Franck–Condon factors in studies of dynamics of chemical reactions. V. Simple construction of quasiadiabatic potential energy surfaces and numerical evaluation of Franck–Condon integrals

Abstract

We test the Franck–Condon (FC) approximation for chemical reactions by prescribing a simple construction of quasiadiabatic potential energy surfaces and evaluating numerically FC overlap integrals for the collinear case of the chemical reactions H2(D2)+F and H+Cl2. The FC model is derivable from the exact transition matrix by the use of four basic approximations: neglect of virtual transitions to excited electronic states; Born–Oppenheimer approximation; neglect of nuclear–electronic couplings; and the Franck–Condon approximation. The wave functions involved in the FC overlap are determined from quasiadiabatic potential surfaces, which were chosen to be constructed from the corresponding LEPS and anti-LEPS adiabatic surfaces for the chemical reaction in question. A coupling function which involves a single free parameter is needed to connect the quasiadiabatic surfaces. Our calculations show that the results are insensitive to this free parameter. We calculate vibrational distributions of reaction products for various initial kinetic energies of reactants and find the results to be in good qualitative agreement with both exact quantal calculations and FC models which include further approximations (with compensatory ease of calculation). Our results agree with the maximum in the vibrational distribution predicted by the other calculations and show similar trends with variation in initial relative kinetic energy and the masses (including isotopic substitution) as well as certain features of the potential surface.