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Microwave spectrum of the CHF2 radical in the 2 A′ ground electronic state: fluorine hyperfine structure alternation in inversion levels
20 February 1998
Chemical Physics Letters 284 Ž1998. 142–146
Microwave spectrum of the CHF2 radical in the 2AX ground electronic state: fluorine hyperfine structure alternation in inversion levels Naomi Inada a , Ko Saito a , Michiro Hayashi a , Hiroyuki Ozeki b, Shuji Saito a
b
Department of Chemistry, Faculty of Science, Hiroshima UniÕersity, Kagami-yama, Higashi-hiroshima 739, Japan b Institute for Molecular Science, Myodaiji, Okazaki 444, Japan Received 13 October 1997; in final form 21 November 1997
Abstract The rotational spectrum of the difluoromethyl radical was observed by microwave spectroscopy. Many b-type R and Q branch transitions accompanied with hyperfine structures due to fluorine and hydrogen nuclei were detected in the 100–400 GHz range. A preliminary analysis of the rotational transitions with I F s 0 and 1, where I F s I ŽF1 . q I ŽF2 ., resulted in finding fluorine hyperfine structure alternation for inversion levels: I F s 0 or 1 components of a particular rotational level correspond to the plus or minus inversion level, depending on the symmetry of the rotational level. The rotational constants and centrifugal distortion constants in both inversion levels were determined by a least-squares analysis for the hypothetical rotational transition frequencies. q 1998 Elsevier Science B.V.
1. Introduction The methyl radical and its halogenated derivatives have offered an interesting problem to high resolution spectroscopy: planarity of molecular structure. Many spectroscopic studies and quantum chemical calculations have been devoted to this problem. The CH 3 radical was concluded to be planar, having a relatively flat potential for its out-of-plane mode w1x. The CH 2 F radical shows a feature of quasiplanarity suggesting a small potential hump at the planar configuration w2x, whereas CH 2 Cl was found to be a well-behaved planar molecule w3x, but CF3 has a definitely pyramidal structure w4x. A tendency found for the 13 C hyperfine coupling constants of the fluorinated derivatives obtained from ESR studies was explained by a change in sp hybridization of C–X
bonds w5x. This was later supported by ab initio analyses w6,7x. The CHF2 radical was first identified in 1965 in an inert matrix by ESR spectroscopy w5x. Fessenden and Schuler studied the ESR spectra of 13 CHF2 as well as CHF2 . They determined the isotropic hyperfine coupling constants of the H, F and C nuclei and concluded that CHF2 has an umbrella angle of 12.78 using a relation between this angle and the carbon isotropic hyperfine coupling constant w5,8x. The infrared spectrum of CHF2 in solid argon was reported by Carver and Andrews in 1969 w9x, and three modes, n 2 , n 5 and n 6 , were assigned to CHF2 and CDF2 . This was confirmed later by Jacox w10x. Dearden et al. w11x studied the electronic spectra of CHF2 and CDF2 by resonance enhanced multiphoton ionization ŽREMPI. spectroscopy, which showed n XX s 1–5 hot
0009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 0 9 - 2 6 1 4 Ž 9 7 . 0 1 3 2 6 - 2
N. Inada et al.r Chemical Physics Letters 284 (1998) 142–146
˜ 2AX state. They modeled the hot bands bands of the X with a quartic double-well potential and obtained an inversion barrier in the ground electronic state, Vi s 2800 Ž500. cmy1 , with an out-of-plane angle of 49 Ž6.8, which predicted a separation between the inversion splitting of ground state to be 0.008 cmy1 . Several quantum chemical calculations were made to estimate various molecular properties of CHF2 and predicted its molecular structure, vibrational frequencies, inversion barrier and the hyperfine coupling constants of the F, H and C nuclei w11–16x. In the present study we detected the pure rotational spectrum of CHF2 with microwave spectroscopy and found fluorine hyperfine structure alternation for the inversion levels in the ground electronic state.
143
frequency region, an initial rotational assignment was made in the 100 GHz region. The assignment of the rotational fine and hyperfine structure transitions was made on the basis of the molecular structure from the ab initio calculation w16x, aided by the program for transition frequency calculation used for H 2 PO w19x and reported hyperfine coupling constants w5x. This analysis concluded that the radical responsible for these spectral lines was CHF2 in the ground electronic state. The optimum conditions for its production were partial pressures of 3 mTorr of CH 2 F2 and 3 mTorr of CF4 at the cell temperature of y100 to y120 8C. Thus, from about 470 observed spectral lines 32 b-type rotational transitions of CHF2 were assigned to 13 R branch and 19 Q branch transitions with K a s 1–0 and 2–1. Typical fine and hyperfine structural patterns are shown in Fig. 1.
2. Experimental The spectral lines of CHF2 were measured using a 100 kHz source-modulated spectrometer reported previously w17x. The radicals were produced by the reaction of CH 2 F2 with 2450 MHz discharge products in CF4 in an 80 cm free space absorption cell, which was pumped by a turbo-molecular pump of 200 lrs w18x. Many line groups were detected in the 100–400 GHz region. They were composed of ten or more spectral lines, closely distributed and assignable to presumably a single paramagnetic molecule. Since the spectral lines were so congested in the higher
Fig. 1. Stick diagram of observed fine and hyperfine structure for the r Q1 branch transitions with N s15–17. Asterisks indicate the hyperfine components of IF s 0.
3. Results and discussion The assignment of the rotational quantum numbers for the spectral lines was established, but it was difficult to derive a set of molecular parameters generally applicable to all observed rotational transitions. The observed spectral lines of the rotational transitions were considered to be composite hyperfine structures of one hydrogen nucleus and two fluorine nuclei giving I F s 0 and I F s 1 Ž I F s I ŽF1 . q I ŽF2 .. and their definite assignments were made as described above. However, a preliminary analysis of the Q branch rotational transitions showed that the line frequencies of I F s 0 changed zigzag relative to those of I F s 1, depending on the evenness or oddness of the rotational quantum number, as exemplified in Fig. 1. This feature resulted in the finding that the I F s 0 or 1 components of a particular rotational level correspond to the plus Ž0q. or minus Ž0y. inversion level, depending on the symmetry of the rotational level, where 0q and 0y denote the symmetric and antisymmetric levels of inversion motion in the Õ s 0 ground state, respectively. As a result, we concluded that for the 0q Žlower. inversion level the K a K c s ee or oo symmetric rotational level combines with the symmetric spin function of I F s 1, giving 12 components in total, and the eo or oe antisymmetric rotational level combines with the an-
N. Inada et al.r Chemical Physics Letters 284 (1998) 142–146
144
tisymmetric spin function of I F s 0, resulting in 4 components in total, whereas for 0y Župper. inversion level, the combination between rotational symmetry and spin symmetry is reversed. This means that the molecular constants for both the inversion levels are so similar that the hyperfine components of the levels are mingled to give a single hyperfine pattern for a rotational transition, as demonstrated in
Fig. 1. Such hyperfine structure alternation in the inversion levels of the free radical generally appears as the nuclear spin statistical weight in a singlet diamagnetic molecule with appropriate symmetry. This is the first case where hyperfine structure alternation was observed for the inversion doubling. The exact assignment of the spectral lines was established, but the analysis of the observed line
Table 1 ˜ 2AX . ŽMHz. Hypothetical rotational transition frequencies obtained from observed spectral line frequencies of CHF2 ŽX X NK aX K cX –
NK a K c
q. b
y. c
G.S.Ž0 nobs
G.S.Ž0 nobs
313 – 2 02 4 14 – 3 03 515 – 4 04 6 16 – 505 717 – 6 06
132357.50Žy11.27. 149585.58Žy0.19. 166261.09Ž0.13. 182489.49Ž0.05.
707 – 6 16 8 08 – 717 9 09 – 818 10 0,10 – 919
99750.07Ž 4.72. d 123542.82Žy0.12. 147339.70Ž0.19. 171011.33Žy0.04.
99750.48Žy0.07. 123549.72Ž1.02. d 147344.67Žy1.22. 171018.33Ž0.02.
10 19 – 10 0,10 111,10 – 11 0,11 12 1,11 – 12 0,12 131,12 – 130,13 14 1,13 – 14 0,14 151,14 – 150,15
105682.30Ž1.55. d 117231.23Ž0.15. 130262.64Žy0.03. 144751.01Žy0.10. 160627.19Žy0.02. 177779.68Ž0.04.
105674.62Žy0.23. 117224.50Žy0.02. 130255.42Ž0.01. 144743.26Ž0.09. 160619.01Ž0.27. 177770.85Žy0.21.
111,10 – 10 29 12 1,11 – 11 2,10 131,12 – 12 2,11 14 1,13 – 132,12
100585.56Ž0.05. 128510.62Žy0.11. 156750.41Žy0.03. 185214.41Ž0.05.
100600.64Ž1.52. d 128525.25Ž0.02. 156764.46Žy0.53. 185227.93Žy0.01.
4 23 – 4 14 524 – 515 6 25 – 6 16 6 24 – 6 15 725 – 716 8 26 – 817 9 27 – 918 152,13 – 151,14 16 2,14 – 16 1,15 172,15 – 171,16 18 2,16 – 181,17 19 2,17 – 191,18 20 2,18 – 20 1,19 a
177843.99Žy0.09. 181490.37Žy0.55. 185886.65Ž0.10.
d
d
157652.92Žy7.49. d 154277.15Žy21.34. d 151047.60Ž27.78. d 148032.47Ž7.55. d 146728.17Žy0.09. 150770.65Žy0.05. 156350.82Žy0.05. 163553.27Ž0.09. 172443.17Ž0.14. 183061.45Žy0.10.
114529.24Žy1.49. 132365.13Žy0.14. 149582.44Ž0.27. 166257.95Ž0.51. d 182486.18Žy0.09.
177843.50Ž0.05. 181489.17Ž0.74. 185885.76Ž3.77.
d
d
d
d d
157654.35Žy1.36. 154290.69Žy1.19. 151010.99Žy0.47. 148014.95Žy0.11. 146716.78Ž0.20. 150759.48Ž0.01. 156339.97Žy0.05. 163542.44Žy0.14. 172432.16Žy0.39. 183051.26Ž0.05.
Calculated frequencies were obtained from the molecular constants given in Table 2. Residuals in the least-squares fit are given in parentheses. Standard deviation of the fit is 0.144 MHz. c Residuals in the least-squares fit are given in parentheses. Standard deviation of the fit is 0.228 MHz. d Not included in the fit. b
d
d d d
d
a
N. Inada et al.r Chemical Physics Letters 284 (1998) 142–146
frequencies was still not straightforward. The molecular constants for one R or Q branch series of transitions were somewhat different. Therefore, the hypothetical rotational transition frequencies without fine and hyperfine structure shifts were calculated from a set of the rotational and centrifugal distortion constants obtained by a least-squares fit of the fine and hyperfine structures of each rotational transition. The hypothetical rotational transition frequencies obtained are listed in Table 1. The spin-rotation coupling constants and the fluorine and hydrogen hyperfine coupling constants obtained depended on the spectral lines fitted. The spin-rotation coupling constants used to derive the hypothetical rotational frequencies are typically ´ a a ; y360, ´ b b ; y54 and ´ cc ; y1 MHz, the fluorine hyperfine coupling constants a F ŽF. ; 250, Ta aŽF. ; y230, and Tb b ŽF. ; y150 MHz and the hydrogen hyperfine coupling constants a F ; 60, Ta aŽH. ; y29 and Tb b ŽH. ; 24 MHz. A more conclusive analysis of the observed fine and hyperfine structures and a discussion on their parameters will be reported in a separate paper. These hypothetical transition frequencies were subjected to a least-squares fit and the rotational and centrifugal distortion constants were determined for both inversion levels, as listed in Table 2. The calculated rotational transition frequencies are comTable 2 ˜ 2AX . ŽMHz. Molecular constants of CHF2 ŽX Constant A0 B0 C0
pared with the hypothetical rotational frequencies in Table 1. Since the errors of the hypothetical frequencies are estimated to be a few hundred kilohertz, most of the hypothetical rotational transition frequencies were reasonably explained within the errors by the molecular constants given in Table 2. An explanation of the local perturbations found in the K a s 2–1 Q branch N s 6–9 transitions and small shifts in other transitions was attempted by an X–Ytype Coriolis tunneling interaction w20,21x. The energy separation between the inversion levels and the interaction term between the inversion doubling were not determinable from the hypothetical line frequencies. However, the close similarity of the molecular constants for both inversion levels suggests that the barrier to inversion is relatively high and the energy separation between the doubling is small, as predicted by an ab initio calculation w11x. After the analysis described above, a trial search for inter-inversion transitions was made, but without success. The molecular structure of CHF2 was determined from the tentative rotational constants for the 0q inversion level of the ground state. When the C-H ˚ bond length is assumed to be 1.087 Afrom an ab initio calculation w16x, the C–F bond length is calcu˚ the FCF angle to be lated to be 1.3245Ž26. A, 111.53Ž15.8, and the HCF angle to be 113.76Ž17.8,
a
G.S.Ž0q . 67204.63Ž36. 11043.301Ž35. 9607.475Ž47.
G.S.Ž0y . 67201.08Ž35. 11042.925Ž66. 9607.801Ž78.
DN DN K DK dN dK
0.01106Ž30. y0.1274Ž51. 1.833Ž77. 0.002129Ž50. 0.068Ž25.
0.00991Ž27. y0.0900Ž58. 0.911Ž80. 0.00229Ž43. y0.153Ž41.
FN FNK FK N FK fN fN K fK
y0.00000179Ž115. 0.000016Ž57. 0.00041Ž112. 0.0 b 0.0 b 0.0 b 0.0055Ž47.
y0.00000433Ž96. y0.000308Ž88. y0.00471Ž136. 0.0 b 0.0 b y0.000132Ž32. y0.0260Ž57.
a b
145
Values in parentheses denote one standard deviation and apply to the last digits. Fixed.
146
N. Inada et al.r Chemical Physics Letters 284 (1998) 142–146
where errors given in parentheses are estimated from the errors in the r 0 structures of similar molecules w22,23x, which mainly arise from the contribution of the zero-point vibrations. The structure determined, gives an umbrella angle of 15.63Ž20.8. The structure obtained in the present study agrees well with that ˚ reported by Barone et al. w16x: r ŽC–F. s 1.327 A, u ŽFCF. s 111.548, u ŽHCF. s 113.698, and the umbrella angle of 16.38. In conclusion, the rotational spectrum of the CHF2 radical in the ground electronic state observed by microwave spectroscopy is assigned to the two lowest inversion levels and the fluorine hyperfine structure alternation due to the symmetry of the inversion levels is observed. This is the first case where hyperfine structure alternation is observed for the inversion doubling. A trial analysis aimed at the determination of the energy separation between the inversion levels and the D K s "1 Coriolis-type tunneling interaction terms was made, but both the parameters were not determinable at present. The rotational constants and centrifugal distortion constants in both inversion levels were determined by a least-squares analysis for the hypothetical rotational frequencies. This preliminary analysis of the hypothetical rotation transition frequencies suggests a high barrier to inversion for CHF2 , with presumably, a small inversion doubling.
Acknowledgements Calculations in the present study were carried out at the Computer Center of the Institute for Molecular Science.
References w1x C. Yamada, E. Hirota, K. Kawaguchi, J. Chem. Phys. 75 Ž1981. 5256. w2x Y. Endo, C. Yamada, S. Saito, E. Hirota, J. Chem. Phys. 79 Ž1983. 1605. w3x Y. Endo, S. Saito, E. Hirota, Can. J. Phys. 62 Ž1984. 1347. w4x Y. Endo, C. Yamada, S. Saito, E. Hirota, J. Chem. Phys. 77 Ž1982. 3376. w5x R.W. Fessenden, R.H. Schuler, J. Chem. Phys. 43 Ž1965. 2074. w6x K. Morokuma, L. Pedersen, M. Karplus, J. Chem. Phys. 48 Ž1968. 4801. w7x D.L. Beveridge, P.A. Dobosh, J.A. Pople, J. Chem. Phys. 48 Ž1968. 4801. w8x D.M. Schrader, M. Karplus, J. Chem. Phys. 40 Ž1964. 1593. w9x T.G. Carver, L. Andrews, J. Chem. Phys. 50 Ž1969. 5100. w10x M.E. Jacox, J. Mol. Spectrosc. 81 Ž1980. 349. w11x D.V. Dearden, J.W. Hudgens, R.D. Johnson III, B.P. Tsai, S.A. Kafafi, J. Phys. Chem. 96 Ž1992. 585. w12x G. Leroy, D. Peeters, J. Mol. Struct. 85 Ž1981. 133. w13x B.T. Luke, G.H. Loew, A.D. McLean, J. Am. Chem. Soc. 109 Ž1987. 1307. w14x C.J. Cramer, J. Org. Chem. 56 Ž1991. 5229. w15x Y. Chen, E. Tschuikow-Roux, J. Phys. Chem. 97 Ž1993. 3742. w16x V. Barone, A. Grand, C. Minichino, R. Subra, J. Chem. Phys. 99 Ž1993. 6787. w17x S. Saito, M. Goto, Astrophys. J. 410 Ž1993. L53. w18x H. Mikami, S. Saito, S. Yamamoto, J. Chem. Phys. 94 Ž1991. 3415. w19x T. Hirao, S. Saito, H. Ozeki, J. Chem. Phys. 105 Ž1996. 3450. w20x D.R. Lide Jr., J. Mol. Spectrosc. 8 Ž1962. 142. w21x D.R. Johnson, R.D. Suenram, W.J. Lafferty, Astrophys. J. 208 Ž1976. L45. w22x W.H. Kirchhoff, D.R. Lide, F.X. Powell, J. Mol. Spectrosc. 47 Ž1973. 491. w23x E. Hirota, T. Tanaka, A. Sakakibara, Y. Ohashi, Y. Morino, J. Mol. Spectrosc. 34 Ž1970. 222.
Chemical Physics Letters 284 Ž1998. 142–146
Microwave spectrum of the CHF2 radical in the 2AX ground electronic state: fluorine hyperfine structure alternation in inversion levels Naomi Inada a , Ko Saito a , Michiro Hayashi a , Hiroyuki Ozeki b, Shuji Saito a
b
Department of Chemistry, Faculty of Science, Hiroshima UniÕersity, Kagami-yama, Higashi-hiroshima 739, Japan b Institute for Molecular Science, Myodaiji, Okazaki 444, Japan Received 13 October 1997; in final form 21 November 1997
Abstract The rotational spectrum of the difluoromethyl radical was observed by microwave spectroscopy. Many b-type R and Q branch transitions accompanied with hyperfine structures due to fluorine and hydrogen nuclei were detected in the 100–400 GHz range. A preliminary analysis of the rotational transitions with I F s 0 and 1, where I F s I ŽF1 . q I ŽF2 ., resulted in finding fluorine hyperfine structure alternation for inversion levels: I F s 0 or 1 components of a particular rotational level correspond to the plus or minus inversion level, depending on the symmetry of the rotational level. The rotational constants and centrifugal distortion constants in both inversion levels were determined by a least-squares analysis for the hypothetical rotational transition frequencies. q 1998 Elsevier Science B.V.
1. Introduction The methyl radical and its halogenated derivatives have offered an interesting problem to high resolution spectroscopy: planarity of molecular structure. Many spectroscopic studies and quantum chemical calculations have been devoted to this problem. The CH 3 radical was concluded to be planar, having a relatively flat potential for its out-of-plane mode w1x. The CH 2 F radical shows a feature of quasiplanarity suggesting a small potential hump at the planar configuration w2x, whereas CH 2 Cl was found to be a well-behaved planar molecule w3x, but CF3 has a definitely pyramidal structure w4x. A tendency found for the 13 C hyperfine coupling constants of the fluorinated derivatives obtained from ESR studies was explained by a change in sp hybridization of C–X
bonds w5x. This was later supported by ab initio analyses w6,7x. The CHF2 radical was first identified in 1965 in an inert matrix by ESR spectroscopy w5x. Fessenden and Schuler studied the ESR spectra of 13 CHF2 as well as CHF2 . They determined the isotropic hyperfine coupling constants of the H, F and C nuclei and concluded that CHF2 has an umbrella angle of 12.78 using a relation between this angle and the carbon isotropic hyperfine coupling constant w5,8x. The infrared spectrum of CHF2 in solid argon was reported by Carver and Andrews in 1969 w9x, and three modes, n 2 , n 5 and n 6 , were assigned to CHF2 and CDF2 . This was confirmed later by Jacox w10x. Dearden et al. w11x studied the electronic spectra of CHF2 and CDF2 by resonance enhanced multiphoton ionization ŽREMPI. spectroscopy, which showed n XX s 1–5 hot
0009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 0 9 - 2 6 1 4 Ž 9 7 . 0 1 3 2 6 - 2
N. Inada et al.r Chemical Physics Letters 284 (1998) 142–146
˜ 2AX state. They modeled the hot bands bands of the X with a quartic double-well potential and obtained an inversion barrier in the ground electronic state, Vi s 2800 Ž500. cmy1 , with an out-of-plane angle of 49 Ž6.8, which predicted a separation between the inversion splitting of ground state to be 0.008 cmy1 . Several quantum chemical calculations were made to estimate various molecular properties of CHF2 and predicted its molecular structure, vibrational frequencies, inversion barrier and the hyperfine coupling constants of the F, H and C nuclei w11–16x. In the present study we detected the pure rotational spectrum of CHF2 with microwave spectroscopy and found fluorine hyperfine structure alternation for the inversion levels in the ground electronic state.
143
frequency region, an initial rotational assignment was made in the 100 GHz region. The assignment of the rotational fine and hyperfine structure transitions was made on the basis of the molecular structure from the ab initio calculation w16x, aided by the program for transition frequency calculation used for H 2 PO w19x and reported hyperfine coupling constants w5x. This analysis concluded that the radical responsible for these spectral lines was CHF2 in the ground electronic state. The optimum conditions for its production were partial pressures of 3 mTorr of CH 2 F2 and 3 mTorr of CF4 at the cell temperature of y100 to y120 8C. Thus, from about 470 observed spectral lines 32 b-type rotational transitions of CHF2 were assigned to 13 R branch and 19 Q branch transitions with K a s 1–0 and 2–1. Typical fine and hyperfine structural patterns are shown in Fig. 1.
2. Experimental The spectral lines of CHF2 were measured using a 100 kHz source-modulated spectrometer reported previously w17x. The radicals were produced by the reaction of CH 2 F2 with 2450 MHz discharge products in CF4 in an 80 cm free space absorption cell, which was pumped by a turbo-molecular pump of 200 lrs w18x. Many line groups were detected in the 100–400 GHz region. They were composed of ten or more spectral lines, closely distributed and assignable to presumably a single paramagnetic molecule. Since the spectral lines were so congested in the higher
Fig. 1. Stick diagram of observed fine and hyperfine structure for the r Q1 branch transitions with N s15–17. Asterisks indicate the hyperfine components of IF s 0.
3. Results and discussion The assignment of the rotational quantum numbers for the spectral lines was established, but it was difficult to derive a set of molecular parameters generally applicable to all observed rotational transitions. The observed spectral lines of the rotational transitions were considered to be composite hyperfine structures of one hydrogen nucleus and two fluorine nuclei giving I F s 0 and I F s 1 Ž I F s I ŽF1 . q I ŽF2 .. and their definite assignments were made as described above. However, a preliminary analysis of the Q branch rotational transitions showed that the line frequencies of I F s 0 changed zigzag relative to those of I F s 1, depending on the evenness or oddness of the rotational quantum number, as exemplified in Fig. 1. This feature resulted in the finding that the I F s 0 or 1 components of a particular rotational level correspond to the plus Ž0q. or minus Ž0y. inversion level, depending on the symmetry of the rotational level, where 0q and 0y denote the symmetric and antisymmetric levels of inversion motion in the Õ s 0 ground state, respectively. As a result, we concluded that for the 0q Žlower. inversion level the K a K c s ee or oo symmetric rotational level combines with the symmetric spin function of I F s 1, giving 12 components in total, and the eo or oe antisymmetric rotational level combines with the an-
N. Inada et al.r Chemical Physics Letters 284 (1998) 142–146
144
tisymmetric spin function of I F s 0, resulting in 4 components in total, whereas for 0y Župper. inversion level, the combination between rotational symmetry and spin symmetry is reversed. This means that the molecular constants for both the inversion levels are so similar that the hyperfine components of the levels are mingled to give a single hyperfine pattern for a rotational transition, as demonstrated in
Fig. 1. Such hyperfine structure alternation in the inversion levels of the free radical generally appears as the nuclear spin statistical weight in a singlet diamagnetic molecule with appropriate symmetry. This is the first case where hyperfine structure alternation was observed for the inversion doubling. The exact assignment of the spectral lines was established, but the analysis of the observed line
Table 1 ˜ 2AX . ŽMHz. Hypothetical rotational transition frequencies obtained from observed spectral line frequencies of CHF2 ŽX X NK aX K cX –
NK a K c
q. b
y. c
G.S.Ž0 nobs
G.S.Ž0 nobs
313 – 2 02 4 14 – 3 03 515 – 4 04 6 16 – 505 717 – 6 06
132357.50Žy11.27. 149585.58Žy0.19. 166261.09Ž0.13. 182489.49Ž0.05.
707 – 6 16 8 08 – 717 9 09 – 818 10 0,10 – 919
99750.07Ž 4.72. d 123542.82Žy0.12. 147339.70Ž0.19. 171011.33Žy0.04.
99750.48Žy0.07. 123549.72Ž1.02. d 147344.67Žy1.22. 171018.33Ž0.02.
10 19 – 10 0,10 111,10 – 11 0,11 12 1,11 – 12 0,12 131,12 – 130,13 14 1,13 – 14 0,14 151,14 – 150,15
105682.30Ž1.55. d 117231.23Ž0.15. 130262.64Žy0.03. 144751.01Žy0.10. 160627.19Žy0.02. 177779.68Ž0.04.
105674.62Žy0.23. 117224.50Žy0.02. 130255.42Ž0.01. 144743.26Ž0.09. 160619.01Ž0.27. 177770.85Žy0.21.
111,10 – 10 29 12 1,11 – 11 2,10 131,12 – 12 2,11 14 1,13 – 132,12
100585.56Ž0.05. 128510.62Žy0.11. 156750.41Žy0.03. 185214.41Ž0.05.
100600.64Ž1.52. d 128525.25Ž0.02. 156764.46Žy0.53. 185227.93Žy0.01.
4 23 – 4 14 524 – 515 6 25 – 6 16 6 24 – 6 15 725 – 716 8 26 – 817 9 27 – 918 152,13 – 151,14 16 2,14 – 16 1,15 172,15 – 171,16 18 2,16 – 181,17 19 2,17 – 191,18 20 2,18 – 20 1,19 a
177843.99Žy0.09. 181490.37Žy0.55. 185886.65Ž0.10.
d
d
157652.92Žy7.49. d 154277.15Žy21.34. d 151047.60Ž27.78. d 148032.47Ž7.55. d 146728.17Žy0.09. 150770.65Žy0.05. 156350.82Žy0.05. 163553.27Ž0.09. 172443.17Ž0.14. 183061.45Žy0.10.
114529.24Žy1.49. 132365.13Žy0.14. 149582.44Ž0.27. 166257.95Ž0.51. d 182486.18Žy0.09.
177843.50Ž0.05. 181489.17Ž0.74. 185885.76Ž3.77.
d
d
d
d d
157654.35Žy1.36. 154290.69Žy1.19. 151010.99Žy0.47. 148014.95Žy0.11. 146716.78Ž0.20. 150759.48Ž0.01. 156339.97Žy0.05. 163542.44Žy0.14. 172432.16Žy0.39. 183051.26Ž0.05.
Calculated frequencies were obtained from the molecular constants given in Table 2. Residuals in the least-squares fit are given in parentheses. Standard deviation of the fit is 0.144 MHz. c Residuals in the least-squares fit are given in parentheses. Standard deviation of the fit is 0.228 MHz. d Not included in the fit. b
d
d d d
d
a
N. Inada et al.r Chemical Physics Letters 284 (1998) 142–146
frequencies was still not straightforward. The molecular constants for one R or Q branch series of transitions were somewhat different. Therefore, the hypothetical rotational transition frequencies without fine and hyperfine structure shifts were calculated from a set of the rotational and centrifugal distortion constants obtained by a least-squares fit of the fine and hyperfine structures of each rotational transition. The hypothetical rotational transition frequencies obtained are listed in Table 1. The spin-rotation coupling constants and the fluorine and hydrogen hyperfine coupling constants obtained depended on the spectral lines fitted. The spin-rotation coupling constants used to derive the hypothetical rotational frequencies are typically ´ a a ; y360, ´ b b ; y54 and ´ cc ; y1 MHz, the fluorine hyperfine coupling constants a F ŽF. ; 250, Ta aŽF. ; y230, and Tb b ŽF. ; y150 MHz and the hydrogen hyperfine coupling constants a F ; 60, Ta aŽH. ; y29 and Tb b ŽH. ; 24 MHz. A more conclusive analysis of the observed fine and hyperfine structures and a discussion on their parameters will be reported in a separate paper. These hypothetical transition frequencies were subjected to a least-squares fit and the rotational and centrifugal distortion constants were determined for both inversion levels, as listed in Table 2. The calculated rotational transition frequencies are comTable 2 ˜ 2AX . ŽMHz. Molecular constants of CHF2 ŽX Constant A0 B0 C0
pared with the hypothetical rotational frequencies in Table 1. Since the errors of the hypothetical frequencies are estimated to be a few hundred kilohertz, most of the hypothetical rotational transition frequencies were reasonably explained within the errors by the molecular constants given in Table 2. An explanation of the local perturbations found in the K a s 2–1 Q branch N s 6–9 transitions and small shifts in other transitions was attempted by an X–Ytype Coriolis tunneling interaction w20,21x. The energy separation between the inversion levels and the interaction term between the inversion doubling were not determinable from the hypothetical line frequencies. However, the close similarity of the molecular constants for both inversion levels suggests that the barrier to inversion is relatively high and the energy separation between the doubling is small, as predicted by an ab initio calculation w11x. After the analysis described above, a trial search for inter-inversion transitions was made, but without success. The molecular structure of CHF2 was determined from the tentative rotational constants for the 0q inversion level of the ground state. When the C-H ˚ bond length is assumed to be 1.087 Afrom an ab initio calculation w16x, the C–F bond length is calcu˚ the FCF angle to be lated to be 1.3245Ž26. A, 111.53Ž15.8, and the HCF angle to be 113.76Ž17.8,
a
G.S.Ž0q . 67204.63Ž36. 11043.301Ž35. 9607.475Ž47.
G.S.Ž0y . 67201.08Ž35. 11042.925Ž66. 9607.801Ž78.
DN DN K DK dN dK
0.01106Ž30. y0.1274Ž51. 1.833Ž77. 0.002129Ž50. 0.068Ž25.
0.00991Ž27. y0.0900Ž58. 0.911Ž80. 0.00229Ž43. y0.153Ž41.
FN FNK FK N FK fN fN K fK
y0.00000179Ž115. 0.000016Ž57. 0.00041Ž112. 0.0 b 0.0 b 0.0 b 0.0055Ž47.
y0.00000433Ž96. y0.000308Ž88. y0.00471Ž136. 0.0 b 0.0 b y0.000132Ž32. y0.0260Ž57.
a b
145
Values in parentheses denote one standard deviation and apply to the last digits. Fixed.
146
N. Inada et al.r Chemical Physics Letters 284 (1998) 142–146
where errors given in parentheses are estimated from the errors in the r 0 structures of similar molecules w22,23x, which mainly arise from the contribution of the zero-point vibrations. The structure determined, gives an umbrella angle of 15.63Ž20.8. The structure obtained in the present study agrees well with that ˚ reported by Barone et al. w16x: r ŽC–F. s 1.327 A, u ŽFCF. s 111.548, u ŽHCF. s 113.698, and the umbrella angle of 16.38. In conclusion, the rotational spectrum of the CHF2 radical in the ground electronic state observed by microwave spectroscopy is assigned to the two lowest inversion levels and the fluorine hyperfine structure alternation due to the symmetry of the inversion levels is observed. This is the first case where hyperfine structure alternation is observed for the inversion doubling. A trial analysis aimed at the determination of the energy separation between the inversion levels and the D K s "1 Coriolis-type tunneling interaction terms was made, but both the parameters were not determinable at present. The rotational constants and centrifugal distortion constants in both inversion levels were determined by a least-squares analysis for the hypothetical rotational frequencies. This preliminary analysis of the hypothetical rotation transition frequencies suggests a high barrier to inversion for CHF2 , with presumably, a small inversion doubling.
Acknowledgements Calculations in the present study were carried out at the Computer Center of the Institute for Molecular Science.
References w1x C. Yamada, E. Hirota, K. Kawaguchi, J. Chem. Phys. 75 Ž1981. 5256. w2x Y. Endo, C. Yamada, S. Saito, E. Hirota, J. Chem. Phys. 79 Ž1983. 1605. w3x Y. Endo, S. Saito, E. Hirota, Can. J. Phys. 62 Ž1984. 1347. w4x Y. Endo, C. Yamada, S. Saito, E. Hirota, J. Chem. Phys. 77 Ž1982. 3376. w5x R.W. Fessenden, R.H. Schuler, J. Chem. Phys. 43 Ž1965. 2074. w6x K. Morokuma, L. Pedersen, M. Karplus, J. Chem. Phys. 48 Ž1968. 4801. w7x D.L. Beveridge, P.A. Dobosh, J.A. Pople, J. Chem. Phys. 48 Ž1968. 4801. w8x D.M. Schrader, M. Karplus, J. Chem. Phys. 40 Ž1964. 1593. w9x T.G. Carver, L. Andrews, J. Chem. Phys. 50 Ž1969. 5100. w10x M.E. Jacox, J. Mol. Spectrosc. 81 Ž1980. 349. w11x D.V. Dearden, J.W. Hudgens, R.D. Johnson III, B.P. Tsai, S.A. Kafafi, J. Phys. Chem. 96 Ž1992. 585. w12x G. Leroy, D. Peeters, J. Mol. Struct. 85 Ž1981. 133. w13x B.T. Luke, G.H. Loew, A.D. McLean, J. Am. Chem. Soc. 109 Ž1987. 1307. w14x C.J. Cramer, J. Org. Chem. 56 Ž1991. 5229. w15x Y. Chen, E. Tschuikow-Roux, J. Phys. Chem. 97 Ž1993. 3742. w16x V. Barone, A. Grand, C. Minichino, R. Subra, J. Chem. Phys. 99 Ž1993. 6787. w17x S. Saito, M. Goto, Astrophys. J. 410 Ž1993. L53. w18x H. Mikami, S. Saito, S. Yamamoto, J. Chem. Phys. 94 Ž1991. 3415. w19x T. Hirao, S. Saito, H. Ozeki, J. Chem. Phys. 105 Ž1996. 3450. w20x D.R. Lide Jr., J. Mol. Spectrosc. 8 Ž1962. 142. w21x D.R. Johnson, R.D. Suenram, W.J. Lafferty, Astrophys. J. 208 Ž1976. L45. w22x W.H. Kirchhoff, D.R. Lide, F.X. Powell, J. Mol. Spectrosc. 47 Ž1973. 491. w23x E. Hirota, T. Tanaka, A. Sakakibara, Y. Ohashi, Y. Morino, J. Mol. Spectrosc. 34 Ž1970. 222.