Electronic relaxation of small molecules in a dense medium

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Abstract

In this paper we present a theoretical study of radiationless transitions in a small molecule embedded in a dense inert medium. Two extreme situations of the molecule-medium coupling were considered, involving the case of zero displacements of the medium modes between the two electronic states (i.e. the Shpolskii matrix) and the limit of strong molecule-medium coupling. The Fourier transform of the non radiative decay probability of a small molecule in a Shpolskii matrix involves exponential damping, while for the strong coupling situation Gaussian damping is involved. In the case of the Shpolskii matrix the decay rate of a small molecule can be expressed in terms of an infinite series where each term corresponds to a product of an (intramolecular) Poisson distribution and a (medium induced) Lorentzian distribution. The Lorentzian widths were explicitly expressed in terms of the vibrational relaxation widths. The Robinson-Frosch formula can be obtained for the extreme case of near degeneracy in a Shpolskii matrix. In the limit of strong molecule-medium coupling the decay rate of a small molecule can be recast in terms of an infinite sum where each term involves a superposition of a Poisson distribution and a Gaussian distribution. The medium induced Gaussian distribution is determined by intramolecular phonon broadening. We have elucidated some new features of the electronic relaxation of a small molecule in a dense medium pertaining to the problem of off-resonance intramolecular coupling which modifies the energy gap law and the deuterium isotope effect.

Original languageEnglish
Pages (from-to)97-116
Number of pages20
JournalTheoretica Chimica Acta
Volume29
Issue number2
DOIs
StatePublished - Jun 1973

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