Rotational spectrum and dynamics of tetrahydrofuran–argon

Chemical Physics 239 Ž1998. 229–234

Rotational spectrum and dynamics of tetrahydrofuran–argon Sonia Melandri

a,b

b , Juan C. Lopez , Paolo G. Favero a , Walther Caminati ´ Jose´ L. Alonso b

a,)

,

a

b

Dipartimento di Chimica ‘‘G. Ciamician’’ dell’UniÕersita, ` Via Selmi 2, I-40126 Bologna, Italy Departamento de Quimica–Fisica, Facultad de Ciencias, UniÕersidad de Valladolid, E-47005 Valladolid, Spain Received 13 July 1998

Abstract The jet-cooled rotational spectrum of the tetrahydrofuran–argon molecular complex has been investigated by millimeterwave absorption and Fourier transform microwave spectroscopies. The argon atom is located nearly over the oxygen atom, almost perpendicularly to the COC plane. Each rotational transition is split in two component lines due to the residual pseudorotational effects of the ring in the complex. The splitting between the two vibrational sublevels has been calculated to be 111.345Ž44. MHz. q 1998 Elsevier Science B.V. All rights reserved.

1. Introduction The combination of the supersonic expansion with spectroscopic techniques w1x has allowed an extensive investigation of the chemistry of the rare gases ŽRG., that is the formation of stable adducts of RG atoms with various molecules. The dynamics of the van der Waals motions and the dissociation energies of the RG atom have been estimated to an extent depending on the spectroscopic resolution power and on the symmetry of the RG partner molecule Žsee, e.g., Ref. w2x.. Several of the investigated van der Waals complexes are between a RG atom and a ring molecule, probably because the high number of interaction centers renders this kind of complexes more stable. After the pioneering work on furan–argon by Kukolich and co-workers w3,4x in 1982 several RG– aromatic molecule complexes have been investigated )

Corresponding author. E-mail: [email protected]

by microwave spectroscopy Žsee Refs. w5–21x for unsubstituted rings.. These studies have generally been performed with pulsed molecular beam microwave Fourier transform spectrometers w3–17x, while only recently a more direct technique — supersonic jet millimeter-wave absorption spectroscopy — has been applied to the investigation of such a kind of complex w18–21x. Only a small number of adducts of RG–non-aromatic rings, has been investigated. They can be grouped in complexes with three-membered rings Žoxirane–Ar w22x, cyclopropane–RG ŽRG s Ne, Ar, Kr. w23x, and dimethylensulphide – Ar w24 x., four-membered rings Žoxetane–Ar w25x., five-membered rings Ž2,5-dihydrofuran–Ar w26,27x, 2,3-dihydrofuran–Ar w28x and 1,3-dioxolane–Ar w29x., and trioxane–Ar w30x for the six-membered ones. In order to investigate the nature of the van der Waals interaction which brings to the formation of molecular complexes, we considered the effects of

0301-0104r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 3 1 9 - X

230

S. Melandri et al.r Chemical Physics 239 (1998) 229–234

withdrawing aromaticity and double bonds from furan. Within the family of five-membered rings containing an oxygen atom we investigated first 2,5-dihydrofuran–Ar. Since isolated 2,5-dihydrofuran is planar, it was not surprising that a complex similar to furan–Ar was observed: the Ar atom was almost over the center of mass of the monomer, tilted ; 108 towards the oxygen w26,27x. We considered then 2,3-dihydrofuran–Ar. In this case the monomer is puckered with a ring puckering barrier of ; 90 cmy1 , and in principle two conformers could have been observed andror interactions of the ring puckering with the argon motions could have been expected. Only one conformer was observed and its behaviour was once again similar to that of furan–Ar w28x. Here we report the rotational spectrum of the fully aliphatic member of the series: tetrahydrofuran–Ar. Fig. 1 shows the monomer ŽTHF. and the adduct ŽTHF–Ar., together with the axes switching that takes place upon formation of the adduct.

2. Experimental part A sample of THF was purchased from Aldrich and used without further purification. Two different experimental setups have been used: a millimeter-wave free jet absorption spectrometer ŽFJ-AMMW, Bologna., and a molecular beam Fourier transform microwave spectrometer ŽMBFTMW, Valladolid., which provided complementary results.

lines allow rapid acquisition of spectra and simplify their assignment. 2.2. MB-FTMW spectroscopy The MB-FTMW spectrometer covers the frequency range 6–18.5 GHz. Details of this instrument have been given elsewhere w27x. Gas mixtures of ; 1% THF in Ar at a stagnation pressures of ; 1 bar were expanded into the Fabry-Perot resonator through a pulsed nozzle ŽGeneral Valve, series 9. with diameter of 0.8 mm. Beam pulses of ; 0.30 ms duration were employed with repetition rates up to 30 Hz. Microwave pulses with peak power of 40 mW and 0.4 ms duration were found to be optimal. The frequencies were determined after transformation of the 8 k data points time-domain signal, recorded with a 40 ns sample interval. The pulsed nozzle valve is located near the centre of one of the mirrors, so that molecular expansion travels parallel to the resonator axis. Consequently, all the transitions appear as doublets due to the Doppler effect. The line positions are determined by averaging the frequencies of the two Doppler components. The accuracy of frequency measurements is estimated to be better that 5 kHz.

3. Analysis of the rotational spectrum In the cases of 2,5- and 2,3-dihydrofuran–Ar complexes, relatively good estimates of the rotational

2.1. FJ-AMMW spectroscopy This relatively simple technique has been only recently systematically applied to the study of molecular adducts. The Stark and pulse modulated free jet absorption millimeter-wave spectrometer used in this study has already been described elsewhere w18,31x. The adducts were formed by expanding the sample seeded in argon, at room temperature and at a pressure of ; 1.0 bar, to ; 5 = 10y3 mbar through a pulsed nozzle Žrepetition rate 5 Hz. with a diameter of 0.35 mm, reaching an estimated ‘rotational’ temperature of ; 8 K. The high speed of the scans Ž10 GHzrday. and the preserved natural intensity of

Fig. 1. Indicative draw of the principal axes of THF and of their switching upon formation of THF–Ar. The representation of the THF distorted ring does not necessarily correspond to the minimum energy configuration associated to the pseudorotation potential.

S. Melandri et al.r Chemical Physics 239 (1998) 229–234 Table 1 Frequencies of all measured transitions of THF–Ar ŽMHz. J

X

ŽKXa , KXc . –

J

Y

ŽKYa , KYc . a

2Ž1, 1. –1Ž0, 1. b 3Ž0, 3. –2Ž0, 2. 3Ž1, 3. –2Ž1, 2. 3Ž1, 2. –2Ž1, 1. 3Ž2, 2. –2Ž2, 1. 3Ž2, 1. –2Ž2, 0. 4Ž0, 4. –3Ž0, 3. 4Ž1, 4. –3Ž1, 3. 4Ž1, 3. –3Ž1, 2. 4Ž2, 3. –3Ž2, 2. 4Ž2, 2. –3Ž2, 1. 5Ž0, 5. –4Ž0, 4. 5Ž1, 5. –4Ž1, 4. 5Ž1, 4. –4Ž1, 3. 5Ž2, 4. –4Ž2, 3. 5Ž2, 3. –4Ž2, 2. 6Ž0, 6. –5Ž0, 5. 6Ž1, 6. –5Ž1, 5. 6Ž1, 5. –5Ž1, 4. 6Ž2, 5. –5Ž2, 4. 6Ž2, 4. –5Ž2, 3. 7Ž0, 7. –6Ž0, 6. 7Ž1, 7. –6Ž1, 6. 7Ž1, 6. –6Ž1, 5. 7Ž2, 6. –6Ž2, 5. 7Ž2, 5. –6Ž2, 4. 7Ž3, 5. –6Ž3, 4. 7Ž3, 4. –6Ž3, 3. 8Ž7. –7Ž6. 8Ž8. –7Ž7. 9Ž7. –8Ž6. 9Ž8. –8Ž7. 9Ž9. –8Ž8. 10Ž7. –9Ž6. 10Ž8. –9Ž7. 10Ž9. –9Ž8. 11Ž6. –10Ž5. 11Ž7. –10Ž6. 11Ž8. –10Ž7. 12Ž6. –11Ž5. 12Ž7. –11Ž6. 12Ž8. –11Ž7. 13Ž6. –12Ž5. 13Ž7. –12Ž6. 14Ž5. –13Ž4. 14Ž6. –13Ž5. 14Ž7. –13Ž6. 15Ž5. –14Ž4. 15Ž6. –14Ž5. 15Ž7. –14Ž6. 16Ž5. –15Ž4. 16Ž6. –15Ž5. 17Ž4, 14. –16Ž3, 14.

q

0

6924.221 6892.356 6906.991 6924.934 6924.736 9231.235 9186.188 9233.176 9232.652 11537.338 11479.972 11595.228 11541.247 11540.27 13842.311 13773.539 13915.697 13849.144 13847.423 16145.919 16066.610 16234.339 16156.626 16154.099 16153.536 16153.474 60409.84 66857.62 62711.89 69158.99 75603.68 65012.71 71459.14 77903.09 60864.29 67312.32 73758.01 63163.21 69610.68 76055.60 65460.76 71907.57 61307.75 67756.78 74202.82 63602.38 70051.11 76496.64 65895.16 72343.88 61722.17

231

Table 1 Žcontinued. X X X Y Y Y J ŽK a , K c . – J ŽK a , K c . a

0q

0y

17Ž4, 13. –16Ž3, 13. 17Ž5. –16Ž4. 17Ž6. –16Ž5.

61733.62 68186.03 74634.56

61727.45 68181.86 74631.04

y

0

7872.450 6921.991 6939.063 6955.836 6922.696 6922.531 9228.275 9276.913 9230.199 9229.791 11533.662 11478.376 11597.048 11537.673 11536.87 13837.932 13770.030 13916.168 13845.144 13843.771 16140.861 16062.083 16234.316 16152.714 16150.634

60410.99 66859.88 62712.13 69160.33 75606.36 65012.24 71459.80 77904.92 60862.24 67311.18 73758.01 63160.69 69608.98 76054.91 65457.86 71905.42 61303.77 67753.54 74200.40 63598.24 70047.64 76493.82 65891.00 72340.18 61717.09

a

Only K a is indicated in the notation when transitions are doubly overlapped due to the near prolate degeneracy of the involved levels. b The vibration–rotation transitions 4 1, 4 Ž0y . § 31, 2 Ž0q . and 4 1, 3 Ž0q . § 31, 3 Ž0y . at 9189.396 and 9270.905 MHz, respectively, have to be included Žsee text..

constants were obtained just attaching an argon atom roughly perpendicular to the ring over its centre of mass. Some complications were expected in the case of THF–Ar because: Ž1. THF is a very floppy molecule undergoing pseudorotation; and Ž2. the lack of p-electronic density in the ring with respect to furan, 2,3- and 2,5-dihydrofuran does not longer favour the location of Ar over the ring. The observed lines of the adduct were not indeed in agreement with a model considering the Ar over the ring, but the Ar needed to be moved over the oxygen atom. In this way it was possible to assign the spectrum. The proposed molecular model is shown in Fig. 1. The r 0 geometry of THF w32,33x has been assumed to be unaltered in the complex. In going from the molecule to the adduct, an inversion of the principal axis of inertia takes place with respect to the ring skeleton Žsee Fig. 1., so that the m a-type spectrum of THF is converted in a predominant m c-type spectrum in the adduct, where also m a has a small value, important for the mmw technique, which is based on Stark modulation. Several high m c –R-type lines, doubly overlapped due to the K a near prolate behaviour were assigned first with FJ-AMMW; later on most of single lines have been measured with MB-FTMW. Due to a tunneling motion in THF–Ar ŽAr motions or residual pseudorotation in THF., all transitions, listed in Table 1, were split in two component lines. They have been fitted with Pickett’s reduced axis Hamiltonian w34,35x giving the 22 spectroscopic constants reported in Table 2. They are the three rotational and five quartic centrifugal distortion constants of the two states, their energy difference Ž D E01 ., the interaction constants Fb c and Fa b , their

S. Melandri et al.r Chemical Physics 239 (1998) 229–234

232

Table 2 Spectroscopic constants Žsee text. of THF–Ar Ž S reduction, I r representation.

A ŽMHz. B ŽMHz. C ŽMHz. DJ ŽkHz. DJ K ŽkHz. DK ŽkHz. d1 ŽkHz. d 2 ŽkHz. D E01 ŽMHz. Fb c ŽMHz. X Fb c ŽkHz. Y Fb c ŽkHz. Fa b ŽMHz. X Fa b ŽkHz. Nb s c ŽMHz.

0q

0y

4372.774Ž62. a 1171.727Ž62. 1146.8943Ž35. 4.754Ž83. 7.41Ž29. 11.451Ž48. 0.067Ž62. y0.0226Ž46. 11.348Ž38. 10.0814Ž5. y0.807Ž30. y55.9Ž57. 184.35Ž54. y20.3Ž18. 109 0.043

4372.935Ž61. 1171.713Ž62. 1146.8913Ž37. 4.765Ž86. 7.29Ž28. 11.403Ž43. 0.111Ž62. y0.0216Ž49.

4. Location of the Ar atom in the complex

a

Error in parentheses are expressed in units of the last digit. Number of transitions in the fit. c Standard deviation of the fit. b

J-dependencies FbX c and FaX b and their K-dependencies FbX c defined in the interaction Hamiltonian Ž H01 .: H s Ý Hi q H01

Ž i s 0, 1 . ,

Ž 1a .

i

where Hi s A Ž i . Pa2 q B Ž i . Pb2 q C Ž i . Pc2 y Dj Ž i . P 4 y DJK Ž i . Pa2 P 2 y DK Ž i . Pa4 q d1 Ž i . P 2 2 2 = Ž Pq q Py . q d 2 Ž i . Ž Pq4 q Py4 .

Ž i s 0, 1 . Ž 1b .

and H01 s Fb c q FbX c J Ž J q 1 . q FbYc K 2 = Ž Pb Pc q Pc Pb . q Fa b q FaX b J Ž J q 1 . = Ž Pa Pb q Pb Pa . q D E01 .

last one is better determined due to the small energy separation Ž D E01 . which is of the same order of magnitude of the rotational spacings between many of the observed K a asymmetry doublets. A final prediction of the centimeter-wave spectra using the obtained parameters allowed to observe, within the estimated accuracy of the MB-FTMW spectrometer, the vibration–rotation transitions 4 1, 4 Ž0y . § 31, 2 Ž0q. and 4 1, 3 Ž0q. § 31, 3 Ž0y. at 9189.396 and 9270.905 MHz Ž nobs y ncalc s 7 kHz., respectively. These transitions have m a-type character due to the strong mixing between the pairs of states 4 1, 4 Ž0y. – 4 1, 3 Ž0q. and 31, 3 Ž0y. –31, 2 Ž0q. produced by Coriolis interactions.

Ž 1c .

Since THF–Ar is an almost prolate symmetric top the S-reduction and the I r-representation have been chosen w36x. The lines were first fitted using only the a-type symmetry coupling terms Ž Fb c . which provided a good value of the energy difference between the tunnelling states and in a second step we included the c-type symmetry coupling terms Ž Fa b .. The Fa b coefficient is larger than Fb c although the

The Coriolis contributions of the van der Waals motions to the moments of inertia Žsee, e.g., Ref. w19x. and the lack of isotopic substitutions make it not easy to determine the position of Ar in the complex. Approximate argon rs coordinates can be obtained applying Kraitchman equations w37x to the rotational constants of isolated THF and of THF–Ar. This corresponds to the substitution of a hypothetical atom of zero mass with an argon atom. The so-obtained rs coordinates are < z < s 3.4080Ž2., < x < s 0.02Ž44., < y < s 1.532Ž7., and < r < s 3.7364Ž3.. These values suggest the Ar atom to lie in the yz plane Žsee Fig. 1., and that the line Ar–CM forms an angle of 248 with the z axis. Assuming that the Ar atom is inclined towards the oxygen atom as in the related adducts furan–Ar w3,4x and 2,5-dihydrofuran–Ar w26,27x, the u angle of Fig. 1 is 668, and that the ˚ behind the projection of the Ar–CM ‘bond’ is 0.27 A position of the oxygen atom, outside of the projection of the heavy atoms of THF on the xy plane. From the present data is not possible, however, to discriminate among the various conformations, related to the nearly free barrier to pseudorotation, that the ring can adopt. 5. Van der Waals vibrations When the argon atom forms the complex with THF, the three translational degrees of freedom of

S. Melandri et al.r Chemical Physics 239 (1998) 229–234

the isolated atom are replaced by three van der Waals vibrational modes: the THF–Ar stretching, and two bendings. Models have been developed to obtain the potential energy surface of van der Waals motions when the ring molecule involved in the complex has at least a C 2v symmetry w11,20,25,26, 38–40x. This is not the case for THF–Ar. In fact, due to the ring pseudorotation, even the equilibrium configuration of THF is not yet established. Furthermore the Ar bending motion are probably mixed with the large amplitude motions of the ring. The Ar stretching motion is probably more isolated. Assuming so the stretching force constant Ž k s . can been estimated by approximating the complex to a molecule made by two rigid parts. For complexes with several symmetry elements Millen w40x and Read et al. w41x for asymmetric top complexes in which the stretching coordinate is near-parallel to the inertial a-axis obtained equations of the type: 2

k s s 16 p 4 Ž m D R CM . 4 BD4 q 4C D4 y Ž BD y C D . 2

= Ž BD q CD . r Ž hDJ . ,

2

Ž 2.

The subscript D denotes a dimer quantity, m D is the pseudo diatomic reduced mass, R CM is the distance between the centers of mass of the monomers ˚ for THF–Ar., and DJ Žs 4.76 kHz average Ž3.736 A value between the two states. is the centrifugal distortion constant. After the analysis of the spectrum with the Hamiltonian of Eq. Ž1a. DJ should be ‘free’ from the ring pseudorotation contributions. For THF–Ar we obtained k s s 1.78 N my1 and corresponding to a harmonic stretching fundamental n k s 34.3 cmy1 . The values 45.8, 48.8 and 48–49 cmy1 are reported for furan–Ar w38x, 2,5-dihydrofuran–Ar w26,27x and 2,3-dihydrofuran–Ar w28x, respectively. By assuming a Lennard-Jones type potential the dissociation energy has been estimated to be E B s 218 cmy1 for THF–Ar. 6. Conclusions By using two complementary free jet spectroscopic techniques we reported the rotational spectrum of THF–Ar. Differently with respect to the spectra of related adducts, as furan–Ar w3,4x, 2,5-dihydrofuran–Ar w25x, 2,3-dihydrofuran–Ar w26x and 1,3-dioxolane–Ar w27x this spectrum has shown a

233

systematic doubling of the rotational lines. This clearly indicates a double minimum potential characterising a large amplitude motion of the complex. This motion could be either the pseudorotation of the ring in the complex, or the tunnelling of Ar between two equivalent minima, for example above and below the C 2 OC 5 , in proximity of the oxygen. The existence of both Fa b and Fb c coupling terms and its relative magnitude are very important data to understand which kind of motion is responsible for the tunnelling splittings. If we first consider pseudorotation of THF we may correlate the observed vibrational levels in THF–Ar with the two lowest energy levels of pseudorotation in the isolated molecule which are connected by an a-type Ž Fb c . coupling term w32,33x. By using the principal inertial axes system this Coriolis coupling would be interpreted in terms of the Pa angular momentum operator w34x. By using a simple vector model it is easy to see with the help of Fig. 1 that classically an angular momentum vector oriented along the a-principal axis of isolated THF must have components mainly along the a and c inertial axes of THF–Ar. Giving the orientation of these two axes with respect to the a axis of THF it can be expected that the projection along the c axis of THF–Ar should be larger than that along the a axis of the complex. This simple description is in good agreement with the facts that a- and c-type coupling terms are observed between the tunnelling states of THF–Ar being larger the c-type coupling. Using the same simple arguments it can be easily seen that a tunnelling motion of Ar between the two equivalent positions in the vicinity of oxygen would generate a b-type Coriolis coupling term between tunnelling states. Thus, the observed Coriolis coupling allow us to conclude that the observed tunnelling splittings should be mainly related to pseudorotation of the THF subunit. Similar behaviour has been observed for some hydrogen bonded complexes involving THF like THF–HCl or THF–HF w42x for wich the rotational spectra also show a doubling due to pseudorotation tunnelling.

Acknowledgements We thank Mr. A. Millemaggi for technical help, and the Ministero dell’ Universita` e della Ricerca

234

S. Melandri et al.r Chemical Physics 239 (1998) 229–234

Scientifica e Tecnologica, and the C.N.R. for financial support. The Direccion ´ General de Ensenanza ˜ Superior ŽDGES Grant PB96-0366. the Junta de Castilla y Leon ´ ŽJCL Grants VA51r96 and VA04r 98. and the European Programme Human Capital and Mobility ŽNetwork SCAMP, Contract ERBCHRXCT930157. are also acknowledged for funds.

References w1x J.B. Anderson, R.P. Andres, J.B. Fenn, in: J. Ross ŽEd.., Advances in Chemical Physics, vol. X, Interscience, New York, 1966, pp. 275–317. w2x P. Hobza, R. Zahradnik, Intermolecular Complexes, Academia, Prague, 1988. w3x S.G. Kukolich, J.A. Shea, J. Chem. Phys. 77 Ž1982. 5242. w4x S.G. Kukolich, J. Am. Chem. Soc. 105 Ž1983. 2207. w5x T.D. Klots, T. Emilsson, R.S. Ruoff, H.S. Gutowsky, J. Phys. Chem. 93 Ž1989. 1255. w6x R.K. Bohn, K.W.D. Hillig II, R.L. Kuczkowski, J. Chem. Phys. 93 Ž1989. 3456. w7x R.M. Spycher, L. Hausser-Primo, G. Grassi, A. Bauder, J. Mol. Struct. 351 Ž1995. 7. w8x R.M. Spycher, D. Petiprez, F.L. Bettens, A. Bauder, J. Phys. Chem. 98 Ž1994. 11863. w9x J.J. Oh, K.W.D. Hillig II, R.L. Kuczkowski, R.K. Bohn, J. Chem. Phys. 94 Ž1990. 4453. w10x Th. Brupbacher, A. Bauder, Chem. Phys. Lett. 173 Ž1990. 435. w11x Th. Brupbacher, J. Makarewicz, A. Bauder, J. Chem. Phys. 101 Ž1994. 9736. w12x T.D. Klots, T. Emilsson, H.S. Gutowsky, J. Chem. Phys. 97 Ž1992. 5335. w13x E. Arunan, T. Emilsson, H.S. Gutowsky, J. Chem. Phys. 99 Ž1993. 6208. w14x T.D. Klots, T. Emilsson, R.S. Ruoff, H.S. Gutowsky, J. Chem. Phys. 93 Ž1989. 1255. w15x U. Kretschmer, W. Stahl, H. Dreizler, J. Mol. Struct. 352,353 Ž1995. 289.

w16x E. Kraka, D. Cremer, U. Spoerel, I. Merke, W. Stahl, H. Dreizler, J. Phys. Chem. 99 Ž1995. 12466. w17x U. Spoerel, H. Dreizler, W. Stahl, E. Kraka, D. Cremer, J. Phys. Chem. 100 Ž1996. 14298. w18x S. Melandri, G. Maccaferri, A. Maris, A. Millemaggi, W. Caminati, P.G. Favero, Chem. Phys. Lett. 261 Ž1996. 267. w19x W. Caminati, S. Melandri, P.G. Favero, R. Meyer, Chem. Phys. Lett. 268 Ž1997. 393. w20x W. Caminati, A. Millemaggi, P.G. Favero, J. Makarewicz, J. Phys. Chem. 101 Ž1997. 9272. w21x W. Caminati, S. Melandri, A. Millemaggi, P.G. Favero, Chem. Phys. Lett. 294 Ž1998. 377. w22x R.A. Collins, A.C. Legon, D.J. Millen, J. Mol. Struct. ŽTheochem. 135 Ž1986. 435. w23x Y. Xu, W. Jager, J. Chem. Phys. 106 Ž1997. 7968. ¨ w24x A.C. Legon, D.G. Lister, Chem. Phys. Lett. 189 Ž1992. 149. w25x F. Lorenzo, A. Lesarri, J.C. Lopez, J.L. Alonso, Chem. Phys. ´ Lett. 286 Ž1998. 272. w26x W. Caminati, P.G. Favero, S. Melandri, J. Makarewicz, Mol. Phys. 91 Ž1997. 663. w27x J.L. Alonso, F.J. Lorenzo, J.C. Lopez, A. Lesarri, S. Mata, H. Dreizler, Chem. Phys. 218 Ž1997. 267. w28x A. Maris, S. Melandri, W. Caminati, P.G. Favero, J. Makarewicz, J. Chem. Phys. 107 Ž1997. 5714. w29x A. Maris, A.C. Fantoni, W. Caminati, P.G. Favero, J. Mol. Spectrosc. 184 Ž1997. 145. w30x A.C. Legon, D.G. Lister, Chem. Phys. Lett. 204 Ž1993. 139. w31x S. Melandri, W. Caminati, L.B. Favero, A. Millemaggi, P.G. Favero, J. Mol. Struct. 352r353 Ž1995. 253. w32x G.G. Engerholm, A.C. Luntz, W.D. Gwinn, D.O. Harris, J. Chem. Phys. 50 Ž1969. 2446. w33x S. Melandri, W. Caminati, P.G. Favero, J.C. Lopez, J.L. Alonso, R. Meyer Žin preparation.. w34x H.M. Pickett, J. Chem. Phys. 56 Ž1972. 1715. w35x H.M. Pickett, J. Mol. Spectrosc. 148 Ž1991. 371. w36x J.K.G. Watson, in: J.R. Durig ŽEd.., Vibrational Spectra and Structure, vol. 6, Elsevier, New York, 1977, pp. 1–89. w37x J. Kraitchman, Am. J. Phys. 21 Ž1953. 17. w38x R.P.A. Bettens, R.M. Spycher, A. Bauder, Mol. Phys. 86 Ž1995. 487. w39x J. Makarewicz, A. Bauder, Mol. Phys. 84 Ž1995. 853. w40x D.J. Millen, Can. J. Chem. 63 Ž1985. 1477. w41x W.G. Read, E.J. Campbell, G. Henderson, J. Chem. Phys. 78 Ž1983. 3501. w42x J.L. Alonso et al. Žto be published..