Constant-pressure and NPT extensions of BABFc

Develop constant-pressure formulations of the constrained Bayesian Adaptive Biasing Force framework that compute restricted Gibbs formation free energies while preserving metastable basin identity under volume fluctuations, pressure-induced basin changes, and biased-to-target measure overlap.

Background

The present BABFc implementation is formulated in the canonical ensemble and therefore yields restricted Helmholtz formation free energies at fixed volume. For applications governed by pressure and temperature, the authors identify two unresolved extensions: evaluating restricted Helmholtz free energies over a volume grid followed by a Legendre transformation, or constructing a direct NPT version of BABFc with cell degrees of freedom. Both approaches must control basin identity under volume fluctuations and pressure-induced changes, as well as maintain sufficient overlap between constrained and target distributions. The authors explicitly defer these extensions to future work.

References

Another possible route would be a direct NPT formulation of BABFc, in which the biased and constrained sampling is extended to include cell degrees of freedom, as in recent developments of NPT thermodynamic integration. Intermediate strategies based on sequences of NVT simulations to approximate NPT behavior may also be considered. These extensions require careful control of basin identity under volume fluctuations, pressure induced changes of metastable basins, and overlap between biased and target measures, and will be the subject of future work.

— Systematic and accurate anharmonic formation free energies of metastable defects via a constrained Bayesian Adaptive Biasing Force framework  (2608.20902 - Lapointe et al., 21 Aug 2026) in Discussions and Conclusion, final methodological-perspectives paragraph before “Amid renewed interest in interatomic interactions”