Microscopic structure factor of liquid parahydrogen: Monte Carlo and molecular dynamics simulations

Abstract

We present a comparison of results on the microscopic structure of liquid parahydrogen as calculated by path-integral Monte Carlo and path-integral-centroid-molecular-dynamics simulations. The radial distribution functions calculated using both approaches are found to be in good agreement. The disagreement between published estimates for the static structure factor are found to arise from different approximations followed for the Fourier transform of heavily truncated data. A comparison of the structure of the real liquid with that of a classical analog is also made and shows that the latter would freeze at the experimental liquid density. Liquid parahydrogen is therefore stabilized by the action of large quantum effects. DOI: 10.1103/PhysRevB.66.212202 PACS number͑s͒: 67.20.ϩk, 61.12.Ϫq, 61.20.Ja The continued interest on the properties of liquid hydrogen stems from different reasons. First, it is known to be one of the dominant constituents of the giant planets 1 where it is found in various states of aggregation stretching over a vast range of densities and temperatures. Second, laboratory efforts to cross the insulator→metal transition resulting in the production of metallic hydrogen continue apace 2 and finally, apart from its use as a cryogenic liquid or as a fuel element in spacecraft technology, the material still constitutes a promising energy source since it is environmentally safe and has a high caloric content.The fundamental difficulties in dealing with this liquid arise from the light masses of its constituent particles and the relatively low temperatures where the liquid exists under its saturated vapor pressure. This makes quantum effects prominent and its first manifestation is the appearance of a discrete spectrum of transitions between molecular rotational levels. The quantum nature of such motions imposes some symmetry constraints to the total molecular wave function. This means that the rotational states and the nuclear spin states of the two protons forming the H 2 molecule are not independent. Coupling of nuclear spin states (Iϭ0 for a molecule having antiparallel proton spins and Iϭ1 for parallel spin states͒ leads to two distinguishable species, para-H 2 (p-H 2 ) and ortho-H 2 (o-H 2 ), respectively. This results in special characteristics of the interaction potential between H 2 molecules. Such constraints imply that p-H 2 molecules interact with its neighbors through an isotropic potential since the total wave function, and therefore the electronic charge distribution, will have spherical symmetry, whereas o-H 2 shows a strong angular dependence of such interactions due to the action of a finite electric quadrupole moment.The liquid structure function of p-H 2 as quantified by the g(r) radial distribution function is now beginning to be understood mostly by recourse to computer simulations where the quantum degrees of freedom are explicitly taken into consideration. A preliminary report on results from pathintegral-centroid-molecular-dynamics ͑PICMD͒ Simulations ͑Ref. 3͒ has shown ...

Static structure factor of liquid parahydrogen

“…Such conditions cannot be matched in neutron work for reasons explained at the beginning, and use of x-ray beams will only provide an estimate for g(r) about one order of magnitude less accurate than neutrons. 19 On the other hand, one expects S centroids (Q) to match the result measured using low incident energies since its dynamic counterpart S centroids (Q, ) was found to be in good agreement with experimental spectra, 5,6 and therefore it should come as no surprise that the quantity derived by recourse to Eq. ͑20͒ in an inelastic-scattering measurement 5 matches the present result shown in Fig.…”

“…As referred to above and already explained in detail, 6 the difference in both measurements cannot explained only be by the rather different conditions employed in both experiments. In fact, the liquid peak becomes barely visible in the single-differential cross section reported in Ref.…”

“…The Silvera-Goldman form is chosen 5,6 to represent the bare interaction potential and the simulation was run for an ensemble of 500 molecules with periodic boundary conditions at Tϭ15 K and a pressure of 1ϫ10 5 Pa that yield a molar volume of 24.513 cm 3 mol Ϫ1 . The statistical ensemble corresponds to isobaric-isothermal conditions and the simulation method followed the Nose-Hoover-chain-Andersentype NPT scheme.…”

“…where S gas (Q, ) is an ideal gas function of free-translating molecules of mass M mol at temperature T and ␥ is a vibrational factor 6 that has a value of 0.12 Å 2 . The phonon components are obtained starting from the one-phonon term …”

“…5͒ from an inelastic-scattering experiment yielded a value for its height well in excess of that predicted from path-integralcentroid-molecular-dynamics ͑PICMD͒ simulations. 6 Here we report on an experiment conducted using a cold neutron diffractometer that allows us to explore d /d⍀ under conditions where most of the scattering arises from liquid structure effects rather than single-particle molecular rotations. Contrary to our previous measurement which was not designed for structure determination, the present experiment allows us to measure d /d⍀ on absolute units from where an estimate of S(Q) for Q-values comprising the liquid diffraction peak is derived.…”