Breaking the Coupled Cluster Barrier for Machine-Learned Potentials of Large Molecules: The Case of 15-Atom Acetylacetone

Abstract

Machine-learned potential energy surfaces (PESs) for molecules with more than 10 atoms are typically forced to use lower-level electronic structure methods such as density functional theory (DFT) and second-order Møller–Plesset perturbation theory (MP2). While these are efficient and realistic, they fall short of the accuracy of the “gold standard” coupled-cluster method, especially with respect to reaction and isomerization barriers. We report a major step forward in applying a Δ-machine learning method to the challenging case of acetylacetone, whose MP2 barrier height for H-atom transfer is low by roughly 1.1 kcal/mol relative to the benchmark CCSD(T) barrier of 3.2 kcal/mol. From a database of 2151 local CCSD(T) energies and training with as few as 430 energies, we obtain a new PES with a barrier of 3.5 kcal/mol in agreement with the LCCSD(T) barrier of 3.5 kcal/mol and close to the benchmark value. Tunneling splittings due to H-atom transfer are calculated using this new PES, providing improved estimates over previous ones obtained using an MP2-based PES.

Transfer learned potential energy surfaces: accurate anharmonic vibrational dynamics and dissociation energies for the formic acid monomer and dimer

“…Here, the unbiased DMC algorithm was used. 14,89,90 A set of thousands to tens of thousands of random walkers is initialized and subsequently the atoms in each walker are displaced randomly at every timestep. The ensemble of walkers represents the nuclear wavefunction of the molecule.…”

“…Based on a walker's potential energy E i with respect to a reference energy, E r , they remain alive and can give birth to new walkers, or can be killed. The walkers die and replicate according to the following probabilities: 14 P death = 1 − e −( E i − E r )Δ τ ( E i > E r ) P birth = e −( E i − E r )Δ τ − 1 ( E i < E r ). Here, Δ τ is the step size in imaginary time.…”

“…Following ref. 14 , the DMC calculations were performed in Cartesian coordinates and in full dimensionality. For both, FAM and FAD, ten independent DMC simulations were performed.…”

“…While calculations at the density functional theory (DFT) or Møller–Plesset perturbation (MP2) levels of theory are cost-efficient, reaction barriers are less accurate. 14 On the other hand, the “gold standard” coupled cluster with perturbative triples (CCSD(T)) approach scales as N 7 (with N being the number of basis functions) 15 which becomes quickly computationally prohibitive for full-dimensional PESs even for moderately sized molecules ( N atoms ∼ 10). Recent applications of novel machine learning (ML) approaches combined with transfer learning (TL) 16–18 and related Δ-ML 19 in physical/computational chemistry 14,18,20–23 were shown to be data and cost-effective alternatives which will also be explored in the present work.…”

Permutation-Invariant-Polynomial Neural-Network-based Δ-Machine Learn-ing Approach: A Case for the HO2 Self-reaction and its Dynamics Study

“…44 The resulting PESs were successfully employed to reproduce finite-temperature infrared spectrum and hydrogen transfer rates. More recently, Bowman and coworkers proposed and tested a Δ-learning approach 51,52 using PIP. 34 Specifically, they expressed the PES as follows,…”