Non‐Condon Approximations and the Static Approach in the Theory of Non‐Radiative Multiphonon Transitions

Abstract

The off-diagonal matrix element of the non-adiabdicity operator, on which usually the theory of non-radiative multiphonon transitions is based, is recast into a form much more convenient for the calculation of the transition probability W in non-Condon approximation. This is demonstrated first for a. two-level system coupled to a single vibrational mode and then extended to the more general case of a complete set of non-degenerate electronic states coupled linearly t o LV normal modes. The strong anharmonicity of the adiabatic potentials due to the mixture of states caused by the electron-phonon interaction operator is stressed, which limits the applicability of the theory to situations where only transitions well below "level crossing" are important, and, consequently, imposes serious restrictions on the parameters of the system and the temperature. Keeping to these restraints and to two electronic levels, the transformed matrix element of the non-adiabaticity operator is identical with that of the perturbation operator used in the static coupling scheme of Haug and Passler, which turns out in this way t o be equivalent to a closed-form of non-Condon approximation based on a well defined set of adiabatic wave functions. Explicit expressions for W are also given, and some aspects of the theory in general are discussed.

Alternative forms for the promoting interaction in radiationless transitions

“…Since no radiationless transitions are possible between true stationary states, the choice ultimately depends on which nonstationary state is prepared in a given experiment (Bixon and Jortner 1969). It has been demonstrated recently by several authors (Huang 1981, Gutsche 1982, Burt 1983) that the two coupling schemes lead to equivalent predictions at a certain level of approximation, although they cannot be precisely equivalent (Denner and Wagner 1984). It has been demonstrated further that, within the adiabatic coupling scheme, the popular 'Condon' approximation introduced by Huang and Rhys (1950) is internally inconsistent, as usually applied, and predicts transition rates which are too small by three orders of magnitude.…”

“…This idealised model is well adapted to clarification of matters of principle, but tends to obscure the procedures appropriate to more realistic models. Generalisation of the idealised model to encompass a larger basis set and several configuration coordinates was undertaken by Gutsche (1982).The object of the present work is to extend these considerations to more realistic models. We proceed from a somewhat different set of assumptions than Gutsche (1982).…”

“…Generalisation of the idealised model to encompass a larger basis set and several configuration coordinates was undertaken by Gutsche (1982).…”

“…This idealised model is well adapted to clarification of matters of principle, but tends to obscure the procedures appropriate to more realistic models. Generalisation of the idealised model to encompass a larger basis set and several configuration coordinates was undertaken by Gutsche (1982).…”

“…However, several authors have advocated an alternative coupling scheme in which radiationless transitions between static states are mediated by off-diagonal elements of the potential energy operator (Helmis 1956, Passler 1974, 1982. Since no radiationless transitions are possible between true stationary states, the choice ultimately depends on which nonstationary state is prepared in a given experiment (Bixon and Jortner 1969).…”