Anharmonic Terms of the Potential Energy Surface: A Group Theoretical Approach

TL;DR

This paper introduces a group theoretical method to efficiently compute anharmonic terms of the potential energy surface in DFT simulations, significantly reducing computational costs by exploiting molecular symmetry.

Contribution

The authors develop and implement a group theoretical approach to decrease the computational effort in calculating anharmonic force constants in DFT, extending previous methods.

Findings

Significant speedups achieved in calculations, up to 76% for MgO.

Method successfully applied to six diverse molecular and crystalline systems.

Group theory reduces the number of configurations needed for energy and force evaluations.

Abstract

In the framework of density functional theory (DFT) simulations of molecules and materials, anharmonic terms of the potential energy surface are commonly computed numerically, with an associated cost that rapidly increases with the size of the system. Recently, an efficient approach to calculate cubic and quartic interatomic force constants in the basis of normal modes [Theor. Chem. Acc., 120, 23 (2008)] was implemented in the Crystal program [J. Chem. Theory Comput., 15, 3755-3765 (2019)]. By applying group theory, we are able to further reduce the associated computational cost, as the exploitation of point symmetry can significantly reduce the number of distinct atomically displaced nuclear configurations to be explicitly explored for energy and forces calculations. Our strategy stems from Wigner's theorem and the fact that normal modes are bases of the irreducible representations (irreps) of the point group. The proposed group theoretical approach is implemented in the Crystal program and its efficiency assessed on six test case systems: four molecules (methane, CH4; tetrahedrane, C4H4; cyclo-exasulfur, S6; cubane, C8H8), and two three-dimensional crystals (Magnesium oxide, MgO; and a prototypical Zinc-imidazolate framework, ZIF-8). The speedup imparted by this approach is consistently very large in all high-symmetry molecular and periodic systems, peaking at 76% for MgO.