Faraday Discuss. Chem. SOC., 1982, 73, 89-108 Infrared Spectra of Hydrogen-Rare-gas Van der Waals Molecules BY A. ROBERT W. MCKELLAR Herzberg Institute of Astrophysics, National Research Council of Canada, Ottawa, Ontario, Canada KIA OR6 Received 17th December, 198 1 Previously measured spectra of the Van der Waals molecules formed from H2 or Dz molecules and Ar, Kr or Xe atoms have been used to derive detailed potential surfaces for these systems. The success of the analyses has prompted a new program to obtain improved high-resolution spectra which may serve as a basis for refined potentials. The first results of these new studies are reported here. The spectra, which lie in the 2-4 pm wavelength region of the hydrogen stretching vibration, are observed in absorption through a long path in a mixture of hydrogen and the rare gas at low temperature. The new results were obtained with a path of 220 m in a 5.5 m multiple-traversal cell at 77 K for H2-Ar, HD-Ar and D2-Ar, and at 97 K for H2-Kr.A 2 m vacuum infrared grating spectrometer was used with electronic signal averaging to record the weak spectra. The resulting spectral linewidths of ca. 0.1 cm-l represent an improvement of from 3 to 6 times over the previous spectra, with the result that much greater detail is revealed in the more crowded regions of the spectra, Furthermore, fully resolved spectra were observed in the Q(0) regions of HD-Ar and Dz-Ar which were previously too weak to be studied in detail. All the spectra studied here are subject to pre- dissociation because the upper states of the observed transitions lie at 3000-5000 cm-l, far above the 40-70 cm-' binding energy of the Van der Waals bond.Predissociation is clearly observed as line broadening in the HD-Ar S(0) region, and also detected for one line of Hz-Kr in the S(0) region. In other regions, the predissociation linewidths must be less than ca. 0.1 cm-'. These observations are of interest since predissociation in Van der Waals molecules is currently an area of considerable theoretical activity and there are relatively few experimental measurements. 1 . INTRODUCTION A discrete infrared spectrum due to the H2-Ar Van der Waals molecule was first observed in 1965 by Kudian et aZ.,l shortly after the discovery of an analogous spectrum due to the (HJ2 dimer. Further studies resulted in similar spectra due to H2-Kr and H2-Xe,3 and aIso in rather more diffuse spectra due to H2-N, and H,-C0.4 These investigations were extended to considerably higher resolution and to the species containing D2 by McKellar and Welsh,5 whose spectra showed direct evidence of the effects of anisotropy in the hydrogen-molecule-rare-gas-atom intermolecular potential functions.Similar experiments were also performed on H2-Ne, D,-Ne and HD-Ar.7 Subsequently there has been a considerable amount of theoretical work 8-14 performed to analyse these high-resolution results and to extract potential-energy surfaces from them. The combination of the spectroscopic data with data from various molecular-beam scattering experiments has thus resulted in increasingly precise determinations of the detailed forms of the hydrogen-rare-gas interaction poten- t i a l ~ .~ ~ J ~ The great success of these studies suggests that new experimental data on the spectra would be very worthwhile as a basis for refined analyses of the inter- molecular potentials. The present paper describes the first results of a program to obtain such improved high-resolution spectra for the hydrogen-rare-gas systems. Spectra of the molecules90 HYDROGEN-RARE-GAS SPECTRA H,-Ar, HD-Ar, D,-Ar and H,-Kr have been measured with the resolution improved by a factor of from 3 to 6 compared with the best previous experiment^,^ higher resolution results in much greater detail being uncovered in the more crowded regions of the spectra. Furthermore, fully resolved spectra have been obtained in spectral regions [Q(O) in HD-Ar and D,-Ar] which were previously too weak to study in detail, and definite evidence has been seen of the effects of predissociation on the spectra: such observations furnish an additional sensitive test of intermolecular potentials.The spectra studied here occur in the region of the middle infrared (A = 2.0-3.5 pm), and they accompany the vibration-rotation transitions in the fundamental bands (u = l+O) of the hydrogen molecules: HZ, HD and D,. They are observed by relying on the very small equilibrium concentrations of the Van der Waals species, and using long absorption paths (> 10 m), moderate gas pressures (0.05-5 atm *) and low temperatures (in the region of the boiling point of the rare gas).If a high-resolu- tion spectrometer is used, the linewidths in the spectra are generally limited by pres- sure broadening. Higher-resolution spectra thus require lower density (pressure) and hence longer pathlength and/or increased sensitivity to weak absorption features. Since the equilibrium concentration of Van der Waals molecules varies approximately as the density squared, the variation in the required pathlength/sensitivity is much stronger than for a normal (monomer) molecule (indeed, for a normal molecule in the pressure-broadened regime, the peak absorption of an isolated line is constant with density). In the present work, the pathlength, sensitivity and instrumental resolution are all increased relative to earlier studies.'- An example of the improve- ment is shown in fig.1, which shows part of the spectrum of the H,-Ar molecule observed with the conditions of ref. (l), (3) and (9, and the present study. As the sample density is further reduced, the resolution in the spectra improves until the linewidths become limited by Doppler broadening or by the finite lifetime of the Van der Waals molecules in their upper states. All the spectra studied here are subject to such predissociation effects, because the upper states lie at energies of 3000- 5000 crn-', which are far above the 40-70 cm-l binding energies of the Van der Waals bonds. However, the predissociation lifetimes may vary greatly with the particular species being studied and with the various quantum states of each species, and in most cases the lifetime-limited linewidths have not been reached experimentally.In one sense, the spectra studied in this paper constitute a component of the well- known collision-induced spectrum l6 of hydrogen. Short-lived binary collisions between, say, H, molecules and Ar atoms in an H, + Ar mixture give rise to charac- teristically broad (ca. 100 cm-l) collision-induced absorption lines, while the few H2 molecules that happen at any moment to be bound to Ar atoms by the weak Van der Waals forces give rise to much sharper spectral lines arising from transitions between bound states of the Van der Waals molecule. In both cases, the mechanism for absorption is the dipole moment induced by the proximity of the H, to the Ar. The overall appearance of the fundamental band with these two contributions may be seen, for example, in fig. 1 of ref.(3) or (7), or fig. 2 of ref. (6). Electric dipole vibration-rotation transitions are, of course, forbidden for isolated H, and DZ, and very weak for HD. Even weaker electric quadrupole transitions occur in all the hydrogen species. A hydrogen-rare-gas molecule is best understood starting with the approxiniation that the hydrogen molecule within the Van der Waals complex is completely free to vibrate and rotate. This assumption is a very good one; even in solid hydrogen, rotation and vibration remain remarkably unperturbed. The energy levels of H,-Ar * 1 atm = 101 325 Pa.A . R . W. MCKELLAR 91 L t- I I 1 I I 4480 4490 4500 4510 4520 wavenumber Icm- FIG. 1,-Spectrum of the H2-Ar Van der Waals molecule accompanying the S(0) transition of H2 under a range of experimental conditions.Traces (a), (b), (c) and ( d ) correspond, respectively, to the results of ref. (l), (3) and ( 5 ) and the present work; the temperature, density and absorption path for each trace are as follows (1 amagat is the density of a gas sample at 1 atm pressure and 0 "C temper- ature): (a) 99 K, 9.6 amagat, 13 m; (b) 91 K, 4.0 amagat, 48 m; (c) 86 K, 1.2 amagat, 165 m; ( d ) 77 K 0.3 amagat, 220 m. The vertical (absorption) scale is not common for the four traces. are then given simply by the sum of two diatomic molecule energies, that of the free H, molecule (quantum numbers v and j ) and that of the pseudodiatomic H,-Ar molecule (quantum numbers n and Z for vibration and rotation).The resulting spectrum consists of small, closely spaced Van der Waals bands centred around each of the widely spaced H2 vibration-rotation transitions. The angular dependence of the induced dipole moment leads to rotational selection rules of Aj = 0, &2 and AZ = & 1, &3 (with only AZ = & l allowed when j = O+O). At the low temperatures used in the experiments, only the Q(0) ( j = O+-0), Q(l) ( l t l ) , S(0) ( 2 ~ 0 ) and S(1) ( 3 t l ) transitions are observed for species containing H,, and only Q(0) and S(0) for those containing HD or DZ. The free vibration and rotation of the hydrogen within the Van der Waals molecule are in fact slightly hindered by the dependence of the intermolecular potential on the hydrogen internuclear distance and by the anisotropy of the potential with respect to hydrogen rotation.The vibrational perturbation is manifested as a slight shift (<0.05%) in the free hydrogen vibrational frequency. The anisotropy couples the angular momenta j and I to form the resultant total rotational angular momentum J.92 HYDROGEN-RARE-GAS SPECTRA Each rotational level denoted by I is split into 25' + 1 (or 21 + 1 if I < j ) sublevels labelled by different values of J. The resulting transitions of the Van der Waals molecule are thus shifted or split, though these effects are only apparent in the spectra a t fairly high resolution. 2. EXPERIMENTAL The results presented here were obtained using a new low-temperature multiple-traversal absorption cell. The cell has a base pathlength of 5.5 m, and was generally used with 40 traversals, giving a total path of 220 m [cf.165 m used in ref. (5)]. It is constructed of stain- less steel, and consists of an innermost tube containing the sample gas and multiple-reflection l7 mirrors, a surrounding space which may be filled with liquid coolant, and an outermost vacuum jacket for thermal insulation. The inner diameter of the sample tube is 12 cm and the outer diameter of the cell is 22 cm. Experiments on the molecular species containing Ar were performed with liquid-nitrogen coolant at 77 K, whereas those involving H,-Kr were performed at ca. 97 K, which was obtained by maintaining an overpressure of ca. 5 atm on the liquid N2 by means of a pressure-relief valve. Spectra were recorded with a 2 m vacuum grating spectrometer,18J9 using a 72 line mm-' grating (in the 7th to 11 th orders), a cooled PbS detector and a carbon-rod continuum source.The instrumental resolution was generally in the range of 0.06 to 0.10 cm-l. The optical path from source to cell and cell to spectrometer was evacuated to minimize the effects of strong atmospheric water-vapour absorption in the 2.5-3.3 pm region. In order to achieve the best possible sensitivity to weak absorption lines, a signal averag- ing technique was used to achieve long integration times (5-30 h) over the relatively limited (ca. 40 cm- ') spectral regions surrounding each hydrogen transition frequency. For this purpose, the spectrometer was operated in a very fine scanning mode achieved by moving its output (" camera ") mirror on a 2 m long pivot arm by a precision lead screw.Provision for this very slow scan mode had been incorporated in the original spectrometer design by Douglas,18 but it was never used because the normal (grating rotation) scanning mode proved satisfactory. By driving the fine scan mode lead screw with a digitally controlled '' stepless " l9 stepping motor, an extremely reproducible scan of any limited wavelength region could be achieved. This mechanical stability made it possible to use a digital signal averager (Nicolet model 535) to accumulate many successive spectral scans without any loss in resolution due to lack of coincidence between scans. Typically, 30 scans of 2048 points and 25 min duration were accumulated during an overnight run; the resulting noise levels were as low as 0.1 % of the continuum.It was thus possible to operate with low sample pressures that gave peak absorptions of only a few percent in the Van der Waals transitions and still obtain good quality spectra. This fact and the increased pathlength were responsible for the improved resolution of the present results. The Nicolet signal averager was inter- faced to a desk-top computer and plotter (Hewlett-Packard models 9825 A and 7225 A) which enabled spectra to be smoothed, calibrated, measured and plotted after each run. The figures presented in this paper result directly from these plots; an example of the raw output of the signal averager is shown in fig. 2. The slope and curvature of the background in this spectrum, which is exaggerated by the suppression of zero on the vertical scale, is due to the variation of the grating, source and detector sensitivities as a function of wavelength, and to the spectral band pass of the spectrometer's order-sorting prism.The appearance of the same spectrum after calibration, smoothing and background flattening is shown below in section 3 ( 4 . Wavelength Cali bration was accomplished using visible neon emission lines recorded in high grating orders before or after each run. The absolute calibration was usually checked using absorption standards recorded simultaneously with the Van der Waals spectra. These standards included the v3 band 'O of CH4 [present as an impurity in the D2-Ar Q(0) spectra], the 2-0 band 21 of CO (introduced at low pressure into the spectrometer tank), the v3 band 24 of H20 (residual water vapour present in the spectrometer vacuum tank), and the hydrogen quadrupole transitions themselves.The frequencies assumed for the free hydrogen tran- sitions are listed in table 1. Le Roy and Van Kranendonk ' point out that there is a problemA . R . W . MCKELLAR 93 70 0 4 0 0 800 1200 1600 2000 channel number FIG. 2.-Raw spectrum of the H,-Kr molecule in the H2 S(0) region. The sample temperature was 97 K, and the total pressure was 108 Torr in an approximately equal mixture of para-Hz and Kr. The spectrum shown is the signal-averager output resulting from the sum of 25 scans of duration 32 min each. The same spectrum after processing is shown later in fig. 11. TABLE 1 .-ASSUMED TRANSITION FREQUENCIES (IN cm- l) FOR FREE HYDROGEN MOLECULES transition H2 a HD Dz Qi(W 4161.166 3632.152 2993.614 Qd 1) 41 55.254 SdO) 4497.8 3 8 3887.681 3166.359 4712.902 a From a fit (unpublished) to available 0-0 and 1-0 band data; fitted values from ref.(22); fitted values from ref. (23). introduced by the practice of calibrating relative to the hydrogen quadrupole lines since these lines are subject to fairly substantial pressure shifts. They also show that this difficulty can be circumvented since the pressure shifts depend on the very potential parameters that are extracted from the Van der Waals spectra. At any rate, the uncertainties introduced by pressure shifts are very small (t0.01 cm-') in the present work because of the low pressures used. Para-H2 and ortho-D, were prepared by the usual technique of liquefying the hydrogen at ca.20 K in the presence of a chrome alumina catalyst. An ortho-H2 separation apparatus such as used previously was not available for the present study, so normal H2 (75OA ortho) was used to obtain spectra in the Q(l) and S(l) regions for H,-Ar and H2-Kr. 3 . RESULTS (a) H2-Ar The spectrum of H2-Ar in the H, Q-branch region is shown in fig. 3 for para-H2 and in fig. 4 for normal H2. These and successive spectra are shown in terms of percentage transmission, rather than absorption coefficient as in earlier papers. The94 100 98 96 HYDROGEN-RARE-GAS SPECTRA -- -- 10 9c 100 95 ~ I I I 1 ** I I I 4155 41 60 4165 wavenumber/cm - FIG. 3.-Spectrum of H2-Ar accompanying the Q(0) transition of H2. The temperature was 77 K and the sample pressures were 350 Torr (upper trace) and 100 Torr (lower trace) in an approximately equal mixture of pura-Hz and Ar.Present in the lower trace, and denoted by asterisks, are lines of the 2-0 band of CO included for wavelength calibration (the 3 weaker lines are due to 13C160). The vertical arrow indicates the Q(0) frequency of free H2 (there is no line at this position); note the shift between this position and the " centre " of the H2-Ar spectrum. para - H, - I I I 4140 4150 41 60 4170 wavenumber/cm- FIG. 4.-Spectrum of H,-Ar accompanying the Q(1) transition of H2 in a normal H2 + Ar mixture at 79 Torr and 77 K. The short upper trace is the H2-Ar Q(0) spectrum (fig. 3) with intensity scaled to match that due to the 25 % para-H2 present in normal H2.The vertical arrow indicates the Q(l) quadrupale transition of free H t .A . R. W . MCKELLAR 95 para-H, spectrum, which is entirely due to the Q(0) ( j = 060) transition, consists of simple P (AZ = - 1) and R (AZ = + 1) branches and is shown for two different sample pressures in fig. 3. The lower trace has some CO 2-0 band lines superimposed for calibration purposes. The normal H2 spectrum is mostly that of the Q(l) transition ( j = l t l ) , but as indicated above the main trace (fig. 4) it also contains weak lines of Q(0) due to the 25%para-H, in normal H,. In each figure, the transition frequencies of free H2 are marked by arrows, and in fig. 4 this coincides with the quadrupole Q(l) transition arising from the unbound H2 in the absorption cell [there is no Q(0) quad- rupole transition].The small shift (ca. 1 cm-') between the apparent centre of the H,-Ar band and the free H, frequency is evident in each case. The S(0) ( j = 2 t 0 ) spectrum of H,-Ar is shown in fig. 1, and a more detailed view of the central part of the spectrum is shown in fig. 5. The upper trace in fig. 5, wavenumberlcm- FIG. 5.-Central portion of the H2-Ar spectrum accompanying the S(0) transition of H2 in a para- H2 + Ar mixture at 77 K: (a) 60, (b) 153 Torr. The whole spectrum is illustrated in fig. 1. The vertical lines below the lower trace indicate lines for which measured positions are listed in table 2. taken with a gas pressure of 153 Torr (20.3 kPa), already shows more detail than the best previous spectrum; the lower trace, taken with 60 Torr, shows almost complete resolution of the H,Ar P- and R-branch lines.The irregular pattern of these lines (cf. fig. 3) is a direct result of anisotropy in the H,-Ar potential. Even more irregular- ity is evident in the S(l) ( j = 3 t l ) region, shown in fig. 6 ; here each line of the N (AZ = -3) and T (A1 = +3) branches may be split by anisotropy into up to 6 com- ponents. The splittings are especially evident in the T branch (lower trace of fig. 6) and they constitute a very sensitive measure of anisotropy which was not previously utilized 599912 because the lines are not well re~olved.~ Many weaker and blended features, especially in the S(1) spectrum, are not listed here Measured positions of the well resolved lines of H,-Ar are given in table 2.96 9 5.- HYDROGEN-RARE-GAS SPECTRA I I I I I I I I (further details may be obtained on request from the author).The assignments of I and J quantum numbers given in table 2 are straightforward except for the S(0) P and R branches and the S( 1) T branch, where they were obtained from calculated spectra.*v9 For blended features, table 2 either gives no assignment, or only that for 1. The absolute calibration of the Q(0) wavenumbers is relative to CO lines 21 (fig. 3) and those of Q(I), S(0) and S(1) are relative to the respective quadrupole lines, with the frequencies assumed in table 1. The uncertainty of these measurements is <0.02 cm-I. The accuracy is thus improved by a factor of ca. 2 compared with previous measurement^,^ but this improvement is unfortunately not as great as the improvement in resolution.The explanation of this discrepancy lies in the signal-averaging tech- nique used here: variations in coincidence between different scans of less than ca. 0.05 cm-I would not significantly affect the resolution in the final averaged spectrum, but they would deteriorate the line-position measurements. Because of such varia- tions, the measurements were not reproducible to the level that one would normally hope for (ca. 1/10 of a linewidth, or better than 0.01 cm-l). (b) HD-Ar The spectrum of HD-Ar was previously studied with an absorption path of 66 m : the resulting rotational structure of the Van der Waals molecule was essentially un- resolved in the Q(0,I) and S(1) regions and fairly well resolved in the S(0) region.The present experiment, with a 220 m path, results in a well resolved Q(0) spectrum but an only marginally improved S(0) spectrum. The Q(0) spectrum is shown in fig. 7; in this region there are two lines due to residual water vapour, and one ofA . R. W . MCKELLAR 97 TABLE 2.-MEASURED POSITIONS OF LINES DUE TO THE H2-Ar MOLECULE ACCOMPANYING THE FUNDAMENTAL BAND OF H2 assignment assignment assignment vlcm - I LJ vlcm-' 4.J vjcm - I 1,J vlcm-' j = 3 t l assignment 4 J 4153.932 41 54.760 41 55.740 4156.776 41 57.880 41 59.001 41 61.256 41 62.3 3 7 41 63.400 4164.417 4165.365 4166.215 41 66.8 17 5,5 t 6,6 4,4445 3,3 4-4,4 2,2+3,3 1,1+2,2 0,o t 1,l 1,l +-0,0 2,2 t l , 1 3,3 t 2 , 2 4,44-3,3 $5 t 4 , 4 6,6+5,5 7,7 4-6,6 4478.1 50 4480.496 448 3.3 63 4486.51 3 4489.847 4490.49 3 449 1.042 4491.863 4492.828 4493.740 4495.134 4497.838 4498.366 4499.125 4499.306 4499.860 4500.261 4500.45 6 4501 -006 450 1.272 4501.522 4502.036 4502.155 4502.48 6 4502.915 4503.320 4505.81 5 450 8,940 451 1.825 4514.304 4,6 t 7 , 7 3,5 t 6 , 6 2,4 t 5 3 1,3 t 4 , 4 0,2 +3,3 1,2+2,2 quad.2,l t l , l 3,l t 2 , 2 2,2 4- 1,l 3,2 4-2,2 4,2 +3,3 3,3+-2,2 4,3 4-3,3 5,3 +4,4 4,4+3,3 5,4 +4,4 6,4 +- 5,5 3,l t O , O 6,5 +- 5,5 6,6 4-53 4 , 2 t l , l 5,3 t 2 , 2 6,4t3,3 7,5t4,4 41 35.96 4138.315 4141.177 4 1 44.28 5 4147.525 4147.982 41 48 327 4 1 49.806 4150.846 4151.938 41 55.254 4 156.370 41 57.453 4 1 58.476 41 59.43 1 41 60.300 4160.825 4164.028 41 67.098 41 69.951 4172.372 4,5 t 7 . 6 3,44-6,5 2,3 t 5,4 1,2+4,3 0,1+3,2 5 t 6 4 t 5 3 +-4 2 t 3 14-2 quad.24-1 3 + 3 44-3 54-4 6 t 5 3,2+0,1 4,3 t 1,2 5,4+2,3 6,5 t 3 , 4 7,6 +4,5 4693.38 5 4695.769 4698.685 4701.860 4705.258 4709.230 471 2.902 4713.415 47 19.945 4720.340 4722.066 4723.545 4724.172 4726.467 4727.067 4728.978 4729.550 4 t 7 3 t 6 2+5 14-4 Oe3 quad." 4,l t l , l 4 , 2 t l , l 4,l +1,0 5,3 +2,2 5-2 6,4 4-3,3 6+3 7,5 t 4 , 4 7 t 4 ' " quad." indicates quadrupole transitions due to free H2 in the absorption cell. these obscures the I = I t 2 HD-Ar transition. The H20 lines were minimized by prolonged pumping on the spectrometer vacuum tank. The S(0) spectrum is shown in fig. 8, and the measured line positions for HD-Ar are listed in table 3. The upper trace in fig. 8 is the spectrum observed after the absorption cell was filled with HD but before argon was added.The R(2) dipole ( j = 3 t 2 ) and S(0) quadrupole ( j = 2 t 0 ) lines of HD are prominent in this background spectrum, and other weak lines are also present: some of these are due to residual H20 in the spectrometer tank, and others due to an impurity (possibly C2H2) in the HD sample. The broad, weak features in the background (ca. 3880, 3885 and 3889 cm-l) may be due to the (HD)2 Van der Waals dimer, which has not previously been studied [CL (H2)2 and (D2)2 spectra 2*25]. When argon is added to the HD (middle trace of fig. 8), the resulting spectrum shows prominent HD-Ar features, but the lines are less sharp than H,-Ar98 HYDROGEN-RARE-GAS SPECTRA 9 5 1 ! : : : : ! : : ; : ! : : : 3625 3630 3635 wavenumber/cm- FIG.7.-Spectrum of HD-Ar accompanying the Q(0) transition of HD in an HD + Ar mixture at 184 Torr and 77 K. Two H20 lines, due to residual water vapour in the spectrometer vacuum tank, are indicated. The vertical arrow indicates the Q(0) transition frequency of free HD (there is no line at this position). 100 90 n x O 100 3 2 b C -g C Y 90 -164 + 138 Torr Y H D + A r I HD S,(O) quadrupole - HD R , [ 2 ) dipole 3870 388 0 389 0 3900 wavenumberlcm- FIG. 8.-Spectrum of HD-Ar accompaning the S(0) transition of HD. The top trace shows the absorption due to the HD sample alone; it shows the prominent R(2) and S(0) transitions as well as weak lines due to residual H20 and another impurity. When Ar is added (middle trace) the spectrum due to HD-Ar appears, but when the total pressure is lowered (bottom trace) this spectrum does not become significantly sharper (see text).A .R. W. MCKELLAR 99 TABLE 3.-MEASURED POSITIONS OF LINES DUE TO THE HD-Ar MOLECULE ACCOMPANYING THE FUNDAMENTAL BAND OF HD Ql(0)j = O t O S , ( O ) j = 24-0 assignment assignment v/crn-' 1, J v/cm-' 1,J 3625.41 3625.978 3 626.65 3 3627.370 3628.130 3628.348 3628.887 3629.644 3630.47 3632.02 3632.838 3633.590 3634.333 3635.055 3635.752 3636.388 3636.966 3637.42 7,7 t 8,8 6,6 4-7,7 5,5 +6,6 4,44-5,5 3,3 +4,4 H20 a 2,24-3,3 H20 O,O+l,l 1,l t O , O 2 , 2 t l , l 3,3 t 2 , 2 4 , 4 t 3 , 3 5,5 t 4 , 4 6,64-5,5 7,7 c 6 , 6 8,8 4-7,7 9,9 4- 8,8 3869.28 3871.13 3873.09 3874.354 3875.26 3877.51 3887.68 1 3895.89 3 8 98 -04 3900.08 3901.89 3903.53 3904.73 6,8 t 9 , 9 5,7 4-8,8 4,6 +7,7 R(2) dipole ' 3,5 +6,6 2,4 t 5,5 S(0) quad.' 5,3 +2,2 6 , 4 t 3 , 3 7,5 t 4 , 4 8,6 c 5 , 5 9,7 4-6,6 10.8 +7,7 ' Line due to residual HzO in spectrometer vacuum tank, used to calibrate this band.24 * Thir The R(2) dipole and S(0) quadrupole lines H 2 0 line is blended with the l , l t 2 , 2 line of HD-Ar.of free HD were used for absolute calibration of this band. under similar conditions. When the total pressure is lower (bottom trace of fig. S), the HD-Ar lines do not become significantly sharper. This behaviour indicates that the region of predissociation-limited linewidth has been reached for HD-Ar S(O), as suspected previ~usly.~ Predissociation is expected to be more rapid in Van der Waals species containing HD than in those containing H, or D2 because of the much greater effective anisotropy in the intermolecular potential, which results from the non-coincidence of the centre of mass and geometric centre in HD.The selection rule A j = 0,1,2, . . , applies to predissociation in HD-Ar, whereas in H,Ar or D2-Ar, the possible channels for predissociation are limited by A j = 0,2,4 . . . In contrast to S(O), it was found that the HD-Ar Q(0) spectrum continued to sharpen as the pressure was lowered. In this case, predissociation of the upper state (u = 1, j = 0) must involve a change in u, and this process is expected to be much slower than the Au = 0 processes possible from the upper state ( u = 1, j = 2) of S(0). The observed linewidths are discussed in more detail in section 3(e). When the previous HD-Ar S(0) measurements were compared with calculations 11 based on the potential function derived from H,-Ar and D,-Ar, relatively large discrepancies were found." These were attributed to a particular sensitivity of HD- Ar energy levels to different portions of the potential.However, it was later realized l4 that the HD-Ar calculations 11*i2 were not valid, in that a larger basis set is required in this case and that shifts due to coupling with the continuum (also responsible for the observed predissociation) cannot be ignored. Such computational difficulties, together with the experimental difficulties in accurately measuring the positions of the100 HYDROGEN-RARE-GAS SPECTRA 100- 99 98 9 7 - 3 L G ." v) *E EJ 100- l-l + broadened lines, render the HD-Ar S(0) spectrum less useful than originally hoped.'J1 However, these problems are considerably less serious for the newly observed HD-Ar Q(0) spectrum. (c) D,-Ar Spectra of D2-Ar accompanying the Q(0) and S(0) transitions of D2 are shown in fig.9, and the measured line positions are listed in table 4. The upper trace in fig. 9 -- -. c H4 I 1 I 2990 2995 300C g5t t I I 1 I I I I 31 50 3160 3170 31 80 wavenumber/cm - FIG. 9.-Spectra of D2-Ar accompanying the Q(0) and S(0) transitions of D2 in an ortho-D2 + Ar mixture at 164 Torr (upper trace), 106 Torr (lower trace), and 77 K. The upper [Q(O)] trace shows absorption due to CH4 impurity; note the shift between the Q(0) frequency of free D2 (marked by the vertical arrow) and the apparent band origin " yo" of the Dz-Ar pattern.The background curvature and relatively poor signal-to-noise ratio of the lower [S(O)] trace are due to absorption by ice on the cell windows (see text). represents the first observation of the resolved Q(0) spectrum for D2-Ar; in previous work this band was too weak and obscured by impurity absorptions to be observed. Some absorption due to an impurity [the P(2) and P(3) lines of the v3 band 2o of CH,] remain in the Q(0) region, and these were used to help fix the absolute wavenumber scale. The observed absorption in these lines corresponds to a methane impurity ofA . R . W . MCKELLAR 101 only ca. 0.5 ppm in the ultra-high-purity (99.9995%) argon sample used. In pre- liminary experiments with high-purity (99.995 %) argon, the CH4 absorption was more than ten times stronger.TABLE 4.-MEASURED POSITIONS OF LINES DUE TO THE D2-Ar MOLECULE ACCOMPANYING THE FUNDAMENTAL BAND OF Dz Ql(0) j = 0 +O S , ( O ) j = 2 c o vlcm - assignment vlcm - 1 assignment 1,J LJ 2987.040 2987.485 2987.988 2988.549 2989.08 a 2989.690 2990.297 2990.904 299 1.542 2994.042 2994.659 2995.287 2995.83 5 2996.402 2996.952 2997.475 2997.955 2998.375 9.9 +10,10 8,8 c9.9 7,7 t 8,8 6,6 +7,7 5,5 t 6 , 6 4,4 + 5,5 3,3+4,4 2,2 +3,3 1,l t 2 , 2 2,2+3,3 3,3 +4,4 4,4 4- 5,5 5,5 +6,6 6,6 t 7 , 7 7,7 +8,8 8,8+9,9 9,9 t10,lO 10,lO + 1 1,ll 3 148.025 3 149.246 3 150.692 3 152.290 3153.995 3 155.768 3 1 57.585 3 159.472 3 161.35 3166.359 3 170.29 3 172.159 3 173.986 3 175.725 3 177.387 3 1 78.964 3 180.41 8 3 18 1.676 3 182.64 8,10+ll,ll 7,9+10,10 6,8+9,9 5,7+8,8 4,6+7,7 3,5+6,6 2,4+5,5 1,3 4-4,4 0,2+3,3 4,24-3,3 5,3 +4,4 6,4+5,5 7,5+6,6 8,6+7,7 9,7 +- 8,8 10,8t9,9 11,9+10,10 12,104-11,ll S(0) quad.* This line is blended with a line due to CH4 impurity (see fig. 9). This is the S(0) quadrupole transition of free DZ. While recording the D,-Ar spectra it was found that the intensity of the infrared radiation transmitted through the absorption cell fell considerably over the period of a few days required to complete an experiment. This effect is believed to be due to the accumulation of a thin layer of ice (H,O) on the side of the (cold) cell windows facing the insulating vacuum space. The ice absorption was especially severe in the D, S(0) region, which lies quite near the peak of the 3.1 pm ice band.The ultimate signal-to-noise ratio obtained for S(0) was limited by this effect, and the spectral background in this region was also affected with the result that the lower trace in fig. 9 has not been " flattened " very successfully. ( d ) H,-Kr Spectra of the H,-Kr molecule are shown in figs. 10-12, and measured line positions are listed in table 5. Most of the comments made regarding H,-Ar in section 2(a) also apply to these H,-Kr results. Analysis * of the previous H,-Kr measurements suggested that they were less satisfactory than those for H,-Ar and H,-Xe, and it is anticipated that the new data in table 5 represent a correspondingly greater improve-102 '00-i, 95- HYDROGEN-RARE-GAS SPECTRA n 90.- x ._ 100- W m v) -g 3 c) 9 5 - 4 155 4 160 4 165 wavenumberlcm- FIG.10.-Spectrum of H2-Kr accompanying the Q(0) transition of Hz in a para-H2 + Kr mixture at 103 Torr and 97 K. The asterisks mark absorption lines of CO present as an impurity in the infrared source chamber. The arrow marks the transition frequency of the free H z molecule; note the shift (ca. 1.6 cm-') between this and the apparent centre of the H2-Kr pattern. r I I I I 4480 4490 4 500 41 50 1 I I 1 1 1 4490 4495 4500 wavenumberlcm- FIG. 11.-Spectrum of Hz-Ar accompanying the S(0) transition of H2 in a para-Hz + Kr mixture at 108 Torr (upper trace) or 69 Tom (lower trace) and 97 K. The arrows mark the S(0) quadrupole transition of free Hz, and the vertical lines indicate features for which measured positions are given in table 5.A . R . W .MCKELLAR e v, .M .- g 100.- c e +a 95.. 103 I I I 1 I I I I I 4 1 4 0 4 150 4160 4170 I I I I ment. In particular, the new Q(l) measurements differ considerably from those of McKellar and Welsh,5 thus confirming the suspicion of Le Roy and Van Kranendonk * that there were serious measurement errors in this region. (e) LINEWIDTH MEASUREMENTS The measured linewidths (full width at half maximum) of typical lines in a number of bands of the H2-Ar and HD-Ar molecules are shown as a function of density in fig. 13(a). The behaviour of widths for D,-Ar and H2-Kr was similar to that shown in fig. 13(a), but the HD-Ar S(0) spectrum was rather different, and is considered separately below. The pressure broadening measurements have been corrected for the effects of instrumental resolution, but they are only accurate to ca.10 or 20%. In particular, the small differences between the different bands in fig. 13(a) are only marginally significant, and may partly be due to the different hydrogen/argon mixing ratios used in each case. From these data, the pressure broadening coefficient for lines of H,-Ar, HD-Ar and D2-Ar appears to be ca. 0.16 cm-’ amagat-l* at 77 K, which is equivalent to 22 MHz Torr-’. As mentioned above, the widths in the HD-Ar S(0) spectrum were found to be limited by predissociation at the pressures used here. The measured widths of re- solved N and T lines (see fig. 8) are plotted in fig. 13(b) as a function of Z‘, the quantum number for end-over-end rotation in the upper state (u = 1, j = 2) of the transition. Note that different J’ substates are involved for N- and T-branch lines, and there may thus be two points for each I’ (this actually occurs only for I’ = 5).The un- * See caption to fig. 1.1 04 HYDROGEN-RARE-GAS SPECTRA TABLE s.-MEASURED POSITIONS OF LINES DUE TO THE H2-Kr MOLECULE ACCOMPANYING THE FUNDAMENTAL BAND OF H2 Ql(0)j = O+-0 S , ( O ) j = 24-0 Ql(l)j = 1-1 S,(l)j = 3 t l v/cm-' assignment v/cm-' assignment v/cm-' assignment v/cm- assignment 1,J LJ 4J 1,J 41 52.207 4152.767 4 1 53.540 41 54.421 4155.365 41 56.361 41 57.390 4158.435 4 1 60.5 1 7 4161.553 4162.551 4163.544 41 64.502 4 1 65.394 41 66.226 41 66.940 7,7 + 8,8 6,6 4-7,7 5,5 t 6 , 6 4,4 t5,5 3,3 t 4 , 4 2,2 +3,3 1,1+2,2 0,0+1,1 1,l t 0 , o 2,2 t 1,l 3,3 t 2 , 2 4,4t3,3 5 3 +4,4 6,6t5,5 7,7 +6,6 8,8t7,7 4475.3 8 8 4477.675 4480.326 448 3.1 96 448 6.220 4489.3 64 4489.886 4490.093 4490.68 5 4490.891 4491.617 4491.779 4492.766 4493.678 4496.462 4497.321 4497.838 4499.027 4501.882 4502.192 4502.739 4503.039 4503.561 4503.758 4504.200 4507.244 45 12.864 451 5.325 45 17.27 5,7 4-83 4,6t7,7 3,5 t 6 , 6 2,4 t 5,5 1,3 t 4 , 4 0.2 t 3 , 3 6,7 t 7 , 7 6,6 t 7 , 7 5,6 t 6,6 5,5 t 6 , 6 4,5 t 5 , 5 4 , 4 4 3 2,o t 1,l 2 , 1 t l , l quad.6,5 t 6 , 6 7,6 t 6 , 6 7,7 c6,6 4,2+1,l 5,3 t 2 , 2 7,5 +4,4 8,6t5,5 9,7 t 6 , 6 4133.351 4135.630 4138.239 4141.027 4143.915 4146.156 41 46.793 4147.5 13 4 1 48.390 4 149.326 4 1 50.300 41 51.285 41 52.234 41 54.510 41 55.254 4155.520 4156.530 4157.542 4158.500 41 59.405 4163.052 4 1 65.944 41 68.739 4171.398 4173.772 5,6 t 8,7 4,5 t 7 , 6 3,5 t 6 , 5 1,2 4-4.3 2,3 +.5,4 0,1+3,2 quad. 4,3 t l , 2 5,44-2,3 6,5t3,4 7,6t4,5 8,7t5,6 4689.03 4690.734 4693.082 4695.775 4698.688 4701.758 4704.972 4712.902 4720.920 4721.663 4722.260 4724.626 4725.266 4727.390 4728.027 4729.866 4730,537 4732,535 6 t 9 5 t 8 44-7 3 t 6 2 t 5 14-4 O t 3 quad. 5,2 t 2 , 2 5,3 t 2 , 2 5,2 t 2 , 1 6,4 t 3,3 6,3 t 3 , 2 7,5 +4,4 7,4 t 4 , 3 8,6t5,5 8,5 t 5 , 4 certainties in the measurements of fig. 13(b) are rather large (10-2073, but the striking trend of narrower widths at higher I' in the T branch is quite definite. It may easily be observed in the spectrum itself (fig. 8), and was in fact noted by Weiss 26 in the earlier results of M~Kellar.~ The open points in fig. 13(b) are calculated widths from the recent work of Corey and Le Roy:27 they reproduce the magnitude and 2'- dependence of the observed widths quite well, though they underestimate all the widths by ca. 20%.There are no calculated widths for 1' = 8 and 9 because these levels lie above the u = 1, j = 2 energy asymptote and are thus subject to direct rotational predissociation. In spite of this, they are the narrowest lines in fig. 13(b). T(7), with 1' = 10, is not plotted in the figure, but it is visible in fig. 8; it definitely shows broadening due to direct rotational predissociation. The calculations of Corey and Le Roy 27 predict that the sharpest levels for HD- Ar with u = 1, j = 2 are those with I' = J', and particularly I = J = 2 with a width of 0.08 cm-'. These particular levels are not involved in N or T transitions, but they do participate in P and R transitions.Intensity calculations for H2-Ar suggest thatA . R. W. MCKELLAR 0 . 0 . 8 - 0.6- 105 I I I 0.5 1 .o 1.5 A A A A o A A A n - A 0 d e n s i t y (amagat) A (b) - a 0 0 0 0.4 r( I E E 4 3 5 f 2 3 . ? c .- I 0.2 0.41 0 0 1 3 5 7 9 I’ FIG. 13.-Measured linewidths (full width at half maximum) for lines in the spectra of hydrogen-rare- gas Van der Waals molecules, corrected (approximately) for instrumental resolution. The upper graph (a) shows pressure-broadening measurements [O, H2-Ar Ql(0); 0, H,-Ar S1(0); +, H2-Ar Ql(l); A , HD-Ar Ql(0)]. The lower graph (6) shows widths of N-branch (A) and T-branch (0) lines in the HD-Ar Sl(0) spectrum as a function of l’, the quantum number for end-over-end rotation in the upper state.These widths are due to predissociation, and they are compared with calculations (open symbols) of Corey and Le Roy.27 Note: in (b) the solid triangles should be moved one unit to the right. P-branch transitions with 1’ = J’ are considerably stronger than the corresponding R- branch lines. Thus one might expect to see a series of relatively sharp lines in the HD-Ar S(0) spectrum P branch. This is indeed the case, as can be seen in fig. 8 where there are 5 or 6 sharper (but unresolved) lines in the 3880-3885 cm-’ region. This observation and the comparison in fig. 13(b) offer strong support for the reli- ability of the secular equation approach used by Corey and Le Corey and Le Roy have also calculated predissociation widths for H2-Ar and D,-Ar S(0) spectra. Their predicted widths generally fall in the range from 0.005 to 0.05 cm-I, which is narrower than can be detected experimentally in the present study.There is, however, one exceptional level predicted to be considerably broader : 1 = 2, J = 0 with a predicted width of 0.123 cm-l in H,-Ar. It turns out that this level is only involved in one possible line of the S(0) spectrum, the R-branch transition with 1,J = 2,0+1,1. Unfortunately, in H,Ar this transition is predicted ‘ 9 ’ to lie106 HYDROGEN-RARE-GAS SPECTRA directly underneath the H, S(0) quadrupole line (see fig. 5) and thus its width cannot easily be checked. And in D2-Ar, the central part of the S(0) spectrum was not sufficiently well-resolved to observe this transition clearly.However, all is not lost: assuming that the relative predissociation lifetimes for H2-Kr will be similar to H2-Ar and D2-Ar, we can turn to the S(0) spectrum of this molecule, in fig. 1 1 . An expanded view of the relevant region is shown in fig. 14. At a total pressure of 69 Torr, the H, l:!;!;!;!;!:!:!;.: 4 4 9 2 L 4 9 4 4 4 9 6 4 4 9 8 4 500 wavenumberlcm- FIG. 14.-Expanded view of the H2-Kr S(0) spectrum shown in fig. 11. The upper trace is calculated using the line positions and intensities of Dunker and G ~ r d o n . ~ Note the line at 4496.46 cm-I whose greater width (0.144 cm-') is believed to be due to predissociation. S(0) quadrupole line has a width of 0.083 cm-' (including instrumental resolution), and most isolated H2-Kr lines have widths of ca.0.10 cm-l. However, one H,-Kr line has a measured width of 0.144 cm-l, as shown in fig. 14, and this line is indeed the Z,J = 2 , 0 t l , l transition, which terminates on the level (2,O) expected 27 to be short- lived. Moreover, this line (at 4496.46 cm-') is predicted 'p9 to be unblended and well isolated, and its observed peak intensity is less than predi~ted,~ just as expected for a line broadened by predissociation. The contribution to the width of this line due to predissociation may be estimated to be ca. 0.1 1 cm-l, which is remarkably close to the value of 0.123 cm-' predicted by Corey and Le Roy 27 for the same transi- tion in H2-Ar. Beswick and Requena 28 have predicted predissociation widths for H,-Ne, H2-Ar and H2-Kr in a few chosen (I,J) levels with j = 2, 4 and 6.Their calculations are for u = 0 rather than v = 1 as required here, but a comparison is still of interest. For H,-Kr with j = 2, I = 2 and J = 0, their calculated width (f.w.h.m.) is 0.022 cm-', which is considerably smaller than the experimental value reported here. 4. DISCUSSION In the above discussion of predissociation, only brief mention was made of the " direct " rotational predissociation process involving levels located above the asymp-A . R. W . MCKELLAR 107 tote of the potential surface and bound only by the centrifugal energy barrier in the potential for larger I values. These effects were well observed in previous ~ p e c t r a , ~ and the relevant widths have been well calculated.8 An interesting aspect of the present work is that transitions involving these quasibound levels tend to " disappear " as the pressure is reduced and the resolution increased, because they do not continue to sharpen below a certain pressure.This effect is apparent at the outer edges of the N and T branches in fig. 1, and may also be seen by comparing many of the present spectra with their earlier eq~ivalents.~. Further work on Van der Waals spectra accompanying the fundamental bands of molecular hydrogen is planned to improve the measurement accuracy of the present results, and to extend these high-resolution studies to other species: HD-Kr, D,-Kr; H,-Xe, HD-Xe, D,-Xe; D,-Ne; (H,),; (D2),; (HD),. Similar spectra may also be studied in other spectral regions. The hydrogen overtone (u = 2 ~ 0 ) spectra in the 1-2 pm region are expected to be ca.25 times weaker than those studied here, but they should yield considerably more information on the dependence of the potential surfaces on. the internal stretching motion of the hydrogen. Van der Waals spectra will also accompany the pure rotational (u = Ot-0) hydrogen transitions in the 20-70 pm far-infrared region. A study of these spectra should yield more precise informa- tion on the anisotropy of the potential for u = 0. This is because the ( u = l+O) spectra studied to date tend l4 to give information on anisotropy for u = 1, since the j = 2 level which supplies a majority of this information is only observed for u = 1. At much lower frequencies, it is also possible to observe pure hyperfine spectra of H,-Ne, H,-Ar and H,-Kr with 21 = 0 and j = 1, as demonstrated recently by Waaijer 29 using molecular-beam magnetic resonance; these results may be used to impose further constraints on parameters of the intermolecular potentials.In summary, new high-resolution spectra of the H,-Ar, HD-Ar, D,-Ar and H,-Kr molecules have been obtained in the regions of the hydrogen fundamental bands. Compared with previous work, the spectral resolution is improved by a factor of 3-6 and the measurement accuracy by a factor of 2 or more. Fully resolved Q(0) spectra for HD-Ar and D,-Ar are reported for the first time. Predissociation broadening due to Au = 0, Aj = 1,2 processes is observed for certain transitions of HD-Ar and H2-Kr. These observations are especially valuable because, in spite of the considerable recent interest in predissociation processes in Van der Waals mole- cules, there are very few experimental measurements involving systems where the relevant potential surfaces are known.I am grateful to J. L. Hunt for providingpara-hydrogen catalyst, to J. G. Potter for construction of the slow-scan drive, to C . A. Harris and J. W. C. Johns for experi- mental assistance and to I. K. M. Strathy for initial assembly of the 5.5 m cell. Special thanks are due to J. R. Austin for invaluable assistance in computer programming and data collection. A. K. Kudian, H. L. Welsh and A. Watanabe, J. Chem. Phys., 1965,43, 3397. A. Watanabe and H. L. Welsh, Phys. Rev. Lett., 1964, 13, 810. A. K. Kudian and H. L. Welsh, Can. J. Phys., 1971, 49, 230. A. K. Kudian, H. L. Welsh and A. Watanabe, J. Chem. Phys., 1967, 47, 1553. A. R. W. McKellar and H. L. Welsh, J . Chem. Phys., 1971, 55, 595. A. R. W. McKellar and H. L. Welsh, Can. J . Phys., 1972,50, 1458. A. R. W. McKellar, J. Chem. Phys., 1974, 61, 4636. R. J. Le Roy and J. Van Kranendonk, J . Chem. Phys., 1974,61,4750; and the Supplement to this work : Chemical Physics Research Report CP-22 (University of Waterloo, Canada, 1974). A. M. Dunker and R. G . Gordon, J . Chem. PhyJ., 1978, 68, 700.108 HYDROGEN-RARE-GAS SPECTRA lo A. N. Petelin, Opt. Spectrosc. (Engl. Transl.), 1975, 38, 21. l1 H. Kreek and R. J. Le Roy, J. Chem. Phys., 1975, 63, 338. It R. J. Le Roy, J. S. Carley and J. E. Grabenstetter, Faraday Discuss. Chem. SOC., 1977, 62, 169. l3 J. S. Carley, Faraday Discuss. Chem. SOC., 1977, 62, 303. I4 R. J. Le Roy and J. S. Carley, Adv. Chem. Phys., 1980, 42, 353. l5 H. Thuis, S. Stolte and J. Reuss, Comments Atom. Mol. Phys., 1979, 8, 123. l6 H. L. Welsh, in Spectroscopy, M.T.P. International Reviews of Science, PhysicaZ Chemistry (Butterworths, London, 1972), vol. 3, p. 33. J. U. White, J. Opt. Soc. Am., 1942, 32, 285. A. E. Douglas and D. Sharma, J. Chem. Phys., 1953, 21, 448. l9 J. W. C. Johns, A. R. W. McKellar and D. Weitz, J. Mol. Spectrosc., 1974,51, 539. 2o A. S. Pine, J. Opt. Soc. Am., 1976, 66, 97. 22 A. R. W. McKellar, W. Goetz and D. A. Ramsay, Astrophys. J., 1976, 207, 663. 23 A. R. W. McKellar and T. Oka, Can. J. Phys., 1978,56, 1315. 24 C. Camy-Peyret, J. M. Flaud, G. Guelachvili and C. Amiot, M d , Phys., 1973, 26, 825. 25 A. R. W. McKellar and H. L. Welsh, Can. J. Phys., 1974,52, 1082. 26 S. Weiss, J. Chem. Phys., 1977, 67, 3840. 27 G. C Corey, MSc. Thesis (University of Waterloo, Waterloo, Canada, 1980); G. C. Corey and R. J. Le Roy, unpublished work, 1981. 28 J. A. Beswick and A. Requena, J. Chem. Phys., 1980,72,3018; see also: J. A. Beswick and A. Requena, J. Chem. Phys., 1980,73,4347. 29 M. Waaijer, Thesis (Katholieke Universiteit, Nijmegen, The Netherlands, 1981). G. Guelachvili, Opt. Commun., 1973, 8, 171.