Analytical Gradients for Molecular-Orbital-Based Machine Learning

TL;DR

This paper develops and demonstrates analytical nuclear gradients for molecular-orbital-based machine learning, enabling accurate and efficient prediction of molecular properties and optimized structures with a general, flexible framework.

Contribution

It introduces a general Lagrangian-based framework for MOB-ML gradients, applicable across different regression methods and feature designs, with demonstrated high accuracy and efficiency.

Findings

MOB-ML gradients are highly accurate compared to other ML methods.

The framework enables accurate structure optimization at low computational cost.

MOB-ML requires training on fewer molecules to achieve high accuracy.

Abstract

Molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 data set while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures, at a computational cost for the gradient evaluation that is comparable to Hartree-Fock theory or hybrid DFT.