A flexible approach to vibrational perturbation theory using sparse matrix methods.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Spectroscopy

Background:

• Vibrational perturbation theory is crucial for understanding molecular spectra.
• Accurate calculation of spectral intensities and transition frequencies requires detailed theoretical models.
• The choice of coordinates can influence the interpretation of theoretical results.

Purpose of the Study:

• To develop and present a sparse linear algebra implementation of Rayleigh-Schrödinger vibrational perturbation theory.
• To investigate the origin of spectral intensity and transition frequencies by analyzing corrections from Hamiltonian and dipole surface expansions.
• To assess the impact of coordinate choice on the interpretation of vibrational anharmonicities.

Main Methods:

• Implementation of Rayleigh-Schrödinger vibrational perturbation theory using sparse linear algebra.
• Expansion of vibrational Hamiltonians and dipole surfaces in various coordinate systems (e.g., Δr, Morse coordinates, Cartesian displacements, internal coordinates).
• Calculation and comparison of corrections to energies, transition intensities, and transition moments for model systems and molecules like H2O and (H2O)2.

Main Results:

• The developed implementation offers flexibility in coordinate choice and perturbation theory order.
• Analysis reveals which terms in Hamiltonian and dipole surface expansions contribute most to spectral corrections.
• Transition frequencies and intensities were found to be independent of the coordinate system used for expansion.

Conclusions:

• A flexible computational tool for vibrational spectroscopy is provided.
• While coordinate choice does not alter physical results, it significantly impacts the interpretability of anharmonic effects.
• Optimal coordinate selection facilitates a clearer understanding of the origins of spectral anharmonicities.