Automatic Differentiation for the Direct Minimization Approach to the Hartree-Fock Method

TL;DR

This paper introduces a novel approach using reverse-mode automatic differentiation to directly minimize Hartree-Fock energy without eigenvalue calculations, improving stability while maintaining accuracy.

Contribution

It presents a new method that applies reverse-mode automatic differentiation to the Hartree-Fock method, bypassing eigenvalue computations for enhanced stability.

Findings

More stable than traditional SCF method

Achieved comparable accuracy to conventional methods

Avoided eigenvalue calculation in optimization

Abstract

Automatic differentiation has become an important tool for optimization problems in computational science, and it has been applied to the Hartree-Fock method. Although the reverse-mode automatic differentiation is more efficient than the forward-mode, eigenvalue calculation in the self-consistent field method has impeded the use of the reverse-mode automatic differentiation. Here, we propose a method to directly minimize Hartree-Fock energy under the orthonormality constraint of the molecular orbitals using reverse-mode automatic differentiation by avoiding eigenvalue calculation. According to our validation, the proposed method was more stable than the conventional self-consistent field method and achieved comparable accuracy.