Fig. 2: Computed chemical potentials and error analysis.
From: Quantum-mechanical exploration of the phase diagram of water

Per-molecule chemical potentials for the phases (meta)stable at 225 K, shown relative to the chemical potential of ice II. The MLP results are in a. In subpanel (i), solid lines show experimentally known bulk phases, dashed lines show various known low-density structures, and dotted lines show other hypothetical phases. Subpanel (ii) shows the same data, but only for the known experimental phases, as labelled. b Shows the chemical potentials at the level of the revPBE0-D3 DFT for classical systems, and c shows DFT results with NQE corrections. d Illustrates representative standard deviations for selected proton-disordered (‘d’), partially proton-disordered (‘p’) and proton-ordered (‘o’) phases. Contributions are split into those arising from (i) the thermodynamic integration to the classical system described by the MLP, with the contribution from proton disorder shown as a lighter hatched area; (ii) the MLP to the revPBE0-D3 correction term; and (iii) the term accounting for NQEs.