Symmetry adapted ro-vibrational basis functions for variational nuclear motion calculations: TROVE approach

TL;DR

This paper introduces a numerically driven method for constructing symmetry-adapted ro-vibrational basis functions, enhancing variational nuclear motion calculations by leveraging Hamiltonian symmetry properties.

Contribution

The paper presents a general approach to build symmetry-adapted basis functions numerically, integrated into the TROVE variational method, applicable to various molecular symmetry groups.

Findings

Successfully applied to multiple molecular symmetry groups.

Demonstrated flexibility with different coordinates and basis sets.

Improved accuracy in ro-vibrational calculations.

Abstract

We present a general, numerically motivated approach to the construction of symmetry adapted basis functions for solving ro-vibrational Schr\"{o}dinger equations. The approach is based on the property of the Hamiltonian operator to commute with the complete set of symmetry operators and hence to reflect the symmetry of the system. The symmetry adapted ro-vibrational basis set is constructed numerically by solving a set of reduced vibrational eigenvalue problems. In order to assign the irreducible representations associated with these eigenfunctions, their symmetry properties are probed on a grid of molecular geometries with the corresponding symmetry operations. The transformation matrices are re-constructed by solving over-determined systems of linear equations related to the transformation properties of the corresponding wavefunctions on the grid. Our method is implemented in the variational approach TROVE and has been successfully applied to a number of problems covering the most important molecular symmetry groups. Several examples are used to illustrate the procedure, which can be easily applied to different types of coordinates, basis sets, and molecular systems.