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Journal of Chemical Education

The Weakest Link: Bonding between Helium Atoms

LAWRENCE L. JUN. LOHR, S. M. Blinder

Published May 1, 2007• 3 citations

Abstract

Van der Waals attraction between helium atoms can lead to the formation of weakly-bound He 2 diatomic molecules stable at temperatures in the millikelvin range. Helium dimers were first detected experimentally in 1993 and 1994. Sophisticated quantum-mechanical computations confirm that the He–He bond is the weakest known, with a binding energy corresponding to 1.176 mK, about 10 -4 eV. The average internuclear distance is computed to be in excess of 50 Å, which makes He 2 the largest known diatomic molecule as well. The authors have introduced an idealized deltafunction model for the helium dimer that succinctly represents its remarkable properties. Despite the weakness of each individual He–He bond, an intriguing mechanism exists for helium to form trimers and larger clusters with much greater binding energies.

DOI: 10.1021/ed084p860

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Models for low‐temperature helium dimers and trimers

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Abstract We have shown that a simple model based on pairwise deltafunction potentials can, with an appropriate choice of parameters, represent the general behavior of ultra‐low temperature helium dimers and trimers, including all possible isotopomers. The species 4He2, 4He3, and 4He23He are stable, with binding energies of approximately 1.3, 100, and 10 mK, respectively. An Efimov state for 4He23He is also predicted, bound by 2.4 mK. The remaining dimers and trimers, 4He 3He, 3He2, 4He 3He2, and 3He3, are evidently unstable. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

International Journal of Quantum Chemistry•Oct 2, 2001•5 citations

Van der Waals attraction between helium atoms can lead to the formation of weakly-bound He 2 diatomic molecules stable at temperatures in the millikelvin range. Helium dimers were first detected experimentally in 1993 and 1994. Sophisticated quantum-mechanical computations confirm that the He–He bond is the weakest known, with a binding energy corresponding to 1.176 mK, about 10 -4 eV. The average internuclear distance is computed to be in excess of 50 Å, which makes He 2 the largest known diatomic molecule as well. The authors have introduced an idealized deltafunction model for the helium dimer that succinctly represents its remarkable properties. Despite the weakness of each individual He–He bond, an intriguing mechanism exists for helium to form trimers and larger clusters with much greater binding energies.

The relative transmissions of helium dimer and helium atom beams through a set of nanoscale sieves were measured as a function of hole size in the range from 98–410 nm. From the relative transmission coefficients, the mean internuclear distance of helium dimer was determined to be 〈r〉=62±10 Å. This enormous bond length—by far the largest known—confirms recent theoretical estimates of the potential energy well depth ε and the extremely small binding energy Eb of helium dimer. The ranges of these parameters corresponding to the experimental uncertainty in 〈r〉 are ε/k=10.88–10.98 K and Eb/k=0.65–1.30 mK, where k is the Boltzmann constant.

Many microscopic properties of the only natural superfluid element helium have become available within the last 18 years through a number of novel experiments. The diffraction of matter-waves of small helium clusters has established the unusually large bond distance (5.2 nm) and extremely weak binding energy (10−7 eV) of the dimer and other exotic properties of small helium clusters. The high-resolution spectroscopy of closed-shell chromophore molecules attached to small clusters or embedded inside large superfluid droplets have revealed that as a result of superfluidity, molecules rotate virtually without friction and that only a handful of He atoms are required for microscopic superfluidity. The frictionless translational motion of atoms and molecules inside the droplets has also been observed. These and a number of other experiments demonstrate that helium droplets are the most gentle and coldest of all cryomatrices with enormous potential for a wide range of future applications.

A molecular beam consisting of small helium clusters is diffracted from a 100 nm period transmission grating. The relative dimer intensities have been measured out to the 7th order and are used to determine the reduction of the effective slit width resulting from the finite size of the dimer. From a theoretical analysis of the data which also takes into account the van der Waals interaction with the grating bars, the bond length (mean internuclear distance) and the binding energy are found to be $〈r〉\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}52\ifmmode\pm\else\textpm\fi{}4\AA{}$ and $|{E}_{b}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.1+0.3/\ensuremath{-}0.2$ mK.

Abstract We have shown that a simple model based on pairwise deltafunction potentials can, with an appropriate choice of parameters, represent the general behavior of ultra‐low temperature helium dimers and trimers, including all possible isotopomers. The species 4He2, 4He3, and 4He23He are stable, with binding energies of approximately 1.3, 100, and 10 mK, respectively. An Efimov state for 4He23He is also predicted, bound by 2.4 mK. The remaining dimers and trimers, 4He 3He, 3He2, 4He 3He2, and 3He3, are evidently unstable. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001