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Diode Laser Spectroscopy of Trifluoroethylene in the 8.6-μm Region
JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.
190, 248 –261 (1998)
MS987598
Diode Laser Spectroscopy of Trifluoroethylene in the 8.6-mm Region R. Visinoni, S. Giorgianni, A. Baldacci, and S. Ghersetti Universita` di Venezia, Dipartimento di Chimica Fisica, D. D. 2137, I-30123 Venezia, Italy Received December 5, 1997; in revised form March 26, 1998
The two mid-infrared bands of the CF2 ACHF molecule, n5 centered at 1172.673 cm21 and n6 1 n9 at 1155.105 cm21, were measured on a tunable diode laser spectrometer with a resolution near the Doppler limit. These vibrations of A9 species give rise to a/b hybrid bands, even though our analysis has pointed out that the intensity of the a-type component is predominant. Most of the J and K structure has been resolved in different subbranches, and the rovibrational analysis led to the assignment of about 1400 (J # 60, Ka # 22, Kc # 60) and 90 (J # 56, Ka # 5, Kc # 56) lines of the n5 and n6 1 n9 bands, respectively. Using Watson’s A-reduction Hamiltonian in the I r representation, a set of accurate spectroscopic constants for the upper states has been derived from transitions free of major resonance effects. The rotational structure of the n5 vibration also exhibits effects of Coriolis perturbation by a state identified as n7 1 n11. Parameters for the perturber were determined from the interaction effects near the observed crossings, using a dyad model including first-order b-Coriolis interaction. © 1998 Academic Press I. INTRODUCTION
As a part of high-resolution infrared studies of the trifluoethylene molecule, initiated with the analysis of the n3 and n4 fundamentals (1, 2), the present paper reports the results of the investigation of the spectral region around 1170 cm21. CF2 ACHF is believed to be a component of a certain importance in the atmospheric chemistry and, since infrared spectroscopy is a very powerful method for detecting trace gases, the determination of accurate spectroscopic parameters becomes useful. Infrared spectra of CF2 ACHF have been already investigated at low resolution many years ago by some workers (3, 4). Besides, microwave spectra have been measured and interpreted to evaluate the molecular parameters for the ground and vibrationally excited states (5, 6); the combined analysis of microwave and electron diffraction data provided some structural information on this molecule (7). This paper deals with the analysis of the rovibrational features arising from the strong n5 fundamental and the weaker n6 1 n9 combination. Upper state molecular parameters and results concerning the observed perturbation effects are reported. II. EXPERIMENTAL DETAILS
The gas sample of CF2 ACHF (99% pure), supplied by Peninsular Chemical Research, Inc., was used without further purification. The infrared spectrum was recorded in the range 1143–1184 cm21 using the tunable diode laser spectrometer at the University of Venice. The arrangement of the instrument is mainly based on the SP-5000 assembly of Laser Analytics, Inc.; in the present version the spectrophotometer setup is in a triple beam configuration so that the sample spectrum, the calibration lines, and the reference signal from a solid germa-
nium e´talon are recorded simultaneously. The instrument is interfaced to a PC that provides data acquisition, storage, and conversion into transmittance of the spectra. The gas sample was contained in a 49-cm cell with KBr windows at a pressure of 0.3 mbar; the temperature was kept at 240 K in order to reduce hot band absorptions. The spectrum was calibrated using standard lines of N2O (8) and the interference patterns from a 2.59-cm germanium e´talon with FSR > 0.0475 cm21. The absolute wavenumber accuracy is estimated to be of the order of 0.001 cm21. The computed Doppler line width (FWHM) is 0.0015 cm21, while the measured full width at half maximum is about 0.002 cm21. III. RESULTS AND DISCUSSION
Trifluoroethylene is a planar near-prolate molecule (k 5 20.74) of CS symmetry with 12 fundamentals; the 9 modes of A9 symmetry (n1 2 n9) give rise to a/b hybrid bands, while the 3 modes of species A0 (n10 2 n12) produce c-type band contours. The spectrum has been analyzed in the range 1143–1184 cm21, where two bands, separated by about 18 cm21, are observed; the stronger absorption at higher wavenumbers (>1173 cm21) corresponds to the n5 fundamental, while the weaker one, located around 1155 cm21 and partially overlapped by the n5 features, has been attributed to the n6 1 n9 vibration. Additional combinations, too weak to be observed, are expected to occur in this region and to interact with the n5 and n6 1 n9 levels. Description of the n5 and n6 1 n9 Bands The spectral analysis started with the assignment of the more prominent features pertaining to the n5 fundamental. This mode, corresponding to the CFH bending vibration, gives rise to an a/b-hybrid band. The high-resolution infrared spectrum
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ANALYSIS OF CF2 ACHF IN THE 8.6 mm REGION
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FIG. 1. A section of the P-branch spectrum of the CF2 ACHF n5 band near 1169.4 cm21 (T 5 240 K, P > 0.3 mbar, 49-cm cell). The fine structure of the PK(15) manifold is indicated; asymmetry splitting is observed.
Q
shows a predominant a-type envelope with a strong partially resolved Q branch degrading toward lower wavenumbers; the P-branch features heavily overlap the weak absorptions of n6 1 n9. Following the selection rules for the a-type transitions (DJ 5 0, 61, DKa 5 0, DKc 5 61) several even and odd subbranches are expected in the P, Q, and R branches depending on (K0a 1 K0c 5 J0) or (K0a 1 K0c 5 J0 1 1), respectively. Basically, the structure of this band is very similar to that of the n4 fundamental (2), and two different types of clusters formed by e,oP(0, 21) and e,oR(0, 1) subbranches have been identified in the P and R branches. The manifolds exhibit regular structure close to the band center, but, as J increases, the lines of contiguous groups overlap each other producing a considerably dense rotational structure. The first type of clusters, with a characteristic spacing of (B 1 C) > 0.22 cm21, is associated with transitions having the same J value and displaying the typical pattern of a parallel band of a symmetric top. As an example, the spectrum of the P branch near 1169 cm21 is illustrated in Fig. 1, where the details of the QPK(15) group are indicated; the asymmetry splitting is observed for Ka # 6. It is worth noting that the transitions with Ka 5 0 and Ka 5 12 are almost degenerate. The second type of clusters is composed of a series of lines defined by a Jmax value and degrading toward higher wave-
numbers. The line that starts the series has J0 5 K 0c and the successive lines have J decreasing by 1 and Kc by 2. The separation between adjacent clusters is 2C > 0.20 cm21. A typical series of lines in the R-branch region around 1181 cm21 is depicted in Fig. 2, which illustrates the structure of the groups with Jmax 5 45– 47. The reproduced details indicate 2 that in many cases levels with K1 a and (Ka 1 1) are almost degenerate. Features of this type, characteristic of spectra of planar molecules, are due to the near coincidence of transitions between energy levels that become degenerate in the oblate symmetric top limit for high Kc values. The degeneration effect appears evident for low Ka values and the computed reduced energy levels (see later in Fig. 4) show that the pairs levels J0,J /J1,J and J1,J21/J2,J21 become almost degenerate for J $ 19 and 25, respectively. The Q branch appears at first glance not easy to be analyzed because the structure is very packed and the subbranches eQ(0, 1) and oQ(0, 21) are mostly overlapped. Nevertheless, once the molecular constants have been determined from the analysis of the P and R branches it was possible to identify many blended transitions. A portion of the Q branch near the band origin is reported in Fig. 3, where the bandheads of several Q QK(J) clusters are also indicated.
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FIG. 2. Details of the R-branch spectrum of the CF2 ACHF n5 band near 1181.4 cm21 (T 5 240 K, P > 0.3 mbar, 49-cm cell). The individual transitions in the RK(J) groups with Jmax 5 45 and 47 are indicated.
FIG. 3. A portion of the CF2 ACHF n5 band near 1172.6 cm21 showing the beginning of the Q-branch (T 5 240 K, P > 0.3 mbar, 49-cm cell). The band heads of the QQK(J) clusters are labelled. 250
ANALYSIS OF CF2 ACHF IN THE 8.6 mm REGION
The n6 1 n9 combination of A9 symmetry gives rise to an a/b hybrid envelope. The band origin is 6 cm21 lower than the harmonic value (1161 cm21) calculated from the data of Ref. (3). Due to symmetry consideration, the n6 1 n9 vibration could have an anharmonic (Fermi) interaction with the n5 fundamental considering the fairly unusual intensity of the combination itself. A few crossings attributable to DKa 5 2 Fermi resonance were found (see later) for transitions with high J values. However, our present understanding of the spectral behavior only allows qualitative appreciation of the perturbation effects. Not surprisingly, the rotational structure of this band is also quite similar to that of the n5 fundamental and therefore its description has been limited to brief comments. The band shows a predominant a-type envelope characterized by a Q branch with unresolved clusters degrading toward lower wavenumbers; the R branch is wholly masked by the stronger P-branch features of the n5 absorption. The rovibrational analysis, only performed in the P branch, appears very difficult owing to the lack of ground state combination differences. As a final point, it should be noted that the weak lines arising from the b-type component for both bands could not be reliably recognized and therefore no rotational analysis has been attempted.
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TABLE 1 Molecular Parameters (cm21) for the n5 and n6 1 n9 Bands of CF2 ACHFa
Data Analysis and Results The ground and excited rotational energy levels have been computed using the Watson’s A-reduced Hamiltonian up to the sixth order in the I r representation, H 5 1/2~B 1 C!P2 1 @A 2 1/2~B 1 C !#P2a 2 DJ P4 2 D JK P 2 P 2a 2 D K P 4a 1 F J P 6 1 F JK P 4 P 2a 1 F KJ P 2 P 4a
a Uncertainties given are one standard deviation in units of the last significant digit. b From Ref. (6). c Constrained to ground state value. d Ground state sextic coefficients (Ref. (6)) fixed for the upper levels.
1 F K P 6a 1 @1/ 2~B 2 C! 2 2 d J P 2 1 2 w J P 4 #~P 2b 2 P 2c ! 1 @~2d K P 2a 1 w JK P 2 P 2a 1 w K P 4a !, ~P 2b 2 P 2c !# 1 , where P is the operator of the total angular momentum and Pa, Pb, and Pc are its components along the principal inertial axes in the molecular-fixed coordinate system. The rovibrational analysis of the n5 band was started from P(J) and R(J) manifolds characterized by low J and Ka quantum numbers. Estimating a satisfactory band center from the high-wavenumber edge of the Q branch, the initial leastsquares routine was carried out keeping the ground state parameters fixed to the values of (6) and refining the upper state constants together with the band origin. The obtained spectroscopic parameters allowed a better estimate of the wavenumbers for transitions with higher J and Ka values, and the refining procedure was iteratively applied until the analysis
was completed. The identification of the transitions did not prove to be very straightforward because of the existence of irregular deviations that were later recognized as due to perturbation effects. From the present analysis about 1400 a-type lines with J # 60, Ka # 22, and Kc # 60 were identified for the n5 fundamental, while about 90 a-type transitions with J # 56, Ka # 5, and Kc # 56 only in the P branch were attributed to the n6 1 n9 combination. The fitted data comprise the whole set of even transitions and only the odd split ones; no additional information is obtained with respect to the determination of the molecular constants by taking into account also the unsplit lines. The Q-branch features of n5, all badly overlapped, as well as the lines affected by perturbations have been eliminated from
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TABLE 2 Observed Line Positions (cm21) in the n5 Band of CF2 ACHF
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TABLE 2—Continued
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TABLE 2—Continued
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TABLE 2—Continued
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TABLE 3 Observed Line Positions (cm21) in the n6 1 n9 Band of CF2 ACHF
the final fit. An uncertainty of 0.001 cm21 was attributed to apparently single lines, while for blended or scarcely resolved features higher uncertainty (0.005 cm21) was assumed. The upper state constants were determined keeping the ground state parameters fixed at the values of (6). The constants obtained for n5 and n6 1 n9 bands, along with the statistical analyses, are summarized in Table 1. As can be seen, about 70% of line positions for n5 and 80% for n6 1 n9 are satisfactorily reproduced within an error of 0.001 cm21, while the rms deviations are about 0.001 cm21, matching the estimated precision of our wavenumber measurements. Most of the larger deviations come from blended lines or weak features easily subjected to overlapping. The sextic distortion constants could not be significantly determined and therefore they were constrained to their ground state values; however, this procedure did not affect the quality of the fit. For the n6 1 n9 level, only two quartic distortion coefficients (DJ and DJK) could be determined. On the whole, the values of the molecular parameters compare satisfactorily with those of the ground state except for the DJK constant of the n5 state, considerably
smaller in magnitude. This behavior might indicate that some weak resonance contributions still persist in the data set. The observed wavenumbers of the assigned transitions of n5 and n6 1 n9 bands are reported in Tables 2 and 3, respectively, which also include the residuals derived from the final fits. Analysis of Perturbations The resolved structure does not reflect a regular displacement in many cases and the observed irregularities clearly reveal that both the analyzed bands are influenced by perturbations. Concerning the n5 state, the small deviations from the expected line positions progressively increase with increasing J, thus indicating a J-dependent resonance. The interacting effects, particularly evident for transitions with K 9a 5 1 2 5 are generally weak and become appreciable near the crossings. The region around 1170 cm21 is rich in binary and ternary combinations, and the spectral positions, calculated employing the vibrational data from Ref. (3) and neglecting the anharmonicity, are predicted at 1178 (n7 1 n11), 1165 (n11 1 2n12), and
Copyright © 1998 by Academic Press
ANALYSIS OF CF2 ACHF IN THE 8.6 mm REGION
TABLE 4 Observed Crossings in the CF2 ACHF n5 Band due to First-Order b-Coriolis Resonance with n7 1 n11 and Obtained Spectroscopic Constants (cm21)
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The procedure was performed employing Watson’s A-reduced Hamiltonian in the I r representation and the Coriolis operator considering only the first-order b-type term, b Pb , H c 5 iZ 5,711
which gives rise to matrix elements of the form ^v 5 5 1, J, K|H c |v 7 5 v 11 5 1, J, K 6 1& 5 ~i/ 2! z Z b5,711 z @ J~ J 1 1! 2 K~K 6 1!# 1/ 2 ,
The 1 and 2 signs associated with Ka correspond to Ka 1 Kc 5 J and Ka 1 Kc 5 J 1 1 components of the energy levels, respectively. Crossings involve the almost 2 degenerate levels K1 a and (Ka 1 1) . b Uncertainties quoted are one standard error. The quartic coefficients (DJK, DK, dJ, dK) and the sextic terms are fixed to the ground state (see Table 1). c Fixed to the ground state value. a
1160 cm21 (n7 1 n9 1 n12); all these modes are of A0 species. Since the observed effects correspond to a perturbation for which the energy levels of the perturber are above those of n5 before the crossing and vice versa after the crossing, the most plausible interpretation is that a b-type Coriolis interaction (E6 7 O6) occurs between Ka levels of n5 and (Ka 2 1) levels of n7 1 n11. The local crossings, covering a limited number of J levels of n5, are reported in Table 4. The weak interaction effects have been found for levels with K9a # 5, while for K9a $ 6 the expected crossings could not be observed since the line assignment was limited to lower J values due to the very high density of the features. The obtained deviations, based on the observed 2 calculated values and their variation with J suggested that it might be possible to obtain a description of the interacting levels with the goal of extracting information on the dark state responsible for the interaction. The n5 transitions were then fitted using the SPFIT program written by Pickett (9), kindly provided to the spectroscopic community by the JPL Molecular Spectroscopy.
where Z b5,711 5 Be z z b5,711 z (v5 1 v711/(v5 z v711)1/2. Initially, the parameters for the n5 state were those of Table 1; for the combination n7 1 n11, the band origin was set 1177 cm21 according to the adjusted value in order to reproduce the observed resonances, while the rotational and distortion constants were taken to be those of the ground state (6). The coupling constant Z b5,711 > 0.004 cm21 was roughly estimated from the residuals of the transitions with Ka 5 31. With these starting values and using all the assigned lines with the exception of those involved in the Fermi resonance (see later), the nonlinear least-squares fit did not produce realistic values for the n7 1 n11 level and the standard deviation became worse than that of Table 1 for the n5 state. One of the reasons may be that weak perturbation effects, due to higher-order interactions or different resonances, involve the transitions employed in the fit and a dyad model including first-order b-Coriolis interaction is not quite satisfactory for all the assigned lines. At this stage, several approaches were attempted and considerable care was taken in deciding which transitions to include in the determination of the excited state parameters. The nonlinear least-squares fit converged to reasonable values only considering the transitions with Ka # 5, which, as above mentioned, are clearly involved in the observed local crossings. The best fit was obtained letting free the band origin, the rotational constants, and the DJ coefficient of n5, the band origin and the rotational constants of n7 1 n11, and the coupling Coriolis term. The results are reported in Table 4, while the residuals for the transitions employed in the fit are included in Table 2; the deviations (observed 2 calculated) near the crossings are notably decreased except in a very few cases, where the anomalous behavior is probably due to the effect of a further perturbation. The n5 band parameters are close to their ground state values and none of the n7 1 n11 state constants have unrealistic values. It is worthwhile to note that the final set of molecular constants accounts satisfactorily for the observed effects of the Coriolis resonance, and the calculated reduced rovibrational energies of n5 and n7 1 n11 levels in the region of the crossings are illustrated in Fig. 4. It can be seen that the crossing positions predicted from such figure are in agreement with the observed ones already given in Table 4.
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FIG. 4. Rovibrational energy levels of n5 ~K 9a 5 0 – 6) and n7 1 n11 ~K 9a 5 0–6) vibrational states of CF2 ACHF. The energies, reduced by 1/2(B 1 C)J(J 1 1), have been computed from the constants of Table 4 without using the coupling term.
As previously mentioned, two local crossings for Ka 5 0 and 11 at J > 48 and 50, respectively, were observed during the subband analyses. In this case the perturbation is much weaker than above and the obtained deviations are consistent with a mechanism where the Ka levels of the perturber are lower in energy than those of the n5 state before the crossing. The most likely candidate for this interaction is the n6 1 n9 vibration lying at 1155 cm21 and the perturbation effects should arise from the Fermi-type resonance (DKa 5 62). This prediction will be satisfactory as long as the data of n6 1 n9 are not contaminated by additional perturbations, whose effects have been observed for low Ka values at J > 30 and 45. Since the n6 1 n9 state can also interact through a- and b-type Coriolis
resonances with the nearby levels n7 1 n9 1 n12 (A0) and n11 1 2n12 (A0), any further discussion on the interaction mechanisms becomes arbitrary at this stage. In conclusion, from this investigation many lines belonging to the most intense a-type component of n5 and n6 1 n9 bands of CF2 ACHF have been identified, and the measurements yielded sufficient information to obtain accurate values of spectroscopic constants. The observed irregularities in the rotational structure of the n5 fundamental have mainly been attributed to the first-order b-type Coriolis resonance with the nearby state n7 1 n11, and the analysis has been performed using a dyad model including the interaction term.
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ANALYSIS OF CF2 ACHF IN THE 8.6 mm REGION
ACKNOWLEDGMENT Financial support by MURST, Roma, is gratefully acknowledged.
REFERENCES 1. R. Visinoni, S. Giorgianni, A. Baldacci, and S. Ghersetti, J. Mol. Spectrosc. 172, 456 – 463 (1995). 2. R. Visinoni, S. Giorgianni, A. Baldacci, M. Pedrali, and S. Ghersetti, J. Mol. Spectrosc. 182, 371–377 (1997). 3. D. E. Mann, N. Acquista, and E. K. Plyler, J. Chem. Phys. 22, 1586–1592 (1954).
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4. D. C. Mc Kean, Spectrochim. Acta, Part A 31, 1167–1186 (1975). 5. A. Bhaumik, W. V. F. Brooks, and S. C. Dass, J. Mol. Struct. 16, 29 –33 (1973). 6. R. Wellington Davis and M. C. L. Gerry, J. Mol. Spectrosc. 103, 187–193 (1984). 7. V. Mom, P. A. G. Huisman, F. C. Mijlhoff, and G. H. Renes, J. Mol. Struct. 62, 95–103 (1980). 8. A. G. Maki and J. S. Wells, ‘‘Wavenumber Calibration Tables From Heterodyne Frequency Measurements,’’ National Institute of Standards and Technology, Washington, DC, 1991. 9. H. M. Pickett, J. Mol. Spectrosc. 148, 371–377 (1991).
Copyright © 1998 by Academic Press
190, 248 –261 (1998)
MS987598
Diode Laser Spectroscopy of Trifluoroethylene in the 8.6-mm Region R. Visinoni, S. Giorgianni, A. Baldacci, and S. Ghersetti Universita` di Venezia, Dipartimento di Chimica Fisica, D. D. 2137, I-30123 Venezia, Italy Received December 5, 1997; in revised form March 26, 1998
The two mid-infrared bands of the CF2 ACHF molecule, n5 centered at 1172.673 cm21 and n6 1 n9 at 1155.105 cm21, were measured on a tunable diode laser spectrometer with a resolution near the Doppler limit. These vibrations of A9 species give rise to a/b hybrid bands, even though our analysis has pointed out that the intensity of the a-type component is predominant. Most of the J and K structure has been resolved in different subbranches, and the rovibrational analysis led to the assignment of about 1400 (J # 60, Ka # 22, Kc # 60) and 90 (J # 56, Ka # 5, Kc # 56) lines of the n5 and n6 1 n9 bands, respectively. Using Watson’s A-reduction Hamiltonian in the I r representation, a set of accurate spectroscopic constants for the upper states has been derived from transitions free of major resonance effects. The rotational structure of the n5 vibration also exhibits effects of Coriolis perturbation by a state identified as n7 1 n11. Parameters for the perturber were determined from the interaction effects near the observed crossings, using a dyad model including first-order b-Coriolis interaction. © 1998 Academic Press I. INTRODUCTION
As a part of high-resolution infrared studies of the trifluoethylene molecule, initiated with the analysis of the n3 and n4 fundamentals (1, 2), the present paper reports the results of the investigation of the spectral region around 1170 cm21. CF2 ACHF is believed to be a component of a certain importance in the atmospheric chemistry and, since infrared spectroscopy is a very powerful method for detecting trace gases, the determination of accurate spectroscopic parameters becomes useful. Infrared spectra of CF2 ACHF have been already investigated at low resolution many years ago by some workers (3, 4). Besides, microwave spectra have been measured and interpreted to evaluate the molecular parameters for the ground and vibrationally excited states (5, 6); the combined analysis of microwave and electron diffraction data provided some structural information on this molecule (7). This paper deals with the analysis of the rovibrational features arising from the strong n5 fundamental and the weaker n6 1 n9 combination. Upper state molecular parameters and results concerning the observed perturbation effects are reported. II. EXPERIMENTAL DETAILS
The gas sample of CF2 ACHF (99% pure), supplied by Peninsular Chemical Research, Inc., was used without further purification. The infrared spectrum was recorded in the range 1143–1184 cm21 using the tunable diode laser spectrometer at the University of Venice. The arrangement of the instrument is mainly based on the SP-5000 assembly of Laser Analytics, Inc.; in the present version the spectrophotometer setup is in a triple beam configuration so that the sample spectrum, the calibration lines, and the reference signal from a solid germa-
nium e´talon are recorded simultaneously. The instrument is interfaced to a PC that provides data acquisition, storage, and conversion into transmittance of the spectra. The gas sample was contained in a 49-cm cell with KBr windows at a pressure of 0.3 mbar; the temperature was kept at 240 K in order to reduce hot band absorptions. The spectrum was calibrated using standard lines of N2O (8) and the interference patterns from a 2.59-cm germanium e´talon with FSR > 0.0475 cm21. The absolute wavenumber accuracy is estimated to be of the order of 0.001 cm21. The computed Doppler line width (FWHM) is 0.0015 cm21, while the measured full width at half maximum is about 0.002 cm21. III. RESULTS AND DISCUSSION
Trifluoroethylene is a planar near-prolate molecule (k 5 20.74) of CS symmetry with 12 fundamentals; the 9 modes of A9 symmetry (n1 2 n9) give rise to a/b hybrid bands, while the 3 modes of species A0 (n10 2 n12) produce c-type band contours. The spectrum has been analyzed in the range 1143–1184 cm21, where two bands, separated by about 18 cm21, are observed; the stronger absorption at higher wavenumbers (>1173 cm21) corresponds to the n5 fundamental, while the weaker one, located around 1155 cm21 and partially overlapped by the n5 features, has been attributed to the n6 1 n9 vibration. Additional combinations, too weak to be observed, are expected to occur in this region and to interact with the n5 and n6 1 n9 levels. Description of the n5 and n6 1 n9 Bands The spectral analysis started with the assignment of the more prominent features pertaining to the n5 fundamental. This mode, corresponding to the CFH bending vibration, gives rise to an a/b-hybrid band. The high-resolution infrared spectrum
248 0022-2852/98 $25.00 Copyright © 1998 by Academic Press All rights of reproduction in any form reserved.
ANALYSIS OF CF2 ACHF IN THE 8.6 mm REGION
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FIG. 1. A section of the P-branch spectrum of the CF2 ACHF n5 band near 1169.4 cm21 (T 5 240 K, P > 0.3 mbar, 49-cm cell). The fine structure of the PK(15) manifold is indicated; asymmetry splitting is observed.
Q
shows a predominant a-type envelope with a strong partially resolved Q branch degrading toward lower wavenumbers; the P-branch features heavily overlap the weak absorptions of n6 1 n9. Following the selection rules for the a-type transitions (DJ 5 0, 61, DKa 5 0, DKc 5 61) several even and odd subbranches are expected in the P, Q, and R branches depending on (K0a 1 K0c 5 J0) or (K0a 1 K0c 5 J0 1 1), respectively. Basically, the structure of this band is very similar to that of the n4 fundamental (2), and two different types of clusters formed by e,oP(0, 21) and e,oR(0, 1) subbranches have been identified in the P and R branches. The manifolds exhibit regular structure close to the band center, but, as J increases, the lines of contiguous groups overlap each other producing a considerably dense rotational structure. The first type of clusters, with a characteristic spacing of (B 1 C) > 0.22 cm21, is associated with transitions having the same J value and displaying the typical pattern of a parallel band of a symmetric top. As an example, the spectrum of the P branch near 1169 cm21 is illustrated in Fig. 1, where the details of the QPK(15) group are indicated; the asymmetry splitting is observed for Ka # 6. It is worth noting that the transitions with Ka 5 0 and Ka 5 12 are almost degenerate. The second type of clusters is composed of a series of lines defined by a Jmax value and degrading toward higher wave-
numbers. The line that starts the series has J0 5 K 0c and the successive lines have J decreasing by 1 and Kc by 2. The separation between adjacent clusters is 2C > 0.20 cm21. A typical series of lines in the R-branch region around 1181 cm21 is depicted in Fig. 2, which illustrates the structure of the groups with Jmax 5 45– 47. The reproduced details indicate 2 that in many cases levels with K1 a and (Ka 1 1) are almost degenerate. Features of this type, characteristic of spectra of planar molecules, are due to the near coincidence of transitions between energy levels that become degenerate in the oblate symmetric top limit for high Kc values. The degeneration effect appears evident for low Ka values and the computed reduced energy levels (see later in Fig. 4) show that the pairs levels J0,J /J1,J and J1,J21/J2,J21 become almost degenerate for J $ 19 and 25, respectively. The Q branch appears at first glance not easy to be analyzed because the structure is very packed and the subbranches eQ(0, 1) and oQ(0, 21) are mostly overlapped. Nevertheless, once the molecular constants have been determined from the analysis of the P and R branches it was possible to identify many blended transitions. A portion of the Q branch near the band origin is reported in Fig. 3, where the bandheads of several Q QK(J) clusters are also indicated.
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FIG. 2. Details of the R-branch spectrum of the CF2 ACHF n5 band near 1181.4 cm21 (T 5 240 K, P > 0.3 mbar, 49-cm cell). The individual transitions in the RK(J) groups with Jmax 5 45 and 47 are indicated.
FIG. 3. A portion of the CF2 ACHF n5 band near 1172.6 cm21 showing the beginning of the Q-branch (T 5 240 K, P > 0.3 mbar, 49-cm cell). The band heads of the QQK(J) clusters are labelled. 250
ANALYSIS OF CF2 ACHF IN THE 8.6 mm REGION
The n6 1 n9 combination of A9 symmetry gives rise to an a/b hybrid envelope. The band origin is 6 cm21 lower than the harmonic value (1161 cm21) calculated from the data of Ref. (3). Due to symmetry consideration, the n6 1 n9 vibration could have an anharmonic (Fermi) interaction with the n5 fundamental considering the fairly unusual intensity of the combination itself. A few crossings attributable to DKa 5 2 Fermi resonance were found (see later) for transitions with high J values. However, our present understanding of the spectral behavior only allows qualitative appreciation of the perturbation effects. Not surprisingly, the rotational structure of this band is also quite similar to that of the n5 fundamental and therefore its description has been limited to brief comments. The band shows a predominant a-type envelope characterized by a Q branch with unresolved clusters degrading toward lower wavenumbers; the R branch is wholly masked by the stronger P-branch features of the n5 absorption. The rovibrational analysis, only performed in the P branch, appears very difficult owing to the lack of ground state combination differences. As a final point, it should be noted that the weak lines arising from the b-type component for both bands could not be reliably recognized and therefore no rotational analysis has been attempted.
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TABLE 1 Molecular Parameters (cm21) for the n5 and n6 1 n9 Bands of CF2 ACHFa
Data Analysis and Results The ground and excited rotational energy levels have been computed using the Watson’s A-reduced Hamiltonian up to the sixth order in the I r representation, H 5 1/2~B 1 C!P2 1 @A 2 1/2~B 1 C !#P2a 2 DJ P4 2 D JK P 2 P 2a 2 D K P 4a 1 F J P 6 1 F JK P 4 P 2a 1 F KJ P 2 P 4a
a Uncertainties given are one standard deviation in units of the last significant digit. b From Ref. (6). c Constrained to ground state value. d Ground state sextic coefficients (Ref. (6)) fixed for the upper levels.
1 F K P 6a 1 @1/ 2~B 2 C! 2 2 d J P 2 1 2 w J P 4 #~P 2b 2 P 2c ! 1 @~2d K P 2a 1 w JK P 2 P 2a 1 w K P 4a !, ~P 2b 2 P 2c !# 1 , where P is the operator of the total angular momentum and Pa, Pb, and Pc are its components along the principal inertial axes in the molecular-fixed coordinate system. The rovibrational analysis of the n5 band was started from P(J) and R(J) manifolds characterized by low J and Ka quantum numbers. Estimating a satisfactory band center from the high-wavenumber edge of the Q branch, the initial leastsquares routine was carried out keeping the ground state parameters fixed to the values of (6) and refining the upper state constants together with the band origin. The obtained spectroscopic parameters allowed a better estimate of the wavenumbers for transitions with higher J and Ka values, and the refining procedure was iteratively applied until the analysis
was completed. The identification of the transitions did not prove to be very straightforward because of the existence of irregular deviations that were later recognized as due to perturbation effects. From the present analysis about 1400 a-type lines with J # 60, Ka # 22, and Kc # 60 were identified for the n5 fundamental, while about 90 a-type transitions with J # 56, Ka # 5, and Kc # 56 only in the P branch were attributed to the n6 1 n9 combination. The fitted data comprise the whole set of even transitions and only the odd split ones; no additional information is obtained with respect to the determination of the molecular constants by taking into account also the unsplit lines. The Q-branch features of n5, all badly overlapped, as well as the lines affected by perturbations have been eliminated from
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TABLE 2 Observed Line Positions (cm21) in the n5 Band of CF2 ACHF
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TABLE 2—Continued
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TABLE 2—Continued
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TABLE 2—Continued
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TABLE 2—Continued
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TABLE 2—Continued
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TABLE 3 Observed Line Positions (cm21) in the n6 1 n9 Band of CF2 ACHF
the final fit. An uncertainty of 0.001 cm21 was attributed to apparently single lines, while for blended or scarcely resolved features higher uncertainty (0.005 cm21) was assumed. The upper state constants were determined keeping the ground state parameters fixed at the values of (6). The constants obtained for n5 and n6 1 n9 bands, along with the statistical analyses, are summarized in Table 1. As can be seen, about 70% of line positions for n5 and 80% for n6 1 n9 are satisfactorily reproduced within an error of 0.001 cm21, while the rms deviations are about 0.001 cm21, matching the estimated precision of our wavenumber measurements. Most of the larger deviations come from blended lines or weak features easily subjected to overlapping. The sextic distortion constants could not be significantly determined and therefore they were constrained to their ground state values; however, this procedure did not affect the quality of the fit. For the n6 1 n9 level, only two quartic distortion coefficients (DJ and DJK) could be determined. On the whole, the values of the molecular parameters compare satisfactorily with those of the ground state except for the DJK constant of the n5 state, considerably
smaller in magnitude. This behavior might indicate that some weak resonance contributions still persist in the data set. The observed wavenumbers of the assigned transitions of n5 and n6 1 n9 bands are reported in Tables 2 and 3, respectively, which also include the residuals derived from the final fits. Analysis of Perturbations The resolved structure does not reflect a regular displacement in many cases and the observed irregularities clearly reveal that both the analyzed bands are influenced by perturbations. Concerning the n5 state, the small deviations from the expected line positions progressively increase with increasing J, thus indicating a J-dependent resonance. The interacting effects, particularly evident for transitions with K 9a 5 1 2 5 are generally weak and become appreciable near the crossings. The region around 1170 cm21 is rich in binary and ternary combinations, and the spectral positions, calculated employing the vibrational data from Ref. (3) and neglecting the anharmonicity, are predicted at 1178 (n7 1 n11), 1165 (n11 1 2n12), and
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ANALYSIS OF CF2 ACHF IN THE 8.6 mm REGION
TABLE 4 Observed Crossings in the CF2 ACHF n5 Band due to First-Order b-Coriolis Resonance with n7 1 n11 and Obtained Spectroscopic Constants (cm21)
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The procedure was performed employing Watson’s A-reduced Hamiltonian in the I r representation and the Coriolis operator considering only the first-order b-type term, b Pb , H c 5 iZ 5,711
which gives rise to matrix elements of the form ^v 5 5 1, J, K|H c |v 7 5 v 11 5 1, J, K 6 1& 5 ~i/ 2! z Z b5,711 z @ J~ J 1 1! 2 K~K 6 1!# 1/ 2 ,
The 1 and 2 signs associated with Ka correspond to Ka 1 Kc 5 J and Ka 1 Kc 5 J 1 1 components of the energy levels, respectively. Crossings involve the almost 2 degenerate levels K1 a and (Ka 1 1) . b Uncertainties quoted are one standard error. The quartic coefficients (DJK, DK, dJ, dK) and the sextic terms are fixed to the ground state (see Table 1). c Fixed to the ground state value. a
1160 cm21 (n7 1 n9 1 n12); all these modes are of A0 species. Since the observed effects correspond to a perturbation for which the energy levels of the perturber are above those of n5 before the crossing and vice versa after the crossing, the most plausible interpretation is that a b-type Coriolis interaction (E6 7 O6) occurs between Ka levels of n5 and (Ka 2 1) levels of n7 1 n11. The local crossings, covering a limited number of J levels of n5, are reported in Table 4. The weak interaction effects have been found for levels with K9a # 5, while for K9a $ 6 the expected crossings could not be observed since the line assignment was limited to lower J values due to the very high density of the features. The obtained deviations, based on the observed 2 calculated values and their variation with J suggested that it might be possible to obtain a description of the interacting levels with the goal of extracting information on the dark state responsible for the interaction. The n5 transitions were then fitted using the SPFIT program written by Pickett (9), kindly provided to the spectroscopic community by the JPL Molecular Spectroscopy.
where Z b5,711 5 Be z z b5,711 z (v5 1 v711/(v5 z v711)1/2. Initially, the parameters for the n5 state were those of Table 1; for the combination n7 1 n11, the band origin was set 1177 cm21 according to the adjusted value in order to reproduce the observed resonances, while the rotational and distortion constants were taken to be those of the ground state (6). The coupling constant Z b5,711 > 0.004 cm21 was roughly estimated from the residuals of the transitions with Ka 5 31. With these starting values and using all the assigned lines with the exception of those involved in the Fermi resonance (see later), the nonlinear least-squares fit did not produce realistic values for the n7 1 n11 level and the standard deviation became worse than that of Table 1 for the n5 state. One of the reasons may be that weak perturbation effects, due to higher-order interactions or different resonances, involve the transitions employed in the fit and a dyad model including first-order b-Coriolis interaction is not quite satisfactory for all the assigned lines. At this stage, several approaches were attempted and considerable care was taken in deciding which transitions to include in the determination of the excited state parameters. The nonlinear least-squares fit converged to reasonable values only considering the transitions with Ka # 5, which, as above mentioned, are clearly involved in the observed local crossings. The best fit was obtained letting free the band origin, the rotational constants, and the DJ coefficient of n5, the band origin and the rotational constants of n7 1 n11, and the coupling Coriolis term. The results are reported in Table 4, while the residuals for the transitions employed in the fit are included in Table 2; the deviations (observed 2 calculated) near the crossings are notably decreased except in a very few cases, where the anomalous behavior is probably due to the effect of a further perturbation. The n5 band parameters are close to their ground state values and none of the n7 1 n11 state constants have unrealistic values. It is worthwhile to note that the final set of molecular constants accounts satisfactorily for the observed effects of the Coriolis resonance, and the calculated reduced rovibrational energies of n5 and n7 1 n11 levels in the region of the crossings are illustrated in Fig. 4. It can be seen that the crossing positions predicted from such figure are in agreement with the observed ones already given in Table 4.
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FIG. 4. Rovibrational energy levels of n5 ~K 9a 5 0 – 6) and n7 1 n11 ~K 9a 5 0–6) vibrational states of CF2 ACHF. The energies, reduced by 1/2(B 1 C)J(J 1 1), have been computed from the constants of Table 4 without using the coupling term.
As previously mentioned, two local crossings for Ka 5 0 and 11 at J > 48 and 50, respectively, were observed during the subband analyses. In this case the perturbation is much weaker than above and the obtained deviations are consistent with a mechanism where the Ka levels of the perturber are lower in energy than those of the n5 state before the crossing. The most likely candidate for this interaction is the n6 1 n9 vibration lying at 1155 cm21 and the perturbation effects should arise from the Fermi-type resonance (DKa 5 62). This prediction will be satisfactory as long as the data of n6 1 n9 are not contaminated by additional perturbations, whose effects have been observed for low Ka values at J > 30 and 45. Since the n6 1 n9 state can also interact through a- and b-type Coriolis
resonances with the nearby levels n7 1 n9 1 n12 (A0) and n11 1 2n12 (A0), any further discussion on the interaction mechanisms becomes arbitrary at this stage. In conclusion, from this investigation many lines belonging to the most intense a-type component of n5 and n6 1 n9 bands of CF2 ACHF have been identified, and the measurements yielded sufficient information to obtain accurate values of spectroscopic constants. The observed irregularities in the rotational structure of the n5 fundamental have mainly been attributed to the first-order b-type Coriolis resonance with the nearby state n7 1 n11, and the analysis has been performed using a dyad model including the interaction term.
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ANALYSIS OF CF2 ACHF IN THE 8.6 mm REGION
ACKNOWLEDGMENT Financial support by MURST, Roma, is gratefully acknowledged.
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4. D. C. Mc Kean, Spectrochim. Acta, Part A 31, 1167–1186 (1975). 5. A. Bhaumik, W. V. F. Brooks, and S. C. Dass, J. Mol. Struct. 16, 29 –33 (1973). 6. R. Wellington Davis and M. C. L. Gerry, J. Mol. Spectrosc. 103, 187–193 (1984). 7. V. Mom, P. A. G. Huisman, F. C. Mijlhoff, and G. H. Renes, J. Mol. Struct. 62, 95–103 (1980). 8. A. G. Maki and J. S. Wells, ‘‘Wavenumber Calibration Tables From Heterodyne Frequency Measurements,’’ National Institute of Standards and Technology, Washington, DC, 1991. 9. H. M. Pickett, J. Mol. Spectrosc. 148, 371–377 (1991).
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