Born—Oppenheimer Approximation and the Calculation of Infrared Intensities

Abstract

In evaluating transition moments it is customary to transform from the momentum representation to the dipole representation by making use of the commutator relations between the Hamiltonian and the particle coordinates. In the present paper we show that in the case of infrared, vibrational transitions it makes quite a difference whether we introduce the Born—Oppenheimer approximation before or after this transformation. In the first case the transition moment depends on the nuclear contribution to the molecular dipole moment and in the second case on the total dipole moment of the molecule. In order to dissolve this discrepancy we calculated the first-order correction to the Born—Oppenheimer approximation. We introduced this correction in the transition moment calculations and we found that the correction terms bring the two different results into agreement with each other. It was found that the correction is quite small in the case where the Born—Oppenheimer approximation is introduced after the momentum—dipole transformation and that the correction is considerable in the case where the Born—Oppenheimer approximation is introduced before the transformation. We conclude that the correct expression for the transition moment contains the derivative of the molecular dipole moment with respect to the normal coordinates of the modes of vibration, in agreement with the expressions that are customarily used.