Translational expansion of radiative interaction operators in molecules

Abstract

The translational expansion of radiative magnetic-dipole operators L o and L ±1 from the center of mass of a molecule to atomic centers is derived here in the right-handed coordinate system. It is shown that the expansion of L ±1 at the atomic centers produces an extra gradient operator which operates on the atomic wavefunction of angular momentum I to generate wavefunctions of different angular momenta l ± 1. This operation is illustrated by applying L ±1 (which is referred to the center of mass) to a LCAO molecular orbital π u, ∓ ( np), resulting in a linear combination of molecular orbital functions σ u( np), σ u(s) and σ u(d). The translational expansion of radiative electric-multipole operators is also given.