DOI: 10.1002/cphc.200600166

New Experimental and Theoretical Results forArgon Broadening and Shift of HCO+ RotationalLinesGiovanni Buffa,[b] Luca Dore,[c] Francesca Tinti,[c] and Markus Meuwly*[a]

1. Introduction

Collisional broadening and the shift of rotational lines of mo-lecular ions are the subject of a number of studies because re-liable values for such parameters are of particular importancefor the interpretation of radio astronomical data.[1–8] HCO+ col-liding with Argon is the most studied case, both experimental-ly and theoretically. However, an important drawback for theo-retical calculations is the absence of a sufficiently reliable inter-action potential valid at short interatomic distances. The theo-retical models used until now, namely capture theory and sem-iclassical approximations, include only the well-known longrange electrostatic part of the interaction in the calculations.This yields quite reliable pressure broadening values, but is in-accurate for the pressure shift calculations.In the capture approach,[9–11] attention is focused on the or-

bital dynamics and on following whether the centrifugal barri-er is crossed and capture occurs. For the rotational state of theion two opposite and extreme possibilities are considered: ifcapture occurs the outgoing rotational state is assumed tohave no correlation with the ingoing one, while no relaxationat all is assumed in the opposite case. The real part of thecross-section, giving rise to pressure broadening, is the capturecross-section sc ¼ pr2c , where rc is the capture radius. Theimaginary part of the cross-section, giving rise to pressureshift, cannot be calculated within such a theoretical frame-work.The semiclassical approximation uses classical dynamics to

describe the orbital motion and quantum mechanics for the in-ternal degrees of the colliding molecules.[12–17] Within theimpact approximation,[18] the collisional relaxation of a line isdescribed by the efficiency function P given in Equation (1).For a line f !i :

P ¼ 1�hijSjii hf jS1rjf i ð1Þ

where S, defined in Equation (2) is the scattering matrix,

S ¼ O exp � 1�h

Zþ1

�1

dteH0 t=�hVðtÞe�H0 t=�h

0@

1A, ð2Þ

H0 is the Hamiltonian of the internal degrees of freedom, V isthe collisional interaction, and O is the time ordering operator.

The linewidth G and lineshift s are related to the real andimaginary parts of the cross-section s and of the efficiencyfunction P via Equations (3) and (4):

G� is ¼ n

Z1

0

f ðnÞnsdv, ð3Þ

s ¼Z1

0

2pbPðbÞdb, ð4Þ

where n is the Argon density, v and b are the relative velocityand the impact parameter, respectively, of the colliding parti-cles, and f(v) is the Maxwell velocity distribution.

[a] Prof. M. MeuwlyDepartment of Chemistry, University of BaselKlingelbergstrasse 80, 4056 Basel (Switzerland)Fax: (+41)61-267-3855E-mail : m.meuwly@unibas.ch

[b] Prof. G. BuffaIPCF-CNR, Largo Pontecorvo 3, 56127 Pisa (Italy)

[c] Prof. L. Dore, F. TintiDipartimento di Chimica “G. Ciamician”, Universit= di BolognaVia Selmi 2, 40126 Bologna (Italy)

An experimental and theoretical study of the pressure broadeningand the pressure shift of three HCO+ rotational lines (j=4 !3,5 !4 and 6 !5) perturbed by collisions with Ar is presented. Themeasurements are carried out at 77 K and are compared toclose-coupling calculations performed on an accurate potentialenergy surface for the Ar–HCO+ interaction extending from smallto very large separations between the ion and the perturber. For

the pressure broadening, agreement between experiment andtheory is satisfactory for both close-coupling and semiclassicalcalculations. For the pressure shift, however, close-coupling calcu-lations are superior. The results agree with experiment in signand order of magnitude, while semiclassical calculations are in-accurate for the shift of the presently studied lines because theyneglect the contribution of strong collisions.

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The semiclassical approximation treats strong and weak col-lisions differently. For weak collisions, at large impact parame-ters, a lowest order (second-order) perturbative expansion ofEquation (2) is used to calculate Pweak. For strong collisions, atsmall impact parameters, the outgoing rotational state of theabsorber is assumed to be completely uncorrelated to the in-going one. This yields Equations (5) and (6):

Re Pstrong ¼ 1, ð5Þ

Im Pstrong ¼ 0: ð6Þ

The interpolation between strong and weak collisions is per-formed either by a cutoff[12,13] or by the exponential smooth-ing[14,17] which is obtained by omitting the time ordering oper-ator O in Equation (2). The latter of the two possibilities allowsfor higher order terms partially, even if not exactly, to be takeninto account and is widely used in recent semiclassical calcula-tions. It yields an efficiency function P ¼ 1� e�P

weak

having theexpected trend in both limits of large and small impact param-eters.The orbital motion can be described either by the assump-

tion of straight line trajectories at constant velocity[6] or by themore accurate numerical integration of the classical motion.[8]

In the latter case, the semiclassical treatment is more accuratethan the capture approach: strong collisions are treated in thesame way by the two methods, while weak collisions arebetter described by the semiclassical perturbative calculationsrather than by the assumption of no relaxation at all of thecapture method.As a consequence of the long-range interaction due to the

charge of the ion, the relaxation is effective even for distantcollisions and the transition from weak to strong collisionsoccurs at large impact parameters. At T=77 K the Langevincapture radius rc for HCO

+-Ar collisions is 8.7 A.[8] Hence, cap-ture and semiclassical calculations are both very weakly affect-ed by the short range part of V. However, the description ofstrong collisions by Equation (1) is questionable, particularly ifthe imaginary part, Equation (6), is considered.Quite good agreement is found between semiclassical calcu-

lations and measurements at 77 K for the pressure broadeningof the rotational lines j=1 !0, 2 !1, and 4 !3 of HCO+ byArgon, where j is the angular momentum of the ion.[6,8] For thepressure shift, good agreement is found for the j=1 !0 line,which is the only pressure shift observed up to now in thespectroscopy of ions. It is a particularly favorable case for ap-plying semiclassical calculations, because, contrary to linescharacterized by higher j values, the large contribution of dis-tant collisions reduces the influence of strong collisions to thepressure shift.Herein we report new experiments for both broadening and

shift of rotational lines from collisions between Argon andHCO+ for higher j values. Understanding the broadening andparticularly the shift of the j=4 !3, 5 !4, and 6 !5 lines islikely to be affected by the assumptions of both the capturemodel and the semiclassical treatment. Indeed, the capturemodel does not allow shift calculations while semiclassical shift

calculations are quite accurate when the main contributioncomes from weak collisions but may be not reliable in the op-posite case. For the HCO+-Ar system they are reliable for theline j=1 !0 but not for the higher rotational lines. The shiftcalculations are more difficult than for the width due also tothe fact that while the width is essentially a sum of the colli-sion effects on the two states involved in the line, the shift isessentially a difference of two effects which are almost equalat high j. Thus, close-coupling calculations on a new 2-dimen-sional potential energy surface (PES) for the Ar–HCO+ complexextending from very short to very long distances are used tocalculate the line broadening and the line shifts. These resultsare compared to estimates from semiclassical calculations.

Experimental Section

The j=4 !3, 5 !4, and 6 !5 rotational lines of HCO+ are observedwith a frequency-modulated millimeter-wave spectrometer equip-ped with a negative glow discharge cell made of a Pyrex tube,3.25 m long and 5 cm in diameter, with two cylindrical hollow elec-trodes 25 cm in length at either end.[19] The radiation source is afrequency multiplier, consisting of a doubler in cascade with a mul-tiplier (RPG—Radiometer Physics GmbH), which is driven by aGunn oscillator working in the region 81–115 GHz (J. E. CarlstromCo). Two phase-lock loops allow the stabilization of the Gunn oscil-lator with respect to a frequency synthesizer, which is driven by a5 MHz rubidium frequency standard. The frequency modulation ofthe radiation is obtained by sine-wave modulating at 16.66 kHzwith low distortion (total harmonic distortion less than 0.01%) thereference signal of the wide-band Gunn-synchronizer. The signal,detected by a liquid-helium-cooled InSb hot electron bolometer(QMC Instr. Ltd. type QFI/2), is demodulated at 2-f by a lock-in am-plifier.

HCO+ was produced in a DC discharge with a current of a few mA(range 0.5–15 mA depending on the cell pressure) by flowing a 1:1mixture of CO and H2 at constant pressure (�1 mTorr) with addi-tion of Ar buffer gas for a total pressure ranging from 5 to35 mTorr. Measurements at higher pressures were prevented bythe failure of the diffusion pump in maintaining a constant flowthrough the cell. The Pyrex cell was cooled at 77 K by liquid nitro-gen circulation, and an axial magnetic field up to about 275 G wasapplied throughout the length of the discharge. With this longitu-dinal magnetic field applied, ions are produced and observed inthe negative glow.[20] In this nearly field free region the ions are ex-pected to show no Doppler shift due to drift velocity, whichoccurs, instead, in the positive column where a low axial electricfield is present.[21] The absence of a Doppler shift is experimentallyverified by comparing the line frequencies measured at invertedelectrode polarity.

A typical spectrum was recorded by sweeping the frequency upand down (several times if signal averaging is needed) in steps of10 kHz at a rate of 2 MHzs�1, with a lock-in amplifier time constantof 10 ms and a frequency modulation depth 3–4 times lower thanthe linewidth. Since we have full flexibility in controlling scanningrate, number of data points and modulation depth, the values ofthese parameters were adjusted to prevent any bias of the meas-ured line frequency. For each line, 6 to 8 series of measurements,at 6 to 7 increasing values of Ar pressure were carried out.

Since the absorption was lower than 6%, collisional linewidths andshifts were recovered from a lineshape analysis of the spectral pro-

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Argon Pressure Broadening and Shifts

file, a procedure which accounts for the frequency modulation andthe line asymmetry due to etalon effects in the cell.[19, 22] In a previ-ous paper we showed that the Voigt profile is not fully adequatein describing the line profile,[6] therefore the Speed DependentVoigt profile has been used as lineshape model,[23] with the Dop-pler width set at its value at 77 K. During the experiment, as per-fect control of the temperature was not achieved, the uncertaintyaffecting the derived collisional parameters was checked: assumingT=90 K, the error is about 2%, which is not the major source ofuncertainty, as explained later.

Table 1 reports the values for collisional line broadening and shift,namely the slope of the straight line describing the width or shiftvs pressure, obtained from least-squares fitting. The new radiation

source employed allowed us to record spectra with a signal-to-noise ratio better than in the previous work,[6] thus a clear negativepressure shift could be revealed for all three lines (see Figure 1).However, there is a discrepancy between present and past broad-ening parameters of the j=4 !3 line which cannot be explainedby the different lineshape analysis carried out. Instead, pressuremeasurements may be affected by the location of the pressuregauge (MKS Baratron with a resolution of 0.1 mTorr) downstreamclose to the pumping port: in the present configuration the meas-ured pressure should be lower than the average value throughoutthe cell. The discrepancy between the pressure measured close tothe pumping port and the cell increases with increasing flow. Acalibration of the system by measuring the j=3 !2 line of CO per-turbed by N2 at 298 K in flow conditions revealed that the broad-ening parameter from the present study is in fact larger than theone obtained under static conditions (see data from ref. [24]).Therefore, the broadening parameters as well as the shift parame-ters are estimated to be systematically larger by a factor of about15%.

2. Results

2.1 Construction and Testing of the PotentialEnergy Surface

The present work uses a standard Jacobi coordinate system, inwhich R is the distance of the Ar atom from the center of massof HCO+ and q is the angle between the CH and the R dis-tance vectors (see Figure 2). For scanning the potential energysurface (PES) the HCO+ monomer is frozen at its minimumenergy structure calculated for the Ar–HCO+ complex at theCCSD(T)/aug-cc-pVQZ level using MOLPRO.[25] The bond

lengths are rCO=1.113 A and rCH=1.112 A, respectively. It is ad-vantageous to choose the grid on which the energies are cal-culated such as to minimize the effort in the bound state andscattering calculations. Evaluation of the necessary angular in-tegrals is the most stable if Gauss-Legendre points are used.[26]

In addition, the representation of the interaction potential issimplified. Thus calculations at angles corresponding to an 11-point quadrature (q=11.988, 27.498, 43.108, 58.738,74.368,90.008, 105.648, 121.278, 136.908, 152.518, and 168.028) are per-formed. In addition, calculations in the two collinear geome-tries are carried out to assess the accuracy of the fit. The radialR grid included 14 regularly spaced points (0.1 A apart) be-tween 2.7 A and 4.0 A, 4 regularly spaced points between4.0 A and 5.0 A, and further points at 5.5, 6.0, 7.0, 8.0, and

Table 1. Measured broadening and shift parameters of HCO+ rotationallines perturbed by argon at 77 K.

Line FrequencyACHTUNGTRENNUNG[MHz]

Broadening[a]

[MHzTorr�1]Shift[a]

[MHzTorr�1]This work Previous[6]

1 !0 89188.53 21.5(6) +2.27(16)2 !1 178375.06 17.5(5)4 !3 356734.223 17.2(5) 14.6(2) �0.59(7)5 !4 445902.872 15.3(3) �0.61(4)6 !5 535061.581 16.3(5) �0.66(7)

[a] 99% confidence intervals are reported in parentheses.

Figure 1. Plots of frequency shifts vs pressure for HCO+ lines perturbed byAr. Least-squares fit : (c).

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M. Meuwly et al.

10.0 A. The total potential VACHTUNGTRENNUNG(R,q) is represented in Equation (7):

VðR; qÞ ¼Xl

VlðRÞPlðcosðqÞÞ ð7Þ

where Vl(R) are the radial strength functions and the sum runsover l=0 to 10. It is advantageous to represent the radialstrength functions as reproducing kernels.[27] This allows theexact reproduction of ab initio points. According to the radialR�4 dependence of the intermolecular potential, the kernel rep-resented in Equation (8):

q2;41 ðx; x0Þ ¼ 215

x�5> � 57x<x>

� �ð8Þ

is used.[27]

Since the main interest herein is on capturing the energeticsclose to dissociation, additional points in the very long range(R=20, 30, and 40 A) were calculated from the long-range po-tential describing the charge-induced dipole and dipole-in-duced dipole interaction [Eq. (9)]:

V ¼ � q2a2R4

� 2qam cos qR5

, ð9Þ

were q is the charge of the ion, m=3.91 D its permanentdipole,[28] and a=1.64M10�24 cm3 is the Argon polarizability.[29]

For the collinear arrangement Ar–HCO+ , the energies ofthese points are also calculated at the CCSD(T)/aug-cc-pVQZlevel, in order to compare with the purely electrostatic ener-gies. As it is unclear how the high-lying regions of the intermo-lecular PES depend upon the vibrational state of the HCO+

monomer, the PES was not adiabatically corrected as done pre-viously for related systems.[30–35]

To test the new PES, the frequencies for the lower boundstates and related spectroscopic observables are calculated.Bound state calculations are carried out with the BOUND com-puter program.[36] The reduced mass of the complex was16.808543 mu and the rotational constant of the monomer wasfixed at B=1.48751 cm�1.[21] The basis set includes internal an-gular momenta up to j=30. This proves to be sufficient forconvergence to better than 10�4 cm�1.Experimentally, the frequency of the intermolecular stretch-

ing mode (146 cm�1) for the vCH=1 state has been directly ob-served[37] while approximate wavenumbers for ns (131 cm�1)and nb (109 cm

�1) corresponding to vCH=1 are calculated fromharmonic force constants derived from microwave spectrosco-py.[38] A further spectroscopic measurement is provided by theground-state rotational constant which is 0.0664 cm�1 from mi-crowave spectroscopy.[38] For the rigid monomer PES, thewavenumbers of the Ar stretching and bending vibrations are132.8 cm�1 and 143.2 cm�1, respectively. The rotational con-stant B0=0.0698 cm�1 for the ground state is calculated fromthe J=0 to 4 levels and fitted to the pseudodiatomic expres-sion EJ�E0+B0M (JACHTUNGTRENNUNG[J+1]). The overestimation of the bendingfrequency on rigid-monomer PESs has already been observedfor other proton bound complexes while the stretching vibra-tions are usually in better agreement with experiments. Com-pared to results on other rigid monomer PESs, the present re-sults suggest that lower bound states are well described andinclusion of vibrational adiabatic corrections would lead to fur-ther improvement.[32,31,39] Overall, the (limited) available experi-mental data for vCH=0 are sufficiently accurately described tojustify further use of the PESs for scattering calculations.

2.2 Comparison between Experiment and Theory

Close-coupling calculations go beyond the semiclassical ap-proximation and allow a quantum treatment of both orbitalmotion and internal degrees of colliding partners. The formal-ism was first developed by Arthurs and Dalgarno for the scat-tering between a rigid linear rotor and a spherical perturber,[40]

which is just our case, since the effect of vibrational transitionsin HCO+ is assumed to be negligible. Herein the MOLSCATcomputer code was used to carry out close-coupling scatteringcalculations to obtain the broadening and shift cross-sec-tions.[41]

We used the potential energy surface and the reduced massas described in Section 2.1. The translational energy was fixedat the average value �Ek ¼ 4kT=p. For the total angular momen-tum J= l+ j, where l is the orbital momentum, we includedvalues ranging from 0 to 300, where the upper limit is fixed bya convergence test. The need for such a high upper limit is re-lated to the long-range nature of the potential : collisions withan impact parameter as large as b=20–30 A and l as large as200–300 still give non-negligible contributions. This is particu-larly true for the imaginary part of the cross-section which, athigh J-values, decreases less rapidly than the real part. Furthertests showed that for converging the scattering matrix it is

Figure 2. Rigid monomer PES for the interaction between Ar and HCO+ atthe CCSD(T)/aug-cc-pVQZ level of theory. R is the HCO+ center of mass toAr distance and q is the angle between the CH vector and the direction ofR. Contours are drawn every 100 cm�1 between �1600 cm�1 and�300 cm�1, at �250, �200, �150, �100, �50, �25, and �10 cm�1, in thebound state region, and at 100, 200, 500, and 1000 cm�1 on the repulsivewall. The inset compares the model potential (c) with ab initio calcula-tions for the two collinear structures, q=0 and q=1808.

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Argon Pressure Broadening and Shifts

necessary to include rotational energy levels of HCO+ up to j=24. The rotational energies were obtained using the rotationalconstants from the literature.[42]

We computed the cross-sections for the six lowest rotationallines. The results are reported in Table 2 and compared to ex-periment and to semiclassical data (SC). In the semiclassical cal-culations, the rotational relaxation is related to the angle-de-pendent part of the long-range potential in Equation (9),

which is dominated by dipole-induced dipole interactionVd�id=�2qamcosq/R5. The orbital motion is obtained by a nu-merical integration that takes into account, as usual, only thespherical part of the potential. In the present calculation weuse the spherical part of the potential described in the previ-ous section. However, this makes negligible difference with re-spect to the calculations of ref.[8] because semiclassical resultsare affected only by the long-range part of the potential whichis given in both cases by charge-induced dipole interactionVc�id=�q2a/2R4. A larger difference (a few %) is due to the factthat in the present case we used exponential interpolation be-tween strong and weak collisions,[14,17] while ref.[8] resorted toassuming a cutoff radius rc.The experimental and theoretical results for pressure broad-

ening are summarized in Table 2. The difference between thesemiclassical and the close-coupling results is less than 5%,while the agreement between calculations and measurementsis worse. As a result, the experimental pressure broadeningdata are not suitable to discriminate between the two theoreti-cal methods. Since the rotational energy depends upon thesquare of the angular momentum quantum number j, higherrotational states require more energy to change the rotationalstate j. Hence, a decreasing broadening is expected for increas-ing j values. This feature is universally observed for the spectraof linear molecules and is also found herein for HCO+ collidingwith Ar. The measured data show a different trend which ismost likely related to the experimental uncertainty. Experimen-tal broadening parameters, in fact, are affected by systematicerrors which limit the accuracy at best to about 2%.[43] For thepresent study, carried out in flow conditions, such an accuracycannot be achieved, as mentioned above.

For the pressure shift data, a first important observation isthat both experiments and theory predict a red shift for alllines. This is in contrast to the j=1 !0 line for which a blueshift (+2.27 MHzTorr�1) was found.[6] This compares with3.37 MHzTorr�1 from the present work for this line. Moreover,the semiclassical shift calculations, which neglect the contribu-tion due to strong collisions, are considerably smaller than theexperimental data. A better, even if not completely satisfactory,

agreement is found for close-coupling calculations. The signand order of magnitude are wellreproduced, but not the trendof j. This may be ascribed toboth the difficulty of the meas-urements as well as to the ap-proximations involved in the cal-culations.

3. Discussion andConclusions

Pressure broadenings of rota-tional linewidths are of consider-able interest for different rea-sons. They are related to colli-sional relaxation cross-sections

and essential to interpret microwave observations of interstel-lar gas,[3, 44] and may serve as a probe for the intermolecular in-teractions between the ion and the perturber molecule. HCO+

as an ion of considerable astrophysical interest is ideal to testand validate current computational methods in comparisonwith experiment. To the best of our knowledge, herein wepresent the first close-coupling calculations of both pressurebroadenings and pressure shifts for an ionic system.New experimental data and a theoretical investigation of

pressure broadenings and pressure shifts for rotational lines inHCO+ perturbed by collisions with Argon are reported. Thenew measurements involve the rotational lines j=4 !3, 5 !4,and 6 !5. To analyze the data, close-coupling calculationswere performed using an accurate 2-dimensional potentialenergy surface for Argon interacting with the HCO+ ion. ThePES covers a sufficiently large grid in R to capture the energet-ics close to dissociation. While close-coupling and semiclassicalcalculations give similar results for pressure broadenings, theyare quite different for the pressure shifts. Of particular interestare the pressure shift data. They show that semiclassical calcu-lations give values which are too small because they neglectthe contribution of strong collisions. Close-coupling calcula-tions and the use of an accurate short-range intermolecularpotential yield better agreement, even if some discrepanciesare still not resolved. A recent investigation of pressure broad-enings in He–CO2, based on an accurate symmetry adaptedperturbation theory (SAPT) potential energy surface, found dif-ferences between calculated and experimental values of 5% to10% at T=123 K.[45] The data at higher temperatures (T=296 Kand T=760 K) suggest that the discrepancies increase at tem-peratures below T=123 K. This is in agreement with the pres-

Table 2. Comparison between measured and calculated broadening and shift parameters of HCO+ rotationallines perturbed by Argon at 77 K.

Line Broadening [MHzTorr�1] Shift [MHzTorr�1]Experiment CC SC Experiment CC SC

1 !0 21.5 22.95 23.82 +2.27 +3.37 +2.472 !1 17.5 19.52 20.88 +0.77 +0.663 !2 16.81 18.29 �0.40 +0.084 !3 17.2/14.6 15.94 16.75 �0.59/�0.50 �0.60 �0.065 !4 15.3/13.0 15.51 15.86 �0.61/�0.52 �0.41 �0.096 !5 16.3/13.9 15.42 15.36 �0.66/�0.56 �0.18 �0.08

For the calculations the present potential energy surface is used. The values for the line broadening and shiftfor j=4 !3, 5 !4, and 6 !5 are given as both the present measurements and values corrected for the flowconditions (see text).

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M. Meuwly et al.

ent work, where differences between experiment (T=77 K)and theory are between 5% and 15% (see Table 2).The remaining disagreement between experiments and

theory indicates that further improvement is required to reacha quantitative understanding of pressure broadenings andpressure shifts. One possible improvement in the calculationswould be to include internal degrees of freedom of the HCO+

ion in constructing the potential energy surface in a mannersimilar to the original adiabatic correction.[30] Also, the currentlyused PES, although of good quality, is not spectroscopically ac-curate which is reflected in the qualitative agreement betweencalculated and observed stretching and bending frequencies.Another improvement could be obtained by integrating overthe thermal energy distribution instead of resorting to calcula-tions at fixed average energy. As for the experiment, improve-ments in controlling external factors (e.g. the pressure) mayhelp to reduce the intrinsic error bars. Nevertheless, combiningexperiments and theory, as done herein, allows to extract im-portant and validated data for further use in astrophysical andastrochemical modeling.

Acknowledgements

M.M. acknowledges financial support from the SchweizerischerNationalfonds through a Fçrderungsprofessur. L.D. and F.T. ac-knowledge financial support from MIUR (Cofin 2005) and Univer-sity of Bologna (RFO funds).

Keywords: ab initio calculations · interaction potentials · ion–atom collisions · line broadening · microwave spectroscopy

[1] E. Herbst, W. Klemperer, Astrophys. J. 1974, 188, 255–256.[2] B. E. Turner, Astrophys. J. 1974, 193, L83–L87.[3] S. Green, Astrophys. J. 1975, 201, 366–372.[4] T. G. Anderson, C. S. Gudeman, T. A. Dixon, R. C. Woods, J. Chem. Phys.

1980, 72, 1332–1336.[5] R. C. Woods in Molecular Ions: Spectroscopy, Structure, and Chemistry

(Eds. : T. A. Miller, V. E. Bondybey), North Holland, Amsterdam, 1983, andreferences cited therein.

[6] G. Buffa, O. Tarrini, G. Cazzoli, L. Dore, Phys. Rev. A 1994, 49, 3557–3565.[7] Q. Liao, E. Herbst, J. Chem. Phys. 1996, 104, 3956–3961.[8] G. Buffa, O. Tarrini, G. Cazzoli, L. Dore, J. Chem. Phys. 1999, 111, 1870–

1874.[9] J. Troe, J. Phys. Chem. 1986, 90, 3485–3492; J. Troe, J. Chem. Phys.

1987, 87, 2773–2780.[10] Q. Liao, E. Herbst, Astrophys. J. 1995, 444, 694–701.[11] “Statistical Adiabatic Channel Model”: M. Quack, J. Troe in Encyclopedia

of Computational Chemistry (Ed. : P. v. R. Schleyer), Wiley, New York,1998.

[12] P. W. Anderson, Phys. Rev. 1949, 76, 647–661.[13] C. T. Tsao, I. Curnutte, J. Quant. Spectrosc. Radiat. Transfer 1962, 2, 41–

91.

[14] J. S. Murphy, J. E. Boggs, J. Phys. Chem. 1967, 71, 691–702.[15] A. Di Giacomo, O. Tarrini, Nuovo Cimento B 1969, 62, 1–12; A. Di Giaco-

mo, O. Tarrini, Nuovo Cimento B 1970, 68, 165–174.[16] B. S. Frost, J. Phys. B 1976, 9, 1001–1020.[17] D. Robert, J. Bonamy, J. Phys. 1979, 40, 923–943.[18] M. Baranger, Phys. Rev. 1958, 111, 481–493; M. Baranger, Phys. Rev.

1958, 111, 494–504; M. Baranger, Phys. Rev. 1958, 112, 855–865.[19] G. Cazzoli, L. Dore, J. Mol. Spectrosc. 1990, 141, 49–58.[20] F. C. De Lucia, E. Herbst, G. M. Plummer, G. A. Blake, J. Chem. Phys. 1982,

78, 2312–2316.[21] K. V. L. N. Sastry, E. Herbst, F. C. De Lucia, J. Chem. Phys. 1981, 75, 4169–

4170.[22] L. Dore, J. Mol. Spectrosc. 2003, 221, 93–98.[23] J.-F. D’Eu, B. Lemoine, F. Rohart, J. Mol. Spectrosc. 2002, 212, 96–110.[24] C. Puzzarini, L. Dore, G. Cazzoli, J. Mol. Spectrosc. 2002, 216, 428–436.[25] MOLPRO is a package of ab initio programs written by H. J. Werner,

with contributions from R. D. Amos, P. J. Knowles, A. Bernhardsson, A.Berning, P. Celani, D. L. Cooper, M. J. O. Deegan, A. J. Dobbyn, F. Eckert,C. Hampel, G. Hetzer, T. Korona, R. Lindh, A. W. Lloyd, S. J. McNicholas,F. R. Manby, W. Meyer, M. E. Mura, A. Nickiass, P. Palmieri, R. Pitzer, G.Rauhut, M. SchRtz, H. Stoll, A. J. Stone, R. Tarroni, T. Thorsteinsson, H. J.Werner and P. J. Knowles. MOLPRO, Version 2000. University of Birming-ham, Birmingham, 2000.

[26] M. Meuwly, J. M. Hutson, J. Chem. Phys. 1999, 110, 3418–3427.[27] T. S. Ho, H. Rabitz, J. Chem. Phys. 1996, 104, 2584–2597.[28] P. Botschwina in Ion and cluster ion spectroscopy and structure (Ed. : J. P.

Maier), Elsevier, Amsterdam, 1989.[29] C. G. Gray, K. E. Gubbins, Theory of molecular fluids, Vol. 1, Clarendon,

Oxford, 1984.[30] M. Meuwly, R. J. Bemish, J. Chem. Phys. 1997, 106, 8672–8680.[31] M. Meuwly, J. Chem. Phys. 1999, 111, 2633–2640.[32] M. Meuwly, J. Chem. Phys. 1999, 110, 4347–4353.[33] A. A. Buchacehnko, N. F. Stepanov, R. V. Krems, S. Nordholm, Phys.

Chem. Chem. Phys. 2002, 4, 4992–4998.[34] M. Meuwly, P. P. Wolynec, E. J. Bieske, J. Chem. Phys. 2002, 116, 4948–

4954.[35] S. P. Belov, B. A. McElmurry, R. R. Lucchese, J. W. Bevana, I. Leonov,

Chem. Phys. Lett. 2003, 370, 528–534.[36] J. M. Hutson. Bound computer program, version 5, distributed by Col-

laborative Computational Project No. 6 of the UK Engineering andPhysical Sciences Research Council, 1993.

[37] S. A. Nizkorodov, O. Dopfer, T. Ruchti, M. Meuwly, J. P. Maier, E. J. Bieske,J. Phys. Chem. 1995, 99, 17118–17129.

[38] Y. Ohshima, Y. Sumiyoshi, Y. Endo, J. Chem. Phys. 1997, 106, 2977–2979.[39] M. Meuwly, J. Phys. Chem. A 2000, 104, 7144–7150.[40] A. M. Arthurs, A. Dalgarno, Proc. R. Soc. London Ser. A 1960, 256, 540–

551.[41] J. M. Hutson, S. Green, MOLSCAT computer code, version 14, distributed

by Collaborative Computational Project No. 6 of the Science and Engi-neering Research Council, UK, 1994.

[42] G. A. Blake, K. B. Laughlin, R. C. Cohen, K. L. Busarow, R. J. Saykally, Astro-phys. J. 1987, 316, L45– L48.

[43] J. M. Colmont, B. Bakri, F. Rohart, G. Wlodarczak, J. Demaison, G. Cazzoli,L. Dore, C. Puzzarini, J. Mol. Spectrosc. 2005, 231, 171–187.

[44] D. R. Flower, Mon. Not. R. Astron. Soc. 1999, 305, 651–653.[45] T. Korona, R. Moszynski, F. Thibault, J. M. Launay, B. Bussery-Honvault, J.

Boissoles, P. E. S. Wormer, J. Chem. Phys. 2001, 115, 3074–3084.

Received: March 19, 2006Published online on July 10, 2006

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Argon Pressure Broadening and Shifts