Two approaches to the calculation of molecular resonance states: Solution of scattering equations and matrix diagonalization

Abstract

AbstractWe have analyzed two approaches to reproduce the resonance expansion of the scattering matrix appropriate for the calculation of molecular resonance states. The first is based on the resonance theory of Siegert‐Humblet‐Rosenfeld (SHR) and the second on the Fano‐Feshbach formalism. The direct method of calculating the resonance expansion characteristics, devised on the basis of the SHR theory, makes it possible to obtain the energies and partial widths (detailed decay rate constants) of resonances. The Fano‐Feshbach formalism, on the other hand, elucidates the resonance state as a concept and facilitates the interpretation of calculation results. The use of computational methods is illustrated by the study of the decay of a model triatomic system and of gas‐phase nucleophilic substitution reactions. Used in the latter case is the division of all degrees of freedom of the reacting system into the adiabatic and dynamic ones along with an algorithm of inclusion of the restricted dynamical treatment in the calculation of reaction rate constants.