Machine-Learned Potential Energy Surfaces for Free Sodium Clusters with Density Functional Accuracy: Applications to Melting

TL;DR

This paper develops machine-learned interatomic potentials for sodium clusters with density-functional accuracy, enabling accurate thermodynamic and melting property predictions for clusters of various sizes.

Contribution

The authors created Gaussian Process Regression-based potentials trained on extensive DFT data, improving force fitting and accuracy for sodium clusters across a range of sizes.

Findings

Accurate heat capacity calculations for Na55 and Na147.

Excellent agreement with experimental melting temperatures.

Mean absolute energy error below 7 meV/atom.

Abstract

Gaussian Process Regression-based Gaussian Approximation Potential has been used to develop machine-learned interatomic potentials having density-functional accuracy for free sodium clusters. The training data was generated from a large sample of over 100,000 data points computed for clusters in the size range of N = 40 - 200, using the density-functional method as implemented in the VASP package. Two models have been developed, model M1 using data for N=55 only, and model M2 using additional data from larger clusters. The models are intended for computing thermodynamic properties using molecular dynamics. Hence, particular attention has been paid to improve the fitting of the forces. Interestingly, it turns out that the best fit can be obtained by carefully selecting a smaller number of data points viz. 1,900 and 1,300 configurations, respectively, for the two models M1 and M2. Although it was possible to obtain a good fit using the data of Na55 only, additional data points from larger clusters were needed to get better accuracies in energies and forces for larger sizes. Surprisingly, the model M1 could be significantly improved by adding about 50 data points per cluster from the larger sizes. Both models have been deployed to compute the heat capacities of Na55 and Na147 and to obtain about 40 isomers for larger clusters of sizes N = 147, 200, 201, and 252. There is an excellent agreement between the computed and experimentally measured melting temperatures. The geometries of these isomers when further optimized by DFT, the mean absolute error in the energies between DFT results and those of our models is about 7 meV/atom or less. The errors in the interatomic bond lengths are estimated to be below 2% in almost all the cases.