Most probable path in phase space for a radiationless transition in a molecule

Alexey V. Sergeev and Bilha Segev


We study a radiationless transition in a polyatomic molecule when the electronic energy of an excited electronic state is transferred to the vibrational degrees of freedom of the nuclei, and when some nuclear coordinates change abruptly. This jump between the donor energy surface to the acceptor one gives the initial conditions for the subsequent dynamics on the acceptor surface, and the partition of energy between competing accepting modes. In the Wigner representation, the physical problem of recognizing the accepting modes for a radiationless vibronic relaxation reduces to the mathematical problem of finding the maximum of a function of many variables under a constraint. The function is the initial Wigner function of the nuclei and the constraint is energy conservation. In a harmonic approximation for the potential surfaces, the problem is equivalent to finding the distance from a given point to a multidimensional ellipsoid. This geometrical problem is solved in closed form. For nonharmonic potentials, the optimization problem is solved perturbatively.

Text of the paper: PDF format (with figures), TeX file.
5 separate figure files: 1, 2, 3, 4, 5.

On-line constraint minimization of the function W(x,y)

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Designed by A. Sergeev.