic polarizability and magnetic susceptibility. The vibronic interaction modifies the temperature dependence by means of the temperature-dependent reduction factors, a part of which was discussed in the investigation of the Kerr effect. 

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