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

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 at the desired pressure and temperature. 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, our new NPT TI scheme provides rigorous and direct Gibbs free energy calculations for solids.