Symmetry-Adapted Ro-vibrational Basis Functions for Variational Nuclear Motion Calculations: TROVE Approach.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Molecular Spectroscopy

Background:

• Solving the ro-vibrational Schrödinger equation is crucial for understanding molecular dynamics.
• Existing methods may face challenges with complex molecular symmetries.
• Symmetry adaptation can simplify calculations and improve efficiency.

Purpose of the Study:

• To develop a general, numerically motivated approach for constructing symmetry-adapted basis functions.
• To enable accurate solutions of ro-vibrational Schrödinger equations for diverse molecular systems.
• To provide a flexible method applicable to various coordinates, basis sets, and symmetry groups.

Main Methods:

• Utilizing the commutation property of the Hamiltonian operator with symmetry operators.
• Numerically constructing the symmetry-adapted basis set via reduced vibrational eigenvalue problems.
• Probing symmetry properties on a grid of molecular geometries to assign irreducible representations.
• Reconstructing transformation matrices by solving overdetermined linear systems.

Main Results:

• A robust and general method for constructing symmetry-adapted basis functions has been developed.
• The approach has been successfully implemented within the TROVE variational method.
• The method has been validated across various important molecular symmetry groups.
• Demonstrated applicability to different coordinate systems, basis sets, and molecular structures.

Conclusions:

• The presented numerical approach offers a powerful tool for theoretical molecular spectroscopy.
• It provides a flexible and efficient way to handle symmetry in ro-vibrational calculations.
• The method is readily adaptable for future studies on complex molecular systems.