J. CHEM. SOC. FARADAY TRANS., 1994, 90(20), 3023-3027 3023

Microwave Spectrum of Tetrolyl Fluoride

Kristine D. Henseit and Michael C. L. Gerry* Department of Chemistry, The University of British Columbia, 2036 Main Mall, Vancouver, B.C. Canada V6T 1Z1

The microwave spectrum of the unstable molecule tetrolyl fluoride (but-2-ynoyl fluoride), CH,-CEC-COF, has been observed for the first time. The a-type rotational spectrum observed with a Stark-modulated microwave spectrometer is very dense, owing to internal rotation of the methyl group. The spectrum has also been mea- sured in the frequency range 9-17 GHz using a pulsed-jet cavity microwave Fourier-transform (MWFT) spec- trometer. Cooling in the jet has removed all internal rotation states other than I rn I = 0 and Irn I = 1, permitting assignment of the microwave spectrum. The threefold barrier to internal rotation has been confirmed to be very low [V, = 2.20(12) cm-' I .

According to the basic concepts of chemical bonding, a methyl group attached to a non-linear acetylene fragment -C=C-R should experience essentially free rotation. Microwave and IR spectroscopic studies of several molecules of the form CH,-C=C-M (where M = CH,,' CD3,2 CF, ,, SiH34 and CHzC15) have confirmed that V, , the three- fold barrier to internal rotation of the methyl group, is indeed low; where V3 has been determined, it has been found to be no greater than ca. 10 cm-'. The IR spectrum of tetrolyl fluoride also gave evidence of free rotation of the methyl group.6

Molecules with low barriers to internal rotation exhibit very crowded mirowave spectra, as lines due to different tor- sional states may be very closely spaced. Assignment is there- fore quite difficult unless some sort of state-selective technique is employed. Microwave-microwave double reson- ance (MW-MW DR) has been used to overcome the problem of spectral congestion in the case of CH,-C~C-CHzCl.5 In the work described here, the microwave spectrum of tet- rolyl fluoride has been obtained using both Stark-modulated and cavity microwave Fourier-transform (MWFT) spectrom- eters. As an alternative to MW-MW DR, the efficient cooling in the molecular beam of the latter spectrometer has been used to 'freeze out' all but the lowest torsional states of tet- rolyl fluoride. This has vastly reduced the congestion in the microwave spectrum, thus permitting the spectrum to be assigned and analysed in detail.

Experimental Tetrolyl fluoride was prepared by heating a mixture of but-2- ynoic acid and benzoyl fluoride, following the method of Olah et al.' The resulting clear distillate (bp 77-78 "C) was identified as tetrolyl fluoride by 'H and 19F NMR, as well as by comparison of the gas-phase IR spectrum with that obtained by Balfour et aL6 As the compound is unstable at room temperature and turns brown over time, the sample was kept at liquid-nitrogen temperatures when not in use and remained colourless over the period of this study.

Preliminary microwave studies were performed on a Stark- modulated spectrometer. For the most part, scans were per- formed in the frequency region 8-18 GHz, as this was the region available on the cavity MWFT spectrometer. Spectra were recorded both with and without dry-ice cooling of the Stark cell. The tetrolyl fluoride was warmed to room tem- perature in order to fill the cell, and spectra were recorded at

t Present address : Physical Chemistry Laboratory, Oxford Uni- versity, South Parks Road, Oxford, UK OX1 342 .

pressures of 30-50 mTorr. At these pressures, the sample remained stable in the cell for at least 1 h, independent of the temperature of the cell.

High-resolution microwave spectra of tetrolyl fluoride were recorded with a cavity MWFT spectrometer which has been described previously.' Gas mixtures of 1-3% tetrolyl fluoride in argon were injected into the microwave cavity using a Bosch fuel-injector nozzle mounted in one of the cavity mirrors. As the molecular beam travelled parallel to the direction of microwave propagation, all lines were doubled by the Doppler effect.

Results and Discussion Given the anticipated structure of tetrolyl fluoride, it was expected that the molecule would be a near-symmetric prolate rotor with its dipole moment lying very nearly along the a inertial axis, resulting in strong a-type rotational tran- sitions. The initial microwave spectra recorded with the Stark spectrometer revealed a typical a-type R-branch pattern, with complex groups of strong, equally spaced, unresolved lines. From this pattern, a rough value for B + C of ca. 3200 MHz was calculated. Very few lines were found in between these groups. Three groups fell within the frequency region of the cavity M WFT spectrometer. Since their frequencies were roughly in the ratio 3 : 4 : 5, they were assigned to the J = 3-2, 4-3 and 5-4 transitions. However, these groups contained far more lines than could be accounted for by a simple rigid-rotor model.

Prediction of Transition Frequencies

A computer program was written to predict rotational tran- sition frequencies for a molecule with one internal rotor and a planar framework. The principal axis method (PAM)9.' was chosen, as the symmetry axis of the methyl group in tet- rolyl fluoride was expected to lie nearly along the a principal axis. When the principal axes of a molecule are chosen such that the frame lies in the ab plane, the Hamiltonian governing internal and overall rotation may be divided as

H = Hrot + Htorsion + Hrot-torsion (1)

Hro, resembles the usual asymmetric rigid-rotor Hamilto- nian, and is a function of the rotational angular momentum operators Jg :

HrOt = A ' e + B'J; + C'J: + Fp,pb(J, J b + Jb J,) (2)

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3024 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90

where A’, B and C are defined in terms of the rotational constants A, B and C as

A‘ = A + FpZ (3)

B‘ = B + Fp,’ (4)

C = C ( 5 )

and

(7)

Ztop is the moment of inertia of the methyl group about its symmetry axis, and is the direction cosine between that symmetry axis and the g principal inertial axis.

Htorsion describes the rotation of the methyl group, and depends on the total angular momentum j of the methyl group about its symmetry axis:

(9)

V(a) is the periodic potential-energy function for rotation of the methyl group through an angle a about its symmetry axis, and is usually expanded as3

v 3 V6

2 2 V(a) = - [l - cos(3a)I + - [l - cos(6a)l + - * * (10)

Hrot-torsion is a term describing the interaction between Je and j :

The computer program has been designed to solve the Hamiltonian in steps, after the method of Anderson and Gwinn.” The rigid-rotor part of the Hamiltonian, Hrot, is treated first, using symmetric-rotor basis functions. The matrix elements of Hrot in this basis are given by

( J K 1 Hrot I JK) = A’K2 + [J(J + 1) - K2] (12) 2

(JK & 1 I Hrot IJK) = - Fpapb (2K f 1) 2

x [J (J + 1) - K(K k 1)]”2 (13)

(B - C’) ( J K 2 I Hrot I JK) = - [J(J + 1) - K(K f 1)]1’2

4

x [ J ( J + 1) - ( K f 1)(K f 2)]”2 (14)

Diagonalization of this part of the Hamiltonian leads to eigenvalues and eigenvectors similar to those of an asym- metric rigid rotor; a Wang transformation does not produce a useful simplication because of the terms off-diagonal by 1 in K.

An analogous procedure is used for the torsional part of the Hamiltonian, Htorsion, using free rotor basis functions of the form U(a) = ( 2 ~ ) - ‘/2exp(irna). Assuming that V6 is suffi- ciently small that V(a) may be truncated after the V3 terms, the matrix elements of the torsional Hamiltonian in the free

rotor basis are given by

The introduction of a non-zero threefold barrier to internal rotation thus introduces off-diagonal elements in Htorsion. Free-rotor states with rn # 0 are doubly degenerate, but the barrier acts to remove the degeneracy for state with rn a multiple of 3. Eltorsion may then be divided into submatrices of A symmetry (rn = . . . -6, -3, 0, 3, 6 . . .) and E symmetry. Since the states with E symmetry are still doubly degenerate, it suffices to consider only half of the E submatrix, i.e. rn = . . . T 5, T 2, & 1, +4, f 7, . . . , where the choice of phase is arbi- trary. Htorsion thus extends from rn = - co to m = + co, and the numerical solutions are necessarily approximate. As trun- cation at sufficiently high I rn I has little effect on small values of I rn I, and only small values of I rn I were expected to be seen for tetrolyl fluoride with the cavity MWFT spectrometer, it was decided to diagonalize a truncated Htorsion directly.

The ‘cross-terms ’ of Hrot-torsion are treated by transforming representations of Ja and Jb in the rigid-rotor basis to repre- sentations in the basis of eigenfunctions of H,,,; j is also transformed to’the basis of eigenfunctions of Htorsion, with A and E submatrices considered separately throughout. If the final Hamiltonian matrix is written in terms of basis functions which are the direct product of the eigenfunctions of Hrot and Htorsion, the cross-terms are easily calculated as the direct pro- ducts (- 2FJa x J) and ( - FJb x J), where the matrix elements of A x B = C are given by

cij, kl = Bjl (17)

As most of the diagonalization of Hrot-torsion has been achieved in the first two steps, the matrix is nearly diagonal and diagonalization proceeds rapidly. The decision to treat the torsional part of the Hamiltonian separately using free- rotor basis functions hinges on the assumption that internal rotation is essentially unhindered, an assumption that was made early in this study of tetrolyl fluoride.

Selection Rules

The selection rules for rotational transitions may be deter- mined by considering the permutation inversion group of a molecule such as tetrolyl fluoride, which has a planar frame and for which the possibility of torsional tunnelling exists. In the G6 permutation inversion group, both the a and b com- ponents of the dipole moment are of symmetry A , . In order to determine the selection rules for rotational transitions, it is necessary to determine the symmetries of the eigenfunctions

The extent to which these eigenfunctions are properly labelled by the K, K, asymmetric rotor labels and the rn tor- sional quantum number depends on both V3 and 8, the angle between the top symmetry axis and the a principal axis. A large barrier to internal rotation results in greater mixing of the free rotor states in Htorsion, while 8 determines the size of F , which in turn determines both the deviation of Hrot from a pure asymmetric rigid-rotor model and the contribution of cross-terms in the final Hamiltonian. V3 was expected to be small for tetrolyl fluoride, in which case lrnl is nearly a good quantum number for torsional states of E symmetry, while states of A symmetry may be approximated as the following

Hrot-torsion *

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linear combinations :

3025

48 kHz f----) 1

- (I + m > + I - rn > ): A , symmetry (18) J 2

J 2

1 - ( 1 i- rn > - 1 - rn > ): A , symmetry. (19)

The angle 8 was also expected to be small (i.e. P b -+ 0, pa -+ l), making the factor Fp,p, in Hro, almost zero. Diagonalization of H,,, will therefore give asymmetric rigid-rotor wavefunc- tions for which the labels K , K , may still be used. The 2Fp, Jb j cross-term in Hrot-torsion will also be small, but the 2Fp, J, j term will be significant. As a consequence, consider- able mixing of asymmetric rigd-rotor states with the same value of K , occurs. The K , label is thus meaningless, although it has been retained in order to distinguish between the resulting K , states. The symmetry species of the rotation- torsion states are preserved in this mixing.

The computer program described above also calculates approximate relative intensities for transitions with low values of I m I. Using the direction cosine matrix elements of Cross, et a1.,12 the dipole moment matrix is calculated in the symmetric rotor basis. This matrix is then transformed to the basis of eigenfunctions of Hrot-,orsion , neglecting intensity effects due to pure torsion, and is then used to calculate intensities of transitions. For the most part, the standard a- and b-type selection rules are retained, in spite of the fact that K , is no longer a good label; allowed transitions must also have Am = 0. However, transitions such as 303-313, which are nominally c-types but which depend on the b component of the dipole moment, are allowed for states of E symmetry. Although these transitions are predicted to have finite inten- sity for large values of 8, the transitions should be vanishingly weak in tetrolyl fluoride, where 8 is expected to be less than ca. 5".

Assignments

The cavity MWFT spectrometer was used to search for some of the strongest lines observed in the Stark spectra. As expected, because of the rotational and torsional cooling, most of the lines observed using the Stark spectrometer dis- appeared in the MWFT spectra, leaving a small number of lines. Some of these could be fitted to a rigid-rotor model as K , = 0 and K , = 2 transitions, with initial rotational con- stants calculated from a trial structure. This made it possible to search for K , = 1 satellites, which had not been identified in the Stark spectra; these were soon found.

Searching was facilitated by the large a component of the dipole moment of tetrolyl fluoride, estimated to be ca. 3 D t by comparison with similar molecules. Thus, despite the small bandwidth of the spectrometer, searches for a-type lines could confidently be performed in 1 MHz steps, with short exciting pulse lengths (0.1 ps). Very strong signals were obtained for many transitions. An example is the line at 12598.412 MHz shown in Fig. 1, later assigned to the I rn I = 0,4,,-3, transition; this transition could be observed with no signal averaging.

With reasonable initial values for the rotational constants, 8 and V,, all the lines observed thus far using the cavity MWFT spectrometer could be assigned. Those lines which corresponded to an asymmetric rigid-rotor spectrum could be assigned to states with I rn I = 0, while the remaining unas-

7 1 D x 3.33564 x C m .

41 4-31 3

I!

1 12598.3 12598.5

frequency/M Hz Fig. 1 The Iml = 0, 4,,-3,3 transition of tetrolyl fluoride. Experi- mental conditions: 2.3% tetrolyl fluoride-Ar gas sample; 12 598.4 MHz excitation frequency; 50 ns sample interval; 8 K FT; one averaging cycle.

signed lines were assigned to states with I rn I = 1. It was then possible to predict the remaining Iml = 1 lines, which were subsequently observed with the cavity spectrometer. The measured transition frequencies and assignments are given in Table 1. In order to obtain spectroscopic constants, the program VC31AM13 was used to fit the data. Although this program uses the internal axis method, frequencies predicted by the PAM prediction program described above agreed with those predicted by VC3IAM.

Although much time was spent trying to locate b-type transitions, no such transitions were observed. This is consis- tent with the spectra recorded using the Stark spectrometer, where no lines were observed in the portions of the spectrum between the groups of a-type lines. The b component of the dipole moment is due entirely to the COF group, and should be relatively small. For the related molecule CH,COF, p b = 0.88 D, cf. pa = 2.83 D.',

As only a-type transitions were observed, the A rotational constant could not be determined. In addition, A and I , , the moment of inertia of the methyl group about its symmetry axis, are highly correlated. If the inertial defect is assumed to be zero, then

I , + I , - I , = I , (20)

since the only out-of-plane atoms are the hydrogens of the methyl group. In fitting the data, I , was assumed to have the value 3.18 u A' and A was released into the fit. However, since the a-type transition frequencies were insensitive to the value of A , it would remain near its initial value. The lowest standard deviation was obtained with A = 11 050 MHz, and so this was used for the initial value in the final fits. The centrifugal distortion constants were set to zero in the fits, as attempts to determine D, and D,, were unsuccessful. Deter- mined in the fit were the B and C rotational constants, 8 and V,, as given in Table 2. As expected, 8 is small; the threefold barrier to internal rotation, V, , is small (ca. 2.2 cm- ') and very comparable to those determined for CH3-C=C-CH3 (5.20 cm-I),' CH3-C=C-CD3 (5.6 cm-'),2 and CH3--C'-C-SiH3 (3.8 cm- 1).4

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Table 1 Measured transitions of tetrolyl fluoride

J m l = 0 Iml= 1

frequency obs. - calc. frequency obs. - calc. J' Kb K: J" Kb' K ; /MHz /MHz /MHz /MHz

3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5

1 0 2 2 1 1 0 2 3 3 2 1 1 0 2 4 4 3 3 2 1

3 3 2 1 2 4 4 3 2 1 2 3 5 5 4 2 1 3 2 3 4

2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4

1 0 2 2 1 1 0 2 3 3 2 1 1 0 2 4 4 3 3 2 1

2 2 1 0 1 3 3 2 1 0 1 2 4 4 3 1 0 2 1 2 3

9452.03 1 9777.556 9793.147' 9808.165'

101 29.989 12598.412 13019.263 13054.608 13064.459' 13064.689' 13092.09 1 13502.172 15741.226 16247.566 163 13.559 16328.843' 16328.843' 16333.820 16334.636 16388.336 16870.396

0.466

0.089 0.139 0.118 0.603

-0.773 0.109

-0.325 -0.327

-0.535

0.217 0.136 0.726 0.367 0.115

- 1.240 - 1.243 -0.411 - 0.407

0.329 0.134

9778.413 9838.027 9746.914' 9796.063' 9798.918

13020.406 13 165.910 12938.029 13075.727' 1306 1.567' 13063.362 13070.045 16246.069 16526.493 16088.505 16335.322' 16327.630' 16356.106

16332.337 16345.380

0.536 0.303 0.485

- 0.533 - 0.089

0.740 0.412 0.512 0.345

- 0.639 -0.716 -0.113 - 0.47 1

0.484 0.464

-0.127 -0.177

0.469 -

- 0.896 -0.127

a K , is retained to distinguish between states with the same values of J and K , . ' These transitions were observed as multiplets with splittings of ca. 10-30 kHz, and the frequency given is an average.

Measurement accuracy is estimated to be better than & 1 kHz.

In the course of searching for b-type transitions, several weak lines were found which could be assigned to I rn / = 0 and I rn I = 1 a-type transitions of a 13C isotopomer of tetrolyl fluoride. The measured transition frequencies and assign- ments are given in Table 3. In order to fit the limited number of lines, A, I , and V, were constrained to the values obtained in the fit for the normal isotopomer; the spectroscopic con- stants obtained are given in Table 2. The isotopic shifts in B and C are quite small, indicating that isotopic substitution has taken place very near the centre of mass. From a rough

calculation of the expected structure of tetrolyl fluoride, the isotopomer is probably CH3-C='3C-COF.

No lines were observed which could be assigned to I rn I = 2 or 3 transitions. The absence of transitions with high values of I rn I is not unreasonable considering the energies of such states (which increase rapidly because of the F i term in Htorsion) and the efficient cooling in the molecular beam. While collisional relaxation of 1 rnl = 1 states to Iml = 0 is symmetry-forbidden, depopulation of torsional states with higher values of Irnl is permitted in the beam. With only

Table 2 Spectroscopic constants of tetrolyl fluoride

AfMHz B/MHz C/MHz IJU A' eldegrees VJcm - nfi,/MHz

normal isotopomer 11 049.705 (90Yb 1745.221 (17) 1519.119 (19) 3.18' 1.5092 (14) 2.20 (12) 0.545 I3C substituted 11 049.705' 1744.601 (54) 1518.056 (93) 3.18' 0.9994 (25) 2.20b 1.118

~

' Numbers in parentheses are one standard deviation in units of the last significant figure. Although the A rotational constant has an apparent small standard deviation, it was insensitive to the data, and remained near its initial value for several reasonable values (see text),

Held constant in the fit.

Table 3 Measured transitions of T-tetrolyl fluoride

J m l = 0 ( m ( = 1

frequency obs. - calc. frequency obs. - calc. J' K:, K? J" Kf K: /MHz /MHz /MHz /MHz

9772.721b - 1.358 - - 3 1 3 2 1 2 3 0 3 2 0 2 9773.601 0.636 9833.142 0.772 3 1 2 2 1 1 101 24.843 - 0.604 4 1 4 3 1 3 12592.392 2.240 13014.021 - 0.304 4 0 4 3 0 3 130 12.853 - 0.285 13 159.336 0.917 4 2 2 3 2 1 13085.58 1 0.337 - 4 1 3 3 1 2 13495.3 17 - 0.803

- -

- - -

K , is retained to distinguish between states with the same value of J and K, . Measurement accuracy is estimated to be better than k 2 kHz.

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Irnl = 0 and Irnl = 1 transitions, it is impossible to test the validity of the assumption that V3 is the dominant term of V(a), as V, cannot be determined.16

It is important to note that the standard deviations in the fits were considerably larger than the uncertainty in the mea- surements; for the larger data set of the normal isotopomer, ofit is roughly 500 times larger than the measurement uncer- tainty. Large discrepancies between observed and calculated transition fequencies have been found in other internal rota- tion studies (e.g. CH,ONO”). A probable source of these discrepancies is the use of rigid-toprigid-frame models, which neglects interactions between internal and overall rota- tion and other vibrational modes.”

As noted in Table 1, several rotational transitions were observed as multiplets. Rotational energy levels with J = K , (2,,, 220, 331, 3 3 0 , 441, 440) seem to be split into two and/or three sublevels, with the splittings of the order of 10-30 kHz. As multiplets were observed for both Irnl = 0 and Iml = 1 states in all cases, it seems unlikely that the mechanism of the splitting is related to the internal rotation. However, none of the likely mechanisms (”F and/or ‘H spin-rotation or spin- spin coupling) split the J = K , levels preferentially, but rather they affect all I J K , K , > states to comparable extents. It is possible that terms which contribute to splittings of the other levels cancel out accidentally, but this is difficult to deter- mine, especially without a fitting program which will simulta- neously fit the hyperfine effects of four coupling nuclei in an asymmetric rotor. Even with such a program, the large residual frequencies mentioned above could make it difficult to fit very small hyperfine parameters.

The authors would like to thank Mike Pungente for his assistance in the synthesis of tetrolyl fluoride, Dr. Nils Heine- king for helpful discussions and Dr. Wolfgang Jager for help with the spectrometer. This work has been supported by the

Natural Sciences and Engineering Research Council of Canada and by the Networks of Centres of Excellence on Molecular and Interfacial Dynamics.

References 1

2

3 4

5

6

7

8

9

10

11 12

13

14

15

16 17

P. R. Bunker, J. W. C. Johns, A. R. W. McKellar and C. di Lauro, J. Mol. Spectrosc., 1993, 162, 142. J. Nakagawa, M. Hayashi, Y. Endo, S. Saito and E. Hirota, J. Chem. Phys., 1984,80,5922. C . C . Lin and J. D. Swalen, Rev. Mod. Phys., 1959, 31, 841. J. Nakagawa, K. Yamada, M. Bester and G. Winnewisser, J. Mol. Spectrosc., 1985, 110, 74. V. M. Stolwijk and B. P. van Eijck, J. Mol. Spectrosc., 1987, 124, 92. W. J. Balfour, K. Beveridge and J. C. M. Zwinkels, Spectrochim. Acta, Part A, 1979, 35, 163. G. A. Olah, R. J. Spear, P. W. Westerman and J. M. Denis, J. Am. Chem. SOC., 1974,%, 5855. Y. Xu, W. Jager, and M. C. L. Gerry, J. Mol. Spectrosc., 1992, 151, 206. E. B. Wilson Jr., C. C. Lin, and D. R. Lide Jr., J. Chem. Phys., 1955,23, 136. J. D. Swalen and D. R. Herschbach, J. Chem. Phys., 1957, 27, 100. R. J. Anderson and W. D. Gwinn, J. Chem. Phys., 1968,49,3988. P. C . Cross, R. M. Hainer and G. W. King, J. Chem. Phys., 1944, 12, 210. B. P. van Eijck, J. van Opheusden, M. M. M. van Schaik and E. van Zoeren, J. Mol. Spectrosc., 1981, 86,465. W. Gordy and R. L. Cook, Microwave Molecular Spectra, Wiley, New York, 3rd edn., 1984. P. H. Turner, M. J. Corkill and A. P. Cox, J. Phys. Chem., 1979, 83, 1473. D. R. Herschbach, J . Chem. Phys., 1959,31,91. J. Koput, J. Mol. Spectrosc., 1986, 115, 131.

Paper 4102938K; Received 17th May, 1994

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