Nondegenerate state

The majority of photochemistry of course deals with nondegenerate states, and here vibronic coupling effects aie also found. A classic example of non-Jahn-Teller vibronic coupling is found in the photoelection spectrum of butatiiene, formed by ejection of electrons from the electronic eigenfunctions [approximately the molecular orbitals). Bands due to the ground and first... 

For the energy, one can make use of first-order perturbation theory for a nondegenerate state. Thus, if the state P is perturbed to the state P = P + P by the one-electron perturbation AV = JT<5v(r,-), the energy change to first order is [1]... 

The other relativistic effect entirely neglected so far is the spin-orbit coupling. For systems in nondegenerate states, the only first-order contribution to TAE comes from the fine structures in the corresponding atoms. Their effects can trivially be obtained from the observed electronic spectra, and hence the computational cost of this correction is fundamentally zero. 

The definitions given in this section are valid both for degenerate and nondegenerate states. 

Much work on the theory of Jahn-Teller and pseudo-Jahn-Teller effects has been reported by Bersuker and co-workers. They have proved that the pJT effect is the only possible source of instabilities of high symmetry molecular systems in nondegenerate states. These researchers have investigated the pJT effect in many systems, including planar BFLf, CH4, BH3, CH3", NH3, octahedral metal complexes MHe (M = Sc3-, V, Cr), and a series of octahedral hexafluoride systems (45, 46, 49, 50). 

A- and C-terms require that either or both the ground and excited states must be degenerate. A B-term signal can occur when both states are nondegenerate, but there is an additional nondegenerate state (TV) that can mix with either due to the applied magnetic field. Figure 1.8a illustrates the effect of TV on the excited state (Te). 

We have also tested numerically the simple analytical formulae for the correction factor, of transitions between nondegenerate states (circular and... 

Table 3. Analytic expressions for the factors vn, and wZlZmv, for magnetic induced corrections to the matrix elements of radiative transitions 7r- and a between nondegenerate states of the hydrogen atoms nlm — n l — 1 m, where l = n — vi, m = n — urn, n = n — un> m = m - for 7r-transitions, m = m — 1 - for -transitions...

A or 5 designate a nondegenerate state. Each set of levels in an A or state is symmetrically occupied. 

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