Assessing the utility of phase-space-localized basis functions: Exploiting direct product structure and a new basis...

Area of Science:

• Quantum Chemistry
• Molecular Spectroscopy
• Computational Physics

Background:

• Accurate computation of molecular vibrational energy levels is crucial for understanding molecular dynamics and spectroscopy.
• Previous methods using symmetrized Gaussian (SG) bases have faced challenges with basis set size and convergence errors.

Purpose of the Study:

• To develop an accurate and efficient computational method for determining vibrational energy levels of small molecules.
• To address limitations in existing SG basis approaches for molecular vibrational energy calculations.

Main Methods:

• Utilizing an iterative eigensolver with Halverson and Poirier's symmetrized Gaussian (SG) basis.
• Solving a regular eigenvalue problem to exploit direct-product structure, avoiding large matrix manipulations.
• Implementing a novel procedure for selecting basis functions to minimize size.

Main Results:

• Achieved accurate vibrational energy levels for molecules with up to five atoms.
• Demonstrated that the developed SG basis approach yields significantly smaller basis sets compared to classical energy criteria.
• Identified and corrected significant convergence errors present in prior SG basis calculations.

Conclusions:

• The proposed iterative eigensolver method with optimized SG bases offers an efficient and accurate route for calculating molecular vibrational energies.
• This approach overcomes the computational burden of large matrices and improves upon previous SG basis implementations.
• The findings pave the way for more precise spectroscopic predictions and molecular simulations.