J. Phys. Chem. 1994, 98, 11863- 11869
11863
Rotational Spectra of Pyridine-(Argon),, n = 1, 2, Complexes and Their Vibrationally Averaged Structures R. M. Spycher, D. Petitprez,? F. L. Bettens, and A. Bauder* Laboratorium f i r Physikalische Chemie, Eidgenossische Technische Hochschule, CH-8092 Zurich, Switzerland Received: June 13, 1994; In Final Form: September 2, 1994@
Rotational spectra of the van der Waals complexes of pyridine-14N- and pyridine-lsN-(argon)2 have been observed in a pulsed nozzle Fourier transform microwave spectrometer over the frequency range 8- 18 GHz. In addition, pyridine-15N- and pyridine-&-argon complexes have been investigated. The rotational spectrum of the pyridine-& monomer has been measured in a conventional Stark spectrometer. The structures of both types of complexes have been determined, accounting for large-amplitude van der Waals vibrations. A C, symmetric structure has been found with the argon above the ring plane at a distance of 3.545( 1) A from the center-of-mass of pyridine and including an angle of 3.2(4)' with the principal axis c of pyridine. The second argon assumes a symmetrically equivalent position below the ring plane where the angles are increased slightly to 3.92(4)', indicating negligible three-body effects.
Introduction A considerable number of complexes between aromatic molecules and argon have been measured by microwave spectro~copy'-~ as well as by resonance-enhanced multiphoton ionization (REMPI) s p e c t r o s ~ o p ywith ~ ~ ~rotational resolution. In all the observed complexes, argon is located above the ring plane of the aromatic molecule in its symmetry plane. Centrifugal distortion effects and the structure of the complex shed light on the intermolecular force field. Even simple aromatic molecules may be complexed by more than one argon atom,1° leading finally to a microdroplet of argon with the aromatic molecule dissolved in it. With two or more argon atoms attached to an aromatic molecule, several isomers were assigned to observed spectral features in REMPI spectra. The different isomers were assumed to be the result of binding argon atoms to the same side of the aromatic ring plane or to both sides.l0 Recently, Weber and Neusser" observed the rotationally resolved REMPI spectrum of benzene-(argon)z. They concluded from the fitted rotational constants that the two argon atoms occupied symmetric positions on both sides of the benzene ring plane. Challenged by these experiments, we tried successfully to measure the microwave spectrum of the corresponding furan-(argon)z complex.12 Furan as a polar aromatic monomer was selected because the permanent electric dipole moment necessary for observing a microwave spectrum vanishes for benzene-(argon)z by symmetry. In an attempt to broaden the experimental basis of such complexes with two argon atoms, we investigated the analogous pyridine-(argon)2 complex. We report here the results of the investigation of the rotational spectra of pyridine-14N- and pyridine-15N-(argon)~. The spectra were measured with a pulsed nozzle Fourier transform microwave (FTMW) spectrometer in the frequency range 8-18 GHz. The structure of the complex was approximated from the experimentally determined rotational constants. The pyridine-argon and pyridine-dl -argon complexes were measured previously by Klots et d4 The authors noticed disturbing effects of large-amplitude van der Waals vibrations t Present address: Laboratoire de Spectroscopie Hertzienne, U.F.R. de Physique, Universitk de Lille, F-59655 Villeneuve d' Ascq, France. @Abstractpublished in Advance ACS Abstracts, October 15, 1994.
0022-3654/94/2098-11863$04.50/0
between pyridine and argon during a structure determination. A specialized method was introduced for the structure determination which considered explicitly the van der Waals bending vibrations. Thereby the moments of inertia of the complex and those of the corresponding pyridine monomer were required. Mean amplitudes of these bending vibrations were estimated in addition to the location of argon above the pyridine ring plane. Questions about the new method for the structure determination of complexes led us to investigate further isotopomers of pyridine-argon. The results of the measurements for the rotational spectra of pyridine-15N- and pyridine-ds-argon are reported here. In addition, the results from Stark spectroscopy are given for the pyridine-d5 monomer, which apparently was never measured before. These results were needed for the structure determination. Experimental Section Spectrometers. The design of our pulsed nozzle FTMW spectrometer is similar to the instrument described by Balle and Flygare.13 The details were reported p r e v i o u ~ l y and , ~ ~only ~~~ a short description of the operating conditions is given here. In order to improve the sensitivity, four microwave pulses of 1ps duration and a power of 0.5 mW were applied to one gas pulse propagating perpendicularly through the cavity axis. The polarization decay signals of the complexes were coadded from a few hundred gas pulses digitized at a rate of 5 MHz for 5 12 channels with an 8-bit analog-to-digital converter. Peak frequencies of rotational transitions were interpolated to an accuracy of 5 kHz from the Fourier transformed power spectrum with a channel separation of 38 kHz. At least two measurements were performed with two slightly different microwave frequencies. Complexes were formed by expanding a gas mixture of 0.5% pyridine in argon at a total pressure of 3 bar through a nozzle of 0.5 mm diameter into the vacuum chamber using a pulsed valve (General Valve, Series 9). The Stark spectrometer with a phase-locked backward wave oscillator as the radiation source was equipped with a 4 m long X-band Stark cell for the frequency range 26.5-40 GHz. Frequency measurements of rotational transitions were made to an accuracy of 50 kHz at pressures of 0.1 Pa and power levels of 0.4 mW with the Stark cell cooled to -30 "C. The final frequency was obtained as the average of two measurements from sweeps in both directions. 0 1994 American Chemical Society
11864 J. Phys. Chem., Vol. 98, No. 46, 1994
Spycher et al.
TABLE 1: Observed Rotational Transition Frequencies (MHz) of the Pyridine-W-(Argon)z Complex
616-505 717-606 221-110 220-111 322-211 321-212 423-312 422-313 52-413 523-414 734-725 633-624 836-827
7 993.9315 8 913.0576 9 196.5370 9 199.6626 10 123.5347 10 132.9172 11 048.9323 11 067.7151 11 972.7252 12 004.0589 12 228.7623 12 229.0141 12 229.0542
-0.9 1.0 -0.6 -1.3 1.7 -0.5 1.2 0.0
0.8 -1.1 2.5 1.4 -1.4
735-726 532-523 634-625 533-524 431-422 432-423 625-514 624-515 533-422 532-423 634-523 633-524
12 229.1371 12 229.2018 12 229.2195 12 229.3058 12 229.3417 12 229.3846 12 894.9040 12 941.9610 16 879.9219 16 879.9697 17 809.8156 17 809.9232
0.9 -0.2 -2.4 -0.9 1.3 -0.6 -1.6 1.3 -1.2 1.7 -1.9 0.9
TABLE 2: Observed Rotational Transition Frequencies (MHz) of the Py~idine-~~N-(Argon)* Complex
616-505 221-110 220-111 322-211
Av = vobs - vcdc in kHz. Chemicals. The samples of pyridine-15N (99% lSN, Cambridge Isotope Laboratories) and pyridine-d5 (99.5% D, Cambridge Isotope Laboratories) were purified by gas chromatography. Pyridine ('99% purity, Fluka) was used as received.
Spectral Analysis and Results Pyridine-(Argon)z. Frequencies of rotational transitions were predicted from a model with C, symmetry assuming that the second argon atom binds to an equivalent position on the opposite side of the ring plane than the first. The principal axis system of the complex had to be relabeled with respect to that of the pyridine monomer. The a axis of pyridine became the b axis of the complex, thus only giving rise to strong pb-type transitions of a nearly prolate symmetric rotor. The microwave spectrum of pyridi~~e-'~N-(argon)z was measured first because the absence of quadrupole hyperfine splittings produced stronger transitions than for the I4N parent species. Rotational transitions were identified near the predicted frequencies from the model. Finally, 16 R-branch and 9 Q-branch transitions were observed and accurately measured, as shown in Table 1. Each transition of the parent pyridine-14N-(argon)2 investigated subsequently was split into a triplet by the quadrupole coupling of the 14N nucleus. All the transitions in the Q-branch accumulated within 2 MHz, and their quadrupole components could not be assigned unambiguously. Thus, only 9 R-branch transitions were observed for this isotopomer due to the reduced intensity of the split transitions. The measured frequencies are listed in Table 2. The transitions of the isotopomers of pyridine-(argon)z were at least 1 order of magnitude weaker than those of pyridineargon. For the parent pyridine-l4N-(argon)2, three rotational constants, two quartic centrifugal distortion constants, and the two diagonal quadrupole coupling constants were fitted simultaneously to the measured transition frequen~ies.'~The centrifugal distortion constants are defined according to Watson's asymmetric reduction in the prolate I' representation.16 Similarly, three rotational and four centrifugal distortion constants were fitted to the frequencies of pyridine-15N-(argon)z. The results of the least-squares fits are collected in Table 3 with uncertainties given in parentheses as one standard deviation. Pyridine- Argon. Rotational transitions for pyridine-15Nargon and pyridine-&-argon were predicted from the structure of the parent pyridine-argon4 and the moments of inertia of pyridine-'5N'7.18and of pyridine-d5 given below. In the absence of quadrupole splittings for py~idine-'~N-argon,even 3 week pu,-typetransitions were measured besides 19pb-type transitions in the isotopically enriched sample. Their frequencies are listed in Table 4. It was subsequently found that the transitions of this isotopomer could be detected in natural abundance.
5 -4 2- 1 3-2 1-0 3-2 2- 1 3-2 4-3 2- 1 4-3 3-2 4-3 5 -4 3-2 3-2 5 -4 4-3 5-4 6-5 4-3 4-3 6-5 5-4
vobs
AV
8 032.1500 9 278.4641 9 279.9937 9 281.2544 9 282.1014 9 282.4663 10 206.7119 10 208.2753 10 209.1464 10 215.0970 10 215.5611 11 133.8456 11 135.2865 11 135.8380 11 149.1201 11 149.3097 11 149.9765 12 059.6724 12 061.0387 12 061.4237 12 084.5696 12 084.7348 12 085.5340
0.0 1.7 -2.2 -2.4 -1.3 4.5 0.9 -1.0 -0.3 0.2 -0.6 1.3 0.6 3.8 -1.3 -1.7 -2.0 -6.3 2.8 0.6 3.9 0.8 -1.9
vcdc in kHz.
TABLE 3: Spectroscopic ConstanW of Pyridine-(Argon)z Complexes from Least-Squares Fits of Rotational Transitions constant pyridine-l4N-(argon)z pyridi~~e-~~N-(argon)~ AMHz BIMHz CIMHz AjikHz AIKWZ A~fldlz d,/kHZ &/kHz x-IMHz XbdMHz x,,/MHz
2938.5064(7) 466.5627( 12) 464.14 18(12) 0.479(15) -0.129(43) 2.001b 0.0029b
0.0'
291 1.03029(38) 466.65273(30) 463.52939(24) 0.3326(34) 1.9099(60) 2.001(40) 0.0029( 16)
0.0'
3.432(8) -4.872(5) 1.440(5)
Numbers in parentheses represent one standard deviation. Transferred from py~idine-'~N-(argon)~.Constrained to zero. The line widths of the rotational transitions of pyridine-dsargon were much broader than those of the former isotopomer. The broadening was attributed to unresolvable quadrupole splittings from five deuteriums. This caused a considerable decrease in line intensity, thus limiting the number of measured pb-type transitions to 9. The frequencies of the more intense quadrupole components due to the 14N nucleus are listed in Table 5 . Three rotational and five quartic centrifugal distortion constants were fitted to the measured transition frequencies of py~idine-'~N-argon.The results are given in Table 6 together with the uncertainties as one standard deviation of the fit. The distortion constant & is only marginally determined, as shown in Table 6 . Besides the three rotational and two centrifugal distortion constants, the two independent diagonal quadrupole coupling constants of 14N were fitted for pyridine-&-argon. The small number of measured transition frequencies did not allow the fitting of all centrifugal distortion constants. Thus the remaining distortion constants were constrained to the values of the former isotopomer. The results are included in Table 6. Pyridine-ds. A set of rotational constants for pyridine-ds was predicted using the differences of the known moments of inertia between the parent and all singly substituted species of pyridine17J8in a fitting procedure.lg It was noticed that the
J. Phys. Chem., Vol. 98, No. 46, 1994 11865
Rotational Spectra of Pyridine-(Argon), Complexes TABLE 4: Observed Rotational Transition Frequencies (MHz) of the Pyridine-’%”Argon Complex J’,
a c
-
633-624 511-574
AV
= Yobs
vobs
AP
8 785.3311 8 791.5440 8 901.9002 8 943.5144 9 242.3628 9 244.9550 9 245.2480 9 579.9860 9 608.6895 10 058.9729 10 073.1599 10 285.0735 11 976.1484 12 439.6518 12 482.3687 13 628.3066 14 812.9095 14 898.7606 15 144.2224 15 981.0314 17 178.6780 17 322.5896
0.4 -6.2 1.6 -1.8 0.9 -2.6 0.8 -1.4 -4.8 -0.3 2.9 -2.9 -1.6 -0.2 -0.9 1.6 -1.0
J’K&
212-101
0.5
3.6 4.3 -1.2 2.3
TABLE 5: Observed Rotational Transition Frequencies (MHz) of the Pyridine-&-Argon Complex
2- 1 3-2 4-3 3-2 2- 1 4-3 3-2 3-2 4-3 2- 1 6-5 5-4 5-4 3-2 6-5 AV
= Yobs
AP
vobs
8 768.478 8 769.980 10 579.268 10 580.896 11 041.947 11 042.210 11 042.660 11 062.145 11 063.664 11 064.525 12 884.555 13 318.117 13 360.527 13 361.064 15 660.511
-3 4 -1
4 -9 -0 -2 2 -5 8 0
2 -4 -2 -1
- Vcdc h kHZ.
TABLE 6: Spectroscopic ConstanW of Two Isotopomers of Pyridine-Argon Complexes from Least-Squares Fits of Rotational Transitions pyridine-I5N-argon
2956.1729(6) 1204.7768(31) 1190.6495(30) 3.4138(46) 19.504(32) -21.949(63) 0.0494(35) 70)
-Jt’qq
202-111
- Vcdc h k H Z .
F-F‘
TABLE 7: Observed Rotational Transition Frequencies (MHz) of Pyridine4 with Resolved Quadrupole Splittings
pyridine-d5-argon
2540.7073(421) 1147.1294(61) 1140.0784(59) 3.020(48) 18.35(43) -61.(8) 0.P 0.P
3.304(17) 1.445(12) -4.749( 12)
a Numbers in parentheses represent one standard deviation. Constrained to zero.
principal a and b axes of pyridine-ds were interchanged with respect to the parent species resulting in a pb-type spectrum. The line widths of the rotational transitions in the Stark spectrum were exceptionally broad (’300 kHz fwhm) despite the care taken to reduce them. The quadrupole splittings due to the 14N nucleus were only resolved for transitions with J 5 5 . A number
F-F‘
vobs
1-0 2-2 3-2 2-1 1-1 2- 1 2-2 3-2 1-0 3-2 2- 1 4-3 3-2 1-0 4-3 5-4 3-2 4-3 5-4 4-3 4-3 5-4 3-2 4-4 5-4 4-3 6-5 5-4 4-3 6-5 4-3 5-4
12 517.051 12 517.571 12 518.664 12 518.986 12 520.720 12 621.690 12 622.130 12 623.280 12 624.480 17 598.648 17 598.834 17 598.964 17 755.228 17 757.070 27 667.064 27 667.549 27 963.880 27 965.160 32 341.650 32 342.509 32 993.879 32 995.294 32 995.728 37 696.935 37 697.275 37 697.585 37 744.374 37 744.930 38 219.390 38 220.515
} }
AP
-36 15 5
-26 -9 -42 9 15 -5 10 -8 1 -6 3 -16 -28 -4 24 -52 -9 63 51 -58 -91 33
{
-:;
{-;:
28
18 11
of low J transitions were measured with the pulsed nozzle FTMW spectrometer in order to determine the quadrupole coupling constants accurately. The quadrupole components of the transitions with J > 5 were not resolved in the Stark spectrum. However, the frequencies of high J transitions were important for the determination of the centrifugal distortion. The measured frequencies of pyridine-ds are collected in Tables 7 and 8 for hyperfine resolved and unresolved transitions, respectively. Three rotational constants, five centrifugal distortion constants, and two quadrupole coupling constants were adjusted simultaneously in a least-squares fit.15 Watson’s16 asymmetric reduction was used in the oblate JIIT representation. The frequency of partially split or unsplit transitions were included for each underlying quadrupole component, but with a reduced statistical weight proportional to the intensity of the component. The result of the fit is given in Table 9 together with the standard deviations in parentheses. Vibrationally Averaged Molecular Structure In all known complexes between an aromatic molecule with CZ, symmetry and a rare gas atom, the latter is located above
the aromatic ring plane in a symmetry plane. The equilibrium structure of the complex is described conveniently with the structural parameters R and 8. As depicted in Figure 1, R measures the distance between the center-of-mass of the aromatic monomer and the rare gas atom and 8 refers to the angle between R and the principal axis c of the aromatic monomer. The same parameters will be used for the [1,1] complex between an aromatic molecule and two rare gas atoms located symmetrically on both sides of the aromatic ring plane. Because the labeling of the principal axis system of the complex
11866 J. Phys. Chem., Vol. 98, No. 46, I994
Spycher et al.
TABLE 8: Observed Rotational Transition Frequencies (MHz) of Pyridine45 with Unresolved Quadrupole Splittings S,,*S c 'qq
vobs
2015.5-2014,6 27 338.560 2016,5-20l5.6 27 376.444 1914.5-1913.6 27 402.529 1915.5-1914,6 27 425.620 1813,5-1812,6 27 455.357 1814.5-1813.6 27 468.999 1712.5-1711,6 27 498.879 1713.5-1712.6 27 506.667 1611.5-1610,6 27 534.704 1612,5-1611.6 27 538.978 1510.5-159.6 27 564.025 1511.5-1510,6 27 566.299 149,5-148,6 27 588.067 14105-149.6 27 588.984 128.5-127.6 27 622.570 127,5-126,6 27 622.570 41.3-32,~ 27 651.930 50.5-41.4 27 657.163 51,5-40,4 27 657.163 27 667.549 42.3-31.2 33,1-22,0 27 965.160 3030.0-3029,1 28 102.327 3030.1-3029,2 28 159.495 3832,6-3831.7 29 107.258 3131.0-3130.1 29 137.195 3131.1-3130.2 29 179.272 3232.0-3231.1 30 168.929 3937,3-3936.4 30 818.455 3226,6-3225,7 31 311.50 3227.6-3226.7 31 657.028 3736.1-3735.2 32 028.098 2721.6-2720,7 32 071.376 2722,6-2721,1 32 122.973 2620,6-2619.7 32 164.950 2621.6-2620,7 32 198.477 2519.6-2518.7 32 245.771 2520,6-2519,7 32 267.086 2418.6-2411,7 32 315.548 2419,6-2418.7 32 328.937 42,2-33,1 32 341.650 2317.6-2316.7 32 376.028 2318,6-2317,7 32 384.060 2216.6-2215.7 32 428.244
AV" Y ~ ~ q - J " q q -76 -69 -83 -62 -72 -66 -101 -109 -88 -109 -82 -77 121 -105 -143 100 143 -37 -38 103 306 130 109 77 86 97 72 -102 27 -45 -42 15 -51 -37 -7 -16 9 -73 69 -267 17 -7 36
v&s
2217,6-2216,7 32 433.044 2115,6-2114,7 32 473.192 2116.6-2115.7 32 476.033 2014,6-2013,7 32 512.073 2015.6-20147 32 513.594 1913,6-1912.7 32 545.098 1914.6-1913,7 32 545.994 1812,6-1811,7 32 573.590 1813.6-1812.7 32 573.875 1711,6-1710,7 32 597.689 1712,6-1711,7 32 597.689 1611.6-1610.7 32 617.848 1610.6-169.7 32 617.848 1510,6-159,7 32 634.795 159.6-158.7 32 634.795 149,6-148,7 32 648.711 148.6-147.7 32 648.711 138.6-137.7 32 660.127 137,6-136,7 32 660.127 127,6-126,7 32 669.276 126.6-125.7 32 669.276 116,6-115,7 32 676.596 115.6-114.7 32 676.596 105,6-104,7 32 682.263 104,6-103,7 32 682.263 61.6-50.5 32 685.684 60.6-51.5 32 685.684 3023,7-3022,8 31 138.881 3024,7-3023,8 37 150.563 2922,7-2921,8 37 214.397 2923.7-2922.8 37 221.643 2821.7-2820.8 37 281.752 2822,7-2821,8 37 286.316 2720.7-2719.8 37 341.573 2721.7-2720,s 37 344.378 2619,7-2618.8 37 394.781 52.3-43.2 37 697.585 70,7-61,6 37 714.036 71.7-60.6 37 714.036 623-51.4 37 715.338 61.5-52.4 37 715.338 53.3-42.2 37 744.930 44.1-33.0 38 220.515
AP 56 -60 21 56 29 -152 -97 -1
-165 56 -166 -118 -11 14 63 23 44 76 84 69 72 127 128 139 139 58 58 -51 138 -105 -112 -37 33 -90 -15 -87 124 -7 -7 -213 -205 220 295
Av = Yobs - vCdcin kHz. TABLE 9: Spectroscopic ConstanW of the Pyridine45 Monomer from a Least-Squares Fit of Rotational Transitions AlMHz 5080.2871(18) BMHz 4979.0161(20) CMHz 2514.2337(11) Ai/kHz 0.741(40) AJ&Hz -1.468(2) A&Hz 0.828(32) &/kHz -0.0330(5) SK/kHZ 0.885(7) xmIMHz 1.297(20) XbdMHz -4.856(73) xccJMHz 3.559(21) Numbers in parentheses represent one standard deviation.
( C ) changed with respect to that of the aromatic monomer (M), the former will be denoted as (xc, yc, zc} and the latter as ($, yM, zM} irrespective of the order of the rotational constants. The principal axis yc is perpendicular to the symmetry plane of the complex and is parallel to yM. The axis zM is perpendicular to the aromatic ring plane with zc rotated by a small angle y . Structural changes in the aromatic molecule are assumed to be negligible in the complex with respect to the free monomer, considering the weak interaction energy in a van der Waals
zM zc
t t
Figure 1. Model of the pyridine-argon and pyridine- argon)^ complexes with the definition of the intermolecular structural parameters and the principal axis systems for the pyridine monomer {XM, yM, z'} and the complex {XC, yc, F } .
TABLE 10: Planar MomenW of the Observed Isotopomers of Pyridine and of Pyridine-(Argon),, n = 1,2, Complexes isotopomer n y z P, PY Pz ref pyridine a b c 87.0799 83.7017 -0.0193 18 b c a 85.9907 83.0132 335.3943 4 pyridine-Ar pyridine-Ar2 b c a 88.8175 83.1670 1OO0.0310 b a b c 88.9890 83.6993 -0.0196 17 pyridine-I5N pyridine-I5N-Ar b c a 87.9672 82.9900 336.4894 b pyridine-l5N-Ar~ b c a 90.4528 83.1555 999.8320 b pyridine-4-dl a b c 93.2604 83.7042 -0.0183 18 pyridine-4-dl -Ar b c a 91.9999 82.9675 337.3318 4 b a c 99.4918 101.5144 -0.0124 pyridine-ds b c b a 98.0940 100.8187 342.4657 b p yridine-d5-Ar Planar moments are given in uAz. This work.
complex. However, if the planar moments of inertia Pg, which are defined as
were compared between the complex and the aromatic monomer, substantial differences were noticed in cases where an exact agreement was e ~ p e c t e d .Table ~ 10 shows the planar moments of inertia for the different isotopomers of the pyridine-argon complex and the corresponding pyridine monomers. Only the nuclei of the pyridine monomer contribute to Py" of the complex, but its value is smaller by approximately 0.7 uA2 than of the corresponding monomer. These differences were attributed to large-amplitude bending vibrations of argon. It is essential to account for the bending vibrations during the structure determination of the complex. Klots et aL4 introduced a model in which the pyridine is rotated at its centerof-mass around $ and yM by arbitrary angles a, and a,, respectively. These motions fulfill the Eckart conditions approximately. The vibrationally averaged angles (ax)and (a,) were expected to be nearly equal. Instead of the angles a, and a, introduced in ref 4, the motion of pyridine may be described first by a rotation with the angle 9, around zM and then with the angle a around xM followed by a rotation with the angle -9,
J. Phys. Chem., Vol. 98, No. 46, 1994 11867
Rotational Spectra of Pyridine-(Argon), Complexes around zM, as shown in Figure 2. The original principal axis system {x', y M ,zM} remains fixed, and only pyridine is rotated. The inertia tensor of the pyridine monomer IM has to be transformed accordingly by the transformation
S = T,T,T-, composed of the transformation matrices
(3) + XM
and (4)
Figure 2. Model for the intermolecular bending motion between pyridine and argon.
The transformed inertia tensor JM is thus given as
The vibrationally averaged inertia tensor (IM)is obtained as an average over the angle
with its elements expressed explicitly in the axis system {xM, yM,zM} as
where
with y corresponding to the angle between the zc and the zM axes. The vibrationally averaged inertia tensor for the pyridine(argon):! complex was derived using the elements of the vibrationally averaged inertia tensor of the pyridine monomer (p) in eq 7 shifted to the center-of-mass of the complex along the xM direction. The contributions of the two argon atoms which are symmetrically located in the axis system {xM,y M , zM} have to be added. No diagonalization is required because the principal axis systems of the monomer and of the complex are parallel to each other. The diagonal elements of the inertia tensor are calculated as
I",= (I",> + 2mR2 cos2 8 The inertia tensor I' of the complex in a coordinate system parallel to {xM,y M ,zM} but shifted to the center-of-mass of the complex is now calculated from the contributions of pyridine in eq 7 and of argon as
I ' ~=
xs= - sin
p ~ 'sin2 e
I'~,= - p ~ ' COS e sin e
(8)
where p = mM/(m
+ 2m[(Rsin 8 - x , ) ~+ R2 cos2 e] I", = (e)+ Mx: + 2m(R sin 8 - x , ) ~ (10) Mx:
2m2yg e
(c)+ pR2
(e)+
(e)+
with
+
I:, = (I",> p~~ cos2 e I'fl =
=
+ M)
is the reduced mass of the complex with m and M representing the masses of the argon atom and of the pyridine mohomer, respectively. The inertia tensor I' is transformed to the principal axis system {xc, yc, zc} by diagonalization
Equations 9 express the principal moments of inertia of the pyridine-argon complex as functions of the structural parameters R and 8 and the average bending angle (a).They are used to determine R, 8, and (a)in an iterative nonlinear leastsquares fit. The results of the fits for each isotopomer are listed in Table 11. The parameters R and 8 refer to the principal axis system of the individual isotopomer of the pyridine monomer. The center-of-mass of the isotopomer is shifted with respect to that of the parent species by
1
Ax=--(
m'i - mi)xiM
Mi where m'i - mi refers to the mass difference of the isotopically substituted nucleus and the summation i is over all substituted nuclei. Corrected parameters R' and 8' were introduced which compensated for this shift of the isotopomers. Their values are.given in Table 12.
11868 J. Phys. Chem., Vol. 98, No. 46, 1994
Spycher et al.
TABLE 11: Intermolecular Structural Parametee of Pyridine-(Argon),, n = 1, 2, Complexes from Fits of All Observed Isotopomers isotopomer pyridine-I4N- Ar pyridine-15N-Ar pyridine-4-d1-k pyridine-ds- Ar pyridine-14N-Ar2 pyridine-l5N-Ar2
R 3.5454 3.5440 3.5410 3.5449 3.5435 3.5422
e
(a)
Y
3.28 2.14 3.41 4.16 3.89 3.66
1.31 1.48 1.62 6.11 6.49 6.54
4.40 3.10 4.67 5.82 0.00 0.00
"The structural parameters are defied in the text (cf. Figure 1). Distances are given in A, and angles, in deg.
TABLE 12: Intermolecular Structural Parameter@ Referring to the Parent Species of Pyridine-(Argon),, n = 1, 2, Complexes Corrected for Center-of-Mass Shifts of Isotopomers B' 3.28 3.02 2.90 3.11 3.89 3.94
R' 3.545 3.545 3.545 3.543 3.544 3.543
isotopomer pyridine-Ar pyridine-lSN-Ar pyridine-dl -Ar pyridine-d5-k pyridine-Ar2 pyridine-I5N-Ar2
(a,) = (a,) 5.20 5.28 5.38 4.14 5.20 5.28
The structural parameters are defined in the text. Distances are given in A, and angles, in deg. (1
It was shown in Table 10 that P; of the complex is of the corresponding pyridine substantially smaller than monomer. Ps is expressed with eqs 9 as
Pc"
Py"= 1/2(rc,
+ I", - &)
+
= q ( 1 - 1/2 sin' a) 1 / 2 e ( s i n 2 a)1/2(pf;l- e>(sin4(a/2>)(12) The second term corresponds to a fourth of the inertia defect of pyridine, which can be neglected safely for a planar molecule. The third term is likewise small due to the fourth power of the trigonometric function of a/2. The first term demonstrates that Ps is reduced with respect to pf;'. The average bending angle (a)may be split into Cartesian components assuming the relation (sin' a)= (sin'
a,>+ (sin' q)
for a curvilinear bending motion. The two angles a, and a, were constrained to be equal in our deviation because of the simple integration over pl in eq 6 . This leads finally to
Py" zz q(cOs2 q) The results for the angles (ax)= (a,)= arcsin(U2 sin2 are included in Table 12. For the two isotopomers of pyridine-(argon);!, the structural parameters R and 8 and the average bending angle (a)were determined in an analogous manner by an iterative nonlinear least-squares fit using eqs 10. The results of the fits are listed in Table 11, and the parameters corrected for the shift of the center-of-mass, in Table 12. Discussion The rotational spectra of pyridine-14N- and pyridine-15N(argon);! provide structural data for a second example of a van der Waals complex between an aromatic molecule and more
than one argon atom that was measured in the microwave region. It was obvious from the rotational constants that the structure was consistent with the [1,1] isomer with the argon atoms attached on both sides of the ring plane similar to the case of furan-(argon)'. l2 Model calculations were performed for the second [2,0] isomer with both argon atoms on the same side of the ring plane. Using a simple Lennard-Jones potential for the intermolecular interaction indicated that the two argon atoms move almost freely above the ring plane as a dimer between several local minima on the potential energy surface. This motion will lead to a complicated rotational spectrum which was not searched for thoroughly. The conventional method for the structure determination of molecules starts from the parent species and a set of singly substituted isotopomers. Only the differences are used between the planar moments of inertia of the substituted species and those of the parent species.20 In this way, the zero-point vibrational contributions are compensated to first order.21 The application of the substitution method would be even more appropriate for the structure determination of van der Waals complexes with their large-amplitude intermolecular vibrations. Unfortunately, no sufficient set of suitably substituted isotopomers was available mainly because of the lack of argon isotopes in adequate natural abundance. One has to resort to taking into account the moments of inertia of the parent species as well. However, then the determination of accurate structures of van der Waals complexes requires consideration of the largeamplitude intermolecular motions of the monomers. A model for the bending vibrations of an argon atom above the ring plane was proposed by Klots et ale4 Similar considerations guided us for the derivation of a vibrationally averaged structure for complexes of the types studied here. The necessary relations were rigorously derived within the initial assumptions. They turned out to be equal to those in ref 4 if terms were neglected which were small for pyridine-argon. Our formulas are appropriate also for complexes between a nonplanar molecule and argon or other rare gas atoms. Analogous relations were obtained for complexes with two argon atoms on both sides of the ring plane. The vibrationally averaged structures of pyridine-14N- and pyridine-l5N-(argon)2 were determined with the help of eqs 9 and 10. The systematic variations of R and 8 for the different isotopomers in Table 11 are a clear indication that the argon atom is shifted from the zM axis toward the nitrogen end of pyridine, corroborating the earlier conclusion^.^ The small differences of these parameters compared to the values reported in ref 4 are due to the additional terms in our formulas. Inspection of Table 12 shows that R' and 8' refemng to the parent species of the complex with one or two argon atoms are remarkably consistent. R' differs by much less than the expected uncertainty of 0.005 A, and 8' varies within lo, approaching the estimated error bounds among the isotopomers. Both parameters have almost equal values for the complexes with one or two argon atoms. These observations show that the binding of the second argon atom to the pyridine-argon complex occurs completely independently at the opposite side of the ring plane. Three-body effects can safely be excluded. Even the average bending angle (a) changes only by approximately 1O. The structural parameters R' and 8' of the complexes of pyridine with one or two argon atoms are similar to those observed in other aromatic molecule-argon complexes. The values of R and 8 were calculated with the same method as for the pyridine-argon complexes for other complexes reported p r e v i o u ~ l y . ~ - ~The ~ ~ results - ~ ~ ~ ~are collected in Table 13.
J. Phys. Chem., Vol. 98, No. 46, 1994 11869
Rotational Spectra of Pyridine-(Argon), Complexes TABLE 13: Comparison of Intermolecular Structures of Aromatic Molecule- Argon ComplexesP pyridine- Ar pyrrole-Ar furan-Ar fluorobenzene- Ar 1,2-difluorobenzene-Ar
R'
e'
RL
3.545 3.554 3.539 3.584 3.583
3.2 5.5 9.7 4.8 8.4
3.539 3.538 3.489 3.572 3.545
Mean values of intermolecular structural parameters for all measured isotopomers calculated with eqs 9 from the combined results of the complexes in refs 2-4, 6, and 7, of the aromatic monomers in refs 17, 18, and 22-27, and of this work. Distances are given in A, and angles, in deg.
TABLE 14: Quadrupole Coupling Constants (MHz) of Pyridine and Pyridine-(Argon),, n = 1,2, Complexes
XU XYY
xu
pyridinez8
pyridine-AP
-4.908(3) 1.434(3) 3.474(3)
-4.8053(20) 1.4406(25) 3.3648(25)
pyridine- A r z -4.872(5) 1.440(5) 3.432(8)
Slightly larger values of R were determined for benzene-, fluorobenzene-, and 1,2-difluorobenzene-argon than for the remaining examples. The center-of-mass of the aromatic molecule is a rather fictitious point. It may be more instructive to compare the perpendicular distance RL of the argon atom from the plane of the aromatic molecule. This parameter should be useful for polycyclic aromatic rings as well. The perpendicular distances are included in Table 13. It must be pointed out that R' and RL are still effective distances in the vibrational ground state and may differ by as much as 0.04 A from the equilibrium values. No attempt was made in the present model to compensate the effects of the zero-point stretching vibration. The pyridine-ds-argon complex was measured as a test for the dependence of (a)on the isotopic composition of pyridine. The moments of inertia of pyridine-d5 were larger by approximately 17% with respect to the parent species (cf. Table 10). (a)is thus expected to be reduced due to the larger mass. A reduction from 7.37" to 6.71" was indeed observed. A similar reduction of 0.37" was noticed previously for the pyridinekrypton complex with respect to the pyridine-argon complex? krypton being twice as heavy as argon. The same argument holds also for the smaller value of 6.49" of the pyridineargon)^ complex. The quadrupole coupling constants of pyridine-14N-(argon)2 are compared in Table 14 to those of pyridine and pyridine14N-argon. Since the principal axis system of the complex with two argon atoms is parallel to that of pyridine, the differences to the latter of 0.036, 0.006, and -0.042 MHz for xm, xyy,and respectively, are exclusively due to effects from the bending
xu,
vibrations. It was noticed that rather similar differences of 0.054, 0.007, and -0.060 MHz remained for pyridine-14Nargon after transforming the quadrupole coupling tensor of pyridine to the principal axis system of the complex. The slightly larger absolute values of the latter differences are completely in line with the larger average bending angle (a) compared to the former complex. Acknowledgment. Financial support by the Schweizerischer Nationalfonds (Project Nos. 20.28474.90 and 4024-027152) is gratefully acknowledged. We thank Mr. G. Grassi for purifying the pyridine samples. References and Notes (1) Kukolich, S. G.; Shea, J. A. J . Chem. Phys. 1982, 77, 5242. (2) Kukolich, S. G. J. Am. Chem. SOC. 1983, 105, 2207. (3) Bohn, R. K.; Hillig, K. W., II; Kuczkowski, R. L. J . Chem. Phys. 1989, 93, 3456. (4) Klots, T. D.; Emilsson, T.; Ruoff, R. S.; Gutowsky, H. S. J . Phys. Chem. 1989, 93, 1255. ( 5 ) Brupbacher, Th.; Bauder, A. Chem. Phys. Lett. 1990, 173, 435. (6) Stahl, W.; Grabow, J.-U. Z. Naturforsch., A 1992, 47, 681. (7) Jochims, E.; Grabow, J.-U.; Stahl,W. J. Mol. Spectrosc. 1993,158, 278. (8) Weber, Th.; von Bargen, A.; Riedle, E.; Neusser, H. J. J . Chem. Phys. 1990, 92, 90. 19) Weber. Th.: Riedle., E.:, Neusser., H. J.:, Schlac. E. W. Chem. Phvs. Lett.'i991, 183. 71.' (10) Schmidt, M.; Mons, M.; Le Calvt, J. Chem. Phys. Lett. 1991,177, Y
371. - . ..
(11) Weber, Th.; Neusser, H. J. J . Chem. Phys. 1991, 94, 7689. (12) Spycher, R. M.; King, P. M.; Bauder, A. Chem. Phys. Lett. 1992, 191, 102. (13) Balle, T. J.; Hygare, W. H. Rev. Sci. Instrum. 1981, 52, 33. (14) Jans-Biirli, S. Ph.D. Thesis, Eidgenossische Technische Hochschule Zurich, 1987. (15) Pickett, H. M. J. Mol. Spectrosc. 1991, 148, 371. (16) Watson, J. K. G. In Vibrational Spectra and Structure; Dung, J. R.,Ed.; Elsevier: Amsterdam, The Netherlands, 1977; p 1. (17) Sgwensen, G. 0.;Mahler, L.; Rastrup-Andersen, N. J . Mol. Struct. 1974, 20, 119. (18) Mata, F.; Quintana, M. J.; Smensen, G. 0. J . Mol. Struct. 1977, 42, 1. (19) Nosberger, P.; Bauder, A.; Gunthard, H. H. Chem. Phys. 1973, I , 418. (20) Kraitchman, J. Am. J . Phys. 1953, 21, 17. (21) Costain, C. C. J . Chem. Phys. 1958, 29, 864. (22) Nygaard, L.; Nielsen, J. T.; Kirchheiner, J.; Maltesen, G.; RastrupAndersen, J.; tiorensen, G. 0. J. Mol. Struct. 1969, 3, 491. (23) Bak, B.; Christensen, D.; Dixon, W. B.; Hansen-Nygaard, L.; Rastrup-Andersen, J.; SchottlXnder, M. J. Mol. Spectrosc. 1962, 9, 124. (24) Mata, F.; Martin, M. C.; Sorensen, G. 0. J. Mol. Struct. 1978, 48, 157. (25) Wlodarczak, G.; Martinache, L.; Demaison, J. J . Mol. Spectrosc. 1988, 127, 200. (26) Nygaard, L.; Bojesen, I.; Pedersen, T.; Rastrup-Andersen, J. J . Mol. Struct. 1968, 2, 209. (27) Stiefvater, 0. L. Z . Naturforsch., A 1988, 43, 147. (28) Heineking, N.; Dreizler, H.; Schwarz, R. Z. Naturforsch., A 1986, 141, 1210.
