$\Delta$-Machine Learning for Potential Energy Surfaces: A PIP approach to bring a DFT-based PES to CCSD(T) Level of Theory

TL;DR

This paper introduces a $ abla$-machine learning approach using permutationally invariant polynomials to efficiently elevate low-level DFT potential energy surfaces to high-accuracy CCSD(T) level, demonstrated on several molecules.

Contribution

It presents a novel $ abla$-machine learning method combining PIP fits to accurately transfer DFT PESs to CCSD(T) level with minimal high-level data.

Findings

High-quality CCSD(T) PESs achieved with as few as 200 energies.

Excellent agreement with benchmark CCSD(T) results for small molecules.

Effective transfer of DFT PESs to CCSD(T) level demonstrated on multiple molecules.

Abstract

``$\Delta$-machine learning" refers to a machine learning approach to bring a property such as a potential energy surface (PES) based on low-level (LL) density functional theory (DFT) energies and gradients to close to a coupled cluster (CC) level of accuracy. Here we present such an approach that uses the permutationally invariant polynomial (PIP) method to fit high-dimensional PESs. The approach is represented by a simple equation, in obvious notation $V_{LL{\rightarrow}CC}=V_{LL}+\Delta{V_{CC-LL}}$, and demonstrated for \ce{CH4}, \ce{H3O+}, and $trans$ and $cis$-$N$-methyl acetamide (NMA), \ce{CH3CONHCH3}. For these molecules, the LL PES, $V_{LL}$, is a PIP fit to DFT/B3LYP/6-31+G(d) energies and gradients, and $\Delta{V_{CC-LL}}$ is a precise PIP fit obtained using a low-order PIP basis set and based on a relatively small number of CCSD(T) energies. For \ce{CH4} these are new calculations adopting an aug-cc-pVDZ basis, for \ce{H3O+} previous CCSD(T)-F12/aug-cc-pVQZ energies are used, while for NMA new CCSD(T)-F12/aug-cc-pVDZ calculations are performed. With as few as 200 CCSD(T) energies, the new PESs are in excellent agreement with benchmark CCSD(T) results for the small molecules, and for 12-atom NMA training is done with 4696 CCSD(T) energies.