Vibronic coupling terms

If the solution of the zero-order Schrodinger equation [i.e., all terms in (17) except V(r, Rq) are neglected] yields an/-fold degenerate electronic term, the degeneracy may be removed by the vibronic coupling terms. If T) and T ) are the two degenerate wave functions, then the vibronic coupling constant... 

The static JT Hamiltonian with the anharmonic vibration and the nonlinear vibronic coupling terms is expressed by... 

Consider the APES of a two-level system with the ground state 1 and excited state 2 and an energy gap A between them, which interact (mix) under the symmetrized nuclear displacement Qr- Using perturbation theory with respect to the linear vibronic coupling term (dH/dQr)o Qr we easily obtain [1] that the primary curvature (the curvature without vibronic coupling) of the ground state K, ... 

The second and third terms in Eq. (7) are vibronic coupling terms and their influence on the electronic properties of the system will be treated by perturbation techniques. In our perturbation treatment we define the zeroth-order electronic Hamiltonian to be... 

In principle, whatever the initial model, after introducing the vibronic coupling terms corresponding to the chosen type of deperturbed potential curves, the experimental energy levels are obtained by diagonalizing one or the other type of interaction matrix. One example will be discussed later (Section 3.3.4). 

The description of the radiationless processes which lead to the transfer of excitation energy from one excited state to another in heavy metal complexes has been discussed by several authors (JI, 17, 22). Spin-orbit coupling must be included in the description of the initial and final states for the radiationless process but may also contribute to the coupling terms responsible for this process (II, 17). There are also vibronic coupling terms which arise from breakdown of the Bom-Oppen-heimer approximation which presumably play some role in radiationless energy transfer processes in both heavy- and light-atom molecules (II, 17). Beyond these electronic terms, there are vibrational contributions to the rate constant for a radiationless process, and these contributions are generally expressed as Franck-Condon factors (II). 

The terms a(Sy/6ga)ga and l/2 V/dQaQ )Q Qp are the linear and quadratic vibronic coupling terms, respectively. For small Ga values, they may be considered as a perturbation. 

The possibility of comparing the magnitude of different vibronic coupling terms on the basis of a qualitative criterion is of great potential use in the... 

A type of analysis of molecular properties and molecular transformations which, unlike the Bom-Oppenheimer approximation, assumes that electronic states depend strongly on nuclear coordinates. If stationary electronic states are obtained as solutions of the Schrodinger equation for fixed nuclei, an accounting for vibronic coupling terms in the Hamiltonian (interaction of electrons with nuclear displacements) mixes these electronic states. This mixing is especially strong in the cases of electronic degeneracy (See Jahn-Teller Effect). 

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