A local anharmonic treatment of vibrations of methane

TL;DR

This paper presents a local anharmonic model for methane vibrations, achieving accurate energy predictions by using symmetry-adapted operators to simplify the eigenvalue problem.

Contribution

It introduces a local anharmonic approach combined with symmetry-adapted operators, providing precise vibrational energy calculations for methane.

Findings

Achieved a standard deviation of 0.81 cm$^{-1}$ in energy fits.

Reduced the eigenvalue problem to block diagonal form.

Successfully modeled 44 observed vibrational energies.

Abstract

The stretching and bending vibrations of methane are studied in a local anharmonic model of molecular vibrations. The use of symmetry-adapted operators reduces the eigenvalue problem to block diagonal form. For the 44 observed energies we obtain a fit with a standard deviation of 0.81 cm$^{-1}$ (and a r.m.s. deviation of 1.16 cm$^{-1}$).