An optimized algebraic basis for molecular potentials

TL;DR

This paper introduces an optimized algebraic basis tailored to molecular potentials, significantly improving the efficiency of vibrational spectra computation for diatomic molecules while maintaining simplicity.

Contribution

It proposes a parameterized basis optimized via minimization, enhancing algebraic methods for molecular vibrational analysis.

Findings

Enhanced computational efficiency for vibrational spectra

Maintains simplicity and numerical light-weightedness

Basis tuning improves accuracy for specific potentials

Abstract

The computation of vibrational spectra of diatomic molecules through the exact diagonalization of algebraically determined matrixes based on powers of Morse coordinates is made substantially more efficient by choosing a properly adapted quantum-mechanical basis, specifically tuned to the molecular potential. A substantial improvement is achieved while still retaining the full advantage of the simplicity and numerical light-weightedness of an algebraic approach. In the scheme we propose, the basis is parameterized by two quantities which can be adjusted to best suit the molecular potential through a simple minimization procedure.