x-y Coriolis interaction in the v, and us bands of propyne-d,

Transcription

1 x-y Coriolis interaction in the v, and us bands of propyne-d, GEETHA RAJAPPAN AND V.A. JOB' Specrroscopy Division, Bhabha Arotnic Research Centre, Bombay, , India Received March 22, 1993 This paper is dedicared to Professor Gerald W. King or1 the occasiotl of his 65th birthday GEETHA RAJAPPAN and V.A. JOB. Can. J. Chem. 71, 1684 (1993). High resolution Fourier transform spectra of the v5 and v, bands of CD,C=CH have been recorded and analyzed tak- ing into account the strong x-y Coriolis interaction between these fundamentals. Fermi resonance of the v, state with the v, + v,, state, 1-type doubling interaction between the +I components of v, and a weak k-type doubling interaction between the v, and v, states have also been included in the perturbation treatment. 'The parameters of the v, and v, states as well as some of the parameters of the unobserved v9 + v,, state have been determined. An estimate of the relative value of the transition moments has been obtained from the line intensities, which are strongly affected by the x-y Coriolis interaction. GEETHA RAJAPPAN et V.A. JOB. Can. J. Chem. 71, 1684 (1993). On a enregistre les spectres 2 haute resolution par transformation de Fourier des bandes v, et v, du CD,C=CH les a analysces en tenant compte de l'importante interaction x-y de Coriolis entre ces fondamentales. Dans le traitement de perturbation, on a aussi inclus la resonance de Fermi de 1'Ctat v, avec 1'Ctat v, + v,,, l'interaction de duplication de type 1 entre les composantes +I de v, et la faible interaction de duplication de type k entre les Ctats v, et v,. On a determine les paramktres des Ctats v, et v, ainsi que d'autres paramktres qui n'ont pas kt6 observes pour I'Ctat v9 + v,,. On a pu evaluk la valeur relative des moments de transition h partir des intensites des raies qui sont fortement affectees par I'interaction x-y de Coriolis. [Traduit par la redaction] I. Introduction A total of 121 scans were coadded. Wavenumber calibration was done with respect to the NH, lines in this region (8), recorded in a The of the v5 and bands of proseparate run. A spectrum at a lower resolution of O. I cm-' was also pyne, CH3C=CH, has been studied by laser Stark spec- recorded at 195 K, troscopy (1-4) and Fourier transform spectroscopy (5). Even though-the possibility of vibration-rotation interactions be Results and discussion tween these two fundamentals has been recognized (5), no Rotation about the x-y axes couples the v, (a,) and v8 (e) attempt was made to include these interactions in the anal- modes of CD3C-CH through a second-order Coriolis inyses. In propyne, these two fundamentals are separated by more than 100 cm-' and, indeed, the interactions are weak. However, in the deuterated s ecies, CD3C=CH, they are P separated by only -4.2 cm- and a strong interaction results. The dominant interaction between a nondegenerate a, mode and a degenerate e mode of a molecule belonging to the C3, point group is x-y Coriolis interaction. It was pointed out by Di Lauro and Mills (6) that, in addition to shifting the line positions, the interaction can have a striking effect on the observed intensities of the spectral lines. The v, and v, bands of CD3C=CH have been studied under medium resolution by Speirs and Duncan (7). The resolution that was available to them permitted only a band contour analysis of the Q subband structure. Nevertheless, they were able to determine some of the molecular parameters, including the x-y Coriolis coupling constant and the relative values of the two transition moments. We have obtained the high-resolution Fourier transform spectrum of CD3C=CH in the v5/v8 band region, and the analysis is presented in this paper. 11. Experimental details A commercial sample of CD,C=CH (Merck, Sharpe & Dohme, Canada) of 99% isotopic purity was used to record the spectrum in the region cm- on a BOMEM DA3.002 Fourier transform spectrometer (globar source, KBr beam splitter, and HgCdTe detector) at an apodized resolution of cm-i. A sample pressure of 66 Pa was used in a folded cell of fixed path length 10 m. 'Author to whom correspondence may be addressed. et on teraction. A comprehensive treatment of this interaction may be found in ref. 6. All interactions as well as the allowed spectroscopic transitions in a C3, molecule follow the selection rule Alk - 1 = 0 mod 3 I and k are signed quantities representing the components of the vibrational and total angular momenta along the C3 axis. In addition, - we have the selection rules based on the classification of the rovibrational levels under the full symmetry group (9), A, o A,, A? o A2, and E o E for all interactions, and A, A2 and E o E for all electric dipole transitions. In x-y Coriolis interaction, the relevant selection rules are A1 = + 1 and Ak = + 1. The energy levels of v, and v, are shown schematically in Fig. 1, with the interacting levels connected by dotted lines. We found that a complete interpretation of the spectrum required that three other interactions - a Fermi resonance with the E component of v9 + ~ 10, "t2,*2" I-type resonance within the v, manifold, and weak k-type doubling interaction between the v5 and v8 states - be taken into account. The Fermi interaction with the v9 + v,, state is also shown in Fig. 1 (broken lines). The I-type resonance connects the -I and +I components differing in k by two units. The t l components connected through this interaction are the same two levels that interact with a particular K level of the v5 state through x-y Coriolis interaction. In addition, the +I components of K = (kl = 1, i.e., k = -1 1 = -1, and k = + 1,1 = + 1, are coupled through

2 RAJAPPAN AND JOB FIG. 1. Energy level diagram of v, and v, states and other interacting levels for J = 10. The levels connected through dotted lines are involved in x-y Coriolis interaction, and those connected by broken lines are in Fermi resonance. this interaction, which results in the splitting of the A, A' pairs: the 1-type doubling. The K = 0 levels of the nondegenerate state belong to either A, or A? species depending on whether J is even or odd. It is thus able to interact with only one component of the A, A, pairs of K = 1 of a degenerate state through x-y Coriolis coupling, leading to the so called "giant 1-type doubling." The k-type doulbing interaction, which is not shown in Fig. 1, connects levels with Ak = -+2 and A1 = This interaction can cause A, A, splittings in the - 1 component of K = 2. An overview of the v, and v8 bands of CD,C=CH, taken at a resolution of 0.1 cm-' at 195 K is shown in Fig. 2. The low temperature suppresses the hot band transitions as well as high J transitions, making the Q branches more prominent. The different shapes of these subbands can easily be understood with the aid of Fig. 1. If two sets of levels are involved in a J-dependent perturbation, the upper(1ower) set is pushed further up(down), the magnitude of the shift increasing with J. The net effect is an apparent increase in the B value of the upper set and an apparent decrease for the lower set. If the unperturbed B value of the upper state involved in a spectroscopic transition is slightly smaller than that of the lower state, the Q branches will be slightly "redndegraded. A change in the apparent B value due to an interaction can increase this degradation or reverse it, depending on the relative position and closeness of the perturbing levels. The B value of the v8 state of CD3C=CH is slightly smaller than that of the ground state, and thus the Q branches are expected to be red-degraded. The branch, the upper state of which is unperturbed by the x-y Coriolis interac- tion, appears with the expected red degradation, in spite of the fact that the 1-type resonance modifies it to some extent. We see from Fig. 1 that the +1 components of K = 1 and K = 2 are below the corresponding interacting levels of v, while for K > 3 they lie above. The branch thus appears strongl~ red-degraded, and the degradation is reversed from Q' onwards. With increasing K, the energy difference between the interacting levels also increases and the "violet" degradation decreases until at K" = 9 the Q-branch appears as a line-like feature. The degradation changes direction for K" > 9. All the K levels of the -1 component of v, lie below the perturbing levels of v,, with the energy difference, AE, increasing with K. Thus the 'Q branches are strongly red-degraded at low K, but become narrower with increasing K. One notices from Fig. 2 that 'Q,, appears shifted towards lower frequencies. All the J components show more or less the same shift, which seems to indicate a Fermi resonance. If the two levels involved in a Fermi resonance are both nondegenerate, all the K levels also are usually uniformly shifted since the AE's are nearly the same. When the interacting levels are degenerate, because of the different values of the z-axis Coriolis coupling constant, the different K stacks can get in and out of resonance.' In the case of the v, state of CD3C=CH, the only suitable candidate as a Fermi res- he same situation prevails even in the case of two nondegenerate states at least one of them is a combination of two degenerate states, for the second-order z-axis Coriolis interaction between the A, A, pairs can produce the same effect (10).

3 CAN. J. CHEM. VOL. 71, R OlO FIG. 2. The spectrum of the v, and v8 bands of CD,C=CH recorded at a resolution of 0.1 cm-' at 195 K. onance partner is the v, + v,, (E) state, with a harmonic value of 942 cm-i for G, (7). With a (A['),,, value of cm-' (7), the k = +9, 1 = k2 component of this (i.e., A([, + c,) state is shifted down by -87 cm-i, while the k.1 = - 9 component of v,, for which (A['),,, is cm-i (7), is shifted up by -21 cm-i by the z-axis Coriolis coupling, bringing them into close resonance. The other K levels in the -I manifold of v8 are also slightly affected by Fermi resonance, but the effect is negligible for the +l components because of the large AE. Energy level calculations The energy levels are calculated by the diagonalization of a combined energy matrix of US, v8, and (v, + v,,), with appropriate off-diagonal interaction matrix elements. The energy matrix can be factored into three smaller submatrices corresponding to the A,, A?, and E rovibrational species. The diagonal matrix elements are the unperturbed energy levels given by the standard polynomial expression, [l] E,,, = G, + B,J(J + 1) + (A, - B,)K' - D:J'(J + 1)' - D:~J(J + 1 )~' - D,K@ ROO K = Ikl and the splitting of the +I components through z-axis Coriolis coupling, given by the terms in square brackets, is relevant only for degenerate states. The choice of the relative vibrational phases is such that all off-diagonal matrix elements are real. The off-diagonal matrix elements we have used are given below and conform with those given by Di Lonardo, Fusina, and Johns (1 1) and Olson, Maki, and Sams (12). The numerical factors preceding these matrix elements and the relative signs are given differently by various authors, and this aspect should be taken into consideration while comparing the various results. X-y Coriolis interaction and

4 RAJAPPAN AND JOB TABLE 1. Molecular parameters of the ground, v5, v8, and vg + vlo states of CD3CCHa Parameter Ground statebc v5 v8 v9 + ~ I O k-type doubling "All values are in cm-'. The standard deviations given in parentheses are in the units of the last digit quoted. "onstrained value. 'From ref. 10. "(A5'),,, value included 11 I. Equations [2] and [5] should be multiplied by K = 0 for the nondegenerate state. "k2, *2" 1-Type resonance Fermi resonance In equations [2]-[8] the upper and lower signs are correlated throughout. Intensity calculations In the calculation of intensities of transitions involving unperturbed states, the relative signs of the direction cosine matrix elements are of little consequence as the intensities are proportional to the square of these matrix elements. In the present case, the upper state is a mixture of v,, the 51 components of v,, and to a smaller extent (v, + v,,). It is necessary to sum the products of appropriate vibrational transition moments, eigenvectors, and direction cosine matrix elements before squaring, and the relative signs of the direction cosine matrix elements become important. The intensity expression and the direction cosine matrix elements we used are consistent with those given by Di Lauro and Mills (6). The nuclear spin statistical weight factors that we used for the A,, A,, and E rovibrational levels were 1 1, 1 1, and 16, respectively. These also include the k-degeneracy factor and it is not necessary to use the factor 2 when K > 0. It is, however, necessary to include a factor of 2 for transitions involving K = 0 of a nondegenerate state and K = 1 of a degenerate state. Analysis of the spectra The initial assignments were made in the R ~, 'P, and 'Q branches of the v, band corresponding to high K values, the perturbation is not severe, and counterchecked with Q(J) - P(J + 1) and R(J) - Q(J + 1 ) combination differences calculated from the known ground state parameters (10). A least-squares fit of these frequencies gave an initial set of paramters that was used to calculate the frequencies and intensities of the low K transitions and make further assignments. The only clearly recognizable feature of the v, band was the Q head. Therefore, in the initial stages of the analysis, the v, state had to be included in the calculations only as a "shadow" state. Recently we carried out the analysis of the v, (13) and 2v, (10) bands of CD,C=CH, it was necessary to include one of more shadow states, i.e., states to which transitions are not directly observed, but which manifest their presence only through the perturbations. Even though we were able to derive some of the parameters of these shadow states from the magnitude of the perturbations, there was always a lingering doubt about their accuracy, as many other parameters were constrained. Therefore, it was gratifying to see that the perturbation treatment predicted the v, and B' of the v, band with fairly good accuracy even when v, was used only as a shadow state. In the final stages it was possible to identify many transitions of the v, band and assign over 2000 transition^.^ The A, A2 splitting in the K. AK = -3 transitions, caused by k-type doubling, was resolvable only for J > 40. Only a few such transitions could be identified because of the diminished intensity at high J values. In the final fit 1592 transitions, 243 of which are parallel type, have been included. In the parallel band, K = 0, 1 are intense in the P branch, while it is the K = 2, 3 that are intense in the R branch. The standard deviation of the fit was cm-i. The parameters derived from our analysis are given in Table 1. 3~ complete list of frequencies and assignments is available from the authors or may be purchased from: The Depository of Unpublished Data, Document Delivery, CISTI, National Research Council Canada, Ottawa, Canada KIA 0S2.

5 1688 CAN. J. CHEM. RP3.47 PP2,17 s L= Rp;: PPI, 22 +zz pp3* FIG. 3. A portion of the high-resolution spectrum of the v, and v, bands. Figure 3 shows a section of the high-resolution spectra and the v, and v8 transitions. The v, transitions do not have the typical parallel band appearance in which the K components of a given J are clustered together. Not only do the K components appear in a haphazard manner, but their relative intensities also are unusual, and it would have been impossible to assign these transitions without the calculation of the perturbed frequencies and intensities. The most striking intensity changes are in the 'Po,'P,,'R,, 'R,, 'R,, 'R,, 'R,, R~O, and R ~ branches, l which are enhanced, and 'P2, 'P,, 'R,, 'R,, 'P,, 'P,, R~O, 'PI, R~z, branches, which are depleted in intensity. Even though we 'Pz, R ~ 3 R, ~ 4, and R ~ 3 have not made any quantitative intensity measurements, from the relative intensities of the spectral lines we estimate the ratio of the transition moments, (CL, k ik): kz, as 1.0:0.6, which corresponds to M,/M, = The value of 1.O for this parameter, used by Speirs and Duncan (7) in their band contour analysis, appears to be on the high side, but their values of 5, and 558 compare well with our values ( and , respectively) derived from the parameters given in Table 1. The intensity perturbation is positive in the sense defined by Di Lauro and Mills (6), i.e., the relative sign of the transition moments is the same as the sign of the x-y Coriolis coupling parameter. It is interesting to note that, in a recent analysis of the corresponding bands of CD3CN, Koivusaari and Anttila (14) have invoked similar perturbations, and the values of the interaction parameters are also comparable. IV. Acknowledgments We thank Dr. V.B. Kartha for his interest in this work and Dr. Romola D'Cunha for a critical reading of the manuscript. The assistance given by S.S. Bhattacharya in the preparation of the manuscript is gratefully acknowledged. 1. P.M. Burrell, E. Bjarnov, and R.H. Schwendeman. J. Mol. Spectrosc. 82, 193 (1980). 2. F. Meyer, J. Dupre, C. Meyer, C. Lambeau, M. De Vleeschouwer, J.G. Lahaye, and A. Fayt. Int. J. Infrared Millimeter Waves, 3, 83 (1982). 3. F. Meyer, J. Dupre, C. Meyer, J.G. Lahaye, and A. Fayt. Can. J. Phys. 63, 1184 (1985). 4. T. A1 Adlouni, F. Meyer, C. Meyer, J.G. Lahaye, and A. Fayt. Int. J. Infrared Millimeter Waves, 7, 405 (1986). 5. T. A1 Adlouni, F. Meyer, C. Meyer, D.E. Jennings, and J.J. Hillman. Int. J. Infrared Millimeter Waves, 8, 1083 (1987). 6. C. Di Lauro and I.M. Mills. J. Mol. Spectrosc. 21, 386 (1966). 7. G.K. Speirs and J.L. Duncan. J. Mol. Spectrosc. 51, 277 (1 974). 8. S. Urban, D. Papousek, J. Kauppinen, K. Yamada, and G. Winnewisser. J. Mol. Spectrosc. 101, 1 (1983). 9. J.T. Hougen. J. Chem. Phys. 37, 1433 (1962). 10. K. Singh, G. Rajappan, V.A. Job, V.B. Kartha, A. Weber, and W.B. Olson. J. Mol. Spectrosc. 157, 467 (1993). 11. G. Di Lonardo, L. Fusina, and J.W.C. Johns. J. Mol. Spectrosc. 104, 282 (1984). 12. W.B. Olson, A.G. Maki, and R.L. Sams. J. Mol. Spectrosc. 55, 252 (1975). 13. N.S. Sule, R.J. Kshirsagar, and V.A. Job. J. Mol. Spectrosc. 160, 502 (1993). 14. M. Koivusaari and R. Anttila. J. Mol. Spectrosc. 155, 201 (1992).