Rotational spectrum of acetone, CH3COCH3, in the ν17 torsional excited state

Journal of Molecular Spectroscopy 251 (2008) 180–184

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Rotational spectrum of acetone, CH3COCH3, in the m17 torsional excited state Peter Groner a,*, Ivan R. Medvedev b, Frank C. De Lucia b, Brian J. Drouin c a b c

Department of Chemistry, University of Missouri—Kansas City, Kansas City, MO 64110-2499, USA Department of Physics, The Ohio State University, Columbus, OH 43210-1106, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109-8099, USA

a r t i c l e

i n f o

Article history: Received 7 February 2008 In revised form 20 February 2008 Available online 7 March 2008 Keywords: Acetone Rotational spectroscopy Internal rotation Torsional excited state

a b s t r a c t The rotational spectrum of acetone in its second torsional excited state (m17, 125 cm1 above the ground state) has been identified and assigned. The interaction between overall rotation and the internal rotation motions causes rotational transitions to split into four components, one for each torsional substate. The splittings in this torsional excited state are significantly larger than any splittings assigned yet for molecules with two methyl internal rotors, making assignments rather difficult. Over 700 frequencies between 72 and 372 GHz in the sub-millimeter wave spectrum have been assigned to bR-transitions in all four torsional substates. Eventually, 32 parameters of an effective rotational Hamiltonian for a molecule with two periodic internal motions were fit to observed frequencies of 612 transitions from all torsional substates with a standard deviation of 0.485 MHz. Ó 2008 Elsevier Inc. All rights reserved.

1. Introduction Acetone is a species of astrophysical interest that has been identified in interstellar clouds of star-forming regions (hot cores) in Sgr B2 and Orion-KL by radio-astronomy [1–3]. It has also been detected as an atmospheric pollutant by using a proton-transfer-reaction mass spectrometer or a chemical ionization mass spectrometer [4,5]. In many regions of the atmosphere, its concentration correlates positively with the concentration of carbon monoxide and it influences the ozone generation and destruction process because it reacts readily with hydroxyl radicals [4]. To better characterize the distribution of astrophysical and atmospheric species and to investigate their environments, spectroscopic studies are preferred because they can be applied remotely over long distances. Astrophysical species are very often studied by radio-astronomy whereas atmospheric species are more commonly investigated by rotationally resolved optical or infrared spectroscopy. Optical or infrared methods cannot be used currently to monitor acetone because the interaction between overall molecular rotation and the internal rotation motions of the methyl groups splits each rotational transition of acetone into four different component lines. Therefore, rotationally resolved spectra of acetone are very dense, and the correct identification of specific lines becomes rather difficult, not least because of the reduced intensity of the split lines. Fifty years ago, Swalen and Costain [6] made the first correct assignments in the rotational spectrum of the first molecule with two methyl internal rotors, acetone. Whereas assignments of rota-

* Corresponding author. Fax: +1 816 235 2290. E-mail address: [email protected] (P. Groner). 0022-2852/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2008.02.018

tional transitions in the lowest vibrational excited states are fairly common for most molecules, no assignments of the rotational spectrum of acetone in any of its vibrational excited states had been published until, a few years ago, the first transitions in the spectrum of acetone in its first torsional excited state (m12) [7] were assigned. Based on this work, lines belonging to the m12 state of acetone have been detected in the interstellar cloud Orion-KL [3]. The unusual delay in assigning the first vibrational excited state of acetone is most certainly due to the fact that the splittings of the rotational transitions caused by the interactions of overall rotation with the internal rotation motions were much larger than anything assigned yet for two-rotor molecules. Even after the successful assignment of m12 in the room temperature sub-millimeter wave spectrum of acetone, many relatively intense lines were left unassigned. This paper reports the assignments of most of the remaining prominent lines to the other torsional excited state of acetone, m17, which is about 45 cm1 higher in energy than m12 [8]. The remaining sections of this paper contain experimental details (Section 2), a summary of the effective Hamiltonian employed to fit the spectrum (Section 3), the analysis of the spectrum and results (Section 4) and the discussion (Section 5). 2. Experimental Room temperature rotational spectra of acetone in the sub-millimeter wave region were acquired at the Ohio State University with the FASSST system (Fast Scan Submillimeter Spectroscopic Technique) [9]. The FASSST spectrometer uses a voltage-tunable backward wave oscillator (BWO) as the primary source of radiation. The BWO is scanned rapidly (104 MHz s1) over a broad fre-

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quency range. Frequencies are calibrated optically by use of a ring cavity. There is no need for active frequency stabilization because of the fast sweep and post-data-acquisition calibration. The detectors used are liquid helium-cooled InSb bolometers. With this system, it is possible to measure thousands of spectral lines per second, with a frequency accuracy of 0.1 MHz. Spectral transitions of acetone were assigned in the region between 119 and 375 GHz. The details of the experimental procedure used at Jet Propulsion Laboratory (JPL) to measure room temperature spectra between 72 and 122 GHz with precision between 0.05 and 0.10 MHz were described in Ref. [7].

R0 ¼ e00 þ 2

X

( eqq cos a0qq þ eqq cos a0qq

q>0

þ

q1 X

)

eqq0 ðcos a0qq0

þ

cos a0q0 q Þ

ð5Þ

q0 ¼qþ1

and Rl ¼ T l00 þ 2

X

( T lqq cos aqq þ T lqq cos aqq

q>0

þ

q1 X

)

T lqq ðcos a 0

qq0

þ cos a Þ q0 q

ð6Þ

q0 ¼qþ1

where a0qq0 ¼ 2pðqðr1  qK 1 Þ þ q0 ðr2  qK 2 ÞÞ=3

3. Theory To fit the rotational transition frequencies and to predict the spectrum of vibrationally excited acetone, the effective rotational Hamiltonian for molecules with one or two periodic large-amplitude motions [10] was used. The application to the m17 excited state of acetone follows the examples described in the papers on the ground states of acetone [11] and dimethyl ether [12], the ground and torsional excited states of 3-methyl-1,2-butadiene [13] and propane [14], and particularly the m12 torsional excited state of acetone [7]. Applications to problems with a different symmetry have been described for ethyl methyl ether [15], dimethyl diselenide [16] and acetone-C13 [17]. The theory has also been applied to the one-rotor molecules 1-C13-methyl formate [18], pyruvic acid [19] and methyl carbamate [20]. In order to give some meaning to the notation of the spectroscopic parameters, the relevant equations are summarized below. The matrix elements of the effective rotational Hamiltonian for molecules with two periodic large-amplitude motions are expressed in the basis j JKMvr1 r2 i ¼j JKMi j vr1 ðKÞr2 ðKÞi

ð1Þ

where |JKMi are symmetric rotor basis functions with the Eulerian angles of the molecule-fixed reference axis system with respect to the space-fixed axes as variables, and |vr1(K)r2(K)i are internal motion basis functions (depending on the projection quantum number K) of states characterized by vibrational quantum numbers v and the torsional symmetry numbers r1 and r2. The general matrix element of the effective rotational Hamiltonian is given by XX hJK 0 Mvr1 r2 j H j JKMvr1 r2 i ¼ Y K 0 K ðK 1 ; K 2 ÞR0 K1

þ

K

X2 0 hJK M j Rl j JKMiRl :

ð2Þ

l

In Eq. (2), Rl are the angular momentum operators of an asymmetric rotor with centrifugal distortion (examples: P4, ðP2b  P2c Þ=4, Pa). The matrix Y K 0 K ðK 1 ; K 2 Þ is defined by Y K 0 K ðK 1 ; K 2 Þ ¼

1 fhJK 0 M j JK 1 MihJK 1 M j JK 2 MihJK 2 M j JKMi 2 þ hJK 0 M j JK 2 MihJK 2 M j JK 1 MihJK 1 M j JKMig

ð3Þ

with hJKM|JKkMi as the matrix element of the rotation between the reference axis system and an axis system with axis zk parallel to the q vector of the k’th internal rotor. It can be expressed in terms of Wigner’s rotation group coefficients [21] ðJÞ

ðJÞ

hJKM j JK k Mi ¼ DK k K ðck ; bk ; ak Þ ¼ eiK k ck dK k K ðbk Þ eiKak :

ð4Þ

The angles ak and ck are zero for acetone whereas b1 = b and b2 = p  b are the angles between the vectors qk and the a principal inertial axis. The symbols R0 and Rl in Eq. (2) are two-dimensional Fourier series. For acetone,

ð7Þ

and aqq0 ¼ pðqð2r1  qðK þ K 0 ÞÞ þ q0 ð2r2 þ qðK þ K 0 ÞÞÞ=3:

ð8Þ

The symbol q is the length of each q vector. Coriolis-type rotational operators like Pa require two-dimensional Fourier series that have no constant term and contain sin aqq0 terms instead of the cos aqq0 terms in Eq. (6). The coefficients in the Fourier series are integrals of torsional operators in a basis of localized functions centered at (s1, s2) = (0, 0) and (2pq/3, 2pq0 /3) with s1 and s2 as the variables of the periodic large-amplitude motions. Together with the angle b and the internal rotation parameter q, they are the spectroscopic constants. The hypothetical unsplit vibrational energy of the torsional state is e00 which cannot be determined from the rotational spectrum alone. The coefficients eqq0 with nonzero q or q0 are the tunneling energy coefficients which also determine the separation of the torsional substates. The parameters Tl00 may be chosen to correspond to the rotational and centrifugal distortion constants of asymmetric rotors. The coefficients T lqq0 (nonzero q or q0 ) are the tunneling contributions to the parameters Tl00 because they arise from the tunneling properties of wave functions. The reader is referred to the original paper [10] for detailed information about the theory leading to Eqs. (1)–(8). The torsional symmetry numbers r1 and r2 can only be 0, 1, or 2 for methyl rotors. For acetone, the combination (r1, r2) = (0, 0) is non-degenerate; it corresponds to the symmetry label AA in the conventional notation for acetone-like molecules [22]. The remaining combinations form a fourfold degenerate set [(0, 1), (1, 0), (0, 2) and (2, 0)] corresponding to label EE and two doubly degenerate pairs: (1, 1) and (2, 2) correspond to AE, whereas (12) and (21) correspond to EA. For all degenerate states, the first member listed above serves as the representative to label the state. Because of the interactions, the substates have slightly different rotational energy levels. This leads to rotational transitions split into four different components, one for each substate. For the ground state of acetone, the width of the quartet splitting extends from a few MHz to more than 1 GHz. The narrowest quartet observed in the first torsional excited state, m12, is spread over about 100 MHz, with most quartets over 1 GHz wide [7]. The splittings in the torsional excited state (m17) are at least twice as large. As a consequence of the symmetry properties, the different rotational quantum numbers and torsional substates have different spin statistical weights, which are factors that take into account the degeneracies of the torsional substates and the allowed nuclear spin functions. The second torsional excited state m17 belongs to the B1 irreducible representation of the point group C2v. Therefore, the spin weights of the rotational states within m17 are different from those in the ground state (A1 symmetry) and the m12 state (A2 symmetry). In the (0, 0) substate, the spin weights are 10 (KaKc: ee M oo) or 6 (KaKc: oe M eo), in the (0, 1) substate the spin weight

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P. Groner et al. / Journal of Molecular Spectroscopy 251 (2008) 180–184

is 16, in the (1, 1) substate, the spin weights are 6 (KaKc: ee M oo) or 2 (KaKc: oe M eo), and in the (1, 2) substate, the spin weight is 4 [22]. 4. Assignment and analysis In the new sub-millimeter wave spectra of acetone recorded by FASSST, there were still many lines not belonging to the ground state [11] or the m12 state [7]. Among these lines, there appeared to be some that looked like unassigned satellites of the low Ka b R-transitions. It was difficult at first to identify the quartet structure because the quartets are spread out even more than in the m12 state [7]. The assignment of a substantial number of quartets to rotational transitions was made much easier by using the program ‘‘Computer Aided Assignment of Asymmetric Rotor Spectra” (CAAARS) [23] which allows us to display experimental and calculated rotational spectra simultaneously in Loomis-Wood type diagrams [24]. The visual comparison afforded by the diagrams facilitates tentative assignments of candidate lines to specific transitions. With a few mouse-clicks, the transition information and the frequencies could be entered directly into a file to be read by the fitting program ‘‘Effective Rotational HAMiltonian” (ERHAM) [10,20] for least-squares fitting of spectroscopic parameters and generating updated predictions. Eventually, over 700 frequencies belonging to transitions within all four torsional substates were assigned in this manner. Some transitions with lower rotational quantum numbers were assigned between 72 and 119 GHz in the spectrum measured earlier at JPL [7]. Reaching a satisfactory fit of the assigned frequencies proved to be a difficult task for several reasons. (i) Because most assigned lines were blends of rotationally degenerate transitions, it was difficult to find a set of reliable spectroscopic parameters. (ii) It was expected that the very large splittings of the rotational transitions required additional tunneling energy terms and tunneling contributions to the rotational and distortion constants. This was the case indeed. The difficulty was in the process of identifying the most significant of these parameters. (iii) The large number of necessary parameters required a large number of assignments of diverse transitions. Because of the rotational degeneracy of most assigned lines and of the failure to make reasonably safe assignments of Q-branch lines, it was impossible to reach a stable fit when the quartic distortion constants DJK or DK were variable spectroscopic parameters. Therefore, DJK and DK and all sextic distortion parameters were kept constant during the least-squares fit. The values of these constants were transferred from a global fit of 3732 and 1434 transitions of the ground and m12 states, respectively, to a parameter set with common q, b and quartic and sextic distortion constants but separate rotational or tunneling constants (unpublished results). Moreover, the final fit for the m17 state with 32 variable parameters was restricted to transitions limited to J < 31 and Ka < 9. Such a fit to 612 frequencies (175, 185, 125, and 127 from the substates (r1r2) = (00), (01), (11) and (12), respectively) including 33 from the JPL measurements resulted in a standard deviation of 0.485 MHz. A selection of assigned and fitted transitions with residuals is listed in Table 1, while the complete list is available in the Supplementary material. Because of the relatively high standard deviation, frequencies and residuals in these tables were rounded off to 0.01 MHz, although the frequencies used in the fit were entered with precisions of 0.001 or 0.0001 MHz. The resulting spectroscopic parameters are shown in Table 2 in comparison with results derived independently for the ground and m12 states. These parameters are q and b, the rotational and centrifugal distortion constants in the A-reduction (the leading terms in Eq. (6)), the tunneling energy parameters eqq0 and the tunneling contributions represented by parameters in

Table 1 Selection of assigned rotational transitions of acetone in its second excited torsional state m17 with observed frequencies and residuals in the least-squares fita r1r2

J0

K 0a

K 0c

J00

K 00a

J 00c

mobs (MHz)

00 01 00 00 01 01 00 01 11 12 00 00 01 01 00 01 11 12

7 7 7 7 7 7 8 8 8 8 8 8 8 8 9 9 9 9

0 0 1 2 1 2 0 0 0 0 1 2 1 2 0 0 0 0

7 7 6 6 6 6 8 8 8 8 7 7 7 7 9 9 9 9

6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8

1 1 2 1 2 1 1 1 1 1 2 1 2 1 1 1 1 1

6 6 5 5 5 5 7 7 7 7 6 6 6 6 8 8 8 8

72868.86 73032.09 81102.51 81113.66 81625.49 81642.18 82691.51 82850.74 83012.22 83017.22 90928.71 90930.73 91438.42 91442.15 92514.09 92669.59 92827.94 92832.19

0.16 0.23 0.05 0.12 1.05 0.49 0.34 0.20 0.67 0.26 0.05 0.42 0.45 0.54 0.34 0.10 0.56 0.42

01 01 00 11 12 01 00 11 12 01 11 12 00 11 12 01 11 12 11 12

27 28 29 28 28 29 30 29 29 30 30 30 30 29 29 30 30 30 30 30

6 5 4 5 5 4 3 4 4 3 3 3 4 5 5 4 4 4 5 5

21 23 25 23 23 25 27 25 25 27 27 27 26 24 24 26 26 26 25 25

26 27 28 27 27 28 29 28 28 29 29 29 29 28 28 29 29 29 29 29

7 6 5 6 6 5 4 5 5 4 4 4 5 6 6 5 5 5 6 6

20 22 24 22 22 24 26 24 24 26 26 26 25 23 23 25 25 25 24 24

321015.38 322148.78 322403.31 323136.53 323161.19 323310.03 323701.75 324205.50 324228.88 324494.28 325278.22 325298.56 332220.25 332907.44 332931.47 333108.72 333986.81 334009.91 342677.84 342701.31

1.93 2.22 0.51 0.43 0.47 1.17 0.10 0.17 0.25 0.03 0.52 0.98 1.11 0.97 0.95 2.06 0.40 0.12 1.74 1.57

mobs  mcalc (MHz)

a The complete table of assigned and fitted transitions is available in the Supplementary material.

square brackets with subscripts q and q0 . [Dab]10, [ga]10 and [gb]10 denote the tunneling contributions associated with the operators PaPb + PbPa, Pa, and Pb, respectively; their non-tunneling coefficients vanish by symmetry. 5. Discussion Even though more than 600 frequencies of the m17 state could be fit and the values of the spectroscopic constants q and b agree well with the independently determined values for the ground and m12 states [7,11], the results from the least-squares fit are nevertheless not quite satisfactory, because of the restrictions that had to be imposed on the centrifugal distortion constants and on the quantum numbers of the transitions. When all quartic distortion constants were included as variable parameters, the least-squares fit did not converge, or all distortion constants ended up with values of much larger magnitudes than for the ground state. As a result of the unknown effect of these restrictions on the other variables, the error limits of some spectroscopic parameters and of derived quantities are certainly larger than those obtained in the least-squares fit. The spectroscopic parameters should therefore be considered as just fitting parameters for this specific set of transitions rather than the true values of these constants. This is also illustrated by the fact that, for instance, the tunneling contribution [A  (B + C)/2]11 is much larger

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P. Groner et al. / Journal of Molecular Spectroscopy 251 (2008) 180–184 Table 2 Spectroscopic constants of acetone in the m17 state compared with the constants obtained for the ground and m12 statea Ground state [11]

m12 [7]

m17

q 0.0621760(60) 0.0625927(50) 0.06342(38) b (°C) 25.8322(93) 25.8860(36) 25.73(13) A (MHz) 10165.21654(80) 10177.2051(41) 10199.05(100) B (MHz) 8515.16477(65) 8502.8490(36) 8480.44(32) C (MHz) 4910.19903(44) 4910.2508(19) 4910.0962(47) DJ (kHz) 4.9055(25) 4.9150(88) 6.88(20) DJK (kHz) 3.620(17) 3.329(62) 3.1765293c DK (kHz) 10.245(17) 9.775(86) 9.8000470c dJ (kHz) 2.0645(12) 2.0786(43) 3.06(10) dK (kHz) 0.7393(56) 0.514(24) 2.87(40) UJ (Hz) 0.0506(34) 0.1016(112) 0.0032929c UJK (Hz) 0.337(20) 0.961(142) 0.0699070c UKJ (Hz) 0.69(38) 0.2616786c UK (Hz) 0.423(20) 0.91(37) 0.2482810c /J (Hz) 0.0254(17) 0.0532(56) 0.0007944c /JK (Hz) 0.0273(41) 0.218(61) 0.0795650c /K (Hz) 0.2215(83) 0.445(118) 0.145657c e11 (MHz) 0.0800(83) 96.553(45) 64(15) e10 (MHz) 763.198(62) 5547.90(46) 13220(97) 1.050(43) 61.96(87) 649(68) e11 (MHz) e21 (MHz) 9.66(96) e20 (MHz) 0.767(13) 15.224(65) 414(21) e21 (MHz) 78.1(85) e30 (MHz) 26.4(12) [A  (B + C)/2]11 (kHz) 1.62(25) 53.0(12) 548(73) [A  (B + C)/2]10 (kHz) 55.07(64) 239.9(29) 970(380) [A  (B + C)/2]11 (kHz) 272.0(26) 6330(650) [A  (B + C)/2]20 (kHz) 0.87(21) 36.84(94) [(B + C)/2]11 (kHz) 1.43(18) 20.97(62) 414(56) [(B + C)/2]10 (kHz) 21.16(56) 208.4(23) 780(150) [(B + C)/2]11 (kHz) 76.0(20) 2240(220) [(B + C)/2]20 (kHz) 0.31(13) 36.95(46) [(B  C)/4]11 (kHz) 0.475(73) 6.39(32) 189(27) [(B  C)/4]10 (kHz) 3.40(27) 68.70(102) 278(74) [(B  C)/4]11 (kHz) 39.46(101) 1110(110) [(B  C)/4]20 (kHz) 0.75(36) 91.8(41) [DJ]10 (kHz) 0.03906(34) 0.1644(28) 1.300(33) [DJK]10 (kHz) 0.0998(17) 0.429(12) 9.3(14) [DK]10 (kHz) 0.0737(17) 0.381(19) 10.7(22) [dJ]10 (kHz) 0.01960(18) 0.0822(14) 0.658(17) [dK]10 (kHz) 0.03427(98) 0.0509(88) 3.93(70) [Dab]10 (kHz) 52.6(63) [ga]10 (MHz) 9.9(17) 35.7(50) [gb]10 (MHz) 0.290(67) 28.4(40) b s (MHz) 0.158 0.238 0.485 a Standard errors from the least-squares fit in units of the last digit in parentheses. b Standard deviation. c Transferred from a common fit of the spectra of m12 and the ground state (see text).

than [A  (B + C)/2]10. This is contrary to expectations and to the observations made in other fits with the effective Hamiltonian [7,11–13]. For these reasons, no predictions of transition frequencies are included in this paper. Table 3 contains the energy differences between the torsional substates (e. g. the energy levels for J = 0) for the assigned vibrational states of acetone as calculated from Eqs. (5) and (7) by setting K1 = K2 = 0. Accordingly, the splitting in the m17 state is about 2.5 times as large as the splitting deduced for the m12 state and about 20 times the splitting of the ground state. For comparison, Table 3 also contains the energy differences between the torsional substates predicted from a torsional potential function that has been derived from a fit of preliminary torsional splittings of the ground and m12 states as well as of torsional transitions [8]. The J = 0 level splittings obtained during this investigation are in reasonable agreement with the predicted ones which lends confidence to the assignment of this state to m17. The consequences

Table 3 Energy differences DE(r1, r2) = E(r1, r2)  E(0, 0) between torsional substates of acetone (MHz)a DE(r1,r2)

Ground stateb

m12c

m17 (this work)

m17d

DE(1, 0) DE(1, 1) DE(1, 2)

2283.91(27) 4571.44(47) 4574.35(44)

17164.9(25) 33564.6(33) 33668.4(30)

43190(270) 83810(540) 82080(590)

41076 82342 82289

a Standard errors from the least-squares fit in units of the last digit in parentheses. b Calculated from the results reported in [11]. c Calculated from the results reported in [7]. d Predicted from the results reported in [8].

of the large splitting of the J = 0 levels are large splittings observed for the rotational transitions. The narrowest splitting pattern observed is spread out over about 220 MHz, whereas the widest splitting pattern assigned and fitted is over 3.0 GHz, as far as we know the largest yet observed for molecules with two methyl internal rotors. The rather large standard deviation of the frequency fit of 0.485 MHz is certainly in part due to the difficulty of fitting these large splittings. However, there are other possibilities: (1) The effective Hamiltonian developed in [10] is expected to eventually reach its limits when torsional energy levels are too close to the barrier to internal rotation where the eigenfunctions are no longer confined to the center of the potential wells. In such a case, more and more tunneling coefficients may have to be used to predict a spectrum accurately because the Fourier series expansions will converge much more slowly. This also means that many additional transitions of great variety need to be assigned to determine the larger number of coefficients. (2) The effective Hamiltonian has been developed for isolated vibrational states that do not interact with other states. Although the general formulas for such interactions have been developed [10], nobody has written a program yet to take them into account. In the specific case of acetone, the m12 and m17 states are 79 and 125 cm1 above the ground state [8]. From the potential reported in [8], the next two torsional states are calculated to be about 42 and 55 cm1 above the m17 state. In other words, neglected interactions of m17 with m12, but also with the higher lying states, will certainly affect the quality of an isolated fit for m17. 6. Summary More than 600 rotational transitions with frequencies between 72 and 372 GHz belonging to all four torsional substates have been identified and assigned in the second torsional excited state of acetone, m17. Their frequencies were used to determine the spectroscopic parameters of an effective rotational Hamiltonian for molecules with two periodic large-amplitude motions by the least-squares method. Observed torsional splittings of the rotational transitions exceed 3 GHz, and the separation between the torsional substates (J = 0 energy levels) is in the order of 2.7 cm1. Acknowledgments Laboratory astrophysics at The Ohio State University is supported by NASA. Portions of this paper present research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of NASA.

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