Selection rules for processes involving photon-molecule interaction: a symmetry-conservation-based approach bypassing transition matrix elements

Abstract

The deduction of selection rule for a photon-induced transition in an atom/molecule is usually a lengthy process involving development of the time-dependent perturbation theory, the mathematical expression for transition probability, and finally the symmetry concepts to identify the transition matrix elements which are zeroes. All these, lengthy mathematical formulae could be bypassed if we invoke the principle that the total symmetry of the initial state is preserved in the final state taking, of course, both molecular and photon wavefunctions into consideration. The parity selection rules for one-photon absorption (electric dipole and magnetic dipole), two-photon absorption, second harmonic generation and optical activity, as well as the angular momentum selection rules are deduced and exemplified by diagrams.