Nuclear velocity perturbation theory for vibrational circular dichroism: An approach based on the exact factorization of the electron-nuclear wave function

TL;DR

This paper introduces a rigorous nuclear velocity perturbation theory for vibrational circular dichroism based on the exact electron-nuclear wave function factorization, enabling new beyond-Born-Oppenheimer corrections to VCD signals.

Contribution

It develops a formalism for NVPT derived from exact factorization, providing a basis for including beyond-BO effects in vibrational circular dichroism calculations.

Findings

New contribution to VCD intensity beyond-BO effects

Numerical validation on chiral and non-chiral systems

Formal derivation from exact electron-nuclear wave function

Abstract

The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similarly to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.