A Novel NPT Thermodynamic Integration Scheme to Derive Rigorous Gibbs Free Energies for Crystalline Solids

TL;DR

This paper introduces a new NPT ensemble thermodynamic integration method that accurately computes Gibbs free energies of crystalline solids by explicitly accounting for cell fluctuations, improving upon conventional approaches.

Contribution

The paper presents a novel two-step NPT thermodynamic integration scheme that eliminates the need for approximate corrections and directly accounts for cell flexibility in solids.

Findings

The new method reproduces conventional results for simple cell-shape distributions.

It provides more accurate Gibbs free energies for complex cell-shape behaviors.

Maintains similar computational cost with a simplified workflow.

Abstract

Thermodynamic Integration (TI) is the state-of-the-art computational technique for accurate Gibbs free energy predictions of solids. Conventional TI schemes start from an NVT harmonic reference and require three successive corrections to recover the Gibbs free energy of the real crystal in the NPT ensemble. However, the NVT-to-NPT correction neglects full cell flexibility. Here, we present a rigorous (and only) two-step TI scheme that operates entirely in the NPT ensemble, eliminating the need for the approximate NVT-to-NPT step. The key methodological advancement is the novel NPT reference that explicitly accounts for full cell fluctuations. The new approach is compared with the conventional one via two complementary case studies. For ice polymorphs, having simple cell-shape distributions, the new approach reproduces conventional TI results with excellent agreement. For CsPbI3, whose black phase exhibits complex cell-shape behavior, we demonstrate that our novel method provides more accurate Gibbs free energy differences than the conventional one. Moreover, the proposed framework maintains comparable computational cost while offering a simplified workflow. Overall, the new NPT TI scheme provides rigorous and direct Gibbs free energy calculations for solids.