Systematic calculation of molecular vibrational spectra through a complete Morse expansion

TL;DR

This paper introduces a precise and efficient algebraic method for calculating molecular vibrational spectra, demonstrated on diatomic molecules with high accuracy, paving the way for scalable multi-dimensional spectral computations.

Contribution

It presents a novel complete Morse expansion approach for vibrational spectra calculation, combining algebraic matrix diagonalization with high accuracy and computational efficiency.

Findings

Achieved cm-1 accuracy for H2 vibrational spectrum

Successfully applied to Lennard-Jones and H2 potentials

Demonstrated computational efficiency with 30x30 matrix diagonalization

Abstract

We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential of diatomic molecules: as typical examples, we apply this method to the standard Lennard-Jones oscillator, and to the ab initio potential of the H2 molecule. Global cm-1 accuracy is exhibited through the H2 spectrum, obtained through the diagonalization of a 30 x 30 matrix. This theory is at the root of a new method to obtain globally accurate vibrational spectral data in the context of the multi-dimensional potential of polyatomic molecules, at an affordable computational cost.