General Symmetry-Based Potential Energy Surface Grid Reduction in Normal Coordinates

Abstract

The construction of a grid-based potential energy surface (PES) can be prohibitively expensive as the number of grid points grows exponentially with molecular size. Molecular symmetry can reduce this cost by eliminating symmetry-equivalent points. We present an algebraic symmetry-based grid reduction method, ASyBGR, that is capable of handling non-Abelian and higher-order cyclic symmetry groups. Non-coordinate-mixing operations are encoded into a vector space bit-string, where Gaussian elimination and closure can identify all symmetry-valid sign change patterns and the coordinate axes whose grids can be halved about the origin. In the presence of degenerate subspaces, we optimize the coordinate basis to maximize reduction. The method was validated by comparing vibrational configuration interaction (VCI) energies calculated using the full and symmetry-reduced fourth-order HDMR PESs for molecules spanning a broad range of symmetries. The number of grid points required to construct the PES was reduced by as much as 81\%, while VCI energies deviated below 1 1/cm for all test cases on average. The relative root-mean-square deviation (RRMSD) between the full and symmetry-reduced potential energy and dipole moment surfaces were at most on the order of 10$^{-3}$ and 10$^{-2}$, respectively.