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Journal of Chemical Information and Computer Sciences

Helium 4 Dimer in Nanotubes

Leandra Vranješ Markić, Ž. Antunović, Srećko Kilić

Published Jun 27, 2001• 5 citations
Publisher

Abstract

The ground state of the helium 4 dimer is considered using the Monte Carlo technique. In a cylinder with a hard core wall, binding depends on its radius. For a small radius binding occurs as in the one-dimensional case. With an increase of the radius, the binding becomes stronger, reaches its maximum value, and then slowly diminishes. In conical geometry, that may be realized as a generalization of a cylindrical one, this dependence of the binding energy on the radius might lead to an effective force which tends to move the molecule toward the region of minimal energy. Thus, in channels, with nonhomogeneous cross-sections, the particles move easier in dimer form. In addition, the square of the momentum and of the particle separation along the cylinder axis and in the plane perpendicular to it are calculated as well.

DOI
10.1021/ci010001q

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arXiv:cond-mat/0310067•Physical Review B•Oct 29, 2004•18 citations
The ground state of the helium 4 dimer is considered using the Monte Carlo technique. In a cylinder with a hard core wall, binding depends on its radius. For a small radius binding occurs as in the one-dimensional case. With an increase of the radius, the binding becomes stronger, reaches its maximum value, and then slowly diminishes. In conical geometry, that may be realized as a generalization of a cylindrical one, this dependence of the binding energy on the radius might lead to an effective force which tends to move the molecule toward the region of minimal energy. Thus, in channels, with nonhomogeneous cross-sections, the particles move easier in dimer form. In addition, the square of the momentum and of the particle separation along the cylinder axis and in the plane perpendicular to it are calculated as well.
The ground-state properties of 3He{}^{3}\mathrm{He}3He and 4He{}^{4}\mathrm{He}4He trimers and tetramers in infinite and restricted two-dimensional and quasi-two-dimensional (2D) space are studied. Using Monte Carlo calculation in two stages successively, simple variational Monte Carlo and diffusion Monte Carlo, we find that all trimers (except one of 3He{}^{3}\mathrm{He}3He with spin 3/2) and tetramers are bound. In infinite 2D space the binding energy of 4He{}^{4}\mathrm{He}4He trimer is $\ensuremath{-}183(1) \mathrm{mK}$ and of tetramer $\ensuremath{-}435(1) \mathrm{mK}.$ In the same environment for 3He,{}^{3}\mathrm{He},3He, using Jastrow-Feenberg-Bruch wave functions trimer (spin 1/2) is bound with $\ensuremath{-}0.013(1) \mathrm{mK}$ and tetramer with $\ensuremath{-}0.021(1) \mathrm{mK}.$ Employing in the same procedure ``dimerlike'' wave functions for 3He{}^{3}\mathrm{He}3He molecules in infinite 2D space it is discovered that trimer prefers the structure of one dimer and one separate particle while a composition of two separate dimers is preferable for tetramer. In this case binding energies are $\ensuremath{-}0.020(1) \mathrm{mK}$ for trimer and $\ensuremath{-}0.040(1) \mathrm{mK}$ for tetramer. The binding energies of mixed molecules in infinite 2D space are $\ensuremath{-}74.3(4)$ mK ${(}^{3}\mathrm{He}{\ensuremath{-}}^{4}{\mathrm{He}}_{2});$ $\ensuremath{-}14(1)$ mK ${(}^{3}{\mathrm{He}}_{2}{\ensuremath{-}}^{4}\mathrm{He});$ $\ensuremath{-}254(4)$ mK ${(}^{3}\mathrm{He}{\ensuremath{-}}^{4}{\mathrm{He}}_{3});$ $\ensuremath{-}118(2)$ mK ${(}^{3}{\mathrm{He}}_{2}{\ensuremath{-}}^{4}{\mathrm{He}}_{2});$ $\ensuremath{-}11(1)$ mK ${(}^{3}{\mathrm{He}}_{3}{\ensuremath{-}}^{4}\mathrm{He}).$ In holding potentials with well-adjusted parameters there is a drastic increase of binding for trimer and tetramer in both sorts of helium atoms.
Abstract The helium dimer 4He2 has recently been detected, confirming earlier ab initio predictions of stability for a single bound state with binding energy of 1.310 mK. The predicted potential minimum is at 2.96 Å, with a radial distribution function peaking at 6.96 Å. We model this system using a Dirac bubble potential, which also admits just one bound j = 0 state. With the bubble located at 6.96 Å, an overlap of 0.9994 with the ab initio wave function is obtained. An average internuclear distance of 52.6 Å is calculated, in good agreement with the ab initio result. The root mean square deviation from the mean, 48.0 Å, indicates an enormous spread of the radial wave function. Also consistent with our model is the absence of bound states for the isotopic variants 3He4He and 3He2. Cross sections for helium‐helium scattering are also computed, using both a partial‐wave expansion and the Born approximation. General trends in the energy dependence of the total cross section are accounted for, in qualitative agreement with experimental results. © 1995 John Wiley & Sons, Inc.
Dimer formation by He atoms confined in a narrow tube is studied and the effect of adsorption potential is clarified. The results are well explained in terms of the effective radius <ρ> and the width of the single-particle ground-state wave function Δρ. For 3 He, adsorption potential promotes dimer formation when ⟨ρ⟩≲3\langle \rho\rangle \lesssim 3⟨ρ⟩≲3 Å, but is unfavorable when ⟨ρ⟩≳3\langle \rho \rangle \gtrsim 3⟨ρ⟩≳3 Å. We discuss the recent experimental results for 3 He atoms confined in nanopores in light of the present results.
Small helium (4He) clusters containing the lighter isotope He3 are studied by means of quantum Monte Carlo methods. Accurate ground state energies and structural properties are obtained using accurate trial wave functions and the Tang–Tonnies–Yiu (TTY) helium–helium pair potential. The dimer He4–3He is not bound; as well as the trimer He4He23. The smallest cluster containing He3 is He24He3 with a nonrigid structure having a marked linear contribution. Interestingly, this weakly bound system, with an energy one order of magnitude less than the He34 trimer, is able to bind another He3 atom, forming the tetramer He24He23, which shows the odd feature of having five out of six unbound pairs. In general, the substitution of a single He4 atom in a pure cluster with a He3 atom leads to an energetic destabilization, as the pair He4–3He is not bound. The isotopic impurity is found to perturb only weakly the distributions of the remaining He4 atoms, which retain the high floppiness already found in the pure clusters. As the number of atoms increases the isotopic impurity has the marked tendency to stay on the surface of the cluster. This behavior is consistent with the formation of the so-called “Andreev states” of a single He3 in liquid He4 helium and droplets, where the impurity tends to form single-particle states on the surface of the pure He4.
We report results of two quantum Monte Carlo methods -- variational Monte Carlo and diffusion Monte Carlo -- on the potential energy curve of the helium dimer. In contrast to previous quantum Monte Carlo calculations on this system, we have employed trial wave functions of the Slater-Jastrow form and used the fixed node approximation for the fermion nodal surface. We find both methods to be in excellent agreement with the best theoretical results at short range. In addition, the diffusion Monte Carlo results give very good agreement across the whole potential energy curve, while the Slater-Jastrow wave function fails to bind the dimer at all.
Helium atoms or hydrogen molecules are believed to be strongly bound within the interstitial channels (between three carbon nanotubes) within a bundle of many nanotubes. The effects on adsorption of a nonuniform distribution of tubes are evaluated. The energy of a single-particle state is the sum of a discrete transverse energy Et{E}_{t}Et​ (that depends on the radii of neighboring tubes) and a quasicontinuous energy Ez{E}_{z}Ez​ of relatively free motion parallel to the axis of the tubes. At low temperature, the particles occupy the lowest-energy states, the focus of this study. The transverse energy attains a global minimum value (Et=Emin)({E}_{t}={E}_{\mathit{min}})(Et​=Emin​) for radii near Rmin=9.95A˚{R}_{\mathit{min}}=9.95\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}Rmin​=9.95A˚ for H2{\mathrm{H}}_{2}H2​ and 8.48A˚8.48\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}8.48A˚ for 4He^{4}\mathrm{He}4He. The density of states N(E)N(E)N(E) near the lowest energy is found to vary linearly above this threshold value, i.e., N(E)N(E)N(E) is proportional to $(E\ensuremath{-}{E}_{\mathit{min}})$. As a result, there occurs a Bose-Einstein condensation of the molecules into the channel with the lowest transverse energy. The transition is characterized approximately as that of a four-dimensional gas, neglecting the interactions between the adsorbed particles. The phenomenon is observable, in principle, from a singular heat capacity. The existence of this transition depends on the sample having a relatively broad distribution of radii values that include some near Rmin{R}_{\mathit{min}}Rmin​.