Polarizability anisotropies of rare gas van der Waals dimers studied bylaser-induced molecular alignmentShinichirou Minemoto, Haruka Tanji, and Hirofumi Sakai Citation: J. Chem. Phys. 119, 7737 (2003); doi: 10.1063/1.1608851 View online: http://dx.doi.org/10.1063/1.1608851 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v119/i15 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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JOURNAL OF CHEMICAL PHYSICS VOLUME 119, NUMBER 15 15 OCTOBER 2003

Polarizability anisotropies of rare gas van der Waals dimers studiedby laser-induced molecular alignment

Shinichirou Minemoto,a) Haruka Tanji, and Hirofumi Sakaib)

Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku,Tokyo 113-0033, Japan

~Received 27 March 2003; accepted 21 July 2003!

The molecular alignment technique utilizing the interaction between the intense nonresonant laserfield and the induced dipole moment is applied to the homonuclear rare gas dimers Rg2 ~Rg5Ar, Kr,and Xe!. The degree of alignment is investigated by Coulomb exploding Rg2 and by measuring theangular distributions of the fragment ions. At the same peak intensity of the laser field, the degreeof alignment!cos2 u @ becomes larger in order of Ar2 , Kr2 , and Xe2 , reflecting the order ofmagnitudes of their polarizability anisotropyDa. By taking I2 molecules as a reference,Da of Ar2 ,Kr2 , and Xe2 are estimated to be 0.5, 0.7, and 1.3 Å3, respectively. ©2003 American Institute ofPhysics. @DOI: 10.1063/1.1608851#

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The rare gas dimers have been studied as model syswhich have van der Waals bonding. An understanding ofweak bonding characteristic of van der Waals dimers isdispensable for the studies of a type of bonding which ofoccurs in many clusters and in transition states and plakey role in determining their electronic and geometricstructures and in chemical reaction dynamics.1,2 So far, theproperties of the neutral rare gas dimers Rg2 have been in-vestigated by measuring the ionization efficiencies orfluorescence from the excited states. One-photon ionizaand resulting photoelectron studies have revealed the iontion potentials of Rg2 .3–5 The resonance-enhanced twphoton ionization and the laser induced fluorescence areplied for the studies of the excitation energies andvibrational constants ofungeradeexcited states.6 Geradeex-cited states are also studied by the resonance-enhancedphoton ionization of Rg2 .7–9

However, despite the long history of the study sincediscovery of rare gas dimers in 1930,10 many of the funda-mental properties such as polarizabilities of Rg2 are still notcompletely understood. The difficulty in studying the phycal and chemical properties arises mostly from the difficuin the preparation and detection of van der Waals dimThe shallow potential of ground state dimers@in the order of100 cm21 ~Ref. 11!# prevents the production of denssamples and requires a highly sensitive technique to chaterize their properties. From the theoretical point of view,shallow potential requires an extensive basis set andelaborate calculation method.12,13

In this paper, we investigate the polarizability anisotroDa[a i2a' of the homonuclear rare gas dimers Rg2 ~Rg5Ar, Kr, and Xe! by the laser-induced alignment techniquThe molecular alignment technique with the intense, nresonant laser field was proposed by Friedrich aHerschbach14 and demonstrated in the adiabatic15 and in the

a!Electronic mail: minemoto@phys.s.u-tokyo.ac.jpb!Electronic mail: hsakai@phys.s.u-tokyo.ac.jp

7730021-9606/2003/119(15)/7737/4/$20.00

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nonadiabatic regimes.16 Since the technique utilizes the polarizability anisotropy interaction between the laser field athe induced dipole moment, the molecular polarizability cbe studied by analyzing the degree of alignment. By taking2

molecules as a reference, the values ofDa are quantitativelyobtained.

The rare gas dimers are produced by a supersonic exsion of a sample gas with the total pressure of 1 atm. Gmixtures of 5% Xe and Kr in Ar are used as sample gasesthe generation of Xe2 and Kr2 , respectively, and pure Ar isused for Ar2 . In these conditions, the production efficiencof Rgn (n>3) is negligible compared with that of Rg2 . Afterpassing through a 0.5-mm-diam skimmer, the collimated mlecular beam is introduced into the interaction region wlaser pulses for the alignment and its probe.

Two laser systems for the alignment and its probe aresame as those used in our molecular orientationperiments.17 For the alignment pulse, we use the fundamenof an injection-seeded Nd:YAG laser~Spectra-PhysicsGCR-130! with the pulse width of;12 ns ~FWHM!. The12-ns-long pulse ensures the adiabatic alignment becauspulse width is much longer than the rotational periods of R2

~in the order of 100 ps!. The alignment pulse is focused bylens (f 5300 mm) to a spot size ofv0

YAG;25mm, yieldingthe maximum peak intensity of 2.631012W/cm2. It is con-firmed that the sample molecules are not ionized byalignment pulses. The probe pulse is delivered from a Ti:sphire amplification system~Spectra-Physics, Super Spitfire!with the pulse width of;45 fs and the center wavelength o;800 nm. The alignment and the probe pulses are spatoverlapped by a dichroic mirror. The probe pulse is focusby the same lens as that used for the alignment pulsespot size ofv0

probe;14mm, giving the peak intensity of 131014W/cm2. The spot size of the probe pulse is carefuadjusted to be smaller than that of the alignment pulseorder to probe only dimers exposed to the alignment puThe femtosecond probe pulse is fired at the peak of the nasecond alignment pulse. The driver for the Ti:sapphire s

7 © 2003 American Institute of Physics

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7738 J. Chem. Phys., Vol. 119, No. 15, 15 October 2003 Minemoto, Tanji, and Sakai

tem serves as the master clock. The temporal overlaptween both pulses is achieved by a digital delay generwith a precision better than60.5 ns.

The fragment ions produced by the probe pulsesmeasured by the velocity map ion imaging technique.18 Theions are accelerated and detected by a microchannel~MCP! backed by a phosphor screen. A homemade posupply provides the MCP with a pulsed high voltage of 1in order to gate the ions with the desired mass-to-charatio. The two-dimensional~2D! ion images on the phosphoscreen are recorded by a CCD camera and are transferrand stored in a personal computer. The 2D images thustained are Abel inverted when the polarization vectorsboth the alignment and the probe pulses are parallel toMCP. The kinetic energy of the fragment ions is calibraton the basis of the precise measurements of their timeflight.

Figure 1 shows typical Abel inverted images of Xe1

under the irradiation of the probe pulses with the polarizatshown by the arrows. The intense signals around the ceare Xe1 ions produced by the ionization of neutral Xe atomWithout the YAG pulse@Fig. 1~a!#, there appears an almoisotropic image. The most prominent ring can be attributedthe Xe11Xe1 channel produced by the Coulomb explosiof transient doubly-charged dimers Xe2

21 as discussed belowWhen the YAG pulses are applied with the polarizati

shown by the arrow@Fig. 1~b!#, the distribution of the Xe1

ions gathers along the polarization direction. The chawith the YAG pulse can be interpreted as the alignmentXe2 along the electric field of the YAG pulse. In fact, whewe rotate the polarization of the YAG pulse by 90°~perpen-dicular to the MCP!, the isotropic image of Xe1 ions almostcompletely disappears and only a circular image peakethe center of the detector is observed. This observation cfirms that neutral Xe2 is aligned perpendicular to the MCP

The thin and thick curves in Fig. 2~a! represent the ki-netic energy distributions obtained by angularly integratthe Abel inverted images of Xe1 ions in Figs. 1~a! and 1~b!,respectively. Apart from strong Xe1 signals peaked at 0 eVand produced from Xe atoms, the distributions have th

FIG. 1. The Abel inverted images of Xe1 produced from Xe2 under theirradiation of the probe pulses~a! without and~b! with the alignment YAGpulses. The polarization directions of the probe and the alignment pulseshown by the arrows. The peak intensity of the alignment pulse is31012 W/cm2.

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peaks at;0.4,;1.2, and;2.4 eV. The 0.4-eV peak is likelydue to the fragment ions from the Xe11Xe channel. Thepeaks at 1.2 and 2.4 eV are reasonably interpreted to beto the fragment ions produced by the Coulomb explosiontransient doubly (Xe2

21) and triply charged dimers (Xe231),

respectively, as shown below. Assuming the equilibriumternuclear distance of the neutral dimer in the ground s@4.4 Å ~Ref. 5!#, the transient Xe2

21 dissociates by the Coulomb explosion to produce two Xe1 fragments with the ki-netic energy of 1.5 eV/fragment, and the transient Xe2

31 dis-sociates to produce Xe1 and Xe21 with the equal kineticenergy of 3.0 eV/fragment. Compared with the measurednetic energy distributions, the 1.2-eV peak can be attributo the Xe11Xe1 channel originating from the transienXe2

21 and the 2.4-eV peak to the Xe11Xe21 channel fromXe2

31 . In fact, the counterpart fragment Xe21 in the Xe1

1Xe21 channel is observed with the kinetic energy centeat ;2.4 eV in the images of Xe21.

Figure 2~b! shows the angular distributions for the Xe1

1Xe1 channel@integrated in the 0.8–1.7 eV range in Fi2~a!# as a function ofu defined in Fig. 1~b!. Without thealignment pulses~thin curve!, the distribution is isotropic.Although slightly anisotropic distributions along the polaization direction are observed for the fragment ions produfrom Xe2

31 as well as Kr2n1 and Ar2

n1 (n52 and 3!, theanisotropy caused by the enhanced ionization19–21 is muchless pronounced compared with that observed in the Clomb explosion of many other diatomic molecules. Espcially, experimental results shown in Fig. 1~a! and Fig. 2~b!present that in the formation of Xe2

21 the constituent atomsin Xe2 behave as if they were independent of each other.less pronounced enhanced ionization might be related toweak bonding characteristics associated with longer inter

re.6

FIG. 2. ~a! The kinetic energy distributions of Xe1 obtained from the Abelinverted images shown in Fig. 1. The thick and thin curves representdistributions with and without the alignment pulses, respectively. The peat 1.2 and 2.4 eV correspond to the Xe11Xe1 and Xe11Xe21 channels,respectively.~b! The angular distributions for the Xe11Xe1 channel@0.8–1.7 eV range in~a!# as a function ofu defined in Fig. 1~b!.

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7739J. Chem. Phys., Vol. 119, No. 15, 15 October 2003 Polarizability anisotropies of rare gas dimers

clear distance of van der Waals dimers. Furthermore,recent experiments reveal that the internuclear distancXe2 does not increase under the present conditions ofwavelength ~;800 nm! and the peak intensity (131014W/cm2) used for the femtosecond probe pulse, thouthat of I2 does increase under the same conditions.22 Thisfinding for Xe2 is also unfavorable for the enhanced ioniztion because its internuclear distance cannot reach the crregion where stronger effect of the enhanced ionizationexpected also for van der Waals dimers.23 A comparativestudy of the Coulomb explosion of Xe2

n1 and I2n1 (n52 and

3! will be reported elsewhere in the near future.22

With the alignment pulse, the angular distribution@thethick curve in Fig. 2~b!# is peaked at 0° and 180°, whichcaused by the alignment of neutral Xe2 dimers. The degreeof alignment is evaluated in terms of the alignment cos!cos2 u @. It is 1/3 for randomly oriented dimers, and 1 foperfectly aligned dimers. The angular distribution for tXe11Xe1 channel yields!cos2 u@50.44560.004 at thepeak intensity of 2.631012W/cm2. At the same peak intensity, !cos2 u @ for the corresponding channels of Kr2 andAr2 are also found to be 0.394 and 0.370, respectively.degree of alignment is enhanced as the mass of the conent atoms increases, i.e., in order of Ar2 , Kr2 , and Xe2 .

The degree of alignment thus obtained is closely relato the polarizability anisotropyDa. When a linear moleculeis exposed to a linearly polarized laser field, the HamiltonH as for the rotational motion is expressed as14

H

B5J22~Dv cos2 u1v'!;

Dv[v i2v' ; v i ,'[a i ,'I

2B, ~1!

whereJ is the rotational angular momentum operator,I is thepeak intensity of the laser pulse,B is the rotational constantanda i anda' are the polarizability components parallel aperpendicular to the molecular axis, respectively. The rotional motion of the molecules is confined in a limited angalong the laser electric field depending on the angular depdent part of the potentialVa(u)[2Dv cos2 u. Given theinitial distribution of the rotational quantum numbersJ’s,!cos2 u @ is determined by the depth ofVa(u).

Since!cos2 u @ is related toVa(u) including Da, thevalues ofDa can be evaluated by comparing the measu!cos2 u @ with that of a reference molecule whoseDa andB are well known. We take I2 molecules as a referenc@Da57 Å3 ~Ref. 24! and B50.037 cm21 ~Ref. 25!#. Thesolid circles in Fig. 3 show!cos2 u @ obtained for the cor-responding channel (I11I1) of I2 as a function of the peakintensity of the alignment pulse. Without the alignmepulse,!cos2 u @50.33~random alignment! and, as the peakintensity increases,!cos2 u @ is enhanced and reaches0.67 at the peak intensity of 2.631012W/cm2. In order torelate !cos2 u @ quantitatively with Va(u), we simulate!cos2 u @ by solving the Schro¨dinger equation with theHamiltonian given by Eq.~1!. Since the initial rotationaltemperatureTrot is not known accurately, the simulationperformed by varyingTrot as the only parameter. The sol

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curves in Fig. 3 show the results of the simulation forTrot

53, 5, 7, and 10 K. The simulated curve at 5 K reproducesthe experimental results best. The rotational temperatureK is consistent with that measured for a molecular besimilar to ours.26

The rotational temperatureTrot of Rg2 is reasonably as-sumed to be the same as that of I2 , i.e., Trot55 K becausethe same pressure~1 atm! of Ar is used as the carrier gas.27,28

However, because of the difference inB, the distribution ofJ’s is different for each dimer and the sameVa(u) does notgive the same!cos2 u @. In order to take account of thedifference in the distribution ofJ’s, we introduce the reducedrotational temperatureY[kBTrot /B. WhenY takes the samevalue, the same magnitude ofVa(u) gives the same!cos2 u @. Considering the difference betweenB of I2 andthat of Xe2 @0.018 cm21 ~Ref. 29!#, one can see that throtational temperatures of 5 K and 10 K give the same valuof Y for Xe2 and I2 , respectively. The alignment cosin!cos2 u @ obtained for Xe2 (0.445) is shown as the dashehorizontal line in Fig. 3. Looking at!cos2 u @ simulated forI2 assumingTrot510 K, the same value of!cos2 u @ isachieved at the peak intensity of 1.031012W/cm2. From theratio of the peak intensities needed to achieve the same vof !cos2 u @, Da of Xe2 is estimated to be 19% that of I2 ,i.e., DaXe2

51.360.3 Å3. In the same way,Da of Kr2 andAr2 are also estimated. Considering the rotational consta@0.029~0.058! cm21 for Kr2 (Ar2) ~Ref. 29!#, the peak inten-sity of 3.5 (1.2)31011W/cm2 is needed for I2 at Trot

56.3 (3) K to achieve the same value of!cos2 u @ as thatobtained for Kr2 (Ar2) at the peak intensity of 2.631012W/cm2. The magnitudes ofDa are thus estimated tobe 0.760.2 and 0.560.2 Å3 for Kr2 and Ar2 , respectively.The magnitudes ofDa thus estimated are compatible witrecent theoretical calculations.12,13 For example,Da of Ar2

and Kr2 are calculated to be 0.3 and 0.6 Å3, respectively. Ourexperimental values are in good agreement with these calated values.

In conclusion, we apply the molecular alignment tec

FIG. 3. Solid circles: The alignment cosine!cos2 u @ measured for I2 as afunction of the peak intensity of the alignment pulse. Solid curves: Tsimulated!cos2 u @ for the rotational temperatures of 3, 5, 7, and 10The simulation at 5 K reproduces the experimental results best. The dashorizontal line represents!cos2 u @50.445 obtained for the Xe11Xe1

channel at the peak intensity of 2.631012 W/cm2.

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7740 J. Chem. Phys., Vol. 119, No. 15, 15 October 2003 Minemoto, Tanji, and Sakai

nique to the weakly bound rare gas dimers Rg2 and measurethe degree of alignment!cos2 u @ for Ar2 , Kr2 , and Xe2 atthe peak intensity of 2.631012W/cm2. By comparing!cos2 u @ with that for I2 molecules, the polarizabilityanisotropiesDa of Ar2 , Kr2 , and Xe2 are estimated to be0.5, 0.7, and 1.3 Å3, respectively. Since the present methutilizes a nonresonant process, it can be a versatile apprto measureDa of any dimer and cluster. Especially foatomic and molecular clusters,Da can serve as a guide fothe determination of their geometric structures whichquite difficult to investigate. The interaction between a lafield and a polarizability can also be applied to extract otproperties of dimers and clusters. In order to evaluateaverage of polarizabilityaave5(a i12a')/3, for example,one can employ the molecular deflection technique witcircularly polarized laser pulse.30 By combining aave withDa obtained from the present technique, the polarizabicomponents can further be extracted which have scarbeen known in dimers and clusters. Furthermore, if we apour molecular orientation technique17 to heteronucleardimers and compare the measured degree of orientationthat of reference molecules, we could evaluate their pernent dipole moments.

The present work is financially supported by the Grain-Aid from Japan Society for the Promotion of Science.

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