Significant contributions of Albrecht's $A$ term to non-resonant Raman scattering processes

TL;DR

This study reveals that Albrecht's A term significantly influences non-resonant Raman scattering for symmetric vibrational modes, challenging the common assumption that it can be neglected in off-resonant conditions.

Contribution

It demonstrates the importance of the A term in off-resonant Raman scattering and verifies the accuracy of perturbation theory under specific energy conditions.

Findings

A term contributes up to 40% of Raman intensity for symmetric modes.

Constructive interference between A and B terms is significant in water molecule.

Perturbation method is accurate when energy difference exceeds five times vibrational energy.

Abstract

The Raman intensity can be well described by the famous Albrecht equation that consists of A and B terms. It is well known that the contribution from Albrecht's A term can be neglected without loss of accuracy for far off-resonant Raman scattering processes. However, as demonstrated in this study, we have found that this widely accepted long-standing assumption fails drastically for totally symmetric vibration modes of molecules in general off-resonant Raman scattering. Perturbed first principles calculations for water molecule show that strong constructive interference between the A and B terms occurs for the Raman intensity of the symmetric O-H stretching mode, which can account for about 40% of the total intensity. Meanwhile, a minor destructive interference is found for the angle bending mode. The state to state mapping between the Albrecht's theory and the perturbation theory allows us to verify the accuracy of the widely employed perturbation method for the dynamic/resonant Raman intensities. The model calculations rationalized from water molecule with the bending mode show that the perturbation method is a good approximation only when the absolute energy difference between the first excited state and the incident light is more than five times of the vibrational energy in ground state.