On algorithms for calculating the SVL-fluorescence spectra of polyatomic molecules

Abstract

A software package for modeling the fluorescence spectra from a single vibrational level (SVL) of excited electron states under resonance laser excitation, in the adiabatic approximation with allowance for the “confusion” of normal coordinates under electron excitation, i.e., the Dushinsky effect, is presented. To algorithmize the calculation of the intensities in resonance fluorescence spectra, thirteen modules for the calculating Franck–Condon integrals are created. To optimize the calculation process, some simpler expressions are derived for the common terms of nested sums in the formulas for calculating Franck–Condon integrals from tone and overtone levels. To accelerate calculations, some constraints in the form of inequalities are additionally imposed on the range of vibrational quantum numbers in the ground electron state. The proposed algorithm for the modeling of SVL-fluorescence spectra of polyatomic molecules is based on quantum models of molecules in the ground and excited electron states calculated within the framework of contemporary ab initio quantum-mechanical methods and methods based on density functional theory.