# Quasiclassical versus phase space approaches to radiationless transitions in molecules

## Alexey V. Sergeev and Bilha Segev

*Department of Chemistry, Ben-Gurion University of the Negev*

POB 653, Beer-Sheva 84105, Israel

We study a radiationless transition in a polyatomic molecule when the electronic energy
of an excited electronic state is transferred to vibrational degrees of freedom of the nuclei,
and when some nuclear coordinates change abruptly.
The rate of the transition is proportional to the square of the Frank - Condon integral,
or an overlap integral between the nuclear components of the wavefunctions.

In the quasiclassical approximation, the bulk of the overlap integral
goes from a vicinity of the point *q*_{L}
in the coordinate space where the
classical momentum on the donor Born - Oppenheimer surface is opposite
to the momentum on the acceptor surface. In the Wigner representation,
the bulk of the phase space overlap integral goes from a region near the
point (*q*_{*}, *p*_{*})
on the surface of constant energy where the Wigner function is maximal.
For illustration, these two approaches in different regimes are compared for two models
with Morse or Poeschl - Teller oscillators.

This research was supported by Grant No. 2000118 from the United States - Israel Binational
Science Foundation (BSF), Jerusalem, Israel.

Abstract and poster

Back to Presentations at conferences.

Designed by A. Sergeev.