"Divide and Conquer" Semiclassical Molecular Dynamics: A practical method for Spectroscopic calculations of High Dimensional Molecular Systems

TL;DR

This paper presents an improved divide-and-conquer semiclassical method for spectroscopic calculations, enabling accurate analysis of high-dimensional molecular systems by dividing the problem into smaller parts, with demonstrated success on complex molecules.

Contribution

The authors introduce a hierarchical subspace-separation criterion based on Liouville's theorem, enhancing the accuracy and applicability of the divide-and-conquer semiclassical approach.

Findings

Improved accuracy reduces errors to about 10 wavenumbers.

Method successfully applied to complex molecules like benzene and Zundel cation.

Facilitates interpretation of experimental IR spectra.

Abstract

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits to perform spectroscopic calculations of high dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Liouville's theorem. Comparisons of calculated vibrational frequencies to exact quantum ones for a set of molecules including benzene show that the new implementation performs better than the original one and that, on average, the loss in accuracy with respect to full-dimensional semiclassical calculations is reduced to only 10 wavenumbers. Furthermore, by investigating the challenging Zundel cation, we also demonstrate that the "divide-and-conquer" approach allows to deal with complex strongly anharmonic molecular systems. Overall the method very much helps the assignment and physical interpretation of experimental IR spectra by providing accurate vibrational fundamentals and overtones decomposed into reduced dimensionality spectra.