Radial distribution functions (RDFs) for (a) O–O, (b) O–H, and (c) H–H atom pairs of liquid water calculated from the expectation values using the SQ models. Also shown are the RDFs obtained from the classical (CL) model and those fitted to experimental x-ray (Ref. 108) and neutron (Ref. 109) diffraction data in reciprocal space using the reverse Monte Carlo (RMC) method without H-bond constraints (Ref. 110). The insets show the magnifications of the corresponding first peaks.
Same as Fig. 1 except that the RDFs for the SQ models are calculated with respect to the WP centers.
(a) Optimized energies of the water dimer as a function of the O–O distance obtained from the SQ and classical (CL) simulations without intramolecular constraints and (b) those with the fixed intramolecular geometry (see text), where the energy is defined as the deviation from the energy of two isolated water molecules and the O–O distance is calculated with respect to the WP centers. The insets show the magnifications of the corresponding minimum regions.
Averaged H-bond exchange trajectories of (a) the jump angle θ and (b) the OaO*Ob angle ψ. The standard deviations are also plotted as error bars. The insets show the corresponding magnifications.
Averaged H-bond exchange trajectories of (a) the O*Oa and O*Ob, and (b) the OaOb distances. The standard deviations are also plotted as error bars.
Averaged H-bond exchange trajectories of the WP width fluctuations of the jumping hydrogen atom H* in the body-fixed axes obtained from the SQ simulation with the EGWP model. Also shown is the graphical definition of the body-fixed axes for the H* atom.
(a) Normalized time correlation functions of the H-bond number fluctuation obtained from the SQ simulations with the thawed GWPs (TGWPs) and (b) those with the frozen GWPs (FGWPs) in which only the rotational and translational degrees of freedom of the WPs are allowed to fluctuate. Also shown is the classical (CL) result. The insets show the corresponding power spectra in arbitrary units. Notice the logarithmic scales of the axes.
Time series of the deviation of the total Hamiltonian from its initial value in liquid water calculated from the EGWP model using the time-reversible second-order explicit symplectic integrator (SI2) and the fourth-order Runge-Kutta method (RK4) with a time step of Δt = 0.02 fs. The inset shows the time step versus the standard deviation (SD) of the total Hamiltonian in kcal/mol using SI2; here, notice the logarithmic scales of the axes. Also shown in the inset is the linear fitting with a slope of 2.00 (dotted line).
Time development of the intra- and intermolecular potential energies obtained from the EGWP model. The average values (the SDs) of the intra- and intermolecular potential energies are 15.0 (0.23) and −10.5 (0.17) kcal/mol, respectively.
Ensemble-averaged static monomer properties in liquid water obtained from the SQ and classical simulations with the f-SPC model. Optimized monomer properties of the isolated water molecule obtained from the SQ simulations are also listed alongside the classical geometric parameters for the f-SPC model. The number in parentheses represents the standard errors in the final digits.
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