Efficient Gaussian process regression for prediction of molecular crystals harmonic free energies

Marcin Krynski,Mariana Rossi

doi:10.1038/s41524-021-00638-x

Abstract

We present a method to accurately predict the Helmholtz harmonic free energies of molecular crystals in high-throughput settings. This is achieved by devising a computationally efficient framework that employs a Gaussian Process Regression model based on local atomic environments. The cost to train the model with ab initio potentials is reduced by starting the optimization of the framework parameters, as well as the training and validation sets, with an empirical potential. This is then transferred to train the model based on density-functional theory potentials, including dispersion-corrections. We benchmarked our framework on a set of 444 hydrocarbon crystal structures, comprising 38 polymorphs and 406 crystal structures either measured in different conditions or derived from these polymorphs. Superior performance and high prediction accuracy, with mean absolute deviation below 0.04 kJ mol−1 per atom at 300 K is achieved by training on as little as 60 crystal structures. Furthermore, we demonstrate the predictive efficiency and accuracy of the developed framework by successfully calculating the thermal lattice expansion of aromatic hydrocarbon crystals within the quasi-harmonic approximation, and predict how lattice expansion affects the polymorph stability ranking.

Highlights

Polymorphism and the prediction of the energetic stability of a crystal polymorph are a fundamental problem of condensed matter physics, especially for the research and applications of molecular crystals
Polymorphism is the capability of solid materials to form more than one distinct crystal structure[1,2]
Even when the vibrational contribution to the relative stability is taken into account in a number of cases, the effect of the thermal expansion of the crystal unit-cell on the free energy is most frequently omitted

Summary

INTRODUCTION

Polymorphism and the prediction of the energetic stability of a crystal polymorph are a fundamental problem of condensed matter physics, especially for the research and applications of molecular crystals. (number of atom environments in the given set) and f is the despite the exceptional performance of many such vector of all, unobserved, atom-wise free energies in the chosen potentials, typical root-mean-square errors on the forces lie around 20 meV Å−1 per atom[34,35,36,37,38,39]. In Eq (3), α is a vector of Nae weights for each atomic environment, such that validation set selection with a computationally cheap empirical potential, confirm its transferability to a first-principles potential, F0 1⁄4 MTCα: Opening up this equation element-wise, the full free energy of a very low cost of training. We analyzed the stability ranking for a few families of hydrocarbon crystal polymorphs up to 300 K, highlighting the power and accuracy of the model This method can predict the anisotropic lattice expansion of these crystals, allowing a cheap evaluation of volume expansion and

RESULTS AND DISCUSSION

V V exp : 2ex9p5K: 2ex7p0K

CODE AVAILABILITY

10 AUTHOR CONTRIBUTIONS