Neural-Network Force Field Backed Nested Sampling: Study of the Silicon p-T Phase Diagram

TL;DR

This study combines neural-network force fields with nested sampling to efficiently compute silicon's phase diagram, achieving results consistent with experiments and emphasizing the importance of training data diversity and functional choice.

Contribution

It introduces an efficient method integrating neural-network force fields with nested sampling for phase diagram calculations, demonstrating accuracy and exploring data diversity impacts.

Findings

Good agreement with experimental phase diagram and melting line

Stable structures within pressure range are observed in simulations

Meta-GGA r2SCAN functional improves thermodynamic accuracy

Abstract

Nested sampling is a promising method for calculating phase diagrams of materials, however, the computational cost limits its applicability if ab-initio accuracy is required. In the present work, we report on the efficient use of a neural-network force field in conjunction with the nested-sampling algorithm. We train our force fields on a recently reported database of silicon structures and demonstrate our approach on the low-pressure region of the silicon pressure-temperature phase diagram between 0 and \SI{16}{GPa}. The simulated phase diagram shows a good agreement with experimental results, closely reproducing the melting line. Furthermore, all of the experimentally stable structures within the investigated pressure range are also observed in our simulations. We point out the importance of the choice of exchange-correlation functional for the training data and show how the meta-GGA r2SCAN plays a pivotal role in achieving accurate thermodynamic behaviour using nested-sampling. We furthermore perform a detailed analysis of the exploration of the potential energy surface and highlight the critical role of a diverse training data set.