Evidence for a bound HeH 2 halo molecule by diffraction from a transmission gratingAnton Kalinin, Oleg Kornilov, Lev. Yu Rusin, and J. Peter Toennies Citation: The Journal of Chemical Physics 121, 625 (2004); doi: 10.1063/1.1768935 View online: http://dx.doi.org/10.1063/1.1768935 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/121/2?ver=pdfcov Published by the AIP Publishing Advertisement:

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Evidence for a bound HeH 2 halo molecule by diffractionfrom a transmission grating

Anton Kalinin,a) Oleg Kornilov,b) Lev. Yu Rusin,c) and J. Peter ToenniesMax-Planck-Institut fu¨r Stromungsforschung, 37073 Go¨ttingen, Germany

~Received 30 March 2004; accepted 17 May 2004!

The HeH2 van der Waals complex has been identified in a molecular beam produced by a cryogenic(T0524.7 K) free jet expansion of a 1% H2 mixture in 99%4He gas. The weakly bound HeH2

complexes in the beam are identified via their first order diffraction angles after passing through a100 nm period transmission grating. An electron impact mass spectrometer analysis of thediffraction patterns is used to discriminate against ion fragments of the constituent gas clusters.© 2004 American Institute of Physics.@DOI: 10.1063/1.1768935#

I. INTRODUCTION

The interaction potential between He and H2 has beenextensively studied theoretically over the last 40 years. For asurvey see Table I of Ref. 1. Since both constituents haveonly two electrons in closed shells it provides the simplesttest of quantum chemical methods for calculating the van derWaals potential between a molecule and an atom. The poten-tial has also been widely studied using a variety of differentexperimental techniques and is of considerable astrophysicalinterest.2,3 This is not surprising since H2 and He are by farthe most prevalent molecule and atom in the solar system.4

The calculated potentials have only recently become suffi-ciently precise to determine if4He forms a bound complexwith H2 . Two recent calculations based on semi-ab initiopotentials predict very small binding energies of onlyEb

520.0428 K~Ref. 5! and20.0246 K~Ref. 6!. Since thesebinding energies are much smaller than the quoted system-atic errors of the order of 190 K in a recent pureab initiocalculation,2 it is highly desirable to have experimental evi-dence that the complex is indeed bound. Despite the recentextensive research on optical spectroscopy of van der Waalscomplexes we are not aware of any experimental evidencefor the existence of the4HeH2 complex. Presumably anyexperiment in this direction would require high pressure lowtemperature cells and under these conditions the more tightlybound and therefore more prevalent H2 complexes wouldmask any spectral features from4HeH2.

The present experiment is based on diffraction from atransmission grating, which previously provided the first un-equivocal evidence for the existence of the weakly bound Hedimer.7 The complexes are formed in a cryogenic expansionof a mixture of the two gases. The diffraction anglesq of the

molecular beam constituents are given by the Bragg equationq>nl/d, wheren is the diffraction order,d the grating pe-riod ~100 nm! andl the de Broglie wavelength given byl5h(Mv)21, hereh is Planck’s constant,M andv are theirmass and velocity, respectively. Thus the diffraction anglesdepend inversely on the neutral particle massM. Typicallyl>1 Å so that the diffraction angles are of the order of1023 rad. Since only those particles passing through the slitswithout a significant shift in phase contribute coherently tothe diffraction pattern the technique is essentially nonde-structive.

II. APPARATUS

The cluster beam diffraction apparatus is an improvedversion of one recently described in detail.8 The 1% normalH2299%4He highly purified gases at a total source pressureof 7 bar are expanded through a 5mm diam pinhole orifice ata source temperature of 24.7 K. The resulting beam is highlycollimated by two 5 mm high 20mm wide slits located at 23and 129 cm downstream from the source orifice. The par-ticles are diffracted by ad>100 nm period SiNx transmis-sion grating9 located at 139 cm from the source. A 70mm slitin front of the detector, located at 266 cm from the source,provides for an angular resolution ofDq>55mrad. Thehomemade electron impact ionization–mass spectrometerdetector rotates about an axis passing through the grating andcan be positioned by a stepping motor to within 1mrad. Thebeam particles are ionized in an open cage ionizer with anelectron energy of 130 eV. The magnetic mass spectrometerhas a resolution ofm/Dm>40.

III. EXPERIMENTAL RESULTS

The coexpansion of the two gases4He and H2 to pro-duce the desired complex presents two major complicationsnot encountered in the earlier study of the4He dimer:7,10 ~1!To avoid massive condensation of the much more stronglybound H2 clusters the H2 concentration had to be limited to1% and for this reason the intensity is about two orders of

a!Permanent address: Institute of Energy Problems of Chemical Physics,Moscow 117334, Russia.

b!Permanent address: St. Petersburg State University, Department of Physics,St. Petersburg 198904, Russia.

c!Permanent address: Institute of Energy Problems of Chemical Physics,Moscow 117334, Russia.

JOURNAL OF CHEMICAL PHYSICS VOLUME 121, NUMBER 2 8 JULY 2004

6250021-9606/2004/121(2)/625/3/$22.00 © 2004 American Institute of Physics

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magnitude smaller than in the4He dimer experiment.~2! Todiscriminate against diffraction peaks at the same diffractionangle from the constituent gases additional diffraction mea-surements of the pure4He and H2 gases were necessary.Figure 1 shows the diffraction pattern of the mixture with themass spectrometer set to the ion massesm53, 4, 5, and 6amu for angles between the specular and the first order Heatom peak atq522.0 mrad. Since the diffraction peaks arealways symmetric with respect to the central specular peakonly one side is shown. The top abscissa indicates the neutralmassesM in amu corresponding to the first order diffractionangles according to the Bragg relationship. These anglesagree with the angle of the first order He atom peak@Fig.1~a!# indicating that all the neutral clusters have the same Heatom velocity of 500 m/sec. These experiments were re-peated with pure para-H2 but no noticeable differenceswithin a few percent could be detected.

Figure 1~a! compares the mixture diffraction pattern withthat measured with a pure4He beam under the same sourceconditions. In both experiments the peak widths are deter-mined by the angular resolution since the beams have verynarrow velocity distributions of aboutDv/v>1%. The twodiffraction patterns coincide within the small statistical errorsexcept in the vicinity of theM56 peak atq521.33 mrad.The small remainingM56 peak in the pure gas diffraction

pattern is due to the second order4He-trimer diffractionpeak. Thus the signal difference of about 7.5 counts/s@seeinset in Fig. 1~a!# can be attributed to an ion fragment ofHeH2. Although no m53 amu ion fragment is expectedfrom HeH2 the diffraction pattern in Fig. 1~b! was made toassess the mole fraction of H2 trimers in the beam. In Fig.1~b! the peak atM54 corresponds to (H2)2 , the peak atM56, (H2)3 , M58, (H2)4 , etc., all of which fragment toH3

1 ions. Experiments with pure H2 carried out under varioussource conditions, reveal for clusters smaller than (H2)5 nodetectable signal on the ion masses 4 and 6 amu correspond-ing to the even H4

1 and H61 fragments nor on mass 5 amu

(H51),11 contrary to earlier literature reports based on less

conclusive evidence. Thus the two weak peaks at ion massesm55 and 6 amu can also be attributed to the HeH2 ionfragments HeH1 and HeH2

1 , respectively. In Fig. 1~c! thevery weak~0.2 counts/s! peak atM510 measured withm55 ions probably is due to He2H2 since it is not found inexpansions of either a pure H2 or pure He beam. Because ofthe large detector background only upper limits on the H1

and H21 fragments could be established. Table I summarizes

the ion fragment ratios of HeH2.

IV. DISCUSSION

The average bond distances^R&514.5~Ref. 5! and 18.1~Ref. 6!, which were calculated from the reported wave func-tions, are both significantly larger than the outer classicalturning point atRot59.5 and 10.3 Å, respectively, and muchlarger than the minimum of the van der Waals potential atRm53.30 Å.2 Thus, if it is assumed that the true values aresimilar, this complex can like the4He2 dimer also be classi-fied as a halo molecule.12 The well-known halo formula^R&5(\2/8muEbu)1/2, wherem is the reduced mass,12,13how-ever, predicts much smaller values of^R&510.3 Å ~Ref. 5!and 13.5 Å~Ref. 6!, respectively. These differences indicatethat the classical allowed region, which is neglected in thehalo formula, makes an important contribution. It is interest-ing to note that the differences are about the same as the sizeof the equilibrium positionRm .

Another interesting aspect of the present study is the ionfragmentation pattern. Since the neutral particles are initiallyvery far apart a fraction of the He1 ions will recoil out ofrange of the remaining neutral partner, which explains thedominantm54 amu signal seen in the experiment. A similarfraction of H2

1 ions is also expected but because of the largebackground only an upper limit could be estimated~Table I!.Those ions which do not receive enough recoil energy toovercome the electrostatic inductive attraction to the neutralpartner are trapped and may take part in one of the followingion–molecule reactions known to occur at low collision en-ergies:

FIG. 1. Diffraction patterns of the atoms, molecules and clusters in a 1%H2 , 99% He mixed free jet expansion (P057 bar, T0524.7 K). In ~a! themass spectrometer detector was set to mass 4 amu and measurements withpure He agreed nearly exactly with that measured with the mixture except at21.33 mrad indicating that the peak shown in the inset can be attributed tothe HeH2 complex. Measurements with pure (H2)N clusters were used torule out an ion fragment contribution on mass 5~c! from the fragmentationof (H2)3 clusters. The scale of the top abscissa gives the masses of thediffracted species.

TABLE I. Ion fragment signal in the ionization of HeH2 by 130 eV elec-trons relative tom54 amu.

Ion fragmentm @amu# 1 2 3 4 5 6

Relative signal ,0.09 ,0.90 0 1.00 0.22 0.08

626 J. Chem. Phys., Vol. 121, No. 2, 8 July 2004 Kalinin et al.

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He11H2→He1H21 , DE529.2 eV ~Ia!

He11H2→He1H11H, DE526.5 eV ~Ib!

He1H21→HeH11H, DE510.8 eV ~II !

He1H21→HeH2

11hn. ~III !

The reactions I and II have been extensively studied in thepast in view of their simplicity14 and astrophysicalimportance.15 The rate for reaction III has recently been pre-dicted to be,0.5310220cm3/sec at 2 K,16 far too small tobe detected. The reactions~Ia! and~Ib! although highly exo-ergic are symmetry forbidden and have cross sections at 15K of only about 0.04 Å2.17 At low collision energies theendoergic reaction~II ! can only occur for vibrationally ex-cited H2

1 in the v>4 vibrational state.18,19 Thus the smallinelastic ionization cross section leading to sufficient vibra-tional excitation of H2

1 ~Ref. 20! can account for the weakm55 amu HeH1 ion signal. Those H2

1 ions with insufficientinternal energy to enable them to relax and escape the weaktrapping potential in a sufficiently short time before they aredetected will contribute to the small HeH2

1 signal at m56 amu.

In summary, the combination of matter-wave diffractionand conventional mass spectroscopy has made it possible todetect the marginally bound HeH2 van der Waals complex.In view of the remaining large errors inab initio potentials,which for HeH2 are estimated to have random energies of 0.2mhartrees~63 K! and systematic errors of about 0.6 mhar-trees~190 K!2 the observation of the HeH2 complex with abinding energy of about<20.04 K provides an importantdiscriminatory test of present-day precision calculations.Other candidates for future study are3HeH2, the alkaliatom–helium atom pairs,21 larger clusters such as alkali at-oms with two attached4He atoms, or two3He atoms or withan 4He and an3He atom,22 (4He)2(3He)2 clusters23 andlarger (4He)m(H2)n clusters.

Note added in proof.F.A. Gianturco and co-workershave recently carried out a discrete variable representation~DVR! calculation for the bound state of4He–para-H2 in theJ50 configuration using the potential of Ref. 2. They findEb520.0523 K and R&513.4 Å.

ACKNOWLEDGMENTS

The authors thank A. Dalgarno, Z. Herman, W. Klem-perer, and B. Whaley for enlightening correspondence and F.Buyvol-Kot for help with the calculations. We are grateful tothe referee for calling attention to our mistake in calculation^R& from the wave functions in Ref. 6.

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627J. Chem. Phys., Vol. 121, No. 2, 8 July 2004 Bound HeH2 halo molecule

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