Quadratic vibronic coupling

With p = (Qg + Ql f being the Jahn-Teller radius, FE the linear vibronic coupling constant, GE the quadratic vibronic coupling constant, KE the force constant for the Eg normal mode of vibration, and Qo, Qe the two degenerate vibrations of eg symmetry. 

In this communication we will give a description of the vibronic E-e interaction in an optical center in a crystal near one of the minima of the trough of the deformed (due to the quadratic vibronic coupling) Mexican-hat-type AP. We will also present a derivation of the nonperturbative formula describing the temperature dependence of the ZPL in the case of an arbitrary change of the elastic springs on the electronic transition. Then we will study a case when the excited state is close to the dynamical instability. Finally, we will apply the obtained general results to the ZPLs in N-V centers in diamond. 

From equation (35), the 30-warping terms arise from the third-order and fifth-order anharmonic vibration and the quadratic vibronic coupling, and the 60-warping terms arise from the sixth-order anharmonic vibration and the fourth-order non-linear vibronic coupling. 

For example, in a triangular molecule X3, if the electronic state belongs to an E representation and only a doubly degenerate e mode is considered, we can obtain the following Jahn-Teller effect with the quadratic vibronic coupling... 

Note added in proof. Very recently, A. Furlan, M. J. Riley, and S. Leutwyler [J. Chem. Phys. 96, 7306 (1992)] have reported a resonant two-photon ionization spectrum of the S, vibronic transitions of supersonically cooled triptycene. The excited state exhibits E (8>e Jahn-Teller activity with linear and quadratic vibronic coupling in a single, degenerate, benzene wagging mode. 

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. 

Here, (r, 6) are polar coordinates of the vibrational mode, (Pr,Pe) the corresponding canonical momenta, A > 0 and g > 0 are the Unear and quadratic vibronic coupling strength, respectively. AT and a are given by... 

In concluding this subsection, we mention that both systems have been treated also by more elaborate calculations beyond the linear-plus-quadratic vibronic-coupling model. The vibronic dynamics of O3 has been... 

In conclusion the fundamentals of the epikernel principle are seen to be a) symmetry contraints imposed on the siuiace by the structure of the configuration space, b) dominance of linear and quadratic vibronic coupling in the breakdown of degeneracy. 

Abstract We present an approach based on the quadratic vibronic coupling (QVC) Hamiltonian [NewJ Chem 17 7-29,1993] and the effective-mode formalism [Phys Rev Lett 94 113003, 2005] for the short-time dynamics through conical intersections in complex molecular systems. Within this scheme the nuclear degrees of freedom of the whole system are split as system modes and as environment modes. To describe the short-time dynamics in the macrosystem precisely, only three effective environmental modes together with the system s modes are needed. 

As the three effective mode model starts from the linear vibronic coupling Hamiltonian (LVC) [9] it may also have some relevance to generalize it and start from the quadratic vibronic coupling Hamiltonian (QVC) to obtain the appropriate quadratically extended (three)-effective mode equations. The motivation for this work has arisen that, in addition to the numerous applications of the LVC model, some other works in which the QVC model is used are also available [32,35], Our aim is to proceed along this direction. Following [21], we set up the QVC three-effective mode Hamiltonian and, using it for the pyrazine molecule we can calculate the autocorrelation function, the spectrum and the diabatic populations. The obtained results can be compared to those calculated by the LVC three-effective mode method. 

Let us start with the Hamiltonian for an N-mode system described by the quadratic vibronic coupling model. For a two state conical intersection in the diabatic representation it has the form... 

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