Structure of SPC/Fw water at 300 K using the HMC and Langevin dynamics approaches. The results are insensitive to the choice of and only results with are shown. For the simulation, sweeps were performed and the last sweeps were used for averaging. A fixed time step of was used. For the HMC simulation with , the starting oxygen positions were based on those of a hard-sphere fluid at a reduced density of 0.3. Results using particles overlap those shown and are not included to preserve clarity. A bin width of 0.04 Å has been used for analyzing the data.
Oxygen-oxygen radial distribution function at 300 K (unless otherwise noted). for SPC/E (dotted line) is used as the standard for comparing different functionals. Data using SPC/Fw are similar to that from SPC/E and are not shown. A bin width of 0.04 Å has been used for analyzing the data.
Oxygen-oxygen radial distribution function using the BLYP density functional. Right panel: BLYP at 300 K (blue curve). Left panel: BLYP at 350 K (light blue curve). The statistical uncertainties at the level are shown. All calculations are based on the CP2K code, the GTH-TZV2P basis set, and cutoff (280 Ry) for the charge density grid. K04: MC with sampling of configurations using an empirical potential; the simulation comprises 64 water molecules (Ref. 38). V05: Born–Oppenheimer molecular dynamics (Ref. 40) on a 32 water molecule system. Uncertainty of about ±10 K was reported around the average temperature noted in the figure (Ref. 40). A bin width of 0.04 Å has been used for analyzing the data.
Left panel: Distribution of coordination numbers around a distinguished water molecule. The coordination radius is 3.0 Å. The curves are translated vertically for clarity. The SPC/E distribution is overlain on the results from each of the density functionals to facilitate comparison. Right panel: Variation of the chemical contribution with coordination radius . Statistical uncertainty at the level is shown.
Left panel: Distribution of water molecules in a cavity of radius 3 Å. The curves are translated vertically for clarity. The SPC/E distribution is overlain on the results from each of the density functionals to facilitate comparison. Right panel: Variation of the packing contribution with coordination radius . Statistical uncertainty at the level is shown.
The packing contribution scaled by the surface area (to within constants) vs the radius of the HS. Compare also with Fig. 2 in Ref. 15. The solid curve is based on the revised scaled particle theory of Ashbaugh and Pratt (Ref. 22). A linear fit to the scaled particle results for is shown (dotted line).
Left panel: The sum of inner-shell chemistry and packing (steric) contributions to the excess free energy of hydration (in units of ). Right panel: The sum of inner-shell chemistry and packing inferred from a two-moment information theory model, that is assuming Gaussian distribution of and (Refs. 5 and 12–14).
Statistics from the HMC simulations of water. The temperature . is the number of molecular dynamics steps between consecutive MC steps. is the total number of sweeps. In the first 2000 sweeps (≈100 ps) of ab initio simulations, was periodically updated to target an acceptance rate of 0.7. Subsequently, was held fixed at the value shown, and the first 500 sweeps of the total time shown were set aside for equilibration. For the SPC/Fw simulation, was used always and the first 2000 sweeps were set aside for equilibration. is the time step for integrating the equations of motion. is the average discretization error between consecutive MC steps. The expected value of is 1. R is the ratio of the observed acceptance rate to that predicted by Eq. (3). Statistical uncertainties at the level are noted, except for the where it is given at the level. is the distance to the first maximum of the . Note that is defined to only within half the bin width of 0.04 Å. The simulation system comprises 32 water molecules.
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