Representing Molecular Ground and Excited Vibrational Eigenstates with Nuclear Densities obtained from Semiclassical Initial Value Representation Molecular Dynamics

TL;DR

This paper introduces and validates a Monte Carlo method for calculating nuclear vibrational densities of molecules, enabling detailed quantum insights into anharmonic effects and vibrational states beyond harmonic approximations.

Contribution

The paper presents a novel Monte Carlo approach for on-the-fly ab initio calculation of anharmonic nuclear densities in molecules, validated on water and applied to protonated glycine.

Findings

Effective visualization of anharmonic vibrational effects

Quantitative analysis of bond-length and angle distributions

Identification of anharmonic deviations in vibrational nodal patterns

Abstract

We present in detail and validate an effective Monte Carlo approach for the calculation of the nuclear vibrational densities via integration of molecular eigenfunctions that we have preliminary employed to calculate the densities of the ground and the excited OH stretch vibrational states in protonated glycine molecule [C. Aieta et. al. Nat. Commun. 11, 4348 (2020)]. Here, we first validate and discuss in detail the features of the method on a benchmark water molecule. Then, we apply it to calculate on-the-fly the ab initio anharmonic nuclear densities in correspondence of the fundamental transitions of NH and CH stretches in protonated glycine. We show how we can gain both qualitative and quantitative physical insight by inspection of different one-nucleus densities and assign a character to spectroscopic absorption peaks using the expansion of vibrational states in terms of harmonic basis functions. The visualization of the nuclear vibrations in a purely quantum picture allows us to observe and quantify the effects of anharmonicity on the molecular structure, and to exploit the effect of IR excitations on specific bonds or functional groups, beyond the harmonic approximation. We also calculate the quantum probability distribution of bond-lengths, angles and dihedrals of the molecule. Notably, we observe how in the case of one type of fundamental NH stretching the typical harmonic nodal pattern is absent in the anharmonic distribution.