On the benefits of localized modes in anharmonic vibrational calculations for small molecules

TL;DR

This paper demonstrates that using localized-mode coordinates in anharmonic vibrational calculations reduces computational costs and improves convergence, enabling more efficient and accurate modeling of small molecules' vibrational spectra.

Contribution

The study introduces the application of localized-mode coordinates to anharmonic vibrational calculations, showing improved convergence and reduced computational effort compared to normal-mode coordinates.

Findings

Localized-mode coordinates reduce mode coupling.

Faster convergence of the n-mode expansion.

Lower computational cost for anharmonic potential energy surfaces.

Abstract

Anharmonic vibrational calculations can already be computationally demanding for relatively small molecules. The main bottlenecks lie in the construction of the potential energy surface and in the size of the excitation space in the vibrational configuration interaction (VCI) calculations. To address these challanges, we use localized-mode coordinates to construct potential energy surfaces and perform vibrational self-consistent field (L-VSCF) and L-VCI calculations [P. T. Panek, Ch. R. Jacob, ChemPhysChem 15, 3365 (2014)] for all vibrational modes of two prototypical test cases, the ethene and furan molecules. We find that the mutual coupling between modes is reduced when switching from normal-mode coordinates to localized-mode coordinates. When using such localized-mode coordinates, we observe a faster convergence of the $n$-mode expansion of the potential energy surface. This makes it possible to neglect higher-order contributions in the $n$-mode expansion of the potential energy surface or to approximate higher-oder contributions in hybrid potential energy surfaces, which reduced the computational effort for the construction of the anharmonic potential energy surface significantly. Moreover, we find that when using localized-mode coordinates, the convergence with respect to the VCI excitation space proceeds more smoothly and that the error at low orders is reduced significantly. This makes it possible to devise low-cost models for obtaining a first approximation of anharmonic corrections. This demonstrates that the use of localized-mode coordinates can be beneficial already in anharmonic vibrational calculations of small molecules, and provides a possible avenue for enabling such accurate calculations also for larger molecules.