Variational Vibrational States of Methanol (12D)

TL;DR

This study computes full-dimensional vibrational states of methanol using advanced numerical methods, achieving high accuracy and providing valuable data for spectroscopy and fundamental physics research.

Contribution

It presents the first comprehensive 12D vibrational energy calculations of methanol with convergence better than 0.5 cm$^{-1}$, validating the potential energy surface and computational approach.

Findings

Vibrational energies agree with experimental data within a few cm$^{-1}$

Approximately seventy torsion-vibration states identified and assigned

Method achieves convergence up to 2000 cm$^{-1}$ beyond zero-point energy

Abstract

Full-dimensional (12D) vibrational states of the methanol molecule (CH$_3$OH) have been computed using the GENIUSH-Smolyak approach and the potential energy surface from Qu and Bowman (2013). All vibrational energies are converged better than 0.5 cm$^{-1}$ with respect to the basis and grid size up to the first overtone of the CO stretch, ca. 2000 cm$^{-1}$ beyond the zero-point vibrational energy. About seventy torsion-vibration states are reported and assigned. The computed vibrational energies agree with the available experimental data within less than a few cm$^{-1}$ in most cases, which confirms the good accuracy of the potential energy surface. The computations are carried out using curvilinear normal coordinates with the option of path-following coefficients which minimize the coupling of the small- and large-amplitude motions. It is important to ensure tight numerical fulfilment of the $C_{3\mathrm{v}}$(M) molecular symmetry for every geometry and coefficient set used to define the curvilinear normal coordinates along the torsional coordinate to obtain a faithful description of degeneracy in this floppy system. The reported values may provide a computational reference for fundamental spectroscopy, astrochemistry, and for the search of the proton-to-electron mass ratio variation using the methanol molecule.