Fitting Potential Energy Surfaces by Learning the Charge Density Matrix with Permutationally Invariant Polynomials

• Type of Material: Article
• Authors: Younos Hashem, Kennesaw State University; Katheryn Foust, Kennesaw State University; Martina Kaledin, Kennesaw State University; Alexey Kaledin, Emory University
• Language: English
• Date: 2023-08-10
• Publisher: American Chemical Society
• Publication Version: Final Published Version
• Copyright Statement: © 2023 The Authors. Published by American Chemical Society
• License: Creative Commons Attribution 4.0 International
• Final Published Version (URL): https://doi.org/10.1021%2Facs.jctc.3c00586
• Title of Journal or Parent Work: Journal of Chemical Theory and Computation
• Volume: 19
• Issue: 17
• Start Page: 5690
• End Page: 5700
• Grant/Funding Information: This material is based upon work supported by the National Science Foundation under Grant No. CHE–1855583.
• Keywords: Charge density matrix; Hartree-Fock theory; Potential energy surface
• Research Categories: Chemistry, Physical

Abstract

The electronic energy in the Hartree–Fock (HF) theory is the trace of the product of the charge density matrix (CDM) with the one-electron and two-electron matrices represented in an atomic orbital basis, where the two-electron matrix is also a function of the same CDM. In this work, we examine a formalism of analytic representation of a generic molecular potential energy surface (PES) as a sum of a linearly parameterized HF and a correction term, the latter formally representing the electron correlation energy, also linearly parameterized, by expressing the elements of CDM using permutationally invariant polynomials (PIPs). We show on a variety of numerical examples, ranging from exemplary two-electron systems HeH+ and H3+ to the more challenging cases of methanium (CH5+) fragmentation and high-energy tautomerization of formamide to formimidic acid that such a formulation requires significantly fewer, 10–20% of PIPs, to accomplish the same accuracy of the fit as the conventional representation at practically the same computational cost.