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At times less than ≈0.5 ps the calculated rotational anisotropy is dominated by librational motion. Capturing the response at this timescale has been demonstrated to be important when comparing simulation to experimental approaches, such as NMR, that give the integrated time correlation function. (28) Because we are here interested principally in longer time behavior and because the rotational response is nonexponential from 0 to 0.5 ps, the exponential fits whose time constants are shown in Figure 3 all reflect rotational anisotropies beyond 0.5 ps.
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83
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These functions are calculated by binning the O·;·;· ;O distance and O-H·;·;·;O angle over all configurations before a hydrogen bond between any two water molecules breaks irrevocably.
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These functions are calculated by binning the O·;·;· ;O distance and O-H·;·;·;O angle over all configurations before a hydrogen bond between any two water molecules breaks irrevocably.
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n, we defined time zero as the first frame in which the angle θ was zero. Because in some fraction of trajectories there are librations during the jump, this criterion results in a slight asymmetry in distances and θ around the jump event. As discussed above, the decay of the rotational anisotropy is dominated by the long time behavior, so we have ignored the loss of rotational correlation in the first 0.5 ps when extracting time constants. In that spirit we also calculate the Δθ for each jump in such a manner as to avoid this asymmetry: we take the difference of the average value of θ in the -0.4 < t < -0.2 ps and +0.5 < t < 1 ps regions. Tests of different criteria found that different averaging windows do not affect our quantitative conclusions.
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n, we defined time zero as the first frame in which the angle θ was zero. Because in some fraction of trajectories there are librations during the jump, this criterion results in a slight asymmetry in distances and θ around the jump event. As discussed above, the decay of the rotational anisotropy is dominated by the long time behavior, so we have ignored the loss of rotational correlation in the first 0.5 ps when extracting time constants. In that spirit we also calculate the Δθ for each jump in such a manner as to avoid this asymmetry: we take the difference of the average value of θ in the -0.4 < t < -0.2 ps and +0.5 < t < 1 ps regions. Tests of different criteria found that different averaging windows do not affect our quantitative conclusions.
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89
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85067776020
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Points with τ < 0.5 were excluded from the fit because rotational motion at these timescales is dominated by libration and does not contribute significantly to the decay of the anisotropy. Points with τ > 13 ps were excluded because of the large uncertainty associated with them.
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Points with τ < 0.5 were excluded from the fit because rotational motion at these timescales is dominated by libration and does not contribute significantly to the decay of the anisotropy. Points with τ > 13 ps were excluded because of the large uncertainty associated with them.
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We emphasize that the SPC/E water model gives a very overstructured O-O rdf: the first peak of the O-O rdf for bulk SPC/E water has a height of 3, whereas the height from experiment is 2.2-2.3. (98-101) As such our conclusions from the free energy differences based on SPC/E rdf's hold because the work presented here uses exclusively the SPC/E water model. The actual values of free energy differences based on rdf's are not transferable to studies using other water models.
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We emphasize that the SPC/E water model gives a very overstructured O-O rdf: the first peak of the O-O rdf for bulk SPC/E water has a height of 3, whereas the height from experiment is 2.2-2.3. (98-101) As such our conclusions from the free energy differences based on SPC/E rdf's hold because the work presented here uses exclusively the SPC/E water model. The actual values of free energy differences based on rdf's are not transferable to studies using other water models.
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We note that the SPC/E water model used in our simulations does not include polarization effects, so we cannot exclude the possibility that the length scale of hydrogen bond perturbation near polar solutes differs from what we observe. Simulations using polarizable water models are necessary to investigate if this is so.
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We note that the SPC/E water model used in our simulations does not include polarization effects, so we cannot exclude the possibility that the length scale of hydrogen bond perturbation near polar solutes differs from what we observe. Simulations using polarizable water models are necessary to investigate if this is so.
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