Simple(r) algebraic equation for transition moments of fundamental transitions in vibrational second-order perturbation theory

Rayleigh–Schrödinger perturbation theory is applied in second order to obtain an expression for the transition moment of vibrational fundamentals. The reported equation is considerably simpler than previous ones. Applications for H2O and HFCO are reported using force fields and dipole functions calculated at the CCSD(T) level of theory with different basis sets.