High resolution infrared spectroscopy and ab initio calculations of HCN–H 2 /D 2 binarycomplexesD. T. Moore, M. Ishiguro, L. Oudejans, and R. E. Miller Citation: The Journal of Chemical Physics 115, 5137 (2001); doi: 10.1063/1.1394743 View online: http://dx.doi.org/10.1063/1.1394743 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/115/11?ver=pdfcov Published by the AIP Publishing

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JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 11 15 SEPTEMBER 2001

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High resolution infrared spectroscopy and ab initio calculationsof HCN–H2 ÕD2 binary complexes

D. T. Moore,a) M. Ishiguro,b) L. Oudejans, and R. E. MillerDepartment of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599

~Received 10 May 2001; accepted 25 June 2001!

High-resolution infrared laser spectroscopy has been used to study HCN–H2 and HCN–D2

complexes in the gas phase. The experimental results are compared withab initio calculations thatare also reported here. The latter calculations reveal two prominent minima on the potential surface,one corresponding to a ‘‘T-shaped’’ complex with the H2 at the hydrogen end of the HCN and theother a ‘‘linear’’ complex with the H2 H-bonded to the nitrogen. The latter minimum is the globalminimum on the surface, in agreement with the fact that this structure is observed experimentally forboth o-H2 andp-D2. © 2001 American Institute of Physics.@DOI: 10.1063/1.1394743#

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INTRODUCTION

The spectroscopy of weakly bound complexes hemerged as a powerful approach for the quantitative studintermolecular forces. The tremendous advances in reyears have provided detailed structural and dynamical inmation for a wide range of species.1 In parallel with theexperimental advances, theoretical methods have develto the point where exact quantum methods can now be uto calculate the spectra of many of these complexes direfrom the potential energy surface.2 Due to the weakness othe bonds associated with these complexes, the intermollar vibrational motion is often highly anharmonic and tassociated spectra contain detailed information on the potial surface.

As a part of our ongoing study of cluster growth adynamics in liquid helium nanodroplets~see companionpaper!3 we carried out the present high resolution gas phstudy of the binary H2/D2–HCN complexes. Complexecontaining hydrogen are particularly interesting becauselow mass of the H2 leads to large zero point energies ahence weak binding. A few complexes containing hydroghave been studied previously, including the detailed specscopic and dynamical studies of H2–HF ~Refs. 4–7! andH2–HCl ~Ref. 8! complexes~as well as various isotopicvariations!. In all of these cases, the H2 is bound to the hy-drogen end of the HX~X5F, Cl! molecule. The corresponding ‘‘T-shaped’’ configuration optimizes the electrostatic iteraction of the molecules, in that it is favorable for both tdipole–quadrupole and quadrupole–quadrupole interactiThis is most vividly illustrated in the case of H2–HF, whereonly the ortho complex is observed, given that these elecstatic interactions are missing for para hydrogen (J50),where the quadrupole moment is averaged to zero. In ctrast, the lower zero point energies associated withD2–HF and H2–HCl complexes make both the ortho an

a!Author to whom correspondence should be addressed. Electronicremiller@unc.edu

b!Department of Chemistry, Faculty of Science, Kyushu UniversFukuoka, 812-8581, Japan.

5130021-9606/2001/115(11)/5137/7/$18.00

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para complexes sufficiently stable to be observexperimentally.6,8 Detailed theoretical studies have also bereported for the H2,D2–HF systems, including a quantitativab initio potential surface, detailed bound state calculatiophotofragment final state distributions and dissociatenergies.9–14 Infrared spectra have also been reported forhydrogen-bonded CO-H2 ~Refs. 15–18! and H2O–H2 ~Ref.19! complexes, in both cases the oxygen acting as the proacceptor.

Our first observation of the HCN–H2 complex was inhelium droplets, as presented in a companion paper.3 Thecorresponding results indicated that ortho-H2 and para-H2bind at opposite ends of the HCN molecule. In order to beunderstand the helium results, we subsequently conduthe gas phase infrared~IR! spectroscopy experiments presented in the current work. Most recently, Ishiguroet al.measured the microwave spectra of these complexes~alsopresented in a companion paper20!, which also indicate thatortho-H2 and para-H2 bind at opposite ends of the HCN. Ithe current IR study, only the HCN–oH2 complex was ob-served.Ab initio calculations are presented that help to uderstand the preference for forming the ortho-H2 complex.The results agree with previous DFT calculations by Welowski and Weber,21 that yielded a linear minimum with theH2 at the N-end of HCN. In addition, we find a ‘‘T-shapedminimum on the potential energy surface, with the H2 bind-ing at the H-end of the HCN.

EXPERIMENTAL METHOD

Rotationally resolved infrared spectra have beentained for HCN–H2 and HCN–D2 in the gas phase using thoptothermal detection method.22,23 In both cases, the fundamental C–H stretching vibration of the HCN~near 3300cm21! was excited. The frequency region of interest wascessed using an F-center laser, operating on the RbCcrystal ~#3! and pumped by a krypton ion laser. A detailedescription of the tuning and calibration of this laser systis given elsewhere.23 In the present case, the absolute ca

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bration of the spectrum was established using theR(0) tran-sition of the HCN monomer, which was also observed inspectrum.

There are two basic configurations for the optothermmethod that are typically used to record infrared specWith the bolometer positioned directly in the path of tmolecular beam, laser induced signals from weakly boucomplexes normally appear with the opposite phase to thof stable monomers, since the complexes often dissocbefore reaching the detector. We have used this ‘‘flop omode of operation extensively to record spectra of macomplexes.24–26 For the purposes of studying the state-state dissociation dynamics of other systems,27,28 we havealso developed an apparatus that works in the ‘‘flopmode,29,30where the bolometer is placed off of the molecubeam axis to detect the fragments that recoil from the mlecular beam upon laser induced vibrational predissociaof the complex. This method has the advantage that thelometer is not exposed to the direct molecular beam fluxthus maintains its high sensitivity throughout the experimeIn particular, the ‘‘flop-out’’ method is problematic since hydrogen condenses on the bolometer~operated at 1.6 K!, re-

FIG. 1. Schematic structures representing the two minima found byab initiocalculations. Energies, frequencies, and structural parameters are surized in Tables I–IV.

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ducing its sensitivity during the course of the day. As asult, the ‘‘flop in’’ mode was used in all of the experimenreported here, with the bolometer positioned 4° from the mlecular beam axis.

A spherical multipass cell27,31 was used to optimize theexcitation efficiency of the molecules in the beam. Since~approximately 60! laser crossings are all at slightly differenangles with respect to the molecular beam, residual Dopbroadening is observed in the spectra. Under these conditthe instrumental linewidths were approximately 20 MHsubstantially greater than the free running linewidth of tlaser~approximately 2 MHz!. Two electrodes placed on ether side of the photolysis volume can be used to apply aelectric field to the complex. Large electric fields can be usto orient the complexes in the laboratory frame using whasometimes referred to as the ‘‘brute force’’ method.32,33 Un-der these conditions the normal spectrum of a free rotorlapses into a group of closely spaced ‘‘pendulatransitions34,35 near the vibrational origin. This electric fieldinduced ‘‘Q branch’’ is generally stronger than the zero fieP- or R-branch transitions, facilitating the initial spectrsearch. Once these transitions are found, the electric fieldbe switched off and a field free spectrum recorded.

The complexes of interest were formed by expandingas mixture composed of 0.5% of HCN and 25% hydrogor deuterium in helium through a 50mm diameter, roomtemperature nozzle maintained at a total pressure of apprmately 500 kPa. The expansion was sampled by a 400mmdiameter skimmer and the resulting molecular beam wasther collimated by a second, 2 mm diameter skimmer.noted above, the photofragments resulting from vibratiopredissociation of the complexes were detected by placthe bolometer 4° from the molecular beam axis. Whenethe laser was tuned through a transition associated withcomplex, photofragments were detected. The techniqumade background free by modulating the laser and usphase sensitive detection of the bolometer signal.

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TABLE I. Ab initio energies for hydrogen-bonded structure1 in Fig. 1.

Basis set

MP2 energies~hartree!De

~cm21!HCNa H2a H2–HCN

6-31111G(2d,2p) 293.222 578 21.162 829 294.385 974 124.46-31111G(2df,2pd) 293.250 517 21.164 692 294.415 804 130.66-31111G(3d f ,3pd) 293.254 614 21.164 992 294.420 268 145.3

aCounterpoise corrected value~see text!.

TABLE II. Ab initio frequencies and selected structural data for structure1.

Basis setRHB

~Å!aRCOM

~Å!aC–H stretch

~cm21!Redshift~cm21!b B ~cm21!c

6-31111G~2d,2p! 2.497 4.126 3459.16 4.61 0.38636-31111G~2df,2pd! 2.474 4.104 3473.44 6.39 0.38946-31111G~3df,3pd! 2.440 4.071 3458.53 6.47 0.3941

aAs indicated in Fig. 1 for structure1.bFrom free HCN optimized with the same basis set.cRepresents average of calculatedB andC rotational constants.

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AB INITIO CALCULATIONS

In parallel with the experimental work,ab initio calcu-lations were performed usingGAUSSIAN 98 ~Ref. 36! on anIBM SP2 platform. Geometry optimizations were performat the MP2 level from various asymmetric starting structurwith the H2 placed near either end of the HCN. The following basis sets were used: 6-31111G~2d,2p!, 6-31111G~2df,2pd!, 6-31111G~3df,3pd!. In all cases only thetwo minima shown schematically in Fig. 1 where found. Fquency calculations were performed for the final geometrand no imaginary frequencies were found. The binding engies (De) were computed by performing counterpoise crected partial optimizations for the monomer units in tfollowing fashion. Starting from the optimized complestructure, the electrons and nuclei of the other monomerwere removed, while leaving the basis functions presThen a partial geometry optimization was performed leavthe internal degrees of freedom of the remaining monomunit as variables. This treatment was used to correctbasis-set superposition error.37

All calculations with the H2 near the H-end of the HCNoptimized to the T-shaped geometry indicated in Fig. 1~a!.The MP2 energies for this structure and the correspondcounterpoise corrected monomer energies are presenteTable I. The frequency data and structural parameterspresented in Table II. All calculations with the H2 near theN-end of the HCN optimized to the linear geometry shoin Fig. 1~b!. The MP2 energies for this structure and tcorresponding counterpoise corrected monomer energiepresented in Table III. The C–H stretching frequencies astructural parameters are presented in Table IV. Thequency shifts due to complex formation were calculatedthe CH stretch using the frequencies~not counterpoise corrected! from calculations on free HCN, optimized with thsame basis set as the complex. These results will becussed in detail below, but for now we simply point out ththe linear geometry~structure2! is more strongly bound thanthe T-shaped~structure1! by ;25 cm21 at all basis sets.

TABLE III. Ab initio energies for structure2 in Fig. 1.

Basis set

MP2 energies~hartree!De

~cm21!HCNa H2a HCN–H2

6-31111G~2d,2p! 293.222 686 21.162 841 294.386 231 154.56-31111G~2df,2pd! 293.250 570 21.164 701 294.416 004 160.96-31111G~3df,3pd! 293.254 601 21.164 965 294.420 355 173.2

aCounterpoise corrected value~see text!.

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EXPERIMENTAL RESULTS

The search for the gas phase spectrum of HCN–H2 wasstraightforward, given that the shift of the C–H vibrationexpected to be small. It was made even easier by carryingthe first searches with a strong electric field applied tointeraction region, thus enhancing the transition intensitying the pendular state method.34,35 Figure 2~a! shows a scanof the region near the ‘‘free’’ C–H stretching region of HCNin the presence of an 18.9 kV/cm electric field. Only twbands are seen in this spectrum; the lower frequencycorresponds to the pendular spectrum of the ‘‘free’’ C–stretch of the linear HCN dimer. The second band, appeaat somewhat higher frequencies, only appeared when H2 wasadded to the gas mixture and is assigned to the HCN–2

complex. Extensive searches were carried out for otHCN–H2 isomers without success.

Having located the pendular state spectrum, a morefinitive assignment of this band to the HCN–H2 complex canbe made by recording the corresponding zero field spectrThis spectrum is shown in Fig. 2~b!, with the closely spacedtransitions to the low frequency side of this spectrum arisfrom the ‘‘free’’ stretch of the HCN dimer, discussed in detapreviously.26 The transition marked with an asterisk is thR(0) transition of the HCN monomer, located

FIG. 2. Experimental spectra of the C–H stretch vibration in tHCN–~ortho!H2 binary complex~a! with 18.9 kV/cm electric field appliedand ~b! zero field condition. The two transitions in~a! are electric fieldinduced ‘‘pendular state’’ transitions near the vibration origins of then1

~‘‘free’’-CH stretch! HCN dimer and the HCN–~ortho!H2 complex. The fieldfree spectrum of the HCN–~ortho!H2 in ~b! consists of regularP and Rbranches, in overlap with theR branch of then1 HCN dimer at lowerfrequencies.

TABLE IV. Ab initio frequencies and selected structural data for structure2.

Basis setRHB

~Å!aRCOM

~Å!aC–H stretch

~cm21!Redshift~cm21!b B ~cm21!c

6-31111G~2d,2p! 2.853 3.787 3462.59 1.41 0.42946-31111G~2df,2pd! 2.848 3.781 3478.84 1.00 0.43046-31111G~3df,3pd! 2.813 3.747 3464.36 0.63 0.4366

aAs indicated in Fig. 1 for structure2.bFrom free HCN optimized with the same basis set.cRepresents average of calculatedB andC rotational constants.

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3314.412 43 cm21.38 The remaining transitions are assignto the HCN–H2 complex, as shown in the figure. Tablecontains a list of the transition frequencies, along withcorresponding residuals obtained from fitting the spectruma simple linear rotor energy level expression. The fit todata is clearly excellent and the resulting molecular constare summarized in Table VI.

It is interesting to note that, as illustrated in the previostudies of H2–HCl ~Ref. 8! and HF–H2,

4 a T-shaped com-plex involving ortho-H2 would give rise to aP←P bandwith a strongQ-branch. Based on the fact that we only oserveP andR branch transition in the present spectrum,presume that the band isS←S, excluding the T-shaped isomer as the source of this spectrum. It is therefore temptin analogy with the H2–HCl results,8 to attribute this spec-trum to the para-H2–HCN hydrogen-bonded complex, whicshould produce aS←S band. However, the small redshiobserved for this band@0.34 cm21 from HCN monomer at3311.48 cm21 ~Ref. 38!# indicates that the CH stretch is onweakly affected by the hydrogen, suggesting that the H2 isbound at the nitrogen end of the HCN monomer. Furthmore, since we observe only one hydrogen related banthe spectrum, it is reasonable to expect that it is associwith the more abundant spin-species~ortho-H2!, particularlysince it interacts more strongly with the HCN than para-H2,in analogy with the HX systems discussed above. Thesesiderations, along with the computational results presenabove and discussed below, lead us to conclude that theperimental spectrum corresponds to the ‘‘linear’’ HCNortho-H2 complex shown in Fig. 1~b!.

TABLE V. A summary of observed transitions, frequencies, and residufrom fit ~Table VI! to a linear rotor spectrum for the HCN–~ortho-H2! com-plex. All frequencies are in cm21.

Transition Observed ~Obs.–Calc.!

P(3) 3308.5958 20.000 49P(2) 3309.4286 0.000 16P(1) 3310.2801 20.000 16R(0) 3311.9972 0.000 01R(1) 3312.8442 0.000 15R(2) 3313.6742 20.000 15R(3) 3314.4839 0.000 04

TABLE VI. A summary of molecular constants for HCN–~ortho-H2! and–~para-D2!

a. All constants are in cm21.

HCN– (o-H2)MW data for

HCN– (o-H2)b HCN– (p-D2)

B9 0.430 65~24! 0.430 289 0.266 27~24!B8 0.429 32~16! 0.266 00~14!D93104 4.20~25! 4.085 0.92~17!D83104 3.38~10! 0.87~7!n0 3311.1399~5! 3311.1228~7!Redshiftc 0.3369 0.3541

aUncertainties in parentheses correspond to one standard deviation~1s!from the least squares fit in the last digit~s!.

bReference 20.cFrom HCN monomer at 3311.476 83 cm21 ~Ref. 38!.

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Further support for this assignment comes from thetational constants determined from the fit. First we note tthe rotational constant decreases slightly~0.3%! upon vibra-tional excitation. A somewhat larger percentage decreasobserved in the case of the HCN monomer38 ~0.7%!, whichcan be explained as being due to the lengthening of thebond upon vibrational excitation. In contrast, vibrational ecitation of a hydrogen-bonded H–X vibration generally leato an increase in the rotational constant due to the cosponding increase in the strength~and hence contraction! ofthe hydrogen bond. Indeed, the rotational constantH2–HF, where the H2 binds to the H atom of HF, increaseby 2.2% in the excited vibrational state.4 Thus the smalldecrease in the rotational constant again suggests that th2

is remote from the hydrogen on HCN.It is interesting to note that the centrifugal distortio

constant is quite large for this complex, indicating that thydrogen molecule is quite weakly bound to the HCN monmer. In fact, the van der Waals stretching frequencyv esti-mated in the pseudodiatomic approximation, usingrelation39

v5A4B3

D

is only 27.6 cm21. If we now assume that the assignmentthe spectrum to a linear complex is correct, we can usefollowing equation for a ‘‘rod–ball’’ system to determine thintermolecular distance:40

I complex5McRi21

~^cos2 u&11!

2I HCN,

Mc5mHCNmH2

mHCN1mH2

,

where I HCN and I complex are the moments of inertia of freHCN and the complex, respectively,Ri is the distance be-tween the centers of mass of the HCN and H2, Mc is thereduced mass of the complex as defined above, and^cos2 u&is the expectation value of the square of the cosine ofHCN bending angle, determined by Ishiguroet al. to be32.65°.20 The distance determined in this fashion~using theB constant given in Table VI! is 3.961 Å.

Isotopic substitution is a standard approach for locatthe positions of certain atoms in a molecule and the abstructural assignment can be confirmed by studying the strum of the corresponding HCN–D2 complex. Here againonly a singleS←S band was observed, as shown in Fig.The correspondingR andP branch transitions are indicatein the figure. The transition frequencies are listed in TaVII and the corresponding molecular constants are sumrized in Table VI. This band is assigned to the HCN–pD2

complex by analogous arguments to those used for the orH2 complex.

Comparing the resulting constants with those for tHCN–oH2 complex reveals some interesting points. Thetermolecular bond length~calculated as above! is 3.911 Å,significantly shorter than for theoH2 complex. Also, the vi-brational redshift of HCN–pD2 is somewhat larger than fo

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the H2 complex. Both of these effects are consistent withlower zero-point energy for thepD2 complex. Furthermorethe centrifugal distortion constant is a factor of 5 smalthan for the H2 complex, indicative of the stronger bindinfor the pD2 complex. In fact, the intermolecular stretchinfrequency for HCN–pD2 ~estimated as above! is 28.6 cm21,which is larger than for HCN–oH2; note that in the har-monic oscillator limit this stretching frequency would bsmaller by a factor of (2)1/2 for HCN–pD2. Clearly, thepD2

andoH2 complexes sample different regions of the potenenergy surface. In light of this, we made several attemptconstruct effective one-dimensional~1D! potentials thatcould simultaneously fit theB andD constants for both theoH2 and pD2 complexes. Our lack of success in these edeavors led us to conclude that a multidimensional modeneeded to quantitatively describe the vibrational dynamicthese systems.

It is now clear that the observed spectra arise from lincomplexes of HCN and ortho-H2 ~or para-D2!, bound at theN-end of the HCN. The question that remains is why tpara-H2 complex was not observed. Although para-H2 ispresent in the gas mixture at 1/3 the abundance of ortho2,we do not believe this difference is sufficient to accountthe absence of this complex in the spectrum, particulasince the missing species in the HCN–D2 case is the moreabundant one~2:1 ortho:para!. @Recall that the spin designa

FIG. 3. Experimental spectrum of the C–H stretching vibration inHCN–~para!D2 binary complex. The spectrum of the HCN–~para!D2 com-plex consists of regularP andR branches, in overlap with theR branch ofthe n1 ~‘‘free’’ stretch! HCN dimer at lower frequencies.

TABLE VII. A summary of observed transitions, frequencies and residufrom linear rotor fit~Table VI! to the spectrum for the HCN–~para-D2!. Allfrequencies are in cm21.

Transition Observed ~Obs.–Calc.!

P(3) 3309.5336 0.000 02P(2) 3310.0601 20.000 05P(1) 3310.5906 0.000 05R(0) 3311.6546 0.000 20R(1) 3312.1832 20.000 20R(2) 3312.7080 0.000 14R(3) 3313.2256 20.000 11

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tions for the boson species D2 ~J odd5para,J even5ortho!are opposite to those for H2.# One possibility is that the paraH2 complex undergoes rapid vibrational predissociation, athe transitions are simply too broad to observe. This is ctainly a reasonable explanation, particularly if the para-H2 isbonded to the hydrogen end of the HCN and thus morerectly coupled to the C–H stretching vibration. Other posible explanations for why the para-H2 complex is missingfrom the spectrum will be explored in the next section.

All of the transitions observed for HCN–pD2 andHCN–oH2 were found to have the same Gaussian linewias the HCN monomer, namely 20 MHz. This can be attruted to Doppler broadening associated with the sphermultipass cell. Since no additional broadening is obserdue to vibrational predissociation of the complex in the ecited vibrational state, the lower limit on the predissociatilifetime is estimated to be 160 ns. This long lifetime is cosistent with the fact that the H2 is remote from the C–Hstretching coordinate, making vibrational predissociatslow.41

COMPARISON OF EXPERIMENT AND AB INITIOCALCULATIONS

The experimental results presented above can be jufied in terms of theab initio calculations, given that~for allbasis sets! the well depths (De) are larger for the linearstructure compared to the T-shaped. Indeed, for the larbasis set the well depths are 173.2 cm21 and 145.3 cm21,respectively. Therefore, it is perhaps not surprising thatobserve the formation of the nitrogen bound complex instof the hydrogen bonded one. However, in view of the larzero-point energies associated with these complexes andsignificant difference between the two nuclear spin speciehydrogen, this simple argument cannot explain everythwe observe. The most important effect is that, as is oftencase in complexes with H2,

42 the anisotropy of the intermolecular potential is not strong enough to significantly mix trotational states of the hydrogen. Thus, for HCN–H2, thepara and ortho complexes have the hydrogen in essentpure j 50 and j 51 states, respectively. To a good appromation, therefore, the effective intermolecular potentialspara and ortho hydrogen can be obtained by averagingthe appropriate free rotor wave function for the hydrogecalculations of this type are presented in the accompanypaper.3 The implications of this averaging are that thej 50hydrogen is completely delocalized in angle at eitherhydrogen or nitrogen end of the HCN molecule, behavessentially like a rare-gas atom. For thej 51 species, thepresence of the HCN splits the degeneracy of the free-rM-states, allowing different projections~k561 and k50!of the H2 angular momentum on the HCN molecular axThe observation of aS←S band for the HCN–oH2 complexindicates that it is in thek50 case~the k561 case givesrise to P←P bands6,8!, so the appropriate free-rotor wavfunction for the averaging is cos(uH2

). This wave functionhas its highest density in the ‘‘linear’’ structure predictedbe the minimum at the N-end of the HCN, and a node wh

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the H2 axis is perpendicular to the HCN. Thus the rotationaveraging will result in a stronger interaction than for thej50 species.

The absence of the para-H2 complexes in our infraredexperiment can now be understood by taking into accothe mechanism of complex formation in the free jet expsion. Close to the nozzle, in the warm part of the expanscomplexes are formed by three-body collisions and thcooled by two-body collisions. However, these two-bocollisions also tend to replace less stable complexes by mstrongly bound ones. For example, if a para-hydrogen cplex ~weakly bound! collides with an ortho-H2 molecule, it isenergetically favorable to form an ortho complex~morestrongly bound! and eject the para-hydrogen. Since theremany two-body collisions downstream of where the coplexes are formed, this exchange process is expected to owith high efficiency at the relative concentrations of orthand para-hydrogen and -deuterium considered here. It isteresting to note that in their recent microwave study, Ishuro et al. did observe the hydrogen-bondedpH2–HCN com-plex, although the intensity was a factor of 5 lower thanHCN–oH2, instead of the factor of 3 that is expected frothe normal abundances.20 Since the exchange process is dpendent on experimental factors such as gas composistagnation pressure, and nozzle geometry, the ratio couleven larger in our case, making the para-H2 signals simplytoo small to detect.

Let us now consider the calculated vibrational frequendata. Although the magnitudes of the vibrational frequencare consistently overestimated byab initio ~harmonic! calcu-lations, relative frequency shifts are often more faithfureproduced. For the largest basis set, the calculatedquency shift is approximately an order of magnitude larfor the T-shaped, H-bonded complex than for the linear oas expected. Also, the agreement between the calculaand the experiment improves with the size of the basisThe best calculations give a shift of 0.63 cm21, comparedwith the experimental values of 0.337 cm21 and 0.354 cm21

for HCN–~ortho!H2 and HCN–~para!D2, respectively. Com-paring rotational constants and bond lengths is more plematic, given that the experimental values represent vibtional averages, while the calculations are for the minimenergy structures. Nevertheless, the agreement is reasonthe best basis set giving B50.4366 cm21 forHCN–~ortho!H2, compared with the experimental grounstate value ofB50.430 71 cm21. A somewhat larger value isindeed expected from the calculation, since vibrational avaging of an anharmonic potential will lengthen the van dWaals bond, making the experimental value smaller.

It is interesting to examine the physical reasons forlinear N-end bonding of the HCN–H2 complex, in contrastwith the T-shaped, hydrogen-bonded H2–HF complex. Aspointed out in the introduction, the T-shaped structure ofortho-H2–HF complex is favorable for both the dipolequadrupole (d–q) and quadrupole–quadrupole (q–q) inter-actions. Since these electrostatic interactions are also dnant in HCN–H2, a linear geometry seems surprisinespecially since it involves a repulsive interaction betwethe quadrupoles. The reason can be seen qualitatively f

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the relative magnitudes of the electrostatic moments of Hand HF. The calculated@MP2/6-31111G~3df,3pd!# dipolemoments~atomic units! are 0.718 and 1.190 for HF anHCN, respectively, while the quadrupole moments are 1.7and 1.669, respectively. Since the dipole–quadrupole termrelatively larger for HCN–oH2, the larger angular factor inthe linear geometry43 compensates for the repulsivquadrupole–quadrupole term. Using the calculated momethe electrostatic contribution to the intermolecular interactcan be evaluated for the two minimum structures usingstandard equations for thed–q and q–q interactions.43 Atthe distances corresponding to the minima, these equatgive 271.1 cm21 for structure1 ~4.07 Å! and 284.8 cm21

for structure2 ~3.74 Å!, respectively. Thus the electrostatinteraction accounts for approximately half of the total cculated well depths, and favors the observed experimegeometry. The remainder of the stabilization in the two weresults from competition between repulsive interactions ainduction/dispersion forces, the latter being always attrtive. For HCN, the dispersion interaction, which dependscharge density, should be stronger for the nitrogen lonethan for the strongly polarized H atom, further favoring tN-end geometry.

SUMMARY

We have presented the first infrared gas phase spectthe complexes formed between H2/D2 and HCN. The obser-vation ofS←S bands in both cases, which are only slightredshifted from the free C–H stretch of HCN, leads to tconclusion that the most stable complexes have linHCN– (J51)H2/D2 structures. This is in agreement with thab initio calculations reported here, which in addition revea somewhat shallower well at the hydrogen end, correspoing to a T-shaped complex. In spite of extensive searchesfind no evidence for the formation of complexes with tH2/D2 at the hydrogen end of the HCN. The absence of paH2 complexes is most likely due to thermodynamically fvored exchanges with more strongly bound ortho-H2 com-plexes in the free jet.

In part, our motivation for studying this system in thgas phase is related to an accompanying paper, which dwith the formation of hydrogen–HCN complexes in liquhelium nano-droplets.3 The interest in hydrogen-containincomplexes in helium arises because they are sufficieweakly bound to consider the possibility that the helium svent modifies the structure of the complex. Having accurmolecular constants for the gas phase complex is clearlyportant for determining such effects. The results obtainhere will be compared with the helium droplet experimein the following paper.

ACKNOWLEDGMENTS

This work was supported by the National Science Fodation ~CHE-99-87740!. The authors also acknowledge thdonors of the Petroleum Research Fund, administered byAmerican Chemical Society, for partial support of this rsearch. One of the authors~M.I.! thanks the financial suppor

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5143J. Chem. Phys., Vol. 115, No. 11, 15 September 2001 Infrared spectroscopy of HCN–H2 /D2 complexes

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of The Japan Society for the Promotion of Science. The coputer time was provided by the North Carolina Supercoputing Center.

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