J. Phys. Chem. 1980, 8 4 , 1765-1767
G.A. Capelle, C. R. (Jones,J. Zorskie, and H. P. Broida, J . Chem. Phvs.. 61. 4777-4779 119741. E. iiemann, Ch. Ryziewi'cz, and T. Torring, Z. Naturforsch. A , 31, 128- 130 ('I976). T. Torrina. J. Mol. Soectrosc., 48, 148-156 (1973). C. A. Mgendres, A. (j.Hebert, and K. Street, Jr., J . Chem. Phys., 51, 855-856 (1969). R. F. Barrow, W. C. Barton, and P. A. Jones in "International Tables of Selected Constants", Vol. 17, "Spectroscopic Data Diatomic Molecules", 8. Rosen, Ed., Pergamon Press, New York, 1970. M. Winnewisser, Z. Angew. Phys., 30, 359-370 (1971).
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(10) M. Winnewisser and B. P. Winnewisser, Z. Naturforsch. A , 29, 633-641 (1974). (1 1) J. B. West; R. S: Bradford, Jr., J. D. Eversole, and C. R. Jones, Rev. Sci. Insfrum., 46, 164-168 (1975). (12) M. A. Kinch and B. V. Rollins, Brit. J. Appl. Phys., 14, 672-676 (1963). (13) E. H. Putley, Phys. Status Solidi, 6, 571-614 (1964). (14) W. Gordy and R. L. Cook, "Microwave Molecular Spectra", WileyInterscience, New York, 1970. (15) J. L. Dunham, Phys. Rev., 41, 721-731 (1932). (16) R. Clegg and S. Wyckoff, Mon. Not. R. Astron. SOC.,179, 417-432 (1977).
New Spectroscopic Constants for Methane Derived by Using Microwave Transitions from the Interstellar Mediumt K. Fox," Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 379 16
D. E. Jennings, Infrarcd and Radio Astronomy Branch, NASA Goddard Space Flight Center, Greenbelt. Maryland 20771
and MI. Dang-Nhu" Laboratoire d' Infrarouge, Universit6 de Paris-Sud, Orsay, France 9 1405 (Received September 17, 1979)
We have computed new spectroscopic constants for the vibronic ground state of I2CH,. Our calculations utilized two sets of microwave transitions: seven interstellar lines recently detected in emission from the Orion molecular cloud, and ten laboratory lines. We obtained the values to = -43516.429 f 0.366, p o = 5.56267 f 0.00312, to co = (1.192 f 0.011) X and do = (-2.300 f 0.063) = -0.487898 f 0.000316, bo = (-6.693 f 0.060) X X 10." Hz. These results are compared with earlier values of ground-state spectroscopic constants for I2CH4 deduced from either microwave or infrared laboratory data alone.
Introduction The determination of spectroscopic constants for tetrahedral XY4 molecules in their vibrational-electronic ground state has, historically, been a challenge. Molecules like methane lack, because of their high symmetry, a permanent electric-dipole moment in their lowest vibronic state. Consequently, no pure-rotational ground-state transitions in the far-infrared and microwave spectral regions were expected,l and the direct determination of ground-state spectroscopic constants for these molecules would be precluded. An important, productive approilch to this problem has been made through conventional vibration-rotation spectroscopy in the near-infrared. Spectra of "forbidden" transitions2 in the infrared-active fundamental ug of 12CH4 and 13CH4 have been analyzed to obtain accurate ground-state constant^.^,^ An alternative, innovative tack has developed because of the unexpected existence of pure-rotational transitions in the vibronic ground state. This effect was first predicted theoretically b$ FOX,^ and later by Watson6 and A l i e ~ .It~ is based on tht?%ypothesis that a tetrahedral XY4 molecule may have an electric-dipole moment induced by vibration-rotation interactions5 or, equivalently, by centrifugal The predictions were first verified in the laboratory by Ozier," and subsequently by several others
using a variety of ingenious experiments on methane, silane, and germaneag-'l The possibility of observing these "forbidden" pure-rotational transitions12 in the interstellar medium was originally pointed out by Transition frequencies accurate enough for radio searches became available for 12CH4as a result of the laboratory spectroscopy by Holt, Gerry, and 0zierl4 and by ~ t h e r s . ~ - lTheir l data led to accurate ground-state constants from which new transition frequencies were calculated. Transition strengths were estimated theoretically,13 having been normalized to the magnitude 5.38 X lo4 D of the transition dipole moment determined by Ozier.8 Fox and Jennings reported the first detection of interstellar methane.15 Six distinct pure-rotational vibronic ground-state 4J = 0 transitions of 12CH4were observed in emission from the Orion molecular cloud. Soon afterward, Jennings and Foxl6J7 detected an additional microwave line of 12CH4in the same source. Observed frequencies for the seven interstellar transitions were obtained by using velocity correlations as described in ref 16. In the present work, we have computed new groundstate constants for W H 4 from both the interstellar and laboratory data, in various combinations. We have considered the statistical significance of these results. The ground-state constants inferred by other workers3J4 are compared with ours.
'Contributed paper D.19 presented a t the Conference on Microwave Spectroscopy and Coherent Radiation, D u k e University, June 18-20, 1979; dedicated t o Professor Walter Gordy.
Calculations The rotational energy for a spherical-top molecule in its
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The Journal of Physical Chemistry, Vol. 84, No. 14, 1980
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Fox et al.
TABLE I : Measured Microwave Transition Frequencies in Methane laboratory
interstellar
J
freq,b MHz
J
transitiona
frea.b MHz
2 7 7 12 13
7.97 046 ( 54 )" 423.02(2)d 1246.55(2)e 10321.91(1O ) f
11 18 18 19 19
E(2)-E(1 1 F1(4)-F2( 1) A1(2)-A2(1) F1(4)-F2( 1) F2(4)-F1(1)
7861.67(10) 1 4 151.81(10 )f 18562.40(20)f 18528.94(2 0 d
19 20
F2( 5)-F1(1) F2(5)-F1(2)
4600.41(4)g 76231.4(5)g 76700.0(5)g 75944.9(5)g 782 34.7 (1O)gsh 78232.1 (4)g3h 94088.6(5)l 82873.7 ( 14)g
14 14 15 16 18
a Ordinal numbers in parentheses distinguish between energy levels of the same symmetry for a given J. Error bars in parentheses are in units of the last digit. Reference 8. R. F. Curl, T. Oka, and D. S. Smith, J. Mol. Spectrosc., 46,518 (1973). e R. F. Curl, J. Mol. Spectrosc., 48, 1 6 5 (1973). f Reference 14. g Reference 15. Reference 20. ' References 1 6 and 17.
TABLE 11: Combinations of Data Used to Obtain Ground-State Constants for Methane ~~
case a b
data all 1 0 laboratory lines from ref 1 4 383 all 10 laboratory lines and only 6 799 interstellar lines, excluding 78.2 GHzb all 1 0 laboratory lines and all 7 1036 interstellar lines, including 78234.7 MHzb 1815 all 1 0 laboratory lines and all 7 interstellar lines, including 78232.1 MHzb 8793 all 7 interstellar lines, including 78234.7 MHzb all 7 interstellar lines, 15673 including 78232.1 MHzb
c d e f
a These overall standard deviations (OSD) between measured and calculated spectral frequencies utilize nor. malized weights only; see eq 2a-c and ref 21. See ref 20.
vibronic ground state was given in a general form to all orders by Michelot, Moret-Bailly, and Fox.18 To sixth order in perturbation theory, this ground-state energy is
Results and Discussion The GSC for 12CH4,calculated by the procedure outlined in the preceding section, are presented in Table 111. While these constants have been computed for each data set in Table 11, only the four cases having an OSD S 2 kHz have been given in Table 111. We have fit the measured transition frequencies using both weighted and unweighted statistical analyses. In the unweighted case, each spectral frequency has simply been assigned the weight unity.21 In the weighted case, we have defined a normalized weight wi for the ith frequency by
9
+ pOJ(J + 1) + b V ( J + 1 ) 2 ] kn= l ( 2 J - 4 + 13 h)1/2(-1)JFfJ'+ [ p + c0J(J + l)] II ( 2 J 6 + k=l .h)1/2(-1)JFfi? + do Icj: ( 2 J - 8 + h)l/z(-l)JFf$) (1) k=l
EO =
begin with the GSC from ref 14. We then calculate the energy-level difference corresponding to each measured laboratory and/or interstellar transition. The GSC are varied until the overall standard deviation (OSD) between measured and calculated spectral frequencies is a minimum. The combinations of laboratory and interstellar data used to obtain GSC, together with their respective OSD, are given in Table 11. Our results are described and discussed in the next section.
-
IF?
(24
wi = ( N / S ) / P i 2
[€O
where pi is the uncertainty in the measurement of the ith frequency (interstellar or laboratory), N is the number of measured frequencies, and N
s = i=l l/p?
(2b) Here J is the total angular-momentum quantum number, and p is an irreducible representation of the point group The OSD is then given by of molecular symmetry. These parameters take the values N J = 0, 1, 2, ,.. and p = Al, A2, E, F1, F2, respe~tive1y.l~ 2 = q ( m ;- Ci)2/(N - P) (2c) The spectroscopic constants e, p , b, 5, c, and d carry the i=l superscript 0 to denote the ground state. The F coeffiwhere P is the number of significant parameters in the fit, cients may be considered as Clebsch-Gordan coefficients and miand ci are the measured and calculated ith freadapted to tetrahedral symmetry.lg In order to implement quencies, respectively. a complete sixth-order calculation, we have included offOur calculation for the ten laboratory lines alone, case diagonal F@)'sin which p' # p, and have done the apa in Table 111, exactly reproduces the values of GSC and propriate matrix diagonalization for each value of J . corresponding errors determinedz2in ref 14. These results The laboratory and interstellar spectral frequenciesm are represent an excellent check on our calculational technique. summarized in Table I. Our calculations to determine the The combination of ten laboratory lines with six or seven ground-state constants (GSC) e , etc. are iterative. We TABLE 111: Ground-State Spectroscopic Constants (Hz)for Methanea
c
case
f"
DO
a
-43515.945(231) -43516.406(291) -43516.429(366) -43516.304(640)
5.55927(249) 5.56235(248) 5.56267(312) 5.56089(544)
b C
d
1 0 4 ~ -0.487648(381) -0.487756(256) -0.487898(316) -0.487103(521)
-6.635(79) -6.684(48) -6.693(60) -6.643(104)
104co
1.183(15) 1.186(9) 1.192(11) 1.157(17)
10'"' -2.305(136) -2.295(50) -2.300(63) -2.274(111)
a Cases a-d consist of the laboratory and/or interstellar lines specified in Table 11. Errors in parentheses are standard deviations, and are in units of the last digit of the value.
J. Phys. Chem. 1980, 84, 1767-1771
interstellar lines, cases b-d in Tables I1 and 111, results in u 5 2 kHz which is small compared to the uncertainties (except for J = 2) recorded in Table I. When the interstellar frequency 78234.7 MHz is replaced by its alternative velocity component at 78232.1 MHz, Q increases significantly. This change reflects the fact that the former frequency has a larger error associated with it; consequently, it has a lower weight in the fit (see eq 2a). When we focus our attention on the calculated errors (in parentheses) in the GSC in Table 111, we note that the addition of six or seven interstellar lines to the ten laboratory lines produces some significant changes. The errors for to,bo, co, and do decrease in cases b and c. Thus, it appears that the interstellar data facilitate the determination of the higher-order GSC. This may be expected because the observed interstellar transitions are predominantly at higher J than the laboratory transitions. In the abstract, we have quoted the GSC from case c as it has the smaller u for the two data sets which include all laboratory and all interstellar lines. When the GSC of case a are used to calculate all 17 transition frequencies, the resultant a = 1194 Hz; this value is larger than u = 1036 Hz for case C.
We have already compared, in Table 111, our calculated GSC with those determined from microwave laboratory datal4 alone. The corresponding values, with their calculated standard deviations, obtained from infrared laboratory data3 alone are to = -43425 f 69, po = 5.300 f 0.378, and to= -0.4803 f 0.0200 Hz. The higher-order GSC bo, co, and do were not determined in ref 3. In that work, the standard deviations for to, po, and toare considerably greater than in ref 1 4 or the present work. References a n d Notes (1) See, for example, G.Herzberg, "Infrared and Raman Spectroscopy of Polyatomic Molecules", Van Nostrand, Princeton, 1945, p 41. (2) K. T. Hecht, J . Mol Spectrosc., 5, 355, 390 (1960). So-called "forbidden" transitions are usually relatively weak compared to "allowed" transitions; they are not absolutely forbidden, with zero
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intensities. G. Tarrago, M. Dang-Nhu, G. Poussigue, G. Guelachvili, and C. Amiot, J . Mol. Spectrosc., 57, 246 (1975). L. W. Pinkley, K. Narahari Rao, M. Dang-Nhu, G. Tarrago, and G. Poussigue, J . Mol. Spectrosc., 63, 402 (1976). K. Fox, Phys. Rev. Lett., 27, 233 (1971). J. K. G. Watson, J. Mol. Spectrosc., 40, 536 (1971). M. R. Aliev, JETPLett. (Engl. Trans.), 14, 417 (1971) [ Z h . Eksp. Teor. Fiz., Pis'ma Red., 14, 600 (1971)]. I. Ozier, Phys. Rev. Lett., 27, 1329 (1971). For a review, see for example, T. Oka in "Molecular Spectroscopy: Modern Research", Vol. 11, K. Narahari Rao, Ed., Academic Press, New York. 1976. DD 229-253. For a review, see {or example, M. R. Aliev, Prog. Phys. Sci., 119, 557 (1976); in Russian. For a revlew, see for example, K. Fox in "The Slgnificance of Nonlinearity in the Natural Sciences", A. Psrlmutter and L. F. Scott., Ed., Plenum Press, New York, 1977, pp 265-292. These "forbidden" transitions are generally much weaker than those alluded to In ref 2. K. Fox, Phys. Rev. A , 6, 907 (1972). C. W. Holt, M. C. L. Gerry, and I. Ozier, Can. J. Phys., 53, 1791 (1975). K. Fox and D. E. Jennings, Bull. Am. Phys. Soc., 23, 318 (1978); Astrophys. J . Lett., 226, L43 (1978). D. E. Jennings and K. Fox, manuscript in preparation. K. Fox and D. E. Jennings in "Proceedings of IAU Symposium No. 87 on Interstellar Molecules", B. H. Andrew, Ed., Reldel, Dordrecht, 1980. F. Mlchelot, J. Moret-Bailly, and K. Fox, J. Chem. Phys., 60, 2606 (1974). The formulation in eq 1 applies equally well to molecules of tetrahedral XY, symmetry, like CH, and octahedral XY8 symmetry, llke SF8. As the present work is on methane only, we have specialized the notation to that of the crystallographic point group Td. Note that the interstellar frequency near 78.2 GHz has two entries in Table I.These correspond to dlfferent observed velocity components, as discussed in detail in ref 16. Both possibilities are included in our calculations. I n Table 11, the only values given for the OSD, u, correspond to normallzed welghts defined In eq 2a-c. For each data set, the value of u computed for the unweighted fit is much greater than that for the weighted one. For example, for the second data set in Table 11, u(unweighted) = 37751 compared to u(weighted) = 799 Hz. Different notations are used for the GSC. The relatlonships between those in ref 14 and in eq 1 and Table 111here are eo = -17,.(3/7)'/*/2~ p o = -H,T(3/7)'/2/2 bo = -L,d3/7)1'2/2 Ea = -H,116(2)"*, c = -LeT/16(2)' *, and do = L8T/66(390)'/d.
Microwave Spectrum and Structure of Pyrrole-2-carbonitrile R. Wellington Davis and M. C. L. Gerry* Department of Chemistty, The University of British Columbia, Vancouver, British Columbia VBT 1WS, Canada (Received August 14, 1979)
Microwave spectra in the frequency region 26-75 GHz have been obtained for two isotopic species of pyrrole-z-carbonitrile. Rotational constants and centrifugal distortion constants have been obtained for both species. The molecule has been shown to be planar. Strong evidence is presented for distortion of the pyrrole ring at the substituted C2 atom.
Introduction The synthesis of pyrrole-Z-carbonitrile (I) was first re-
I
ported by Anderson,] and since then improved methods have been reported.2J It has recently been found as part of the neutral fraction of tobacco smoke condensate^.^ 0022-3654/80/2084-1767$01 .OO/O
There has been only a little spectroscopic study in both the and ultraviolet6g7regions. The electric dipole moment has, however, been measured by dielectric methods and has been found to be equal in magnitude to the vector sum of the dipole moments of pyrrole and benzonitrileS8 Pyrrole itself is one of a series of heterocyclic molecules with considerable aromatic character. There is much evidence for this, such as its planar structure, the close similarity of its nominally single and double CC bond lengths (1.417 and 1.382 A, respectivelyg), its ability to undergo
0 1980 American
Chemical Society
