THE ASTROPHYSICAL JOURNAL, 499 : 517È519, 1998 May 20 ( 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A. THE MILLIMETER- AND SUBMILLIMETER-WAVE SPECTRUM OF ETHYLENE OXIDE (c-C H O) 2 4 J. PAN AND SIEGHARD ALBERT Department of Physics, Ohio State University, Columbus, OH 43210-1106 K. V. L. N. SASTRY Department of Physics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3 ERIC HERBST Departments of Physics and Astronomy, Ohio State University, Columbus, OH 43210-1106 ; herbst=ohstpy.mps.ohio-state.edu AND FRANK C. DE LUCIA Department of Physics, Ohio State University, Columbus, OH 43210-1106 Received 1997 October 14 ; accepted 1998 January 5 ABSTRACT The cyclic molecule ethylene oxide (c-C H O) has recently been detected in the interstellar source Sgr 2 4 B2N. Previous laboratory work on the rotational spectrum of this molecule extends only to a frequency of 123 GHz. We report here the extension of the laboratory rotational spectrum of this species through the frequency range 262È358 GHz using a new fast scan spectrometer (FASSST). The newly measured lines have been combined with previous data at lower frequencies to form a data set consisting of 662 lines that has been assigned and Ðtted via a standard semirigid asymmetric top analysis. The spectral constants obtained from the Ðt have allowed us to predict the frequencies of many additional lines. Subject headings : ISM : molecules È methods : laboratory È molecular data È radio lines : ISM 1. 1991 ; Blake et al. 1987). Whether or not such a scenario pertains to ethylene oxide is uncertain, since the speciÐc gas phase reactions for its formation are not well studied. The rotational spectrum of ethylene oxide in its ground vibrational state has been studied through 123 GHz by a number of investigators, most recently by Creswell & Schwendeman (1974) and by Hirose (1974). References to earlier work can be found in Townes & Schawlow (1975). The molecule is a semirigid asymmetric top which is oblate in character, and the analysis of its rotational spectrum can be handled by standard means. The transitions are all b-type in character ; the dipole moment, k , is 1.89 D b (Cunningham et al. 1951). Using the constants reported by Hirose (1974), Dickens et al. (1997) calculated frequencies for transitions through 300 GHz, with estimated uncertainties less than 1 MHz for transitions up to J \ 10, an estimate conÐrmed by a preliminary version of the analysis discussed here. In this paper, we report the measurement and assignment of over 500 rotational transitions in the frequency range 262È358 GHz for J \ 50. These lines have been added to many of the previously measured lower frequency lines to form a global data set of 662 transitions, which has been Ðtted to experimental accuracy. The spectral constants determined from the Ðt have allowed us to predict accurately a large number of lines through 400 GHz in frequency. INTRODUCTION Ethylene oxide (c-C H O), a small cyclic molecule, is a 2 4 ““ metastable ÏÏ isomer of acetaldehyde (CH CHO), lying 3 more than 1 eV higher in energy than the lowest energy form. Interestingly, ethylene oxide is kinetically stable in the laboratory, whereas a lower energy metastable isomerÈ vinyl alcohol (CH CHOH)Èrequires unusual conditions 2 for its laboratory preparation because it tends to isomerize into acetaldehyde. Acetaldehyde has been detected in the interstellar medium, while earlier searches for ethylene oxide and vinyl alcohol had not been successful (Irvine et al. 1989 ; Hollis et al. 1980). Recently, however, Dickens et al. (1997) detected 10 rotational transitions of ethylene oxide in the source Sgr B2N and deduced a rotational temperature of 18 K and a column density of 3.3 ] 1014 cm~2. Despite the rather low rotational temperature, which is consistent with other oxygen-containing molecules found in Sgr B2N, this source is considered to be of the ““ hot core ÏÏ type (Miao et al. 1995) and is known to be the home for a variety of complex hydrogenated species. Although the chemistry of such regions is far from understood (Charnley et al. 1995 ; Caselli, Hasegawa, & Herbst 1993 ; Brown, Charnley, & Millar 1988), the general picture is one in which rising temperatures associated with star formation drive previously synthesized molecules o† the grains into the gas, where they are the precursors for a hightemperature gas-phase chemistry. The precursor molecules can be synthesized directly on grains or in the gas followed by adsorption onto the cold dust particles. Strong laboratory evidence for formation on cold grains has been found for the molecule methanol, which can be directly synthesized via successive H atom additions to condensed CO (Hiraoka et al. 1994 ; Charnley, Tielens, & Rogers 1997) as long as the temperature is low enough for CO to remain on dust surfaces (Caselli et al. 1993). Once methanol is released into the gas, it acts as a precursor for a variety of oxygencontaining organic molecules (Millar, Herbst, & Charnley 2. EXPERIMENT AND SPECTRAL ANALYSIS The spectrum of ethylene oxide in the frequency range 262È358 GHz has been taken with a new type of fast scan submillimeter system that we have dubbed FASSST (fast scan submillimeter spectroscopic technique ; Petkie et al. 1997). In this system, the submillimeter-wave radiation is provided by a voltage-tunable backward wave oscillator (BWO), which is scanned rapidly through a large frequency range. The frequencies are calibrated optically by use of a Fabry-Perot cavity. Since the sweep is so rapid, frequency 517 518 PAN ET AL. Vol. 499 TABLE 1 ASSIGNED AND FITTED TRANSITION FREQUENCIES OF ETHYLENE OXIDE IN THE GROUND VIBRATIONAL STATE J@ K@ a 3 2 3 1 0 4 0 4 2 4 5 3 5 1 3 2 1 4 5 2 3 3 4 2 6 5 4 4 2 6 7 5 6 1 3 4 3 4 5 3 K@ c 0 1 1 1 6 1 4 0 1 2 2 2 1 1 1 2 2 1 0 2 JA 3 3 4 2 5 5 3 4 2 6 7 5 6 0 3 4 3 4 5 3 K@@ a 2 1 2 0 3 3 3 3 1 3 4 2 4 0 2 1 0 3 4 1 K@@ c 1 2 2 2 3 2 1 1 2 3 3 3 2 0 2 3 3 2 1 3 Measured Frequency (MHz) Calculated Frequency (MHz) O[C (MHz) 23134.160 23610.420 24834.300 24923.690 26267.940 29687.080 33588.910 34147.760 34157.040 35790.570 37328.780 37780.740 38701.050 39581.640 39680.050 41579.440 45177.530 47094.930 47556.890 49000.880 23134.215 23610.370 24834.257 24923.644 26267.982 29687.034 33588.972 34147.727 34156.986 35790.548 37328.826 37780.693 38701.078 39581.607 39680.087 41579.454 45177.565 47094.971 47556.920 49000.971 [0.055 0.050 0.043 0.046 [0.042 0.046 [0.062 0.033 0.054 0.022 [0.046 0.047 [0.028 0.033 [0.037 [0.014 [0.035 [0.041 [0.030 [0.091 Referencea 1, 1, 1, 1, 2 1, 2 1, 1, 1, 1, 1, 1, 1, 1, 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 NOTE.ÈTable 1 appears in its entirety in the electronic edition of the Astrophysical Journal. a The lack of a reference indicates that the line is reported here for the Ðrst time. REFERENCES.È(1) Hirose 1974 ; (2) Creswell & Schwendeman 1974. drifts and instabilities are frozen out, and there is no need for active frequency stabilization. With the new system, it is possible to measure thousands of spectral lines each second, with a typical accuracy of B0.1 MHz. In the spectral region studied, we were able to assign all of the strong lines and TABLE 2 SPECTROSCOPIC PARAMETERS FOR ETHYLENE OXIDE IN THE GROUND VIBRATIONAL STATE Parameter Valuea A (MHz) . . . . . . . . . . . . . . . . . . . . . B (MHz) . . . . . . . . . . . . . . . . . . . . . C (MHz) . . . . . . . . . . . . . . . . . . . . . * (kHz) . . . . . . . . . . . . . . . . . . . . . *J (kHz) . . . . . . . . . . . . . . . . . . . . *JK(kHz) . . . . . . . . . . . . . . . . . . . . . d K (kHz) . . . . . . . . . . . . . . . . . . . . . . dJ (kHz) . . . . . . . . . . . . . . . . . . . . . 'K (Hz) . . . . . . . . . . . . . . . . . . . . . . 'J (Hz) . . . . . . . . . . . . . . . . . . . . . 'JK (Hz) . . . . . . . . . . . . . . . . . . . . . 'KJ(Hz) . . . . . . . . . . . . . . . . . . . . . . / K (Hz) . . . . . . . . . . . . . . . . . . . . . . . /J (Hz) . . . . . . . . . . . . . . . . . . . . . /JK(Hz) . . . . . . . . . . . . . . . . . . . . . . L K (mHz) . . . . . . . . . . . . . . . . . . . . L J (mHz) . . . . . . . . . . . . . . . . . . L JJK(mHz) . . . . . . . . . . . . . . . . . . . L JK (mHz) . . . . . . . . . . . . . . . . . . L KKJ (mHz) . . . . . . . . . . . . . . . . . . . . l K(mHz) . . . . . . . . . . . . . . . . . . . . . J l (mHz) . . . . . . . . . . . . . . . . . . . . lJK (mHz) . . . . . . . . . . . . . . . . . . . . lKJ(mHz) . . . . . . . . . . . . . . . . . . . . . PK (kHz) . . . . . . . . . . . . . . . . . . . . . pbK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25483.88812(224) 22120.84830(224) 14097.83999(271) 51.1883(173) [70.4938(116) 27.6541(226) [9.01689(109) 3.3491(118) 0.2456(483) [5.2164(452) 15.7370(964) [10.638(121) [0.05097(206) 1.4297(327) [17.8633(989) [0.1210(427) [0.1288(397) 0.624(179) [0.800(293) 0.892(251) [0.00367(120) 0.0921(250) [0.448(121) 0.679(193) [1.114(172) 1.38 a Standard error in units of last digit in parentheses ; IIIl basis used. b Weighted standard deviation (dimensionless). approximately 50% of the total of all lines detected ; the remaining weak lines are mainly from excited vibrational states. The measured and assigned lines, along with previous data at lower frequencies, were combined into a global data set of 662 transitions and Ðt to an asymmetric top Hamiltonian with centrifugal distortion using WatsonÏs A reduction (Watson 1977). A root mean square deviation of 138 kHz was determined by the Ðt, which is comparable with the experimental uncertainty in the lines. The Ðtted spectral transitions are listed in Table 1 (only the Ðrst 20 rows of Table 1 appear in the paper edition ; for the complete version, see the electronic edition) along with quantum assignments, residuals (observed minus calculated frequencies), and, for previously measured lines, the most recent reference. The spectroscopic constants determined by the Ðt are listed in Table 2. These include the standard rotational constants, full sets of fourth-order, sixth-order, and eighth-order centrifugal distortion constants, and one tenth-order constant. 3. DISCUSSION Using the spectroscopic constants in Table 2, we can predict the frequencies of unmeasured lines both outside of the measured frequency range and/or, to a limited extent, involving higher quantum numbers than the measured transitions. These are listed in Table 3 (only the Ðrst 20 rows of Table 3 appear in the paper edition ; for the complete version, see the electronic edition), which contains quantum assignments, predicted frequencies and uncertainties, intensities, and upper state energies. The intensities are expressed as S-values (Townes & Schawlow 1975) multiplied by the square of the dipole moment in units of debye squared. Only transitions with rotational quantum number J ¹ 60, k2S º 0.10, E ¹ 700 cm~1, frequency ¹400 GHz, and upper predicted uncertainty less than 0.5 MHz are included in Table 3 (a more complete table is also available from the No. 1, 1998 SPECTRUM OF ETHYLENE OXIDE 519 TABLE 3 PREDICTED TRANSITION FREQUENCIES OF ETHYLENE OXIDE IN THE GROUND VIBRATIONAL STATE J@ 1 2 3 3 4 2 5 4 2 6 7 5 6 1 3 4 8 3 4 9 K@ a 1 2 3 2 3 1 4 4 2 4 5 3 5 1 3 2 6 1 4 6 K@ c 0 0 0 1 1 1 1 0 1 2 2 2 1 1 1 2 2 2 1 3 JA 1 2 3 3 4 2 5 4 2 6 7 5 6 0 3 4 8 3 4 9 K@@ a 0 1 2 1 2 0 3 3 1 3 4 2 4 0 2 1 5 0 3 5 K@@ c 1 1 1 2 2 2 2 1 2 3 3 3 2 0 2 3 3 3 2 4 Frequency (MHz) Uncertainty (MHz) k2S E upper (cm~1) 11385.905 15603.557 23134.215 23610.370 24834.257 24923.644 29687.034 34147.727 34156.986 35790.548 37328.826 37780.693 38701.078 39581.607 39680.086 41579.454 43397.469 45177.565 47094.971 47145.517 0.001 0.002 0.003 0.004 0.003 0.004 0.003 0.005 0.004 0.005 0.004 0.006 0.006 0.005 0.004 0.007 0.005 0.007 0.005 0.005 5.36 7.33 7.59 9.23 13.08 4.59 14.83 7.03 2.98 17.66 21.26 12.63 14.56 3.57 4.61 7.90 22.31 3.96 5.53 26.27 1.588 4.792 9.660 8.888 15.087 4.272 22.918 16.227 4.608 31.139 41.942 21.927 32.430 1.320 9.556 14.259 54.395 8.100 16.177 66.745 NOTE.ÈTable 3 appears in its entirety in the electronic edition of the Astrophysical Journal. authors). Those assigned and Ðtted lines listed in Table 1 that meet the constraints are included in Table 3 with their predicted frequencies so that the additional information concerning these lines (intensities, upper state energies) is readily available for astronomical use. A comparison of those frequencies in Table 3 corresponding with the predictions in Tables 1 and 2 of Dickens et al. (1997) shows that the predicted frequencies of these authors, based on the earlier data of Hirose (1974), are generally accurate to 1 MHz for low J-values. In computing the actual line intensities, the nuclear spin statistics of the hydrogen nuclei must be considered. The di†erent rotational quantum states possess di†erent spin weights due to the C symmetry of the molecule and the 2v existence of four hydrogen nuclei, each with spin I \ 1 . These spin weights are 10 for states in which the K and K2 a c quantum numbers are both odd or both even, and 6 for states in which one of these quantum numbers is odd and the other even. Note that b-type transitions occur between states with the same spin weights. The partition function, q, for the rotational levels of the ground vibrational state of ethylene oxide is well approximated by the standard asymmetric top expression (Townes & Schawlow 1975) multiplied by the total spin weight, (2I ] 1)4 \ 16, and divided by the symmetry number, p \ 2. The result is q \ 15.13T 3@2, where T is the temperature in kelvins. The fractional population f for any rotational state is then given by the expression f \ g (2J ] 1) exp ([E/kT )/q , (1) s where g stands for the proper spin weight (10 or 6), E is the s rotational energy, and k is the Boltzmann constant. We would like to thank NASA for their support of laboratory astrophysics at Ohio State University, the AFOSR for an Instrumentation Grant, and the Ohio State University Supercomputer Center for the award of time on their Cray Y-MP8 computer. S. A. thanks the Alexander von Humboldt Stiftung for a Feodor-Lynen research stipend. REFERENCES Blake, G. A., Sutton, E. C., Masson, C. R., & Phillips, T. G. 1987, ApJ, 315, Hirose, C. 1974, ApJ, 189, L145 621 Hollis, J. M., Snyder, L. E., Suenram, R. D., & Lovas, F. J. 1980, ApJ, 241, Brown, P. D., Charnley, S. B., & Millar, T. J. 1988, MNRAS, 231, 409 1001 Caselli, P., Hasegawa, T. I., & Herbst, E. 1993, ApJ, 408, 548 Irvine, W. M., et al. 1989, ApJ, 342, 871 Charnley, S. B., Kress, M. E., Tielens, A. G. G. M., & Millar, T. J. 1995, Miao, Y., Mehringer, D. M., Kuan, Y.-J., & Snyder, L. E. 1995, ApJ, 445, ApJ, 448, 232 L59 Charnley, S. B., Tielens, A. G. G. M., & Rogers, S. D. 1997, ApJ, 482, L203 Millar, T. J., Herbst, E., & Charnley, S. 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