Reaction rate assessment of multiphonon relaxation

TL;DR

This paper extends the reaction rate formalism to inelastic tunneling vibronic processes involving phonons, linking reaction rates with multiphonon relaxation and confirming traditional temperature dependence patterns.

Contribution

It proposes that Bardeen-Christov's quantum-mechanical approach can be extended to inelastic tunneling, connecting reaction rate theory with multiphonon relaxation processes.

Findings

Transition probabilities relate to Franck-Condon factors.

Relaxation rate of 1-phonon processes increases linearly with temperature at low T.

The theory aligns well with numerical calculations on experimental systems.

Abstract

An investigation is made into whether the reaction rate formalism also applies to describing inelastic tunneling vibronic processes associated with the absorption and emission of phonons. We propose that Bardeen-Christov's quantum-mechanical approach to the transition (tunneling) probabilities originally intended for elastic tunneling alone can formally be extended to cover inelastic tunneling as well. Namely, we show that inelastic tunneling through the absorption of p phonons can be regarded as an exothermic reaction with zero-point reaction heat H = -phv. Alternatively, inelastic tunneling through the emission of p phonons will be equivalent to an endothermic reaction with zero-point reaction heat H = +phv. An analysis made indicates that the transition (tunneling) probabilities expand into Franck-Condon factors revealing the interconnection between reaction-rate and multiphonon relaxation rates. Our proposal confirms to a good approximation the traditional multiphonon fingerprint that the relaxation rate of 1-phonon processes increases linearly with the temperature T at low T. The combined reaction rate theory compares favorably with numerical calculations on specific experimental systems.