The Rotational Spectra of H 2 CCSi and H 2 C 4 Si

Transcription

1 Journal of Molecular Spectroscopy 211, (2002) doi: /jmsp , available online at on The Rotational Spectra of 2 CCSi and 2 C 4 Si M. C. McCarthy and P. Thaddeus arvard Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, and Division of Engineering and Applied Sciences, arvard University, 29 Oxford Street, Cambridge, Massachusetts Received July 26, 2001; in revised form October 3, 2001 The microwave rotational spectra of two singlet chains 2 CCSi and 2 C 4 Si, have been observed in a pulsed supersonic molecular beam by Fourier transform microwave spectroscopy. Following detection of the singly substituted rare isotopic species and D 2 CCSi, an experimental structure (r 0 ) has been determined to high accuracy for 2 CCSi by isotopic substitution. In addition, the rotational transitions of the 29 Si and the two 13 C isotopic species of 2 CCSi exhibit nuclear spin rotation hyperfine structure. The component of the spin rotation tensor along the a-inertial axis is abnormally large for each of these isotopic species, especially for that with 29 Si, where the magnitude of C aa is in excess of 700 kz. I. INTRODUCTION Although silicon analogs of many pure carbon clusters (C n ) and acetylenic free radicals (C n ) have recently been characterized by high-resolution spectroscopy (1, 2), only 2 CSi, the silicon analog of vinylidene ( 2 CC:), has been reported in the gas phase (3, 4). Because small silicon-bearing molecules such as SiS, SiC, and SiC 2, and the cumulene carbenes 2 C 3 (5), 2 C 4 (6), and 2 C 6 (7) are abundant in the circumstellar shells of evolved carbon stars (8), 2 CCSi and longer silacumulenes are plausible candidates for astronomical detection. In the laboratory, these chains may serve as intermediates in chemical vapor deposition and in the formation of thin films (9), so experimental studies of the spectroscopy and structure of silacumulenes is of general interest. There is presently little experimental or theoretical data on 2 C n Si clusters beyond 2 CSi. The photochemical interconversion between isomers of 2 C 2 Si and 2 C 4 Si was studied by matrix isolation spectroscopy (10, 11), and silacyclopropenylidene, a low-lying singlet cyclic isomer of 2 C 2 Si, was detected in the gas-phase by millimeter-wave spectroscopy and its molecular structure determined by isotopic substitution (12). The relative stabilities, structures, and dipole moments of the 2 C 2 Si isomers have been the subject on several theoretical investigations (13 15), but no calculations are available for 2 C 3 Si or larger analogs. We describe here the laboratory detection of the two new silicon carbon chains 2 C 2 Si and 2 C 4 Si shown in Fig. 1. Each has a singlet electronic ground state ( 1 A 1 ) and a linear heavy-atom backbone with two equivalent off-axis atoms. As a consequence the rotational spectrum of each is that of a nearly prolate rotor with C 2v symmetry and ortho and para nuclear spin statistics for the K a rotational levels. An effective structure (r 0 )of 2 CCSi has been determined by detection of the singly-substituted isotopic species and the doubly-substituted D 2 CCSi. In addition, rotational lines of the 29 Si and both 13 C isotopic species exhibit hyperfine structure owing to the interaction between the nuclear spins and the overall rotation of the molecule. The diagonal elements of the nuclear spin rotation tensor have been derived for all three species; C aa, the element along the a-inertial axis, for each is large relative to that of other closed-shell molecules of similar symmetry. Because this hyperfine interaction is proportional to the radial expectation value of the valence electrons, the determination of C aa at different atomic positions along the carbon chain may provide a sensitive probe of the molecular wave function. II. EXPERIMENTAL Rotational lines of the two molecules here were detected in a supersonic molecular beam at centimeter-wavelengths with a Fourier transform microwave (FTM) spectrometer that has been previously described (16). This instrument operates from 5 to 43 Gz and employs a liquid nitrogen-cooled receiver and cold optics for high sensitivity; computer control provides rapid data acquisition and analysis. A gate valve allows the small discharge source in the throat of the supersonic nozzle to be readily serviced without breaking vacuum, so continuous operation over many tens of hours or days is achieved. The same discharge source used to detect many new silicon carbides SiC n and radicals SiC n was employed in the present investigation. The best gas mixture and source conditions were similar to those used before (1, 2): silane and diacetylene (0.1% each) heavily diluted in neon, a gas pulse of 200 µsec duration (15 20 sccm flow), a 1000-V dc discharge, and a stagnation pressure behind the nozzle of 2.5 ktorr (3.2 atm). To detect the isotopic species of 2 CCSi, deuterated diacetylene was used in place of normal diacetylene for D 2 CCSi, and a statistical mixture of carbon-13 CC (25% CC, 50% 13 CC, and 25% 13 C 13 C) was used in place of normal diacetylene to observe the two single 13 C isotopic species; 2 CC 29 Si was observed in natural abundance. Carbon-13 CC was produced /02 $35.00 All rights reserved. 228

2 ROTATIONAL SPECTRA OF 2 CCSi AND 2 C 4 Si Å C C Si b Å Å C C C a C Si shown in the energy level diagram in Fig. 2, the K a =±1 rotational ladders of 2 CCSi lie about 14 K above ground, but these are metastable owing to ortho para nuclear spin statistics, and therefore are well populated in our rotationally cold molecular beam (T rot 3 K). The rotational spectrum of 2 CCSi as a result consists of fairly tightly spaced triplets with an intensity ratio of 3 : 2 : 3. At least three successive triplets were measured in 2 CCSi and each of its isotopic species (Table 1). The spacing between the triplets is determined by the asymmetry splitting of the K a =±1 transitions; for the transitions near 20 Gz, the triplet splitting is about 100 Mz. The spectrum of 2 CCSi and its isotopic species were analyzed with Watson s S-reduced amiltonian (19) which reproduces the observed spectra of each species to the measurement FIG. 1. Structures of the two new silacumulenes, 2 CCSi and 2 C 4 Si. The bond lengths and angle of 2 CCSi were obtained by isotopic substitution (see Section. III.D). by the hydrolysis of 13 C-enriched Li 2 C 2 which was prepared at the NI Stable Isotope Resource, Los Alamos National Laboratory. The lines of 2 CCSi are about twice as weak with acetylene as with diacetylene in the discharge, but lines of the two 13 C species are fivefold stronger with carbon-13 enriched acetylene than with normal acetylene, about the enhancement expected. The laboratory detection of 2 CCSi and 2 CCCCSi benefited from theoretical calculations that significantly narrowed the search range for the rotational transitions. On the basis of several calculations (14, 15), 2 CCSi was detected first, its rotational constants differing by only 0.3% from those predicted by Cooper (14). For D 2 CCSi and the singly substituted isotopic species, rotational constants calculated from Cooper s theoretical structure were scaled by the ratio of the experimental rotational constant to that calculated for the normal species. Such scaling predicts the transition frequencies of the isotopic lines to better than 1% of the frequency shift from the lines of the normal species, so a search of only a few Mz in the vicinity of 20 Gz was required for detection. Because no theoretical geometries are available for 2 C 4 Si, laboratory searches were based on a high-level ab initio geometry of SiC 4 (17) in which two hydrogen atoms were appended to the terminal carbon atom of the chain with a C bond of 1.06 Å length and an internal C angle of 116 a procedure previously used for the detection of four new thiocumulene chains similar in structure to the molecules here (18). Rotational transitions predicted in this way turned out to be accurate to about 1%. III. RESULTS AND ANALYSIS A. Rotational Spectrum of 2 CCSi The rotational spectrum of 2 CCSi is similar to that of formaldehyde, a molecule with similar structure that also possesses C 2v symmetry and two equivalent off-axis protons. As FIG. 2. Lowest rotational energy levels of 2 CCSi, showing the transitions detected in the normal isotopic species (arrows) and the singly substituted isotopic species and D 2 CCSi (dots). Owing to the ortho para nuclear spin statistics, the K a =±1rotational levels are metastable in our rotationally cold molecular beam.

3 230 MCCARTY AND TADDEUS TABLE 1 Measured Transitions of the Isotopic Species of 2 CCSi (in Mz) J K a,k c J K a,k c 2 CCSi 13 2 CCSi 2C 13 CSi 2 CC 29 Si D 2 CCSi 1 0,1 0 0, ,2 0 1, ,2 1 0, ,1 1 1, ,3 2 1, ,3 2 0, ,2 2 1, ,4 3 1, ,4 3 0, ,3 3 1, Note. Centroid of hyperfine-split line is given; estimated experimental uncertainties (1σ ) are 2 kz. Observed minus calculated frequencies are 0 2 kz; the best-fit constants are given in Table 2. uncertainty (2 kz) with only four free parameters: the rotational constants B and C, and the two leading centrifugal distortion constants D J and D JK (Table 2). The A rotational constant, however, could not be determined from the present data set; it was instead constrained to the theoretical value derived by Cooper (14). B. Rotational Spectrum of 2 C 4 Si The rotational spectrum of 2 C 4 Si is very similar to that of 2 CCSi, but the rotational lines are weaker by a factor of 10; five rather than three rotational transitions, each with the predicted triplet structure, were measured between 8 and 20 Gz (Table 3). Owing to the small difference between the B and C rotational constants, the asymmetry splitting in the K a = ±1 transitions is only about 25 Mz for the transitions near 20 Gz. Five spectroscopic constants (Table 2) were again adequate to reproduce the observed transition frequencies of 2 C 4 Si. The spectroscopic and chemical evidence for our assignments is extremely good. The rotational constants of each molecule are within 1% of those predicted, and the centrifugal distortion constants (D J and D JK ) are close to those of other silicon carbon or hydrocarbon chains of similar size and structure. The absence of lines at subharmonic frequencies indicates that the carriers of the observed lines are not from larger or heavier molecules, and the relative intensity ratio of the triplet components of each transition closely agrees with that expected from the nuclear spin statistics. The observed lines also pass several other tests: they are only found in the presence of an electrical discharge through gas containing Si 4, as expected for a silicon-bearing molecule, and they vanish when diacetylene is replaced with deuterated diacetylene, indicating a molecule containing hydrogen. The intensities of the observed lines are also unaffected when a permanent magnet is brought near the molecular beam, as expected for molecules with closed-shell, singlet electronic ground states. Crucial conformation of the 2 CCSi assignment is finally provided by isotopic substitution: lines of 29 Si and the 13 C isotopic species were observed within 0.3% of those calculated from the theoretical structure, and those of the doubly deuterated isotopic species of 2 CCSi were observed within 0.4% of those similarly calculated. TABLE 2 Spectroscopic Constants of 2 CCSi and 2 CCCCSi Isotopic Species (in Mz) 2 CCSi Constant Measured Expected a 2 13 CCSi 2 C 13 CSi 2 CC 29 Si D 2 CCSi 2 CCCCSi A b b b b b b B (4) (5) (5) (4) (4) (1) C (6) (5) (5) (4) (4) (1) D J (1) 0.86 c 1.19(3) 1.29(3) 1.21(1) 1.02(1) 0.041(1) D JK (3) d (3) (3) (3) (2) (6) Note. 1σ uncertainties (in parentheses) are in the last significant digit. a From Ref. (14). b Constrained to theoretical A constant of 2 CCSi or D 2 CCSi (Ref. 14). c From C 4 (Ref. 35). d From 2 C 4 (Ref. 36).

4 ROTATIONAL SPECTRA OF 2 CCSi AND 2 C 4 Si 231 TABLE 3 Measured Transitions of 2 CCCCSi (in Mz) J K a,k c J K a,k c 2 CCCCSi 3 1,3 2 1, ,3 2 0, ,2 2 1, ,4 3 1, ,4 3 0, ,3 3 1, ,5 4 1, ,5 4 0, ,4 4 1, ,6 5 1, ,6 5 0, ,3 3 1, ,7 6 1, ,7 6 0, ,6 6 1, Note. Estimated experimental uncertainties (1σ ) are 2 kz. Observed minus calculated frequencies are 0 2 kz; the best fit constants are given in Table 2. C. Nuclear Spin Rotation yperfine Structure in 2 CCSi Spin rotation hfs (hyperfine structure) has also been observed in the lowest- J rotational transitions of the three singly substituted isotopic species of 2 CCSi; it is a consequence of the interaction of the 29 Si or 13 C nuclei with the small magnetic field produced by molecular rotation. Other possible hyperfine interactions such as - spin spin, spin rotation, or 13 C- spin spin have been ruled out because the additional hfs is only observed when 13 C is present, and the magnitude of the observed splittings generally becomes larger as the distance between the two nuclei increases. The nuclear spin rotation amiltonian can be written as nsr = i I i C i J, [1] where C i is the spin rotation coupling tensor of the ith nuclei (20). The measured hfs for the 29 Si and the two 13 C species of 2 CCSi is given in Table 4, and the diagonal elements of the nuclear spin rotation tensor are given in Table 5. Sample lines of 2 CC 29 Si with resolved hfs are shown in Fig. 3. Owing to lower signal to noise, it has not been possible to detect the rare isotopic species of 2 C 4 Si. The theory of nuclear spin rotation has been developed by Ramsey and co-workers, (20, 21), Flygare and co-workers, (22, 23), and others (24). General expressions for the coupling constants can be written as C gg = g g n B gg a n0 0 L g n n L g 0 E n E 0, [2] TABLE 4 Observed hfs of 2 CCSi Isotopic Species (in kz) J K a,k c J K a,k c F F 13 2 CCSi 2C 13 CSi 2 CC 29 Si 1 0,1 0 0,0 3/2 1/ /2 1/2 2 1,2 1 1,1 5/2 3/ /2 1/ ,2 1 0,1 5/2 3/ /2 1/2 2 1,1 1 1,0 5/2 3/ /2 1/ ,3 2 1,2 7/2 5/ /2 3/ ,3 2 0,2 7/2 5/ /2 3/2 3 1,2 2 1,1 7/2 5/ /2 3/ ,4 3 1,3 9/2 7/2 18 7/2 5/ ,3 3 1,2 9/2 7/2 13 7/2 5/2 29 Note. Experimental uncertainties (1σ ) are 2 kz. where the summations are over the principal inertial axes (g = a, b, c), all electrons i, and excited states n; B gg is the rotational constant; a n0 = 1 hc µ Bg N µ N i r 3 i is an off-diagonal radially dependent hfs constant; and the orbital angular momentum matrix elements are between the ground and excited states. Since hyperfine interactions are generally very small, normally it is only the diagonal elements of the spin rotation tensor that are important. If the orbital angular momentum matrix elements are with respect to each atomic nucleus rather than with respect to the center of mass, and if centrifugal and vibration effects are neglected, Eq. [2] simplifies to C gg = 4B gg n a n0 0 L g n 2 E n E 0 + effects of nuclear charges, where g = a, b, c. The contribution to Eq. [3] from the rotation of the nuclear frame of the molecule is readily calculated from the molecular structure. For 2 CCSi it is of order 10 kz or less, and can be neglected in the present analysis. TABLE 5 Diagonal Elements of the Nuclear Spin Rotation Tensor for 2 CCSi Isotopic Species (in kz) Isotopic Species C aa C bb C cc 13 2 CCSi 112(14) 8(4) 6(4) 2 C 13 CSi a 142(14) 2 CC 29 Si a 723(30) Note. The 1σ uncertainties (in parentheses) are in the last significant digit. a C bb and C cc constrained to zero. [3]

5 232 MCCARTY AND TADDEUS FIG. 3. Sample spectra of 2 CC 29 Si showing nuclear spin rotation hyperfine splitting in rotational transitions near 31 Gz in the K a = 0 and the two K a =±1ladders. Each hyperfine transition has a double peaked line profile as a result of the Doppler shift between the fast-moving molecular beam and the two traveling waves that compose the confocal Fabry Perot mode. Typical integration times were 8 min per spectrum. There are several points worth emphasizing. First, the C aa values determined here (Table 5) are all large. In other closed-shell molecules where nuclear spin rotation hfs has also been observed, coupling constants are typically on the order of a few kilohertz (25, 26). One notable exception is difluorcarbene, CF 2, where C aa is comparable to that here, presumably because of the presence of a low-lying excited electronic state (27). The large C aa values here, however, arise for a different reason: as Eqs. [2] and [3] show, the magnitude of the diagonal elements is proportional to the rotational constant along that axis. Because the A rotational constant is more than 50 times larger than either B or C in 2 CCSi, the hfs splitting in the K a =±1 levels is much larger than the hfs splitting in the K a = 0 level, and consequently C aa is much larger than either C bb or C cc. The sign of C aa for 2 CC 29 Si is the opposite of that of the two 13 C isotopic species, because of the opposite sign of the nuclear magnetic moments (28). The three C aa values in Table 5 differ considerably in magnitude because a n0 in Eq. [2] is proportional to r 3, and this expectation value apparently changes considerably along the carbon chain. D. The Structure of 2 CCSi An experimental (r 0 ) structure of 2 CCSi was obtained by a least-squares adjustment of the three bonds and the C bond angle in Fig. 1 to reproduce the measured rotational constants in Table 2, i.e., those of the three rare isotopic species and D 2 CCSi, plus that of the normal species. Our calculation assumes that 2 CCSi is planar and possesses C 2v symmetry. The bond lengths and angle are compared in Table 6 with equilibrium r e structures calculated ab initio using different basis sets at the self-consistent field (SCF) level of theory. Uncertainties in the r 0 structure are derived on the assumption that the largest source of error is zero-point vibration. The magnitude of this error and how it is partitioned among the three moments of inertia are unknown, but it was estimated by assigning to each rotational constant an uncertainty which yields a χ 2 of 7, the most probable value for six degrees of freedom (29). The same uncertainty in B and C was assumed for each isotopic species: Mz. One advantage of the approach used here and elsewhere (30) is that since the present

6 ROTATIONAL SPECTRA OF 2 CCSi AND 2 C 4 Si 233 TABLE 6 2 CCSi Structures Theoretical Experimental Parameter (r 0 ) DZ SCF a DZ+P SCF a CASSCF b r(-c (1) )/Å 1.099(1) r(c (1) -C (2) )/Å 1.321(1) r(c (1) -Si)/Å 1.703(1) C (1) /(deg) 117.3(1) Note. Structure that best reproduces the observed rotational transitions of the five isotopic species (see Sect. III.D). Estimated uncertainties in the last significant digit are given in parentheses. a From Ref. (13). b From Ref. (14). molecules possess large vibrational rotational coupling constants (owing to the light mass of hydrogen) zero-point vibration is explicitly taken into account in a simple and systematic way. The r o structure here is in reasonable agreement with the r e structures of 2 CCSi at the SCF level of theory (13), calculated with a double-ζ basis set either alone (DZ SCF) or augmented with polarization functions (DZ + P SCF), or at the complete active-space SCF level of theory (14) using the TZVP basis set (CASSCF). Not surprisingly, the C bond differs by the largest amount between the r 0 and r e structures ( 0.02 Å), but the experimental C C and C Si bond lengths are within Åof the theoretical values using the three basis sets, and with the DZ basis set for example the theoretical and experimental bonds differ by no more than Å. The experimental C (1) bond angle of ± 0.1 also closely matches that from theory, the difference between the two amounting to less than 1.3 for either of the three r e structures. The C C and C Si bond lengths are close to the standard value for double bonds, indicating that the bonding in the heavy atom backbone of 2 CCSi is cumulenic. IV. DISCUSSION As the present work demonstrates, cumulenic chains terminated with oxygen, sulfur, and now silicon are readily produced in certain gas discharges, and can be detected in the laboratory by FTM spectroscopy. It is likely that the rotational spectra of other cumulenic chains, including those terminated with phosphorus, germanium, etc. are also stable and detectable. Phosphorus molecules such as 2 CCP and 2 CCCP are especially good candidates for laboratory detection because the isovalent nitrogen chains have been well characterized in the laboratory (31) and because phosphorus-bearing molecules can be readily produced through discharges containing P 3 (32). The present silacumulenes are candidates for astronomical detection for several reasons: (1) they are similar in structure and composition to known astronomical silicon-bearing chains, (2) 2 CCSi is isovalent to 2 C 3, which has been detected in several astronomical sources, including the circumstellar envelope of the evolved carbon star IRC , and (3) astrochemical models of dense molecular clouds (33) predict that the simplest silacumulene chain, 2 CSi, has a fractional abundance comparable to SiC 2, which is quite abundant in IRC Preliminary radioastronomical searches by Saito and co-workers (3) failed to detect 2 CSi toward several astronomical sources, but this failure may be the result of its small dipole moment, estimated to be only 0.3 D. The dipole moment of 2 CCSi is calculated by Cooper (14) to be considerably larger (µ = 1.21 D, i.e., a factor of 4), so 2 CCSi may be much easier to detect in space than 2 CSi, even if less abundant. With the spectroscopic constants listed in Table 2 the astronomically most interesting lines of 2 CCSi can be predicted to better than 1 ppm up to 150 Gz, and those of 2 C 4 Si can be predicted to the same level of accuracy up to 75 Gz. Other isomers of 2 C 2 Si may be detectable with our present spectrometer because rotational lines of silacyclopropenylidene (c-sic 2 2 ) and vinylidenesilene, the cumulene isomer detected here, are fairly strong. The next best candidate is silylenylacetylene, a low-lying isomer that is calculated to possess a nearly linear Si-C-C backbone in which a hydrogen atom is attached to each end of the chain. It is calculated ab initio (13) to lie 22 kcal/mol above the cyclic ground state isomer, but only 5 kcal/mol higher in energy than the cumulene isomer. Because silylenylacetylene is a nearly prolate, asymmetric top, with transitions that are harmonically related in frequency by integer quantum numbers, its rotational spectrum should be fairly easy to identify. The determination of nuclear spin rotation coupling constants at different atomic positions along a carbon chain may be useful in elucidating the electronic structure and bonding in closed-shell molecules such as 2 CCSi with an even number of electrons and a 1 A 1 electronic ground state, and hence no magnetic interactions between the nuclei and electrons in the absence of molecular rotation. Isotopic substitution combined with rotation gives rise to a perturbation which slightly excites higher orbitals of the valence electrons and produces a small internal magnetic field. Because the coupling constants that describe the magnitude and projection of this interaction onto the molecular axes are proportional to the average distribution of valence electrons in the vicinity of each atomic nucleus, these constants may prove to be a sensitive probe of the molecular wave function a key feature for molecules which otherwise lack magnetic hyperfine interactions. Although coupling constants apparently have not yet been calculated ab initio, it may be worthwhile doing so now that experimental data is available. The spin rotation coupling constant C aa at each nucleus along a chain can be compared with little ambiguity because isotopic substitution has a negligible effect on excited state energies, on the radial and angular expectation values of the valence electrons, and on the A rotational constant. Our results, for example,

7 234 MCCARTY AND TADDEUS suggest that the unpaired electron density is highest on the silicon atom of 2 CCSi, owing to the pair of singlet-coupled electrons which are formally located on this atom. This interpretation is in good agreement with the 13 C spin rotation coupling constants of 2 C 3, 2 C 4, and 2 C 5, which were measured by the same technique and are described in the accompanying paper (34). For each of these molecules, the largest coupling constant (by a factor of 2 or more) was at the carbene carbon terminating the chain. ACKNOWLEDGMENTS The authors thank C. A. Gottlieb and J. K. G. Watson for helpful discussions, A. J. Apponi for assistance with some of the early experiments, J. Dudek for the synthesis of diacetylene, and E. S. Palmer for help with the microwave electronics and cryogenic system. We also gratefully acknowledge L.A. Silks III of the NI Stable Isotope Resource at The Los Alamos National Laboratory for assistance in the production of the carbon-13 enriched lithium carbide. The Los Alamos Isotope Resource was supported by USPS Grant RR02231 and by the U.S. Department of Energy. The present research is supported by NASA Grant NAG and NSF Grant AST REFERENCES 1. M. C. McCarthy, A. J. Apponi, C. A. Gottlieb, and P. Thaddeus, Astrophys. J. 538, (2000). 2. M. C. McCarthy, A. J. Apponi, C. A. Gottlieb, and P. Thaddeus, J. Chem. Phys. 115, (2001). 3. M. Izuha, S. Yamamoto, and S. Saito, J. Chem. Phys. 105, (1996). 4. W. W. arper, K. W. Waddell, and D. J. Clouthier, J. Chem. Phys. 107, (1997), and references therein. 5. J. Cernicharo, C. A. Gottlieb, M. Guélin, T. C. Killian, G. Paubert, P. Thaddeus, and J. M. Vrtliek, Astrophys. J. Lett. 368, L39 L41 (1991). 6. J. Cernicharo, C. A. Gottlieb, M. Guélin, T. C. Killian, P. Thaddeus, and J. M. Vrtliek, Astrophys. J. Lett. 368, L43 L45 (1991). 7. M. Guélin, S. Muller, J. Cernicharo, A. J. Apponi, M. C. McCarthy, C. A. Gottlieb, and P. Thaddeus, Astro. Astrophys. 363, L9 L12 (2000). 8. A. E. Glassgold and G. A. Mamon in Chemistry and Spectroscopy of Interstellar Molecules (D. K. Bohme et al., Eds.), p Univ. of Tokyo Press,Tokyo, M. D. Allendorf, Energy Res. Abstr. 17, No (1992). 10. G. Maier,. P. Reisenauer, and. Egenolf, Eur. J. Org. Chem. 7, (1998), and references therein. 11. G. Maier,. P. Reisenauer, and A. Meudt, Eur. J. Org. Chem. 7, (1998). 12. M. Izuha, S. Yamamoto, and S. Saito, Can. J. Phys. 72, (1994). 13. G. Frenking, R. B. Remington, and. F. Schaefer III, J. Am. Chem. Soc. 108, (1986). 14. D. L. Cooper, Astrophys. J. 354, (1990). 15. C. D. Sherrill, C. G. Brandow, W. D. Allen, and. F. Schaefer III, J. Am. Chem. Soc. 118, (1996). 16. M. C. McCarthy, W. Chen, M. J. Travers, and P. Thaddeus, Astrophys. J. Suppl. 129, (2000). 17. V. D. Gordon, E. S. Nathan, A. J. Apponi, M. C. McCarthy, P. Thaddeus, and P. Botschwina, J. Chem. Phys. 113, (2000). 18. V. D. Gordon, M. C. McCarthy, A. J. Apponi, and P. Thaddeus, Astrophys. J. Suppl. 134, (2001). 19. J. K. G. Watson, in Vibrational Spectra and Structure (J. R. Durig, Ed.), Vol. 6, Chap. 1. Elsevier, New York, N. F. Ramsey, Phys. Rev. 78, (1950). 21. I. Ozier, L. M. Crapo, and N. F. Ramsey, J. Chem. Phys. 49, (1968), and references therein. 22. W.. Flygare, J. Chem. Phys. 41, (1964). 23. W.. Flygare and J. Goodisman, J. Chem. Phys. 49, (1968), and references therein. 24. C. Deverell, Mol. Phys. 18, (1970). 25. P. Thaddeus, L. C. Krisher, and J.. N. Loubser, J. Chem. Phys. 40, (1964). 26. B. Gatehouse,. S. P. Muller, and M. C. L. Gerry, J. Chem. Phys. 106, (1997). 27. N. ansen,. Mäder, and F. Temps, Chem. Phys. Lett. 327, (2000). 28. C.. Townes and A. L. Schawlow, Microwave Spectroscopy. Dover, New York, W.. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, p Cambridge. Univ. Press, Cambridge, UK, M. C. McCarthy, E. S. Levine, A. J. Apponi, and P. Thaddeus, J. Mol. Spectrosc. 203, (2000). 31. W. Chen, M. C. McCarthy, M. J. Travers, E. W. Gottlieb, M. R. Munrow, S. E. Novick, C. A. Gottlieb, and P. Thaddeus, Astrophys. J. 492, (1998), and references therein. 32. S. Saito and S. Yamamoto, J. Chem. Phys. 111, (1999). 33. E. erbst, T. J. Millar, S. Wlodek, and D. K. Bohme, Astron. Astrophys. 222, (1989). 34. M. C. McCarthy and P. Thaddeus, J. Mol. Spectrosc. 211, (2002). 35. W. Chen, S. E. Novick, M. C. McCarthy, C. A. Gottlieb, and P. Thaddeus, J. Chem. Phys. 103, (1995). 36. T. C. Killian, J. M. Vrtilek, C. A. Gottlieb, E. W. Gottlieb, and P. Thaddeus, Astrophys. J. 365, L89-L92 (1990).