$\Delta$-Machine Learning to Elevate DFT-based Potentials and a Force Field to the CCSD(T) Level Illustrated for Ethanol

TL;DR

This paper demonstrates that $ riangle$-machine learning can effectively elevate DFT-based potentials and force fields to CCSD(T) accuracy, using ethanol as a test case, across various functionals with consistent improvements.

Contribution

The study extends $ riangle$-machine learning to multiple DFT functionals for ethanol, showing its broad applicability and effectiveness in improving potential energy surfaces and force fields.

Findings

Significant reduction in RMSE for PES with $ riangle$-ML across all tested functionals.

Notable improvement in DFT gradient accuracy without using coupled cluster gradients.

Successful correction of a molecular mechanics force field for ethanol.

Abstract

Progress in machine learning has facilitated the development of potentials that offer both the accuracy of first-principles techniques and vast increases in the speed of evaluation. Recently,"$\Delta$-machine learning" has been used to elevate the quality of a potential energy surface (PES) based on low-level, e.g., density functional theory (DFT) energies and gradients to close to the gold-standard coupled cluster level of accuracy. We have demonstrated the success of this approach for molecules, ranging in size from H$_3$O$^+$ to 15-atom acetyl-acetone and tropolone. These were all done using the B3LYP functional. Here we investigate the generality of this approach for the PBE, M06, M06-2X, and PBE0+MBD functionals, using ethanol as the example molecule. Linear regression with permutationally invariant polynomials is used to fit both low-level and correction PESs. These PESs are employed for standard RMSE analysis for training and test datasets, and then general fidelity tests such as energetics of stationary points, normal mode frequencies, and torsional potentials are examined. We achieve similar improvements in all cases. Interestingly, we obtained significant improvement over DFT gradients where coupled cluster gradients were not used to correct the low-level PES. Finally, we present some results for correcting a recent molecular mechanics force field for ethanol and comment on the possible generality of this approach.