The Ground and First Torsional States of CD3CHO

Journal of Molecular Spectroscopy 197, 275–288 (1999) Article ID jmsp.1999.7923, available online at http://www.idealibrary.com on

The Ground and First Torsional States of CD 3CHO I. Kleiner,* Juan C. Lopez,† S. Blanco,† A. R. W. McKellar,‡ and N. Moazzen-Ahmadi§ ,1 *Laboratoire de Photophysique Mole´culaire, Universite´ Paris Sud, Baˆtiment 210, 91405 Orsay Cedex, France; †Departamento de Quimica-Fisica, Facultad de Ciencias, Universitad de Valladolid, 47071 Valladolid, Spain; ‡Steacie Institute for Molecular Sciences, National Research Council, Ottawa, Ontario, K1A0R6, Canada; and §Department of Physics, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada Received April 21, 1999; in revised form June 10, 1999

The rotational spectra for the ground and first excited torsional states v t 5 0 and 1 in the frequency region of 8 –254 GHz and the v t 5 1 4 0 band high-resolution far-infrared spectrum of 2,2,2-d 3 -acetaldehyde (CD 3CHO) were measured. We fitted a data set consisting of 1016 v t 5 1 4 0 far-infrared lines together with 195 microwave lines in v t 5 0 and 79 microwave lines in v t 5 1 to near-experimental accuracy, using a global model from the earlier literature. The final fit includes lines with J # 20 and requires 25 parameters to achieve root-mean-square deviations of 87 and 88 kHz for the microwave v t 5 0 and 1 lines, respectively, and of 0.00048 cm 21 for the far-infrared v t 5 1–0 lines. This can be considered a good starting point for future analysis of CD 3CHO. © 1999 Academic Press I. INTRODUCTION

There is a fair amount of ground state spectroscopic work available for the normal species of acetaldehyde, CH 3CHO (1–16). Its microwave spectrum was well characterized in the ground, first, second, third, and to a more modest extent, even in the fourth torsional excited state (16). The torsional modes were also studied directly using far-infrared spectroscopy (10, 17–19). These microwave and far-infrared data were fitted globally for CH 3CHO to almost experimental precision using an internal rotation Hamiltonian to determine a V 3 barrier term of 407.716(10) cm 21, and V 6 , V 9 , and V 12 barrier terms of 212.918(87), 20.186(2), and 0.1076(2) cm 21, respectively, in the Fourier series expansion of the internal rotation potential (16). Deuterated species, on the other hand, are less studied. Since the work of Kilb et al. (1), only one microwave study on acetaldehyde-1-d 1 species, CH 3CDO (20), was performed in the 8 – 40 GHz range. Fateley and Miller (17) and then Souter and Wood (18) observed the torsional transition region at low resolution for CH 3CHO and CD 3CHO. They determined torsional fundamental frequencies but no internal rotation splittings could be obtained at this resolution. Acetaldehyde is one of the simplest molecules with an internal rotor and is thus used as a prototype molecule for studying some complex internal rotation effects in spectroscopy (21). One of the objectives of the high resolution which have accompanied the ground state works of acetaldehyde as well as the recent infrared studies of the normal species (22– 24) was to understand the spectroscopy of this molecule at lower energies and then use this information in higher energy

regions where state densities are larger and intramolecular vibrational relaxation (IVR) could occur. In this context, the study of the 2,2,2-trideuteratoacetaldehyde (CD 3CHO) can serve as another prototype molecule where the effects of deuteration on the rate of IVR can be tested and compared to the results in the literature (25). The CH vibrational overtone spectra of CD 3CHO (26) was also shown to be less complex than the CH overtone spectra of the normal species, which are dominated by the hydrogen–methyl group absorptions (27, 28), and therefore, CD 3CHO is a good candidate for further high-resolution spectroscopy at higher energies. The acetaldehyde torsional barrier has also been the subject of many theoretical studies. Ab initio determinations of torsional transition frequencies (29) can now be compared to the present experimentally determined values for CD 3CHO. Finally, even though the nuclear quadrupole moment of deuterium is rather small and the corresponding splittings of rotational transitions are not usually resolved with conventional Stark spectrometers, they were observed for CH 3CDO with pulsed nozzle beam microwave Fourier transform spectroscopy (20). II. EXPERIMENTAL DETAILS

1 Permanent address: Department of Physics and Astronomy, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada.

The sample of CD 3CHO (used to measure the microwave spectra) was obtained from Eurisotop and used without further purification. The rotational spectrum was measured in Valladolid in the range 8 –250 GHz using different spectrometers. A computer-controlled Stark modulation spectrometer described elsewhere (30) was used to record the spectra between 26.5 and 72 GHz. For the range 40 –72 GHz, the source was a 12.4 –19 GHz BWO followed by Spazek Labs frequency tripler Q-3X or quadrupler V-4X. The Stark cell was cooled to temperatures of

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FIG. 1. Sections of the microwave spectrum of CD 3CHO showing the frequency and intensity patterns of the 2 12 4 1 11 and 2 02 4 1 01 transitions in the v t 5 0 and 1 states.

about 260 K with sample pressures of 5–20 mTorr. Measurements in the frequency regions 80 –120 and 230 –250 GHz were carried out with a computer-controlled source-modulation millimeter-wave spectrometer (31) working at room temperature with sample pressures below 30 mTorr. A waveguide Fourier transform microwave spectrometer (WG-FTMW) (32) was used in the frequency range 8 –18 GHz. Microwave pulses of 20 –120 ns duration with peak power of 1–5 W polarized the molecules in the 12-m waveguide cell. The spectra were taken at sample pressures below 1 mTorr with the cell cooled to about 230 K. The estimated accuracy of frequency measurements is 50 kHz for the absorption spectrometers and 10 kHz for the WG-FTMW spectrometer. The far-infrared measurements were made in Ottawa using a modified (33) Bomem DA3 Fourier transform spectrometer operating at a resolution of 0.002 cm 21 (unapodized). The 2-m multiple-traversal cell was set for an absorption path of 56 m and cooled to about 194 K. This reduced temperature provided a significant simplification of the rather congested spectrum of acetaldehyde. Spectra were obtained in the overlapping regions covering from 45–95 and 90 –200 cm 21, with sample pressures of 180 and 270 mTorr, respectively, and data acquisition times of about 16 h each. A small region from 131.7 to 132.3 cm 21 was obscured due to the absorption in quartz filter used in the

Si bolometer infrared detector. The estimated accuracy of the measurements is 0.0004 cm 21. The CD 3CHO sample, rated as 98% D substituted, was obtained from MSD isotopes. THEORETICAL MODEL

Rather complete descriptions of the theoretical model used in the present study exist in the literature. We give here only the main characteristics. The Hamiltonian used is the so-called “RAM” (rho axis method) internal-rotation Hamiltonian based on the work of Kirtman (34), Lees and Baker (35), and Herbst et al. (36). The method takes its name from the choice of the axis system (21), the “rho axis system,” which is related to the principal axis system a, b, c by a rotation choosen to eliminate the 22Fp a r x J x and 22Fp a r y J y coupling terms in the kinetic energy where F is the internal rotation constant, p a is the internal angular momentum, J x and J y are the usual x and y components of the global rotation angular momentum, and r is a vector that expresses the coupling between the internal rotation p a and global rotation J angular momenta. This rotation corresponds to making the new z axis coincident with the r vector, since r x 5 r y 5 0 by definition. The advantage of the resulting RAM Hamiltonian for computation arises from the

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FIG. 2. WG-FTMW spectrum of the 5 14 4 5 15 transition of the CD 3CHO showing that the E species are split.

fact that all operators containing the torsional angle a and its conjugate momentum p a are diagonal in the rotational quantum number K. All operators off-diagonal in K come in the purely rotational part of the problem. The method starts with a onedimensional potential function V( a ) together with a torsion– rotation kinetic energy operator diagonal in K. First a set of torsional calculations, one for each value of K, is carried out using a 21 3 21 torsional basis set. This basis set is then reduced in size by discarding all but the nine lowest torsional eigenfunctions for a given K. We checked that those two truncations of the Hamiltonian matrix did not modify the energy levels at the measurement accuracy. Finally, the torsional eigenfunctions are multiplied by the symmetric top rotational function uJ, K, M& to form a basis set which is then used to diagonalize, in a second step, zeroth-order asymmetric rotor terms and higher order terms in the Hamiltonian, obtained by multiplying torsional operators with rotational operators. ASSIGNMENTS

The assignment procedure began by locating and remeasuring 18 of the 23 ground state microwave lines listed in Table III of Ref. (1). For the ground torsional A-species transitions initial assignments, we used a “conventional” I r Watson-type Hamiltonian (37). The identification of the corresponding E species transitions for low J and K values was not difficult because they occur at frequencies not far from the A-species transitions. These assignments were based on intensity patterns

and, when working on the 26.5–72 GHz region, also on Stark patterns. Note that the A and E members of a doublet in a given rotational transition do not have equal intensities as shown in Fig. 1. The ratio of intensities is 16/11 with the transitions in the degenerate E sublevel being stronger. Once we had a sufficient number of ground states A and E species transitions, the same program written for the normal acetaldehyde species (16) in the RAM approach, as described in the previous section, was used to predict new lines. A fit of the ground torsional state v t 5 0 ( A and E species) with a root-mean-square deviation of 37 kHz was obtained by floating four pure rotational parameters, A, B, C, and D ab , five centrifugal distortion terms, D J , D K , D JK , d J , and d K , three torsional parameters, F, V 3 , and r, and four higher order torsion–rotation interaction terms, F v , c 2 , k 5 , and k 6 . These constants were then used to provide a prediction of the v t 5 1 transitions. The conventional Stark-modulation microwave spectrometer was used to make a number of frequency measurements between 26.5 and 72 GHz any time that an initial search of the transitions was needed. The 80 –120 and 230 –250 GHz ranges which often correspond to higher J values complemented the search. Some measurements for v t 5 0 were carried out using the Fourier transform microwave spectrometer. Finally, the internal consistency of the microwave data set was checked by using an IAM approach where v t 5 0 and 1 microwave transitions are fitted separately (38). In the initial stages of the assignment of the ground state transitions v t 5 0, we observed that some low J A- and

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TABLE 1A Assignments, a Observed v t 5 0 and 1 Microwave Transitions in MHz, b and Observed Minus Calculated Values c from the Global v t 5 0 and 1 Fit with Parameters Given in Table 4 and Weighted Root-Mean-Square Residuals Given in Table 3

Upper and lower state quantum numbers are indicated by 9 and 0, respectively. Torsion–rotation levels of A species, only given in the first part of the table, have a 6 parity label; levels of the E species, given in the second part of the table, have a signed K a value. b Observed v t 5 0 and 1 microwave transitions in MHz, with estimated uncertainties in parentheses. c Observed minus calculated values in MHz. a

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TABLE 1A—Continued

E-species transitions show different shapes. These lines were found to be broader and, in some cases, at very low pressures with the Stark modulation spectrometer or with the WGFTMW spectrometer, it was possible to resolve a doublet for the E species as shown in Fig. 2. This effect is attributable to

the quadrupole coupling of the three D nuclei, which is expected to be different for A and E species. The hyperfine structure for the ground state transitions was recently measured using a molecular beam Fourier transform microwave spectrometer and is now under analysis.

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TABLE 1B Assignments, a Observed v t 5 1 4 0 Far-Infrared Transitions b in cm 21, and Observed Minus Calculated Values c from the Global v t 5 0 and 1 Fit with Parameters Given in Table 4 and Weighted Root-Mean Square Residuals Given in Table 3

a Upper and lower state quantum numbers are indicated by 9 and 0, respectively. Torsion–rotation levels of A species, only given in the first part of the table, have a 6 parity label; levels of the E species, given in the second part of the table, have a signed K a value. b Observed v t 5 1 4 0 far-infrared transitions in cm 21, with estimated uncertainties in parentheses. c Observed minus calculated values in cm 21.

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TABLE 1B—Continued

The far-infrared spectrum of CD 3CHO offers a number of similarities with the far-infrared spectrum of CH 3CHO (10). In particular, the n 15 fundamental torsional band follows perpendicular-type selection rules (DK 5 61) as summarized in Table 1 of Ref. (10). We used the same quantum numbers defined in Ref. (7) for CH 3CHO, with the symbol 6 corre-

sponding to a “parity” designation for rotation–torsion A states. Each DK DJ K0 ( J0) symmetric rotor transition is split into four components, but unlike the normal species, the statistical weights are not the same for the A and the E species (see above). At higher K values, the two A-type lines (1 3 2 and 2 3 1) are degenerate and A-type lines become twice as

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TABLE 1B—Continued

intense. For the E species, there is no energy grouping into nearly degenerate pairs. As explained in Ref. (21), the usual method for associating K C labels with E species rotational energy levels in internal rotors molecules involves reasoning with the energy ordering of rotational level in a rigid asymetric top molecule and assuming that the J Ka ,J2Ka levels always lie

above J Ka ,J2Ka 11. As in CH 3CHO, we can establish the energy ordering of E levels for CD 3CHO in v t 5 0 and 1, knowing that the energy separation DE of the two degenerate pairs of E levels (E(1K, s 5 11, and 2K, s 5 21) 2 E(2K, s 5 11 and 1K, s 5 21) can be approximated by (using Eq. [6] of Ref. (21))

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TABLE 1B—Continued

DE 5 E~1K! 2 E~2K! 5 2 Î3Fa 1 sin~2 pr K/3!,

[1]

where F is the internal rotation constant and a 1 is a Fourier coefficient depending on the barrier height. Note that in order to be consistent with the phase convention used in our pro-

gram, and contrary to Eqs. [4] and [6] of (21), we have used here a positive sign in the expression of the Fourier cosine series describing the torsional contribution to the energy level, i.e., Fa 1 cos[(2 p /3)(K r 1 s )], and therefore, we obtain the negative sign in front of the right member of Eq. [1]. As it can

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TABLE 1B—Continued

be approximated from the E–A J 5 K 5 0 splittings, the value of the coefficient Fa 1 for CD 3CHO is negative in the ground torsional state v t 5 0 and positive in v t 5 1 as in CH 3CHO (21). For CD 3CHO, the r parameter is almost 21 (instead of almost 31 in CH 3CHO), and the sine function sin(2 pr K/3) of Eq. [6] from Ref. (21) goes to zero for K a 5 0, 3, 6, 9, . . . ,

is positive for K a 5 1, 2, 7, 8, 13, 14, . . . , and is negative for K a 5 4, 5, 10, 11, . . . . When the sine function is positive, the uv t 5 0, 1K& or uv t 5 1, 2K& wavefunctions (for s 5 11) correspond to the J Ka ,J2Ka levels (lying above the J Ka ,J2Ka 11) following traditional asymmetric rotor ordering considerations; when the sine function is negative, the uv t 5 0,

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TABLE 1B—Continued

2K& and uv t 5 1, 1K& functions (for s 5 11) correspond to the J Ka ,J2Ka. The usual assignment techniques (ground state combination differences) allowed us to identify R, P, and Q branches in the fundamental band v t 5 1–0. No attempt to assign hot band

transitions (v t 5 2–1, for example) was made. The analysis led to the assignment of about 1300 A- and E-type lines in the far-infrared range, with J values up to 20 and K values up to 10. From this data set, 1016 unblended lines were selected for the final fit.

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TABLE 1B—Continued

TABLE 3 Root-Mean-Square Deviations from the Global Fit of Table 1

COMBINED FIR AND MICROWAVE LEAST-SQUARES FIT

The 195 microwave v t 5 0–0, the 79 v t 5 1–1, and the 1016 far-infrared v t 5 1–0 frequencies used in the combined global fit are given in Table 1A and 1B, respectively, along with their assignments in the notation of Refs. (7) or (36) and experimental uncertainties (50 kHz for the absorption MW spectrometers, 10 kHz for the WG-FTMW spectrometer and 0.0004 cm 21 for the far-infrared data, and 200 kHz for four lines measured by Kilb (1) around 21 GHz). Weights used in the fits were taken equal to the inverse square of the experimental uncertainties. The observed 2 calculated values are also presented in Table 1 and provide our best understanding of the FIR and MW v t 5 0 and 1 spectra of CD 3CHO at the present time. Three lines which were measured in the second excited torsional state v t 5 2 but not included in the fit are also shown in Table 2. The global fit chosen as the “best” fit allowed 25 parameters to vary and gives far-infrared and microwave rms deviations of 0.00048 cm 21 (for 1016 lines), 87 kHz (for 195 lines), and 88 kHz (for 79 lines) for v t 5 0 and 1, respectively. The overall quality of the fit is given in Table 3, which gives the unitless (weighted) rms deviations for transitions grouped according to their measurement uncertainties (weight in the fit). Table 4 presents values and one-standard-deviation uncertainties for the 25 parameters used in our model to fit transitions in both v t 5 0 and 1 torsional states. For comparison, we also show in Table 4 all the parameters that were required in

a

Number of MW lines in each uncertainty group. Experimental uncertainty in MHz. c Dimensionless root-mean-square deviation for each group, which should be unity if the fit is good to experimental uncertainty. b

the global fit of transitions involving the v t 5 0 and v t 5 1 torsional states of the normal species CH 3CHO (12). The addition of other parameters did not improve significantly the fit of the deuterated species and led to fitting instabilities. We thus set those parameters to zero in the present fit. Moreover, three additional parameters, namely k 6 , and its J and K dependence k 6J and k 6K which were not needed in the CH 3CHO fit of the two lowest torsional states, were found to decrease significantly the standard deviation in the case of CD 3CHO. The rotational constant A is reduced substantially (by 26%) from the values obtained for this constant in the similar fit of the unsubstituted species (12), but the change for the rotational constants B and C are smaller (by 16 and 14%, respectively). A similar effect was also observed for the rotational constants

TABLE 2 Assignments, a Observed v t 5 2 Microwave Transitions in MHz, b and Observed Minus Calculated Values c from the Global v t 5 0 and 1 Fit with Parameters Given in Table 4 and Weighted Root-Mean-Square Residuals Given in Table 3

Note. Transitions presented in this table are not included in the fit and are marked by an asterisk. a Upper and lower state quantum numbers are indicated by 9 and 0, respectively. Only the torsion–rotation levels of A species are given in the table and have a 6 “parity” label. b Observed v t 5 2 microwave transitions in MHz. c Observed minus calculated values in MHz.

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GROUND AND FIRST TORSIONAL STATES OF CD 3CHO

TABLE 4 Torsion–Rotation Parameters Needed for the Global Fit of Transitions Involving v t 5 0 and v t 5 1 Torsional Energy Levels of Acetaldehyde CD 3CHO

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of CH 3CDO (20). The value obtained in the present work for the rotational constant D ab is a measure of the Q RAM angle between the RAM and the PAM axis system (21). As we have tg~2 u RAM! 5

D ab , 1/ 2~ A 2 B!

[2]

we can estimate the value of the u RAM angle for CD 3CHO. Its value (4.82°) is not very different than the value of 4.54° for CH 3CHO estimated from the rotational constants of Ref. (15). The values we obtained in the present work for the torsional barrier height V 3 (399.02(2) cm 21) and for V 6 (213.76(2) cm 21) are rather close to the values of 399.9 and ;13.6 cm 21 found by Kilb et al. (1) and to the values of 397.5 and 27.75 cm 21 evaluated by Souter and Wood (18). This represents a 2% decrease in the barrier height from the parent molecule CH 3CHO (407.72(1) cm 21). The rotationless torsional frequency v t 5 1–0 is found to be 115.61 cm 21 for the A species and 115.38 cm 21 for the E species, slightly lower than the mean value of 117.5(5) cm 21 estimated by Souter and Wood (18) for the A and E torsional subbands and also lower than the ab initio values of 118.92 and 118.56 cm 21 for the A and E species, respectively, by Ozkabak and Goodman (29). Note that although the barrier height V 3 for the normal and deuterated species are not very different, the reduced height s 5 4V 3 /9F is bigger for CD 3CHO (s 5 36.60) than for CH 3CHO (s 5 23.95). Therefore, as expected, the internal rotation splittings are about 10 times smaller in the deuterated species than in the normal species for the rotationless ground torsional state in the deuterated species (0.007 cm 21) and about 7.5 times for the first excited state v t 5 1 (0.23 cm 21). In conclusion, we present here the first global study involving the two lowest torsional states of the deuterated species of acetaldehyde CD 3CHO using a global rotation–torsion Hamiltonian which has now proved to be a powerful tool in the analysis of the microwave, millimeter-wave, and far-infrared data of internal C 3v rotors. This study can thus be considered as a starting point for further investigation of the torsional manifold of CD 3CHO. As shown in this paper, the satisfactory fit of v t 5 0 and 1 of CD 3CHO can serve as a starting point for measurement and identification of transitions with higher J and K values and higher excited torsional states. ACKNOWLEDGMENTS The authors are indebted to L. H. Coudert for running separate v t 5 0 and 1 fits. This work was done under the Picasso Project (Reference 9119 in France and HF 1997-0185 in Spain). J.C.L. and S.B. thank the Direccion General de Ensenanza Superior (DGES, Grant PB 96-0366) and the Junta de Castilla y Leon (Grant VA04/98).

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