- Email: [email protected]
Rotational spectrum and structure of the oxetane–argon Van der Waals complex
10 April 1998
Chemical Physics Letters 286 Ž1998. 272–276
Rotational spectrum and structure of the oxetane–argon Van der Waals complex F. Lorenzo, A. Lesarri, J.C. Lopez, J.L. Alonso ´
)
Departamento de Quımica Fısica, Facultad de Ciencias, UniÕersidad de Valladolid, E-47005 Valladolid, Spain ´ ´ Received 4 December 1997; in final form 20 January 1998
Abstract The rotational spectrum of the Van der Waals complex oxetane–argon has been observed using a molecular beam–Fourier transform microwave spectrometer in the frequency range of 5–18.5 GHz. The complex has C s symmetry with the argon ˚ from the center of mass of the ring. The line joining the Ar atom with the atom located above the plane of oxetane, 3.57 A center of mass of oxetane makes an angle of ; 108 with the normal to the oxetane plane. q 1998 Elsevier Science B.V.
1. Introduction Despite the number of spectroscopic studies of Van der Waals complexes using molecular beam– Fourier transform microwave spectroscopy ŽMB– FTMW., there are few studies involving nonaromatic cyclic molecules. We have recently reported the Van der Waals complex 2,5-dihydro˚ furan–argon ŽAr. w1x, where the Ar atom lies 3.5 A w x w above the ring. Oxirane–Ar 2 and thiirane–Ar 3x have also been studied. The authors found these complexes to have a symmetric structure, with the Ar atom located above the ring, displaced away from the hetero-atom. Oxirane–Ar showed inversion splittings due to argon tunnelling between equivalent sites. For bare oxetane the substitution structure w4x and the dipole moment w5x have been previously determined by microwave spectroscopy. This molecule
)
Corresponding author. E-mail: [email protected]
has a double minimum potential energy function for the ring puckering vibration Žw5x and references therein. with a barrier-to-ring planarity close to 15 cmy1 . The ground vibrational state lies 12 cmy1 above the barrier, so a near-planar ring equilibrium configuration has been established for the molecule. We have studied the rotational spectrum of oxetane–Ar in an attempt to find the conformation and structure of the complex. The determination of the force constant for the complexing bond is also interesting. The latter is available from the centrifugal distortion constants usually obtained in the rotational study.
2. Experimental The rotational spectrum was observed using a MB–FTMW spectrometer operating between 5 and 18.5 GHz, with the molecular beam parallel to the Fabry–Perot ´ resonator axis w1x. In this configuration
0009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 0 0 9 5 - 5
F. Lorenzo et al.r Chemical Physics Letters 286 (1998) 272–276 Table 1 Observed line frequencies Žin MHz. for oxetane–Ar and their differences Žin kHz. with those calculated from the spectroscopic constants of Table 2 for the S reduction and I r representation J 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 8 8 8 8
X
X Ky1
X Kq1
1 0 1 1 2 2 1 0 1 1 2 2 2 2 1 0 1 1 2 2 2 2 1 0 0 1 1 2 2 3 3 2 2 0 0 1 1 2 2 3 3 2 2 0 2 2 0 2 2 0 1
1 2 2 1 1 0 2 3 3 2 2 1 2 1 3 4 4 3 3 2 3 2 4 4 5 5 4 4 3 3 2 4 3 5 6 6 5 5 4 4 3 5 4 6 6 5 7 7 6 8 8
§ J 0 1 1 1 2 2 1 2 2 2 2 2 3 3 2 3 3 3 3 3 4 4 3 3 4 4 4 4 4 4 4 5 5 4 5 5 5 5 5 5 5 6 6 5 7 7 6 8 8 7 7
Y
Y Ky1
Y Kq1
Obs.
0 0 1 1 1 1 0 0 1 1 2 2 1 1 0 0 1 1 2 2 1 1 0 1 0 1 1 2 2 3 3 1 1 1 0 1 1 2 2 3 3 1 1 1 1 1 1 1 1 1 2
0 1 1 0 2 1 1 2 2 1 1 0 3 2 2 3 3 2 2 1 4 3 3 3 4 4 3 3 2 2 1 5 4 4 5 5 4 4 3 3 2 6 5 5 7 6 6 8 7 7 5
8321.209 2 5868.449 1 5865.902 5 5870.685 0 16167.775 5 16160.581 y8 11252.802 2 8802.272 1 8798.451 5 8805.628 2 8801.315 y11 8801.332 4 16170.646 y3 16156.295 4 14182.798 0 11735.612 1 11730.515 0 11740.089 2 11734.343 y9 11734.352 y8 16174.484 y1 16150.561 y2 17111.042 0 6355.085 1 14668.313 4 14661.945 2 14673.904 y2 14666.739 2 14666.752 1 14664.757 y1 14664.757 y1 16179.280 1 16143.410 1 9292.878 0 17600.202 0 17592.570 0 17606.919 y3 17598.316 y3 17598.343 y1 17595.944 4 17595.944 4 16185.029 1 16134.833 0 12231.136 0 16191.729 1 16124.838 2 15169.694 1 16199.377 y1 16113.429 2 18108.387 3 7258.954 y1
Obs.–Cal.
273
Table 1 Žcontinued. J
X
8 9 9 10
X
X
Ky1
Kq1 § J
1 2 2 2
7 8 7 8
Y
7 9 9 10
Y
Y
Ky1 Kq1 Obs. 2 1 1 1
6 9 8 9
Obs.–Cal.
7345.152 y2 16207.976 0 16100.607 y4 16086.393 1
the lines appear as Doppler doublets Žsee Fig. 1.. The linewidth of the Doppler components is about 7 kHz full width at half maximum ŽFWHM., and allowed frequencies are measured with an estimated accuracy of 1 kHz. The transition frequencies are taken as the arithmetic mean of the Doppler doublets. The weakly bound complex was generated by a pulsed supersonic expansion of a gas mixture of ; 1% oxetane ŽAldrich. in argon at a total pressure of 2 bar through a nozzle 0.8 mm in diameter ŽGeneral Valve, series 9.. Beam pulses of about 300 ms duration were employed with repetition rates up to 30 Hz. A microwave pulse with a peak power of 40 mW and 0.8 ms duration was applied to each gas pulse. Timing of the gas and microwave pulses was coordinated to obtain an optimal SrN ratio. Typically 500–2000 beam pulses were signal averaged and Fourier transformed to obtain the spectrum in the frequency domain. In the initial search for oxetane–Ar lines, the spectrometer was operated in a scanning mode, recording the spectra at discrete
Fig. 1. Doppler doublet for the 4 0,4 §30,3 rotational transition of the oxetane–Ar Van der Waals complex.
F. Lorenzo et al.r Chemical Physics Letters 286 (1998) 272–276
274
Table 2 Spectroscopic constants for oxetane–Ar in the I r representation for both A and S reductions A reduction
S reduction
rotational constants and asymmetry parameter ŽMHz. 6855.3145 Ž18. a A ŽMHz. 1468.410 Ž13. B ŽMHz. 1465.921 Ž13. C k y0.999076 centrifugal distortion constants D J ŽkHz. 6.6600 Ž82. DJ ŽkHz. D J K ŽkHz. 39.460 Ž29. DJ K ŽkHz. DK ŽkHz. y29.56 Ž37. DK ŽkHz. d J ŽkHz. 0.00728 Ž82. d1 ŽkHz. d K ŽkHz. 23.7 Ž6.3. d 2 ŽkHz. F J ŽHz. y0.110 Ž68. H J ŽHz. F J K ŽHz. y3.78 Ž32. H J K ŽHz. Nb 55 s c ŽkHz. 3 ˚2. I a ŽmA 73.720775 Ž19. d Ib
˚2. ŽmA
Ic
˚2. ŽmA
Pc
˚2. ŽmA
344.1676 Ž30. 344.7519 Ž30. 36.5682 Ž60. e
6855.3144 Ž18. 1468.36251 Ž29. 1465.96859 Ž30. y0.999112 6.6572 Ž82. 39.470 Ž29. y29.57 Ž37. y0.00725 Ž82. y0.00126 Ž34. y0.112 Ž69. y3.95 Ž30. 55 3 73.720776 Ž19. 344.178700 Ž68. 344.740742 Ž71. 36.57937 Ž16.
enabled us to make a better prediction. In this way further R-branch transitions were found at 8321, 11252, 14182 and 17111 MHz. They were initially assigned as c-type transitions, which gave a good fit except for the fact that the B constant was smaller than C. By reassigning the quantum numbers to the related b-type transitions, a total of 12 R-branch and 17 Q-branch b-type were finally assigned. All measured frequencies are collected in Table 1. As oxetane–Ar is close to the near-prolate limit Ž k ; y0.999. different fits were carried out using both A- and S-reduced Watson Hamiltonians w6x in the I r representation. Three rotational constants, five quartic and two sextic centrifugal distortion constants were determined from the measured lines. The spectroscopic parameters and standard deviation of the fits are shown in Table 2. The derived rotational constants B and C are determined with smaller standard errors when using the S-reduced Hamiltonian.
a
Standard error in parentheses in units of the last digit. Number of fitted transitions. c Standard deviation of the fit. d ˚ 2 MHz. Conversion factor: 505379.1 mA e Pc s 12 Ž Ia q Ib y Ic . s im i c i2 b
Ý
polarizing frequencies with a step width of 0.25 MHz.
4. Structural analysis Assuming that the oxetane structure is unchanged upon complexation, three coordinates are required to describe the structure of the oxetane–Ar complex Žsee Fig. 2.. R is the distance from the center of
3. Data analysis and results The spectrum of oxetane–Ar was predicted from a model based on the structures of oxetane w4x and 2,5-dihydrofuran–Ar w1x considering a planar equilibrium structure for oxetane. This molecule is an oblate near symmetric top with its a-axis coincident with the C 2 axis through the oxygen atom. Binding of an Ar atom above the ring then gives a prolate near symmetric top. In this event the a-axis of the heterocycle becomes the b- or c-axis of the dimer. Our search began for a-type R-branch rotational transitions. After scanning the range from 8500 to 8900 MHz the 3 § 2 transitions were soon found at 8798, 8802 and 8805 MHz. The assignment of other a-type R-branch lines then followed, giving a total of 26 transitions assigned for Ky1 s 0–3. A semirigid rotor fit of the measured a-type lines
Fig. 2. Structure of the oxetane–Ar Van der Waals complex.
F. Lorenzo et al.r Chemical Physics Letters 286 (1998) 272–276 Table 3 Spectroscopic constants for oxetane taken from Ref. w5x
C k DJ
˚ 2 . 41.9559891 Ž28. b ŽMHz. 12045.45788 Ž79. a Iam ŽmA m ˚ 2 . 43.0694599 Ž29. ŽMHz. 11734.04778 Ž78. Ib ŽmA m ˚ 2 . 75.0861576 Ž18. ŽMHz. 6730.65604 Ž16. Ic ŽmA 0.882814 ŽHz. 4.8756 Ž16.
DJK DK dJ dK
ŽkHz. ŽkHz. ŽHz. ŽHz.
A B
y1.2253 Ž44. 4.5705 Ž33. y1.61102 Ž40. 0.91804 Ž74.
˚ 2 . 36.9863434 Ž75. c Pb ŽmA
275
The inertial tensor I X of the complex in the center of mass axis system Ž xX , yX , zX . depicted in Fig. 2 can be expressed in terms of R and u by mean of the following set of equations w8x: I xX x s Iam q m Ž y 2 q z 2 . s Iam q m R 2 cos 2u I yX y s Ibm q m Ž x 2 q z 2 . s Ibm q m R 2 IzX z s Icm q m Ž x 2 q y 2 . s Icm q m R 2 sin2 u I xX y s ym xy s 0
a
Standard error in parentheses in units of the last digit. ˚ 2 MHz. Conversion factor: 505379.1 mA c Pb s 12 Ž Ia q Ic y Ib . s im i bi2 b
I xX z s ym xz s ym R 2 sin u cos u
Ý
I yX z s ym yz s 0 mass of oxetane to the Ar atom, u is the angle between R and the principal axis c of oxetane, and w is the angle between R and the ac symmetry plane of the ring. The principal axis system of the complex and the monomer have been denoted Ž a, b, c . and Ž a m , b m , c m ., respectively, with the principal axis c parallel to b m . Tables 2 and 3 show the planar moments of inertia Pc for the complex and Pb for the monomer. The first describes the mass located out of the ab plane of the complex, while the latter refers to the mass located out of the symmetry plane of oxetane. A good agreement between them is expected if the Ar atom is situated on this plane. As in the case of 2,5-dihydrofuran–Ar w1x, the difference ˚ 2 may be attributed to the large amplitude of 0.41 mA vibrations of the complex w7x and a C s equilibrium symmetry can be assumed.
where x, y, z are the coordinates of the Ar atom in the principal axis system of oxetane and m s Ž mŽoxetane. mŽAr..rŽ mŽoxetane. q mŽAr.. is the pseudodiatomic reduced mass for the dimer. The moments of inertia for the monomer are given in Table 3. The above inertial tensor is diagonalized to get the principal inertial moments Ia , Ib , Ic for the complex in terms of R and u , establishing a way for fitting these parameters to the experimental values of the dimer. An ro-like structure was then derived by fitting R and u to the pairs of inertial moments Ž Ia , Ib ., Ž Ia , Ic ., Ž Ib , Ic .. The results obtained are given in Table 4, along with the calculated inertial moments for each set of coordinates. The different sets of rotational constants give different coordinates R and u due to large amplitude vibrations, which have
Table 4 Determination of the coordinates R and u Žsee Fig. 2. of the oxetane–Ar complex from r o - and r s-like procedures r 0 structure Iac , Ibc
rs structure Iac , Icc
Ibc , Icc
Average
Ibc q Icc , Iac y Ibc
3.565 11.069
Iac
˚. ŽA Ž8. ˚2. ŽmA
73.7207
73.7207
74.5347
74.0308
73.9922
74.1278
Ibc
˚2. ŽmA
344.1138
344.9582
344.1442
344.3102
344.5178
344.5846
Icc
˚2. ŽmA
343.8619
344.7062
344.7062
344.3683
344.5373
344.7397
R u
3.570 11.071
3.568 Ž3. a 9.7 Ž2.3.
3.570 6.999
For each set of derived parameters the resulting moments of inertia are given. a Standard error in units of the last digit.
3.569 9.892
3.570 9.251
F. Lorenzo et al.r Chemical Physics Letters 286 (1998) 272–276
276
Table 5 Comparison of R distances, stretching harmonic frequencies n and force constants K s for complexes formed between Ar and oxirane, oxetane and 2,5-dihydrofuran Complex
R ˚. ŽA
n Žcmy1 .
Ks ŽN my1 .
oxirane PPP argon oxetane PPP argonc 2,5-dihydrofuran–argond
3.61a 3.57 3.53
44 b 46 47
2.4 b 3.0 3.3
a
Ref. w11x. Calculated using the pseudodiatomic model from the rotational parameters given in Ref. w11x. c This work. d Ref. w1x. b
been omitted in interpreting the moments of inertia w9x. In this situation the averaged values R s 3.568Ž3. ˚ and u s 9.78 Ž2.3. can be considered as the most A reliable ones. In the absence of isotopic substitution the sign of the angle u cannot be determined. Values for an rs structure can be obtained using Kraitchman’s equations w10x. This can be done considering the complex with an Ar atom of zero mass as the parent molecule and using the real mass in the substituted molecule. The assumed C s symmetry of the complex leads to < a < s 0.574, < b < s 0 and < c < s ˚ giving the values of R and u listed in 3.524 A, Table 4 for comparison with the r 0 values. Again in this procedure the sign of angle u cannot be determined. The harmonic frequency n and stretching force constant K s associated to the weak bond between Ar and oxetane have been estimated from the centrifu-
gal distortion constant DJ and the rotational constant B using the pseudodiatomic model relationship w11x DJ s
4B3
. Ž 2. n2 The resulting values are compared in Table 5 with those calculated using the same approximation for the related complexes oxirane–Ar and 2,5-dihydrofuran–Ar. The model precludes definitive interpretations of the data. However, the trend of the determined values for R and K s Žor n . may indicate a strengthening of the bond to argon with the increasing of the ring size. References w1x J.L. Alonso, F.J. Lorenzo, J.C. Lopez, A. Lesarri, S. Mata, ´ H. Dreizler, Chem. Phys. 218 Ž1997. 267. w2x R.A. Collins, A.C. Legon, D.J. Millen, J. Mol. Struct. 135 Ž1986. 435. w3x A.C. Legon, D.G. Lister, Chem. Phys. Lett. 189 Ž1991. 149. w4x R.A. Creswell, Mol. Phys. 30 Ž1975. 217. w5x A. Lesarri, S. Blanco, J.C. Lopez, J. Mol. Struct. 354 Ž1995. ´ 237. w6x J.K.G. Watson, in: J.R. Durig ŽEd.. Vibrational Spectra and Structure, Vol. 6 ŽElsevier, Amsterdam, 1977., pp. 1–89. w7x T.D. Klots, T. Emilsson, R.S. Ruoff, H.S. Gutowsky, J. Phys. Chem. 93 Ž1989. 1255. w8x W. Gordy, R.L. Cook, Microwave Molecular Spectra ŽWiley–Interscience, New York, 1984. Ch. 13, p. 657. w9x R.K. Bohn, K.W. Hillig, R.L. Kuczkowski, J. Phys. Chem. 93 Ž1989. 3456. w10x W. Gordy, R.L. Cook, Microwave Molecular Spectra ŽWiley–Interscience, New York, 1984. Ch. 13, p. 663. w11x W. Gordy, R.L. Cook, Microwave Molecular Spectra ŽWiley–Interscience, New York, 1984. Ch. 8, p. 304.
Chemical Physics Letters 286 Ž1998. 272–276
Rotational spectrum and structure of the oxetane–argon Van der Waals complex F. Lorenzo, A. Lesarri, J.C. Lopez, J.L. Alonso ´
)
Departamento de Quımica Fısica, Facultad de Ciencias, UniÕersidad de Valladolid, E-47005 Valladolid, Spain ´ ´ Received 4 December 1997; in final form 20 January 1998
Abstract The rotational spectrum of the Van der Waals complex oxetane–argon has been observed using a molecular beam–Fourier transform microwave spectrometer in the frequency range of 5–18.5 GHz. The complex has C s symmetry with the argon ˚ from the center of mass of the ring. The line joining the Ar atom with the atom located above the plane of oxetane, 3.57 A center of mass of oxetane makes an angle of ; 108 with the normal to the oxetane plane. q 1998 Elsevier Science B.V.
1. Introduction Despite the number of spectroscopic studies of Van der Waals complexes using molecular beam– Fourier transform microwave spectroscopy ŽMB– FTMW., there are few studies involving nonaromatic cyclic molecules. We have recently reported the Van der Waals complex 2,5-dihydro˚ furan–argon ŽAr. w1x, where the Ar atom lies 3.5 A w x w above the ring. Oxirane–Ar 2 and thiirane–Ar 3x have also been studied. The authors found these complexes to have a symmetric structure, with the Ar atom located above the ring, displaced away from the hetero-atom. Oxirane–Ar showed inversion splittings due to argon tunnelling between equivalent sites. For bare oxetane the substitution structure w4x and the dipole moment w5x have been previously determined by microwave spectroscopy. This molecule
)
Corresponding author. E-mail: [email protected]
has a double minimum potential energy function for the ring puckering vibration Žw5x and references therein. with a barrier-to-ring planarity close to 15 cmy1 . The ground vibrational state lies 12 cmy1 above the barrier, so a near-planar ring equilibrium configuration has been established for the molecule. We have studied the rotational spectrum of oxetane–Ar in an attempt to find the conformation and structure of the complex. The determination of the force constant for the complexing bond is also interesting. The latter is available from the centrifugal distortion constants usually obtained in the rotational study.
2. Experimental The rotational spectrum was observed using a MB–FTMW spectrometer operating between 5 and 18.5 GHz, with the molecular beam parallel to the Fabry–Perot ´ resonator axis w1x. In this configuration
0009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 0 0 9 5 - 5
F. Lorenzo et al.r Chemical Physics Letters 286 (1998) 272–276 Table 1 Observed line frequencies Žin MHz. for oxetane–Ar and their differences Žin kHz. with those calculated from the spectroscopic constants of Table 2 for the S reduction and I r representation J 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 8 8 8 8
X
X Ky1
X Kq1
1 0 1 1 2 2 1 0 1 1 2 2 2 2 1 0 1 1 2 2 2 2 1 0 0 1 1 2 2 3 3 2 2 0 0 1 1 2 2 3 3 2 2 0 2 2 0 2 2 0 1
1 2 2 1 1 0 2 3 3 2 2 1 2 1 3 4 4 3 3 2 3 2 4 4 5 5 4 4 3 3 2 4 3 5 6 6 5 5 4 4 3 5 4 6 6 5 7 7 6 8 8
§ J 0 1 1 1 2 2 1 2 2 2 2 2 3 3 2 3 3 3 3 3 4 4 3 3 4 4 4 4 4 4 4 5 5 4 5 5 5 5 5 5 5 6 6 5 7 7 6 8 8 7 7
Y
Y Ky1
Y Kq1
Obs.
0 0 1 1 1 1 0 0 1 1 2 2 1 1 0 0 1 1 2 2 1 1 0 1 0 1 1 2 2 3 3 1 1 1 0 1 1 2 2 3 3 1 1 1 1 1 1 1 1 1 2
0 1 1 0 2 1 1 2 2 1 1 0 3 2 2 3 3 2 2 1 4 3 3 3 4 4 3 3 2 2 1 5 4 4 5 5 4 4 3 3 2 6 5 5 7 6 6 8 7 7 5
8321.209 2 5868.449 1 5865.902 5 5870.685 0 16167.775 5 16160.581 y8 11252.802 2 8802.272 1 8798.451 5 8805.628 2 8801.315 y11 8801.332 4 16170.646 y3 16156.295 4 14182.798 0 11735.612 1 11730.515 0 11740.089 2 11734.343 y9 11734.352 y8 16174.484 y1 16150.561 y2 17111.042 0 6355.085 1 14668.313 4 14661.945 2 14673.904 y2 14666.739 2 14666.752 1 14664.757 y1 14664.757 y1 16179.280 1 16143.410 1 9292.878 0 17600.202 0 17592.570 0 17606.919 y3 17598.316 y3 17598.343 y1 17595.944 4 17595.944 4 16185.029 1 16134.833 0 12231.136 0 16191.729 1 16124.838 2 15169.694 1 16199.377 y1 16113.429 2 18108.387 3 7258.954 y1
Obs.–Cal.
273
Table 1 Žcontinued. J
X
8 9 9 10
X
X
Ky1
Kq1 § J
1 2 2 2
7 8 7 8
Y
7 9 9 10
Y
Y
Ky1 Kq1 Obs. 2 1 1 1
6 9 8 9
Obs.–Cal.
7345.152 y2 16207.976 0 16100.607 y4 16086.393 1
the lines appear as Doppler doublets Žsee Fig. 1.. The linewidth of the Doppler components is about 7 kHz full width at half maximum ŽFWHM., and allowed frequencies are measured with an estimated accuracy of 1 kHz. The transition frequencies are taken as the arithmetic mean of the Doppler doublets. The weakly bound complex was generated by a pulsed supersonic expansion of a gas mixture of ; 1% oxetane ŽAldrich. in argon at a total pressure of 2 bar through a nozzle 0.8 mm in diameter ŽGeneral Valve, series 9.. Beam pulses of about 300 ms duration were employed with repetition rates up to 30 Hz. A microwave pulse with a peak power of 40 mW and 0.8 ms duration was applied to each gas pulse. Timing of the gas and microwave pulses was coordinated to obtain an optimal SrN ratio. Typically 500–2000 beam pulses were signal averaged and Fourier transformed to obtain the spectrum in the frequency domain. In the initial search for oxetane–Ar lines, the spectrometer was operated in a scanning mode, recording the spectra at discrete
Fig. 1. Doppler doublet for the 4 0,4 §30,3 rotational transition of the oxetane–Ar Van der Waals complex.
F. Lorenzo et al.r Chemical Physics Letters 286 (1998) 272–276
274
Table 2 Spectroscopic constants for oxetane–Ar in the I r representation for both A and S reductions A reduction
S reduction
rotational constants and asymmetry parameter ŽMHz. 6855.3145 Ž18. a A ŽMHz. 1468.410 Ž13. B ŽMHz. 1465.921 Ž13. C k y0.999076 centrifugal distortion constants D J ŽkHz. 6.6600 Ž82. DJ ŽkHz. D J K ŽkHz. 39.460 Ž29. DJ K ŽkHz. DK ŽkHz. y29.56 Ž37. DK ŽkHz. d J ŽkHz. 0.00728 Ž82. d1 ŽkHz. d K ŽkHz. 23.7 Ž6.3. d 2 ŽkHz. F J ŽHz. y0.110 Ž68. H J ŽHz. F J K ŽHz. y3.78 Ž32. H J K ŽHz. Nb 55 s c ŽkHz. 3 ˚2. I a ŽmA 73.720775 Ž19. d Ib
˚2. ŽmA
Ic
˚2. ŽmA
Pc
˚2. ŽmA
344.1676 Ž30. 344.7519 Ž30. 36.5682 Ž60. e
6855.3144 Ž18. 1468.36251 Ž29. 1465.96859 Ž30. y0.999112 6.6572 Ž82. 39.470 Ž29. y29.57 Ž37. y0.00725 Ž82. y0.00126 Ž34. y0.112 Ž69. y3.95 Ž30. 55 3 73.720776 Ž19. 344.178700 Ž68. 344.740742 Ž71. 36.57937 Ž16.
enabled us to make a better prediction. In this way further R-branch transitions were found at 8321, 11252, 14182 and 17111 MHz. They were initially assigned as c-type transitions, which gave a good fit except for the fact that the B constant was smaller than C. By reassigning the quantum numbers to the related b-type transitions, a total of 12 R-branch and 17 Q-branch b-type were finally assigned. All measured frequencies are collected in Table 1. As oxetane–Ar is close to the near-prolate limit Ž k ; y0.999. different fits were carried out using both A- and S-reduced Watson Hamiltonians w6x in the I r representation. Three rotational constants, five quartic and two sextic centrifugal distortion constants were determined from the measured lines. The spectroscopic parameters and standard deviation of the fits are shown in Table 2. The derived rotational constants B and C are determined with smaller standard errors when using the S-reduced Hamiltonian.
a
Standard error in parentheses in units of the last digit. Number of fitted transitions. c Standard deviation of the fit. d ˚ 2 MHz. Conversion factor: 505379.1 mA e Pc s 12 Ž Ia q Ib y Ic . s im i c i2 b
Ý
polarizing frequencies with a step width of 0.25 MHz.
4. Structural analysis Assuming that the oxetane structure is unchanged upon complexation, three coordinates are required to describe the structure of the oxetane–Ar complex Žsee Fig. 2.. R is the distance from the center of
3. Data analysis and results The spectrum of oxetane–Ar was predicted from a model based on the structures of oxetane w4x and 2,5-dihydrofuran–Ar w1x considering a planar equilibrium structure for oxetane. This molecule is an oblate near symmetric top with its a-axis coincident with the C 2 axis through the oxygen atom. Binding of an Ar atom above the ring then gives a prolate near symmetric top. In this event the a-axis of the heterocycle becomes the b- or c-axis of the dimer. Our search began for a-type R-branch rotational transitions. After scanning the range from 8500 to 8900 MHz the 3 § 2 transitions were soon found at 8798, 8802 and 8805 MHz. The assignment of other a-type R-branch lines then followed, giving a total of 26 transitions assigned for Ky1 s 0–3. A semirigid rotor fit of the measured a-type lines
Fig. 2. Structure of the oxetane–Ar Van der Waals complex.
F. Lorenzo et al.r Chemical Physics Letters 286 (1998) 272–276 Table 3 Spectroscopic constants for oxetane taken from Ref. w5x
C k DJ
˚ 2 . 41.9559891 Ž28. b ŽMHz. 12045.45788 Ž79. a Iam ŽmA m ˚ 2 . 43.0694599 Ž29. ŽMHz. 11734.04778 Ž78. Ib ŽmA m ˚ 2 . 75.0861576 Ž18. ŽMHz. 6730.65604 Ž16. Ic ŽmA 0.882814 ŽHz. 4.8756 Ž16.
DJK DK dJ dK
ŽkHz. ŽkHz. ŽHz. ŽHz.
A B
y1.2253 Ž44. 4.5705 Ž33. y1.61102 Ž40. 0.91804 Ž74.
˚ 2 . 36.9863434 Ž75. c Pb ŽmA
275
The inertial tensor I X of the complex in the center of mass axis system Ž xX , yX , zX . depicted in Fig. 2 can be expressed in terms of R and u by mean of the following set of equations w8x: I xX x s Iam q m Ž y 2 q z 2 . s Iam q m R 2 cos 2u I yX y s Ibm q m Ž x 2 q z 2 . s Ibm q m R 2 IzX z s Icm q m Ž x 2 q y 2 . s Icm q m R 2 sin2 u I xX y s ym xy s 0
a
Standard error in parentheses in units of the last digit. ˚ 2 MHz. Conversion factor: 505379.1 mA c Pb s 12 Ž Ia q Ic y Ib . s im i bi2 b
I xX z s ym xz s ym R 2 sin u cos u
Ý
I yX z s ym yz s 0 mass of oxetane to the Ar atom, u is the angle between R and the principal axis c of oxetane, and w is the angle between R and the ac symmetry plane of the ring. The principal axis system of the complex and the monomer have been denoted Ž a, b, c . and Ž a m , b m , c m ., respectively, with the principal axis c parallel to b m . Tables 2 and 3 show the planar moments of inertia Pc for the complex and Pb for the monomer. The first describes the mass located out of the ab plane of the complex, while the latter refers to the mass located out of the symmetry plane of oxetane. A good agreement between them is expected if the Ar atom is situated on this plane. As in the case of 2,5-dihydrofuran–Ar w1x, the difference ˚ 2 may be attributed to the large amplitude of 0.41 mA vibrations of the complex w7x and a C s equilibrium symmetry can be assumed.
where x, y, z are the coordinates of the Ar atom in the principal axis system of oxetane and m s Ž mŽoxetane. mŽAr..rŽ mŽoxetane. q mŽAr.. is the pseudodiatomic reduced mass for the dimer. The moments of inertia for the monomer are given in Table 3. The above inertial tensor is diagonalized to get the principal inertial moments Ia , Ib , Ic for the complex in terms of R and u , establishing a way for fitting these parameters to the experimental values of the dimer. An ro-like structure was then derived by fitting R and u to the pairs of inertial moments Ž Ia , Ib ., Ž Ia , Ic ., Ž Ib , Ic .. The results obtained are given in Table 4, along with the calculated inertial moments for each set of coordinates. The different sets of rotational constants give different coordinates R and u due to large amplitude vibrations, which have
Table 4 Determination of the coordinates R and u Žsee Fig. 2. of the oxetane–Ar complex from r o - and r s-like procedures r 0 structure Iac , Ibc
rs structure Iac , Icc
Ibc , Icc
Average
Ibc q Icc , Iac y Ibc
3.565 11.069
Iac
˚. ŽA Ž8. ˚2. ŽmA
73.7207
73.7207
74.5347
74.0308
73.9922
74.1278
Ibc
˚2. ŽmA
344.1138
344.9582
344.1442
344.3102
344.5178
344.5846
Icc
˚2. ŽmA
343.8619
344.7062
344.7062
344.3683
344.5373
344.7397
R u
3.570 11.071
3.568 Ž3. a 9.7 Ž2.3.
3.570 6.999
For each set of derived parameters the resulting moments of inertia are given. a Standard error in units of the last digit.
3.569 9.892
3.570 9.251
F. Lorenzo et al.r Chemical Physics Letters 286 (1998) 272–276
276
Table 5 Comparison of R distances, stretching harmonic frequencies n and force constants K s for complexes formed between Ar and oxirane, oxetane and 2,5-dihydrofuran Complex
R ˚. ŽA
n Žcmy1 .
Ks ŽN my1 .
oxirane PPP argon oxetane PPP argonc 2,5-dihydrofuran–argond
3.61a 3.57 3.53
44 b 46 47
2.4 b 3.0 3.3
a
Ref. w11x. Calculated using the pseudodiatomic model from the rotational parameters given in Ref. w11x. c This work. d Ref. w1x. b
been omitted in interpreting the moments of inertia w9x. In this situation the averaged values R s 3.568Ž3. ˚ and u s 9.78 Ž2.3. can be considered as the most A reliable ones. In the absence of isotopic substitution the sign of the angle u cannot be determined. Values for an rs structure can be obtained using Kraitchman’s equations w10x. This can be done considering the complex with an Ar atom of zero mass as the parent molecule and using the real mass in the substituted molecule. The assumed C s symmetry of the complex leads to < a < s 0.574, < b < s 0 and < c < s ˚ giving the values of R and u listed in 3.524 A, Table 4 for comparison with the r 0 values. Again in this procedure the sign of angle u cannot be determined. The harmonic frequency n and stretching force constant K s associated to the weak bond between Ar and oxetane have been estimated from the centrifu-
gal distortion constant DJ and the rotational constant B using the pseudodiatomic model relationship w11x DJ s
4B3
. Ž 2. n2 The resulting values are compared in Table 5 with those calculated using the same approximation for the related complexes oxirane–Ar and 2,5-dihydrofuran–Ar. The model precludes definitive interpretations of the data. However, the trend of the determined values for R and K s Žor n . may indicate a strengthening of the bond to argon with the increasing of the ring size. References w1x J.L. Alonso, F.J. Lorenzo, J.C. Lopez, A. Lesarri, S. Mata, ´ H. Dreizler, Chem. Phys. 218 Ž1997. 267. w2x R.A. Collins, A.C. Legon, D.J. Millen, J. Mol. Struct. 135 Ž1986. 435. w3x A.C. Legon, D.G. Lister, Chem. Phys. Lett. 189 Ž1991. 149. w4x R.A. Creswell, Mol. Phys. 30 Ž1975. 217. w5x A. Lesarri, S. Blanco, J.C. Lopez, J. Mol. Struct. 354 Ž1995. ´ 237. w6x J.K.G. Watson, in: J.R. Durig ŽEd.. Vibrational Spectra and Structure, Vol. 6 ŽElsevier, Amsterdam, 1977., pp. 1–89. w7x T.D. Klots, T. Emilsson, R.S. Ruoff, H.S. Gutowsky, J. Phys. Chem. 93 Ž1989. 1255. w8x W. Gordy, R.L. Cook, Microwave Molecular Spectra ŽWiley–Interscience, New York, 1984. Ch. 13, p. 657. w9x R.K. Bohn, K.W. Hillig, R.L. Kuczkowski, J. Phys. Chem. 93 Ž1989. 3456. w10x W. Gordy, R.L. Cook, Microwave Molecular Spectra ŽWiley–Interscience, New York, 1984. Ch. 13, p. 663. w11x W. Gordy, R.L. Cook, Microwave Molecular Spectra ŽWiley–Interscience, New York, 1984. Ch. 8, p. 304.