Vibronic perturbations, evaluation

To compute the intensity of the vibronic transition, S->-N, all we need do is evaluate the vibronic perturbation AVgj, it is assumed that we have experimental or theoretical knowledge of the energies AE j, hv S —> N), and hv TN) and the electronically allowed oscillator strength f TN). [Experimentally, the latter may be obtained by the evaluation of the area under the absorption curve when its ordinate is the extinction coefficient. e v), and its abscissa is the frequency of absorption, r(cm ), according to the formula / = 4.33 Theoretically, it... 

The vibronic coupling features are evaluated in a perturbation treatment by taking acconnt of temperature and electric field dependence (5). 

In the above formula, Q is the nuclear coordinate, p, and I/r are the ground state and excited electronic terms. Here Kv is provided through the traditional Rayleigh-Schrodinger perturbation formula and K0 have an electrostatic meaning. This expression will be called traditional approach, which has, in principle, quantum correctness, but requires some amendments when different particular approaches of electronic structure calculation are employed (see the Bersuker s work in this volume). In the traditional formalism the vibronic constants P0 dH/dQ Pr) can be tackled with the electric field integrals at nuclei, while the K0 is ultimately related with electric field gradients. Computationally, these are easy to evaluate but the literally use of equations (1) and (2) definitions does not recover the total curvature computed by the ab initio method at hand. 

The evaluation of the transition moment is straightforward now. Even though the energy difference between a5 B and ll A2 is small and the Tx level is strongly perturbed, the dipole transition to the ground state is forbidden as long as the molecule remains planar because of the dipole selection rules this transition would require an operator of A2 symmetry, but x, y, and z transform like B1, B2, and A, respectively. The transition may gain some intensity due to second-order spin-vibronic interactions, however. 

The beauty of Ham s theory is its simplicity. The Ham factors for any particular problem can be classified by symmetry. This means that any other operator which is a function of the Ua2 will be reduced by the same factor. Note that Ham s treatment implies that that the linear coupling is large compared to the additional terms in the Hamiltonian that are subsequently evaluated as perturbations of the ground vibronic energy levels. 

There has been considerable controversy in the literature as to whether the nonradiative decay rates kn T are to be evaluated using the adiabatic Bom-Oppen-heimer (ABO) or the crude Born-Oppenheimer (CBO) approximation mo,31,39-43) In Sect. 5 it was noted that the complimentary principle of quantum mechanics requires that the rates exactly calculated within these two schemes be the same provided that 4>s in both schemes is, as expected, a reasonable approximation to the true physical state. As noted also, in both the ABO and the CBO approximations. we have the same mechanistic schemes of (f>s coupled to the effective quasicontinuum 0,. Thus, both cases represent differing, yet reasonable representations of s and 10,). In the present discussion it is necessary to consider the remainder of the vibronic states of the moleculae, 0C in addition to f coupling matrix elements are no longer the effective values, but are actual matrix elements of the perturbing Hamiltonian. 

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