The origin of the well-defined collective excitations found in liquid para-H 2 by recent experiments is investigated. The persistence of their relatively long lifetimes down to microscopic scales is well accounted for by calculations carried out by means of path-integral-centroid molecular dynamics. In contrast only overdamped excitations are found in calculations carried within the classical limit. The results provide fully quantitative evidence of quantum effects on the dynamics of a simple liquid. PACS numbers: 67.20. + k, 62.10. + s, 62.60. + v In spite of being composed of the simplest stable molecules, the transport and kinetic properties of liquid hydrogen still resist a quantitative understanding [1]. Such peculiar behaviors are usually thought to arise because of the light masses of the particles forming the liquid (M ഠ 2 amu) and the relatively low temperatures where it exists under its saturated vapor pressure. Quantum effects are thus expected to be noticeable although their relevance for understanding quantitatively most of the transport properties awaits to be established in full. These effects are first manifested by 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. In particular, the rotational and nuclear spin states of the two protons forming the H 2 molecule are coupled, leading to two distinguishable species, para͑p͒-H 2 and ortho͑o͒-H 2 corresponding to molecules having antiparallel (I 0), and parallel (I 1) spin states, respectively. This has an immediate consequence on the symmetry of the interaction potential between H 2 molecules which is isotropic for p-H 2 molecules but angular dependent for o-H 2 . It is so because the orientational distribution of the internuclear bond in the laboratory frame is spherically symmetric (s-like) for the former and axially symmetric (p-like) for the latter. A noticeable manifestation of quantum behavior is expected concerning the spatial smearing of the molecular wave function. This comes because of the low molecular mass and the low temperatures in question (about 10-20 K) which makes the thermal (de Broglie ) wavelength l ͑2ph 2 ͞Mk B T ͒ to reach values larger than the molecular dimensions. In fact, close to triple point, l ഠ 3.3 Å which becomes comparable to the equilibrium separation between two p-H 2 molecules, r 0 ഠ 3.5 Å. In addition to the spatial spread of the wave function a delocalization time t d can be defined in terms of the fluid number density r and the particle mass through [2] t d M͞2ph͑r͞2.612͒ 2͞3 , which for the triple point density yields an estimate for t d ഠ 1.2 ps. Finally, exchange effects arising because of the indistinguishability of the molecules are deemed to play a very minor role since the temperatures in question are well above the quantum degeneracy temperature T 0 h͞k B t d 6.5 K and therefore most particles will be accommodated in excited levels [3].Two sets of recent in...
Several fundamental transport properties of a quantum liquid para-hydrogen (p-H2) at 17 K have been numerically evaluated by means of the quantum dynamics simulation called the path integral centroid molecular dynamics (CMD). For comparison, classical molecular dynamics (MD) simulations have also been performed under the same condition. In accordance with the previous path integral simulations, the calculated static properties of the liquid agree well with the experimental results. For the diffusion coefficient, thermal conductivity, and shear viscosity, the CMD predicts the values closer to the experimental ones though the classical MD results are far from the reality. The agreement of the CMD result with the experimental one is especially good for the shear viscosity with the difference less than 5%. The calculated diffusion coefficient and the thermal conductivity agree with the experimental values at least in the same order. We predict that the ratio of bulk viscosity to shear viscosity for liquid p-H2 is much larger than classical van der Waals simple liquids such as rare gas liquids.
Fundamental transport properties of liquid para-hydrogen (p-H(2)), i.e., diffusion coefficients, thermal conductivity, shear viscosity, and bulk viscosity, have been evaluated by means of the path integral centroid molecular dynamics (CMD) calculations. These transport properties have been obtained over the wide temperature range, 14-32 K. Calculated values of the diffusion coefficients and the shear viscosity are in good agreement with the experimental values at all the investigated temperatures. Although a relatively large deviation is found for the thermal conductivity, the calculated values are less than three times the amount of the experimental values at any temperature. On the other hand, the classical molecular dynamics has led all the transport properties to much larger deviation. For the bulk viscosity of liquid p-H(2), which was never known from experiments, the present CMD has given a clear temperature dependence. In addition, from the comparison based on the principle of corresponding states, it has been shown that the marked deviation of the transport properties of liquid p-H(2) from the feature which is expected from the molecular parameters is due to the quantum effect.
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 ...
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