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The Journal of Chemical Physics

Direct measurement of the size of the helium dimer

Fei Luo, Clayton F. Giese, W. Ronald Gentry

Published Jan 15, 1996• 166 citations
Publisher

Abstract

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.

DOI
10.1063/1.470771

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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.
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.
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.
Abstract Small helium clusters Hen (n = 2, 3, ... , 10) in molecular beams produced by supersonic expansion of gaseous helium have been observed in several different experiments. Among these clusters the dimer, which has a single very slightly bound state, and the trimer, which could have many bound states, have especially unusual properties which QMC calculations can explain in detail. In this paper, diffusion QMC calculations were used to determine ground state properties for clusters (n = 2, ... , 10) using two accurate, but slightly different pairwise-additive potential energy expressions, a perturbation-based potential by Tang et al.a and an empirical potential (HFD-B) proposed by Aziz et al.b Trial functions for importance sampling were based on those determined earlier by Rick et alc. Expectation values and probability distributions were determined by the descendent-weighting technique to give results independent of the trial functions. As expected, a single bound state of the dimer was found, and its average internuclear distance was predicted to be 51.5 A. Energies for clusters with n = 2, 7 with the HFD-B potential were in good agreement with those of earlier calculations. Comparisons of the results for the two different potential energy expressions showed energies differing by a few percent. Tests of possible nonadditive interactions showed these to be far less important in their effects on predicted energies.