Neural-network force field backed nested sampling: Study of the silicon 𝑝-𝑇 phase diagram

Abstract

Nested sampling is a promising method for calculating phase diagrams of materials. However, if accuracy at the level of ab initio calculations is required, the computational cost limits its applicability. 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 evaluated at the level of density functional theory and demonstrate our approach on the low-pressure region of the silicon pressure-temperature phase diagram between 0 and 16GPa. The simulated phase diagram shows 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 r2SCAN meta-generalized gradient approximation plays a pivotal role in achieving accurate thermodynamic behavior. We furthermore perform a detailed analysis of the potential energy surface exploration and highlight the critical role of a diverse and representative training data set.