Algorithmic Design of Geometric Data for Molecular Potential Energy Surfaces

Abstract

A code MolecGeom, based on algorithms for stepwise distortions of bond lengths, bond angles and dihedral angles of polyatomic molecules, is presented. Potential energy surfaces (PESs) are curated in terms of the energy for each molecular geometry. PESs based on the Born–Oppenheimer approximation, by which the atomic nuclei within a molecule are assumed stationary with respect to the motion of its electrons, are calculated. Applications requiring PESs involve the effects of nuclear motion on molecular properties. These include determining equilibrium geometries corresponding to stationary and saddle point energies, calculating reaction rates and predicting vibrational spectra. This multi-objective study focuses on the development of a new method for the calculation of PESs and the analysis of the molecular geometry components in terms of incremental changes that provide comprehensive sampling while preserving the precision of PES points. MolecGeom is applied to generate geometric data to calculate PESs for theoretical calculations of vibrational-rotational spectra of water and formaldehyde. An ab initio PES comprising 525 and 2160 intramolecular nuclear configurations results in vibrational frequencies in agreement with experiment, having errors less than 0.08% and 0.8%, respectively. Vinyl alcohol, with a total of 14 internal coordinates, generates a PES of 1458 unique geometries. Ascorbic acid, with 54 internal coordinates, generates a 1,899,776 point PES.

Keywords

• vibrational-rotational analysis
• potential energy surfaces
• internal displacement coordinates