Fig. 1: Outline of the developed methodology. | npj Computational Materials

Fig. 1: Outline of the developed methodology.

From: Free-energy perturbation in the exchange-correlation space accelerated by machine learning: application to silica polymorphs

Fig. 1: Outline of the developed methodology.

Within the lower rungs of Jacob’s ladder of DFT, Helmholtz energy surfaces F(V, T) are computed, yielding the full set of thermodynamic properties (bottom panel). Precise free energy perturbation is then guaranteed by small second-order terms, making all rungs efficiently accessible at selected volume-temperature points (top panel). The correlation with the β-quartz–β-cristobalite Helmholtz energy difference \(\Delta\)Fq−c allows an accurate estimate of the transition temperature Tq−c and further transition characteristics.

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