^{1,a)}, Q. Mei

^{1}, C. J. Benmore

^{2,b)}, J. C. Neuefeind

^{3}, J. F. C. Turner

^{4}, M. Dolgos

^{4}, B. Tomberli

^{5}and P. A. Egelstaff

^{5}

### Abstract

We have measured the difference in electronic structure factors between liquid and at temperatures of 268 and with high energyx-ray diffraction. These are compared to our previously published data measured from . We find that the total structural isotope effect increases by a factor of 3.5 over the entire range, as the temperature is decreased. Structural isochoric temperature differential and isothermal density differential functions have been used to compare these data to a thermodynamic model based upon a simple offset in the state function. The model works well in describing the magnitude of the structural differences above , but fails at lower temperatures. The experimental results are discussed in light of several quantum molecular dynamics simulations and are in good qualitative agreement with recent temperature dependent, rotationally quantized rigid molecule simulations.

The authors would like to thank Dr. P. G. Kusalik for sending us the rigid body TIP4P quantum and classical simulation data as a function of temperature (the solid lines in Figs. 8 and 10), that are associated with Refs. 21 and 31. Dr. Yang Ren of BESSRC-CAT is thanked for his assistance with experiments at APS. The work performed at the IPNS and APS Divisions of Argonne National Laboratory were supported under the U.S. DOE Contract No. W31-109-ENG-38.

I. INTRODUCTION

II. BACKGROUND AND CONVENTIONS

III. EXPERIMENT

IV. RESULTS AND DISCUSSION

A. difference functions

B. Magnitude of the structural isotopequantum effect

C. Comparison to low density amorphous ice

D. Test of thermodynamic shift model

E. Comparison to quantum simulations

F. substitution

V. CONCLUSIONS

### Key Topics

- Quantum effects
- 26.0
- Electronic structure
- 9.0
- Water energy interactions
- 9.0
- Isotopes
- 8.0
- Photons
- 8.0

## Figures

(solid line) scaled to the isotropic scattering (dashed line) for at . The curves have been offset for clarity.

(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 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).

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 .

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).

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).

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 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).

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

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).

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).

Article metrics loading...

Full text loading...

Commenting has been disabled for this content