Using Weighted and Chopped Rectangular Collocation Methods with Tensor-Product Contracted Bases To Compute...

Area of Science:

• Computational chemistry
• Molecular spectroscopy
• Quantum mechanics

Background:

• Product contracted (PC) bases are efficient for computing molecular vibrational spectra.
• Previous PC methods require costly quadrature for subsystem coupling calculations, increasing with molecular dimensionality.

Purpose of the Study:

• To develop a novel method that obviates quadrature in PC-based vibrational spectra calculations.
• To improve the accuracy and efficiency of computing (ro-)vibrational spectra for complex molecules.

Main Methods:

• Proposed a weighted and chopped rectangular collocation (WC-RC) method.
• Utilized Christoffel weights and Christoffel-Fekete (CF) collocation points for near-optimal fitting.
• Employed matrix chopping to enhance energy level accuracy and enable symmetry adaptation (SA).

Main Results:

• Achieved sub-0.1 cm^-1 accuracy for 9-D CH₂NH and 6-D HF dimer.
• Demonstrated significant reduction in the number of points required compared to quadrature methods.
• Successfully implemented symmetry adaptation through additional matrix chopping.

Conclusions:

• The WC-RC method offers a more efficient and accurate alternative to traditional quadrature-based PC methods for computing vibrational spectra.
• This approach is particularly advantageous for high-dimensional molecular systems.
• The method provides a pathway for accurate and computationally feasible spectroscopic calculations.