Calculating the Raman Signal Beyond Perturbation Theory for a Diatomic Molecular Crystal

TL;DR

This paper models the eigenstates of diatomic molecules in mean-field potentials to understand how their Raman spectra evolve with field strength, revealing complex mode behaviors and challenging the use of spectral changes as phase transition indicators.

Contribution

It introduces a non-perturbative approach to calculating Raman spectra of diatomic molecules, accounting for mixed modes and symmetry-preserving spectral changes.

Findings

Raman spectra exhibit significant changes without symmetry breaking.

Non-harmonic potentials split Raman active modes and alter selection rules.

Mass dependence varies among modes, aiding isotope-based mode identification.

Abstract

We calculate the eigenstates of a diatomic molecule in a range of model mean-field potentials, and evaluate the evolution of their associated Raman spectra with field strength. We demonstrate that dramatic changes in the appearance of the Raman spectrum for a diatomic molecule occur without any associated change in the symmetry of the surrounding potential. The limiting cases of the quantum eigenstates correspond, in the classical sense, to free rotation, and libration of well-oriented molecules. However, there are also many mixed modes which are neither rotons nor librons. The consequence for Raman spectroscopy is a series of complications - the non-harmonic potential splits the Raman active modes, and breaks the selection rules on forbidden modes. The mass-dependence of the various states is different - rotors, oscillators and reorientations have $1/m$, $1/\sqrt{m}$ and weaker mass dependence respectively. This may allow one to identify the character of the mode with isotope spectroscopy. However it is complicated by mixed modes and transitions between two different eigenstates with different character. We conclude that significant changes in the Raman spectrum of molecular systems are insufficient to demonstrate a phase transition since such changes can also occur in a fixed symmetry potential upon increasing field strength.