(solid line) scaled to the isotropic scattering (dashed line) for at . The curves have been offset for clarity.
for minus at 273 (shifted by ) and shown with the error bars as the lines through the data points.
for minus from obtained by dividing by the number of electrons per molecule and Fourier transforming with the mean electron number density for and . The data for were published previously in Hart et al. (Ref. 20).
Plot of the summed modulus of with the predicted structural isotopic quantum effect from the thermodynamic shift model presented in the text. The open squares are the experimental data, the circles are the isochoric temperature derivative, the triangles are the isothermal density derivative, and the closed squares are the sums of the two derivatives. The solid lines on this plot are guides to the eye. Insert: the line represents a least-squares fit to the residual between the experimental data (open squares) and thermodynamic model (solid squares) using the form . and .
Molecular densities of (solid) and (dashed) as a function of temperature, after Badyal et al. (Ref. 3) and Kell and Whalley (Ref. 27). The arrows show and for the density maxima and boiling points used to define the coefficients of the isothermal density derivative and isochoric temperature derivative in Eq. (4).
Top: isochoric temperature derivative measured at atmospheric pressure for of (average taken from digitized data sets , 23.3, and in Ref. 28). Middle: isothermal density derivative measured at for of (average taken from digitized data sets , 2.44, 3.36, 4.10, 4.88, 5.47, 5.95, and in Ref. 29). Bottom: isothermal density derivative measured at for of (average taken from data sets and in Ref. 30).
Comparison of the measured minus difference compared to various types of molecular dynamics simulations. Top: digitized curve of the ab initio path integral Car-Parinello results (Ref. 6) calculated using the modified form factors of Hura et al. (Ref. 23). Bottom: Feynman-Hibbs with a modified central force potential (Ref. 4) (also shown reduced by an arbitrary factor of 5 to directly compare to the shape of the curve). These data have been digitized and converted from an independent atom to modified form factor representation (Ref. 23).
Comparison of measured minus difference at (open circles), with simulation data of Refs. 21 and 31 using the rigid body T1P4P potential at , obtained using the modified atomic form factors of Hura et al. (Ref. 23). Also shown are the relative contributions from the differences between the oxygen-oxygen and oxygen-hydrogen partial electronic structure factors (lines).
Schematic of water structure showing the looselyn hydrogen bonded interstitial molecule that exists with some probability at , predicted by the simulation in Ref. 4
Comparison of the measured difference in difference between minus (circles) with the full quantum minus classical simulations of de la Peña and Kusalik (Ref. 21) (lines) in Fig. 1 of Refs. 21 and 31, divided by a factor of 2 to give essentially the same curve as the total solid line in Fig. 8. It is assumed that the factor of 2 arises because the quantum mechanical contribution for heavy water is approximately halfway between that for light water and the purely classical case (Ref. 4).
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