Automatic differentiation in quantum chemistry with an application to fully variational Hartree-Fock

TL;DR

This paper demonstrates the use of Automatic Differentiation (AD) to compute gradients in quantum chemistry, specifically implementing a fully autodifferentiable Hartree-Fock method and optimizing basis set parameters.

Contribution

It introduces DiffiQult, the first fully autodifferentiable Hartree-Fock algorithm, showcasing AD's potential in quantum chemistry for gradient calculations and parameter optimization.

Findings

Successfully implemented a fully autodifferentiable Hartree-Fock method.

Demonstrated gradient-based optimization of basis set parameters.

Showcased AD's potential to simplify derivative calculations in quantum chemistry.

Abstract

Automatic Differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that automatic differentiation can be used to compute gradients with respect to any parameter throughout a complete quantum chemistry method. We implement DiffiQult, a fully autodifferentiable Hartree-Fock (HF) algorithm, which serves as a proof-of-concept that illustrates the capabilities of AD for quantum chemistry. We leverage the obtained gradients to optimize the parameters of one-particle basis sets in the context of the floating Gaussian framework.