Molecular Spectra Calculations Using an Optimized Quasi-Regular Gaussian Basis and the Collocation Method.

Area of Science:

• Quantum chemistry
• Molecular spectroscopy
• Computational physics

Background:

• The collocation method offers a simplified approach to computing molecular vibrational spectra.
• Distributed localized basis sets, like Gaussian functions, are key to this method.
• Optimizing basis function placement and shape is crucial for efficiency.

Purpose of the Study:

• To explore the optimization of basis function placement and shape within the collocation method.
• To investigate the efficacy of quasi-regular grids (QRGs) for basis set optimization.
• To improve the accuracy and efficiency of calculating molecular vibrational energies.

Main Methods:

• Revisiting the Manzhos and Carrington collocation method.
• Employing a distributed localized Gaussian basis set.
• Utilizing quasi-regular grids (QRGs) for basis function optimization.
• Solving the generalized eigenvalue problem for the molecular vibrational Hamiltonian.

Main Results:

• Demonstrated the superiority of QRG-based distributed Gaussian basis sets.
• Achieved accurate computation of eigenenergies for formaldehyde.
• Showcased significant reduction in basis size through optimized basis functions.

Conclusions:

• Quasi-regular grids represent an effective strategy for optimizing basis sets in the collocation method.
• The enhanced method offers a computationally efficient and accurate route to molecular vibrational spectra.
• This approach provides a flexible and numerically stable alternative for vibrational structure calculations.