Quantum Effects on Liquid Dynamics as Evidenced by the Presence of Well-Defined Collective Excitations in Liquidpara-Hydrogen

Abstract

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...

Static structure factor of liquid parahydrogen

“…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.…”

“…In fact, the employed conditions are such that one can expect to find a relatively large inelasticity component to the interference term of the single-differential cross section since our sampling time will become comparable to the lifetime of the excitations. 5 To our knowledge, there is no established route to estimate the magnitude of the correction referred to above. To proceed, we will make recourse to our previous knowledge of S(Q, ) and calculate an inelasticity correction due to collective vibrations.…”

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

“…A vivid example of such effects is shown in Fig. 1 that depicts experimental data for ⌺ Q derived from an inelastic neutronscattering experiment 6,8 where the experimentally accessible quantity was the double-differential cross section. An esti- mate of the contributions of the rotational cross section is then made by integrating over energy transfers the measured double-differential cross section.…”

“…1 of Ref. 8 show that the statistical accuracy of the measured liquid structure factor leaves much to be desired and calls for an accurate determination of this quantity.…”

“…The differences in S(Q) are thus attributable to the different inversion procedures used to deal with heavily truncated data. We made use of direct Fourier transform 8 while Zoppi et al use an extrapolation of g(r) to large distances by means of the formula suggested by Verlet. 13 To enable a direct comparison of both sets of data we have followed the same procedure employed by Zoppi et al 12 The large-r part of the g(r)'s have been fitted to a decaying sine function 12,13 and the fitted function extrapolated to rϭ30 Å previous to Fourier inversion.…”