Quantum effects on the structure of water at constant temperature and constant atomic density

To explore quantum effects on the structure of liquid water, we have carried out high-energy x-ray diffraction measurements of quantum differences both under isothermal conditions at 24.5 °C and under isochoral conditions at 0.0997 atom/ų. The measured isothermal difference correlation function is approximately equivalent to an isochoric temperature differential (ITD) of 5.5 °C, reflecting the tendency of quantum effects to introduce more disorder into the liquid. The measured isochoral correlation function is about three times higher in amplitude and is approximately equivalent to an ITD of 19 °C. Since the isochoral measurements for ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ were made at temperatures 13.5 °C apart, the isothermal and isochoral functions are roughly consistent. The discrepancies are discussed with reference to data on the pressure dependence in the literature. They are comparable with differences in results obtained with different potential functions in path-integral molecular dynamics simulations. The present results lend further validity to the notion that quantum effects on the structure of liquid water are similar to those of thermal disorder, as long as the effects of differences in the equation-of-state of ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ are taken into account.