- Email: [email protected]
A Reinvestigation of the c3Π–X1Σ+ (0–0) Absorption Band of Carbon Monoxide
Journal of Molecular Spectroscopy 203, 314 –319 (2000) doi:10.1006/jmsp.2000.8185, available online at http://www.idealibrary.com on
A Reinvestigation of the c 3⌸–X 1⌺ ⴙ (0 – 0) Absorption Band of Carbon Monoxide Jacob Baker,* ,1 Franc¸oise Launay,† Miche´le Eidelsberg,† and Franc¸ois Rostas† *Division of Environmental Health and Risk Management, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom; and †DAMAp et UMR 8588 du CNRS, Observatoire de Paris, Section de Meudon, 92195 Meudon Cedex, France Received May 22, 2000
The forbidden c 3 ⌸–X 1 ⌺ ⫹ (0–0) absorption band of carbon monoxide has been reinvestigated under different pressure conditions using the 10.7-m VUV spectrograph at Meudon. Overlap with the allowed C 1 ⌸–X 1 ⌺ ⫹ (0–0) band at lower transition energy has been taken into account. We have identified a new rotational branch corresponding to an S-type branch and extended the analysis to both higher and lower J. An analysis of the band structure and the low J transition lines suggests that the band gains its intensity predominantly as a result of an interaction of the c 3 ⌸ state with a 1⌺ ⫹ state, most likely the C 1 ⌺ ⫹ (v ⫽ 0) state. Molecular constants have been obtained for the c 3 ⌸ state that are in reasonable agreement with those previously published. The apparently anomalous small value for the centrifugal distortion constant is explained by a homogeneous perturbation with the k 3 ⌸ valence state. © 2000 Academic Press INTRODUCTION
The c 3 ⌸ state of carbon monoxide was first observed experimentally in emission as the upper state of the 3A band system (c–a 3 ⌸) but was initially believed to be a 3⌺ state (1, 2). These emission bands are overlapped with those of the fourth positive system ( A–X emission bands) and hence are difficult to identify. Later Tilford (3) recorded the absorption band of the spin-forbidden c–X 1 ⌺ ⫹ transition and observed a P- and R-type branch and a condensed Q-type branch. This was inconsistent with the initial assignment to a 3⌺ state and led Tilford to reassign the c state to a 3⌸ state of approximately pure Hund’s case b character. This reassignment was supported by the work of Ginter and Tilford (4) who reanalyzed the 3A band system under higher resolution and observed ⌳-type doubling in the c state. Rytel and co-workers (5– 8) have since investigated the 3A band system for various different isotopomers of CO. However, analysis of the 3A band system has been somewhat limited by poor data at low J due to overlapping rotational structure and the presence of perturbations. Dabrowski et al. (9) observed the near-infrared c 3 ⌸–b 3 ⌺ ⫹ (0–0) emission band of carbon monoxide in a radiofrequency discharge. Difficulties were reported in the analysis of this band due to both states being heavily perturbed, particularly the b state. “Empirical parameters” for both states were given where the analysis was limited to transition lines with N⬙ ⬍ 10. These lines did not appear to be severely perturbed and hence in the analysis perturbations were neglected. A spin– orbit constant of A ⫽ 1.5 cm ⫺1 for the c 3 ⌸ state was determined in the work. This value was said to be similar to a 1
previous study by Klopotek and Vidal (10) that examined high-lying states of carbon monoxide by means of a two-step excitation from the ground state. This earlier study observed triplet splitting in the c 3 ⌸ state for N ⫽ 1–5, but no line positions were presented. Although Klopotek and Vidal reported a fine-structure constant of A ⫽ 1.49 cm ⫺1, this related to only one of the parity components of the c state. In fact, Klopotek and Vidal report observing different fine-structure splittings depending on whether the intermediate state, the a⬘ 3 ⫹ ⌺ state, had plus or minus parity. This was said to be most likely due to a perturbation of the c state with a ⌺ ⫹ state. Clearly, there is some uncertainty in the nature of the perturbations and the molecular constants of the c state of carbon monoxide, which explains our interest in reinvestigating the c–X band. The advantage of studying the c–X band is that the lower state, the ground state, is unperturbed and well characterized such that the fine-structure assignment and analysis of the upper c state is greatly simplified. Also, the band structure is quite simple and hence relatively easy to interpret. However, this band is partially overlapped with the allowed C–X (0–0) absorption band that occurs to the red (i.e., to longer wavelengths) of the c–X band and it is important to take this into account. Fortunately, the C–X (0–0) band has been well characterized in previous studies. The initial impetus for reinvestigating the c–X band was the identification of unassigned lines in Tilford’s (3) published c–X spectrum. SPECTROSCOPIC DATA
To whom correspondence should be addressed.
Photographic absorption spectra were obtained at room temperature over the wavelength range 102–115 nm using the 10.68-m VUV spectrograph at the Meudon observatory
314 0022-2852/00 $35.00 Copyright © 2000 by Academic Press All rights of reproduction in any form reserved.
A REINVESTIGATION OF THE c 3 ⌸–X 1 ⌺ ⫹ (0–0) BAND OF CO
315
FIG. 1. The c 3 ⌸–X 1 ⌺ ⫹ (0–0) absorption band of CO recorded in the transition energy range 92 300 –91 950 cm ⫺1 (wavelength range 1083.6 –1087.3 Å) at four different pressures. (A) 1.5 Torr, (B) 0.5 Torr, (C) 0.15 Torr, and (D) 0.07 Torr. A simulation of the band is also shown, where T ⫽ 298 K, ⫽ 20, and a Gaussian linewidth of 0.4 cm ⫺1 (FWHM) was used (see text for further details). Overlapping rotational structure from the C 1 ⌸–X 1 ⌺ ⫹ (0–0) band of CO and the various isotopomers are also indicated.
(21.4-m effective path length). The experimental and calibration procedure has been described elsewhere (11, 12). Calibration was achieved by recording atomic emission lines from a windowless hollow-cathode lamp. The small wavelength shift between the hollow-cathode reference lamp and the VUV light source (due to slightly different optical paths within the spectrometer) was corrected for by reference to two Ar I impurity lines appearing in the background continuum. In addition, rotational lines of the C–X (0–0) absorption band of 12C 16O (13, 14) were also used for calibration. Natural isotopic composition carbon monoxide gas (99 and 99.997% purity) was used in this study. The c–X (0–0) ab-
sorption band was rotationally analyzed from measurements of photographic plate spectra recorded at four different pressures 1.5, 0.5, 0.15, and 0.07 Torr. Toward the red, i.e., to longer wavelength, the c–X (0–0) band is interleaved and overlapped with high J R-branch rotational lines of the C–X (0–0) band. Increasing the gas pressure results in stronger absorption of the lines of the forbidden c–X (0–0) band but also results in a widening zone of saturation from the band center of the C–X (0–0) band. Hence, a range of pressures was needed for examining the spectrum (see Fig. 1). In identifying rotational lines of the c–X (0–0) band it was necessary to take into account the rotational lines of the C–X
Copyright © 2000 by Academic Press
316
BAKER ET AL.
TABLE 1 Line Positions for the c 3⌸ (vv ⴝ 0)–X 1⌺ ⴙ (vv ⴝ 0) Transition a
(0–0) band, which overlap in particular the P-type and O-type branches. Since the C–X (0–0) absorption band is very much stronger than the c–X band, all the naturally occurring isotopomers of CO were considered. From isotopic abundance tables (15) the following relative fractional abundances are expected (given in parentheses): 12C 16O (1); 13C 16O (1.11 ⫻ 10 ⫺2); 12C 18O (2.00 ⫻ 10 ⫺3); 12C 17O (3.81 ⫻ 10 ⫺4); 13C 18O (2.23 ⫻ 10 ⫺5). All these isotopomers, except for 12C 17O, have well-determined C 1 ⌺ ⫹ state molecular constants (13, 14, 16, 17) and their C–X (0–0) transition lines were readily determined and accounted for in the spectrum. During this investigation some new lines were observed that could be assigned to the C–X (0–0) band of 12C 17O (13). These will be considered elsewhere. RESULTS AND DISCUSSION
Figure 1 shows the c 3 ⌸–X 1 ⌺ ⫹ (0–0) absorption band of carbon monoxide photographed over the transition energy range 92 300 –91 950 cm ⫺1 (wavelength range 1083.4 –1087.5
Å) at four different pressures. This band has a prominent blue-degraded Q-type bandhead at 92 076.8 ⫾ 1.0 cm ⫺1, indicating that B⬘ ⬎ B⬙. Tilford (3), over 30 years ago, performed the only other study of this band. He identified the P-, Q-, and R-type branches and was the first to assign the upper state to a 3 ⌸ state. However, he was only able to perform a partial rotational analysis. As seen from Fig. 1, a most prominent feature of the band is a regular series of lines extending to higher transition energy that has a line spacing about twice that of the R-type branch. This line spacing is that which would be expected for an S-type branch, where ⌬N ⫽ 2. This branch is in fact the S R branch. This branch was not identified by Tilford (3) even though three of its lines are evident in his published spectrum (for example, in Fig. 1 of Ref. (3), the S R(6) line lies between “R(45)” and “R(46)” of C–X (0–0), while the S R(5) line lies between “R(43)” and “R(44)”). The line positions and assignments of the observed spectral lines of the c 3 ⌸–X 1 ⌺ ⫹ (0–0) band are given in Table 1. The
Copyright © 2000 by Academic Press
A REINVESTIGATION OF THE c 3 ⌸–X 1 ⌺ ⫹ (0–0) BAND OF CO
TABLE 2 Possible Rotational Branch and Upper Level Assignments for the c–X (0 – 0) Band a
a
The upper level assignments in terms of spin component and parity (e/f ) are given in parentheses.
measurements and estimated errors were obtained from several spectra recorded under the various pressure conditions described in the previous section. Figure 1 also shows a simulation of the absorption band assuming a rotational temperature of T ⫽ 298 K and a Gaussian linewidth of 0.4 cm ⫺1 (FWHM). In this simulation the energy levels of the c 3 ⌸ state were obtained using molecular constants derived from a weighted least-squares fit of the measured line position given in Table 1. The 3⌸– 1⌺ ⫹ linestrength factors were taken from Kovacs (18) in which the 3⌸ state is treated in the intermediate Hund’s case a/b framework. In the simulation no attempt was made to account for the threshold characteristics of the photographic plate nor its nonlinear response above threshold. The linestrength formulas contain a parameter labeled ⫽ D/E, where D and E correspond in the present case to the effective transition moments arising from mixing of 1⌺ ⫹ and 1⌸ character into the c 3 ⌸ state, respectively. If we consider the linestrength factor of the S R rotational branch, we find for ⫽ 1 there is a cancellation of terms that results in a negligible absorption intensity that exponentially decreases with J. Since the S R branch is observed to be relatively strong, cancellation does not occur, implying that Ⰷ 1 or Ⰶ 1. Hence, the c–X (0–0) transition predominantly gains intensity through the mixing of the c 3 ⌸ state with either a 1⌺ ⫹ state or a 1⌸ state but not both. This mixing can occur through spin– orbit interaction. There are two obvious candidates, the C 1 ⌺ ⫹ and E 1 ⌸ Rydberg states, respectively. Table 2 gives the main branch assignments for both cases. To distinguish between the two cases, the c–X band needs to be examined at low J. From Table 2 it can be seen that the S-, Q-, and O-type branches are the same for the two cases but the R- and P-type branches are different. We note that the Q-type branch is an overlap of two branches; however, for the lines that were observed in this study, the two branches could not be resolved and appeared as a single branch. At medium and high J ( J⬙ ⬎ 5), as the c 3 ⌸ state is essentially of pure Hund’s case b character, there is very little difference in line position between the two cases. However, there are small differences in line positions at low J and more importantly different branches may start at different J⬙ values. We find for the P-type branch the first nonzero line occurs at J⬙ ⫽ 2 in both cases. However, for the R-type branch we find the R R rotational branch (case 1)
317
begins at J⬙ ⫽ 0, while the R Q branch (case 2) begins at J⬙ ⫽ 2. Hence, by examining the R-type branch at low J⬙, we might be able to distinguish between the two cases. Figure 2 is a densitometer recording showing the central region of the c–X (0–0) band photographed at 0.15 Torr. Considering the low J lines of the R-type rotational branch, the R(0) line would be expected to be hidden in the Q-type bandhead while the R(1) line would be overlapped with the Q(15) line. From Fig. 2, when we compare the relative intensities of the Q-type lines, Q(13), Q(15), Q(16), and Q(17), we do see a large enhancement of the intensity of the Q(15) line (note that the Q(14) line is overlapped with the R(35) line of the C–X (0–0) band). This observation is consistent with the existence of a strong R(1) line and the case 1 assignment. We also obtain a better fit to the low J⬙ line positions assuming the case 1 assignment. Hence, we adopt the case 1 assignment, i.e., the band gains its intensity predominantly through the mixing of the c 3 ⌸ state with a 1⌺ ⫹ state, most likely the C 1 ⌺ ⫹ (v ⫽ 0) state. There is a further observation to support this assignment. Klopotek and Vidal (10) looked at the two-step excitation to the c 3 ⌸ state from the ground state via the a⬘ 3 ⌺ ⫹ state. Giving limited details, they noted an anomalous finestructure splitting at low J for the c 3 ⌸ state “indicating a perturbation most likely due to a ⌺ ⫹ state.” Table 3 gives molecular parameters obtained from the results of weighted least-squares rotational fits. For fit 1 no explicit perturbations were included for the upper state whose
FIG. 2. A densitometer recording of the central region of the c 3 ⌸–X 1 ⌺ ⫹ (0–0) band photographed at 0.15 Torr and room temperature. The R R(1) line overlaps the Q-type, Q(15) line. (The Q-type bandhead has a “flat top” due to saturation of the photographic plate.)
Copyright © 2000 by Academic Press
318
BAKER ET AL.
TABLE 3 Molecular Constants for the c 3⌸ (vv ⴝ 0) State a
a All parameters are in units of cm ⫺1. Values between parentheses are errors, to one standard deviation, in the least significant figure resulting from the fit. For T 00 , the error given is that obtained from the fit and hence neglects possible calibration errors (estimated to be up to 0.2 cm ⫺1). is the standard deviation of the weighted fit. For both fits the following molecular constants of the c 3 ⌸ (v ⫽ 0) state were fixed at the nonzero values of Dabrowski et al. (9); ⫽ 0.064 cm ⫺1, (o ⫹ p ⫹ q) ⫽ 0.087 cm ⫺1, ( p ⫹ 2q) ⫽ 0.0209 cm ⫺1. (See text for further details.) b In the fitting procedure the molecular constants of the k state were fixed to those values given by Mellinger and Vidal (Table V of Ref. (21)).
rotational energy levels were fitted to the eigenvalues of the effective 3⌸ Hamiltonian matrix given by Brown and Merer (19), while the X 1 ⌺ ⫹ ground state rotational energy levels were fitted simply to the expression F共 J兲 ⫽ BJ共 J ⫹ 1兲 ⫺ D共 J共 J ⫹ 1兲兲 2
[1]
using B ⫽ 1.9225288 cm ⫺1 and D ⫽ 6.120 ⫻ 10 ⫺6 cm ⫺1, from Ref. (20). The upper state molecular parameters that could not be readily determined were fixed to those obtained by Dabrowski et al. (9) rather than fixed to zero. The second fit takes into account a perturbation with the k 3 ⌸ state (vide infra). There are some points to note regarding the c 3 ⌸ state from the fits. First, it has a well-determined lambda doubling parameter q ⫽ 0.0098 cm ⫺1. This arises mainly as a result of the interaction of the c 3 ⌸ 3p Rydberg state with the j 3 ⌺ ⫹ 3p Rydberg state which in the pure precession model yields a value of q ⫽ 0.012 cm ⫺1 (21). The actual value is also similar to that of the isoconfigurational E 1 ⌸ 3p state, where q ⫽ 0.0119 cm ⫺1 (22). Second, the spin– orbit constant determined is very small, as expected for a Hund’s case (b)-type state. The electronic configuration of the c 3 ⌸ state consists of a 2⌺ ⫹ ionic core and a 3p Rydberg electron. Hence, only the Rydberg electron contributes to the spin– orbit splitting and the Rydberg nature of the orbital leads to the small value. The value obtained is in fact smaller than that previously obtained in other studies (ca., 1.0 –1.5 cm ⫺1) and may effectively be zero. The only direct attempt at observing the spin– orbit splitting of the c 3 ⌸ state
(Klopotek and Vidal (10)) gave conflicting results: A ⫽ 1.49 cm ⫺1 for an “unperturbed” parity component and a “different” fine-structure splitting for the other parity component. Finally, for fit 1, where no explicit perturbation was considered, the centrifugal distortion coefficient obtained is smaller than expected and is effectively zero from the fit. This has been noted previously where a negative value for the distortion coefficient has been reported (9). This can be explained by a homogeneous perturbation with another 3⌸ state at lower energy. In fact there does exist such a state, the k 3 ⌸ valence state (12, 23–25), the v ⫽ 2 level of which lies at 91 959 cm ⫺1 (21), i.e., approximately 118 cm ⫺1 lower in energy than the c 3 ⌸ (v ⫽ 0) state. We note that Berden et al. (25) have correctly reassigned the vibrational numbering of the k state, which has been independently confirmed (26). The vibrational numbering of the k state in studies prior to that work needs incrementing by one unit. Hence a second rotational fit was performed which included explicitly a possible homogeneous interaction with the k 3 ⌸ (v ⫽ 2) state. In the fitting procedure, a 6 ⫻ 6 Hamiltonian matrix with a Hund’s case (a) basis was used with two 3 ⫻ 3 submatrices (19) to represent the c 3 ⌸ (v ⫽ 0) state and the k 3 ⌸ (v ⫽ 2) state, respectively. The rotational levels of the k 3 ⌸ (v ⫽ 2) state were determined using the molecular constants given by Mellinger and Vidal (21). The homogeneous interaction between the two states was represented by including the off-diagonal terms, 具c 3 ⌸ x 兩H兩k 3 ⌸ x 典 ⫽ W, where x ⫽ 0, 1, and 2, in the 6 ⫻ 6 Hamiltonian matrix (6, 27). The ground state was treated as before. The results of the fit are given in the final column of Table 3. By including this interaction we obtained a better fit to the line positions of the c–X (0–0) band and a more realistic value for the centrifugal distortion constant, D. We have also observed a few weak lines emerging from the long wavelength side of the C–X (0–0) absorption band which should be attributable to the k–X (2–0) transition. The main part of the k–X (2–0) band is completely overlapped with the C–X (0–0) band. However, the lines that we have observed present some apparent anomalies which we are currently investigating. We are also planning to reanalyze the 3A band system and the c–b near-infrared band in order to resolve some small discrepancies in the literature concerning the c 3 ⌸ state. CONCLUSION
We have reinvestigated the c 3 ⌸–X 1 ⌺ ⫹ (0–0) absorption band of carbon monoxide taking into account overlap with the allowed C 1 ⌸–X 1 ⌺ ⫹ (0–0) band at lower transition energies. We have identified a new rotational branch corresponding to an S-type branch and extended the analysis to both higher and lower J. An analysis of the band structure and the low J transition lines suggests that the band gains its intensity predominantly as a result of an interaction of the c 3 ⌸ state with a 1 ⫹ ⌺ state, most likely the C 1 ⌺ ⫹ (v ⫽ 0) state. Molecular
Copyright © 2000 by Academic Press
A REINVESTIGATION OF THE c 3 ⌸–X 1 ⌺ ⫹ (0–0) BAND OF CO
constants have been obtained for the c 3 ⌸ state which are in reasonable agreement with those previously published. The apparently anomalous small value for the centrifugal distortion constant is explained by a homogeneous perturbation with the k 3 ⌸ (v ⫽ 2) valence state. ACKNOWLEDGMENTS We are grateful to Dr. Claudina Cossart for use of a densitometer at Orsay and to Maurice Benharrous for technical assistance in the experiments.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
R. Schmid and L. Gero¨, Nature 139, 928 (1937). L. Gero¨, Z. Phys. 109, 210 –215 (1938). S. G. Tilford, J. Chem. Phys. 50, 3126 –3127 (1969). M. L. Ginter and S. G. Tilford, J. Mol. Spectrosc. 31, 292–307 (1969). T. Siwiec-Rytel, J. Mol. Spectrosc. 97, 234 –243 (1983). T. Rytel and M. Rytel, Acta Phys. Hung. 55, 69 – 84 (1984). T. Rytel and M. Rytel, Acta Phys. Hung. 59, 355–369 (1986). R. Hakalla, R. Kepa, M. Rytel, and M. Zachwieja, J. Mol. Spectrosc. 197, 199 –211 (1999). 9. I. Dabrowski, M. Vervloet, and D.-C. Wang, Can. J. Phys. 65, 1171–1177 (1987). 10. P. Klopotek and C. R. Vidal, J. Opt. Soc. Am. B: Opt. Phys. 2, 869 – 876 (1985).
319
11. M. Eidelsberg, J.-Y. Roncin, A. Le Floch, F. Launay, C. Letzelter, and J. Rostas, J. Mol. Spectrosc. 121, 309 –336 (1987). 12. J. Baker and F. Launay, J. Mol. Spectrosc. 165, 75– 87 (1994). 13. W. Ubachs, P. C. Hinnen, P. Hansen, S. Stolte, W. Hogervorst, and P. Cacciani, J. Mol. Spectrosc. 174, 388 –396 (1995). 14. M. Eidelsberg, A. Le Floch, F. Launay, J. Rostas, J-Y. Roncin, and M. Vervloet, unpublished manuscript. 15. D. R. Lide, (Ed.), “CRC Handbook of Chemistry and Physics, 75th ed.,” CRC Press, Boca Raton, FL, 1994. 16. M. Eidelsberg and F. Rostas, Astron. Astrophys. 235, 472– 489 (1990). 17. M. Eidelsberg, J. J. Benayoun, Y. Viala, and F. Rostas, Astron. Astrophys. Suppl. 90, 231–282 (1991). 18. I. Kovacs, “Rotational Structure in the Spectra of Diatomic Molecules,” Hilger, London, 1969. 19. J. M. Brown and A. J. Merer, J. Mol. Spectrosc. 74, 488 – 494 (1979). 20. G. Guelachvili, D. De Villeneuve, R. Farrenq, W. Urban, and J. Verges, J. Mol. Spectrosc. 98, 64 –79 (1983). 21. A. Mellinger and C. R. Vidal, J. Chem. Phys. 101, 104 –110 (1994). 22. C. Amiot, J.-Y. Roncin, and J. Verges, J. Phys. B: At., Mol. Opt. Phys. 19, L19 –L23 (1986). 23. J. Baker, J. L. Lemaire, S. Couris, A. Vient, D. Malmasson, and F. Rostas, Chem. Phys. 178, 569 –579 (1993). 24. J. Baker, J. Mol. Spectrosc. 167, 323–333 (1994). 25. G. Berden, R. T. Jongma, D. Van der Zande, and G. Meijer, J. Chem. Phys. 107, 8303– 8310 (1997). 26. J. Baker and F. Launay, J. Mol. Spectrosc. 203, 196 –199 (2000). 27. H. Lefebvre-Brion and R. W. Field, “Perturbations in the Spectra of Diatomic Molecules,” Academic Press, Orlando, 1986.
Copyright © 2000 by Academic Press
A Reinvestigation of the c 3⌸–X 1⌺ ⴙ (0 – 0) Absorption Band of Carbon Monoxide Jacob Baker,* ,1 Franc¸oise Launay,† Miche´le Eidelsberg,† and Franc¸ois Rostas† *Division of Environmental Health and Risk Management, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom; and †DAMAp et UMR 8588 du CNRS, Observatoire de Paris, Section de Meudon, 92195 Meudon Cedex, France Received May 22, 2000
The forbidden c 3 ⌸–X 1 ⌺ ⫹ (0–0) absorption band of carbon monoxide has been reinvestigated under different pressure conditions using the 10.7-m VUV spectrograph at Meudon. Overlap with the allowed C 1 ⌸–X 1 ⌺ ⫹ (0–0) band at lower transition energy has been taken into account. We have identified a new rotational branch corresponding to an S-type branch and extended the analysis to both higher and lower J. An analysis of the band structure and the low J transition lines suggests that the band gains its intensity predominantly as a result of an interaction of the c 3 ⌸ state with a 1⌺ ⫹ state, most likely the C 1 ⌺ ⫹ (v ⫽ 0) state. Molecular constants have been obtained for the c 3 ⌸ state that are in reasonable agreement with those previously published. The apparently anomalous small value for the centrifugal distortion constant is explained by a homogeneous perturbation with the k 3 ⌸ valence state. © 2000 Academic Press INTRODUCTION
The c 3 ⌸ state of carbon monoxide was first observed experimentally in emission as the upper state of the 3A band system (c–a 3 ⌸) but was initially believed to be a 3⌺ state (1, 2). These emission bands are overlapped with those of the fourth positive system ( A–X emission bands) and hence are difficult to identify. Later Tilford (3) recorded the absorption band of the spin-forbidden c–X 1 ⌺ ⫹ transition and observed a P- and R-type branch and a condensed Q-type branch. This was inconsistent with the initial assignment to a 3⌺ state and led Tilford to reassign the c state to a 3⌸ state of approximately pure Hund’s case b character. This reassignment was supported by the work of Ginter and Tilford (4) who reanalyzed the 3A band system under higher resolution and observed ⌳-type doubling in the c state. Rytel and co-workers (5– 8) have since investigated the 3A band system for various different isotopomers of CO. However, analysis of the 3A band system has been somewhat limited by poor data at low J due to overlapping rotational structure and the presence of perturbations. Dabrowski et al. (9) observed the near-infrared c 3 ⌸–b 3 ⌺ ⫹ (0–0) emission band of carbon monoxide in a radiofrequency discharge. Difficulties were reported in the analysis of this band due to both states being heavily perturbed, particularly the b state. “Empirical parameters” for both states were given where the analysis was limited to transition lines with N⬙ ⬍ 10. These lines did not appear to be severely perturbed and hence in the analysis perturbations were neglected. A spin– orbit constant of A ⫽ 1.5 cm ⫺1 for the c 3 ⌸ state was determined in the work. This value was said to be similar to a 1
previous study by Klopotek and Vidal (10) that examined high-lying states of carbon monoxide by means of a two-step excitation from the ground state. This earlier study observed triplet splitting in the c 3 ⌸ state for N ⫽ 1–5, but no line positions were presented. Although Klopotek and Vidal reported a fine-structure constant of A ⫽ 1.49 cm ⫺1, this related to only one of the parity components of the c state. In fact, Klopotek and Vidal report observing different fine-structure splittings depending on whether the intermediate state, the a⬘ 3 ⫹ ⌺ state, had plus or minus parity. This was said to be most likely due to a perturbation of the c state with a ⌺ ⫹ state. Clearly, there is some uncertainty in the nature of the perturbations and the molecular constants of the c state of carbon monoxide, which explains our interest in reinvestigating the c–X band. The advantage of studying the c–X band is that the lower state, the ground state, is unperturbed and well characterized such that the fine-structure assignment and analysis of the upper c state is greatly simplified. Also, the band structure is quite simple and hence relatively easy to interpret. However, this band is partially overlapped with the allowed C–X (0–0) absorption band that occurs to the red (i.e., to longer wavelengths) of the c–X band and it is important to take this into account. Fortunately, the C–X (0–0) band has been well characterized in previous studies. The initial impetus for reinvestigating the c–X band was the identification of unassigned lines in Tilford’s (3) published c–X spectrum. SPECTROSCOPIC DATA
To whom correspondence should be addressed.
Photographic absorption spectra were obtained at room temperature over the wavelength range 102–115 nm using the 10.68-m VUV spectrograph at the Meudon observatory
314 0022-2852/00 $35.00 Copyright © 2000 by Academic Press All rights of reproduction in any form reserved.
A REINVESTIGATION OF THE c 3 ⌸–X 1 ⌺ ⫹ (0–0) BAND OF CO
315
FIG. 1. The c 3 ⌸–X 1 ⌺ ⫹ (0–0) absorption band of CO recorded in the transition energy range 92 300 –91 950 cm ⫺1 (wavelength range 1083.6 –1087.3 Å) at four different pressures. (A) 1.5 Torr, (B) 0.5 Torr, (C) 0.15 Torr, and (D) 0.07 Torr. A simulation of the band is also shown, where T ⫽ 298 K, ⫽ 20, and a Gaussian linewidth of 0.4 cm ⫺1 (FWHM) was used (see text for further details). Overlapping rotational structure from the C 1 ⌸–X 1 ⌺ ⫹ (0–0) band of CO and the various isotopomers are also indicated.
(21.4-m effective path length). The experimental and calibration procedure has been described elsewhere (11, 12). Calibration was achieved by recording atomic emission lines from a windowless hollow-cathode lamp. The small wavelength shift between the hollow-cathode reference lamp and the VUV light source (due to slightly different optical paths within the spectrometer) was corrected for by reference to two Ar I impurity lines appearing in the background continuum. In addition, rotational lines of the C–X (0–0) absorption band of 12C 16O (13, 14) were also used for calibration. Natural isotopic composition carbon monoxide gas (99 and 99.997% purity) was used in this study. The c–X (0–0) ab-
sorption band was rotationally analyzed from measurements of photographic plate spectra recorded at four different pressures 1.5, 0.5, 0.15, and 0.07 Torr. Toward the red, i.e., to longer wavelength, the c–X (0–0) band is interleaved and overlapped with high J R-branch rotational lines of the C–X (0–0) band. Increasing the gas pressure results in stronger absorption of the lines of the forbidden c–X (0–0) band but also results in a widening zone of saturation from the band center of the C–X (0–0) band. Hence, a range of pressures was needed for examining the spectrum (see Fig. 1). In identifying rotational lines of the c–X (0–0) band it was necessary to take into account the rotational lines of the C–X
Copyright © 2000 by Academic Press
316
BAKER ET AL.
TABLE 1 Line Positions for the c 3⌸ (vv ⴝ 0)–X 1⌺ ⴙ (vv ⴝ 0) Transition a
(0–0) band, which overlap in particular the P-type and O-type branches. Since the C–X (0–0) absorption band is very much stronger than the c–X band, all the naturally occurring isotopomers of CO were considered. From isotopic abundance tables (15) the following relative fractional abundances are expected (given in parentheses): 12C 16O (1); 13C 16O (1.11 ⫻ 10 ⫺2); 12C 18O (2.00 ⫻ 10 ⫺3); 12C 17O (3.81 ⫻ 10 ⫺4); 13C 18O (2.23 ⫻ 10 ⫺5). All these isotopomers, except for 12C 17O, have well-determined C 1 ⌺ ⫹ state molecular constants (13, 14, 16, 17) and their C–X (0–0) transition lines were readily determined and accounted for in the spectrum. During this investigation some new lines were observed that could be assigned to the C–X (0–0) band of 12C 17O (13). These will be considered elsewhere. RESULTS AND DISCUSSION
Figure 1 shows the c 3 ⌸–X 1 ⌺ ⫹ (0–0) absorption band of carbon monoxide photographed over the transition energy range 92 300 –91 950 cm ⫺1 (wavelength range 1083.4 –1087.5
Å) at four different pressures. This band has a prominent blue-degraded Q-type bandhead at 92 076.8 ⫾ 1.0 cm ⫺1, indicating that B⬘ ⬎ B⬙. Tilford (3), over 30 years ago, performed the only other study of this band. He identified the P-, Q-, and R-type branches and was the first to assign the upper state to a 3 ⌸ state. However, he was only able to perform a partial rotational analysis. As seen from Fig. 1, a most prominent feature of the band is a regular series of lines extending to higher transition energy that has a line spacing about twice that of the R-type branch. This line spacing is that which would be expected for an S-type branch, where ⌬N ⫽ 2. This branch is in fact the S R branch. This branch was not identified by Tilford (3) even though three of its lines are evident in his published spectrum (for example, in Fig. 1 of Ref. (3), the S R(6) line lies between “R(45)” and “R(46)” of C–X (0–0), while the S R(5) line lies between “R(43)” and “R(44)”). The line positions and assignments of the observed spectral lines of the c 3 ⌸–X 1 ⌺ ⫹ (0–0) band are given in Table 1. The
Copyright © 2000 by Academic Press
A REINVESTIGATION OF THE c 3 ⌸–X 1 ⌺ ⫹ (0–0) BAND OF CO
TABLE 2 Possible Rotational Branch and Upper Level Assignments for the c–X (0 – 0) Band a
a
The upper level assignments in terms of spin component and parity (e/f ) are given in parentheses.
measurements and estimated errors were obtained from several spectra recorded under the various pressure conditions described in the previous section. Figure 1 also shows a simulation of the absorption band assuming a rotational temperature of T ⫽ 298 K and a Gaussian linewidth of 0.4 cm ⫺1 (FWHM). In this simulation the energy levels of the c 3 ⌸ state were obtained using molecular constants derived from a weighted least-squares fit of the measured line position given in Table 1. The 3⌸– 1⌺ ⫹ linestrength factors were taken from Kovacs (18) in which the 3⌸ state is treated in the intermediate Hund’s case a/b framework. In the simulation no attempt was made to account for the threshold characteristics of the photographic plate nor its nonlinear response above threshold. The linestrength formulas contain a parameter labeled ⫽ D/E, where D and E correspond in the present case to the effective transition moments arising from mixing of 1⌺ ⫹ and 1⌸ character into the c 3 ⌸ state, respectively. If we consider the linestrength factor of the S R rotational branch, we find for ⫽ 1 there is a cancellation of terms that results in a negligible absorption intensity that exponentially decreases with J. Since the S R branch is observed to be relatively strong, cancellation does not occur, implying that Ⰷ 1 or Ⰶ 1. Hence, the c–X (0–0) transition predominantly gains intensity through the mixing of the c 3 ⌸ state with either a 1⌺ ⫹ state or a 1⌸ state but not both. This mixing can occur through spin– orbit interaction. There are two obvious candidates, the C 1 ⌺ ⫹ and E 1 ⌸ Rydberg states, respectively. Table 2 gives the main branch assignments for both cases. To distinguish between the two cases, the c–X band needs to be examined at low J. From Table 2 it can be seen that the S-, Q-, and O-type branches are the same for the two cases but the R- and P-type branches are different. We note that the Q-type branch is an overlap of two branches; however, for the lines that were observed in this study, the two branches could not be resolved and appeared as a single branch. At medium and high J ( J⬙ ⬎ 5), as the c 3 ⌸ state is essentially of pure Hund’s case b character, there is very little difference in line position between the two cases. However, there are small differences in line positions at low J and more importantly different branches may start at different J⬙ values. We find for the P-type branch the first nonzero line occurs at J⬙ ⫽ 2 in both cases. However, for the R-type branch we find the R R rotational branch (case 1)
317
begins at J⬙ ⫽ 0, while the R Q branch (case 2) begins at J⬙ ⫽ 2. Hence, by examining the R-type branch at low J⬙, we might be able to distinguish between the two cases. Figure 2 is a densitometer recording showing the central region of the c–X (0–0) band photographed at 0.15 Torr. Considering the low J lines of the R-type rotational branch, the R(0) line would be expected to be hidden in the Q-type bandhead while the R(1) line would be overlapped with the Q(15) line. From Fig. 2, when we compare the relative intensities of the Q-type lines, Q(13), Q(15), Q(16), and Q(17), we do see a large enhancement of the intensity of the Q(15) line (note that the Q(14) line is overlapped with the R(35) line of the C–X (0–0) band). This observation is consistent with the existence of a strong R(1) line and the case 1 assignment. We also obtain a better fit to the low J⬙ line positions assuming the case 1 assignment. Hence, we adopt the case 1 assignment, i.e., the band gains its intensity predominantly through the mixing of the c 3 ⌸ state with a 1⌺ ⫹ state, most likely the C 1 ⌺ ⫹ (v ⫽ 0) state. There is a further observation to support this assignment. Klopotek and Vidal (10) looked at the two-step excitation to the c 3 ⌸ state from the ground state via the a⬘ 3 ⌺ ⫹ state. Giving limited details, they noted an anomalous finestructure splitting at low J for the c 3 ⌸ state “indicating a perturbation most likely due to a ⌺ ⫹ state.” Table 3 gives molecular parameters obtained from the results of weighted least-squares rotational fits. For fit 1 no explicit perturbations were included for the upper state whose
FIG. 2. A densitometer recording of the central region of the c 3 ⌸–X 1 ⌺ ⫹ (0–0) band photographed at 0.15 Torr and room temperature. The R R(1) line overlaps the Q-type, Q(15) line. (The Q-type bandhead has a “flat top” due to saturation of the photographic plate.)
Copyright © 2000 by Academic Press
318
BAKER ET AL.
TABLE 3 Molecular Constants for the c 3⌸ (vv ⴝ 0) State a
a All parameters are in units of cm ⫺1. Values between parentheses are errors, to one standard deviation, in the least significant figure resulting from the fit. For T 00 , the error given is that obtained from the fit and hence neglects possible calibration errors (estimated to be up to 0.2 cm ⫺1). is the standard deviation of the weighted fit. For both fits the following molecular constants of the c 3 ⌸ (v ⫽ 0) state were fixed at the nonzero values of Dabrowski et al. (9); ⫽ 0.064 cm ⫺1, (o ⫹ p ⫹ q) ⫽ 0.087 cm ⫺1, ( p ⫹ 2q) ⫽ 0.0209 cm ⫺1. (See text for further details.) b In the fitting procedure the molecular constants of the k state were fixed to those values given by Mellinger and Vidal (Table V of Ref. (21)).
rotational energy levels were fitted to the eigenvalues of the effective 3⌸ Hamiltonian matrix given by Brown and Merer (19), while the X 1 ⌺ ⫹ ground state rotational energy levels were fitted simply to the expression F共 J兲 ⫽ BJ共 J ⫹ 1兲 ⫺ D共 J共 J ⫹ 1兲兲 2
[1]
using B ⫽ 1.9225288 cm ⫺1 and D ⫽ 6.120 ⫻ 10 ⫺6 cm ⫺1, from Ref. (20). The upper state molecular parameters that could not be readily determined were fixed to those obtained by Dabrowski et al. (9) rather than fixed to zero. The second fit takes into account a perturbation with the k 3 ⌸ state (vide infra). There are some points to note regarding the c 3 ⌸ state from the fits. First, it has a well-determined lambda doubling parameter q ⫽ 0.0098 cm ⫺1. This arises mainly as a result of the interaction of the c 3 ⌸ 3p Rydberg state with the j 3 ⌺ ⫹ 3p Rydberg state which in the pure precession model yields a value of q ⫽ 0.012 cm ⫺1 (21). The actual value is also similar to that of the isoconfigurational E 1 ⌸ 3p state, where q ⫽ 0.0119 cm ⫺1 (22). Second, the spin– orbit constant determined is very small, as expected for a Hund’s case (b)-type state. The electronic configuration of the c 3 ⌸ state consists of a 2⌺ ⫹ ionic core and a 3p Rydberg electron. Hence, only the Rydberg electron contributes to the spin– orbit splitting and the Rydberg nature of the orbital leads to the small value. The value obtained is in fact smaller than that previously obtained in other studies (ca., 1.0 –1.5 cm ⫺1) and may effectively be zero. The only direct attempt at observing the spin– orbit splitting of the c 3 ⌸ state
(Klopotek and Vidal (10)) gave conflicting results: A ⫽ 1.49 cm ⫺1 for an “unperturbed” parity component and a “different” fine-structure splitting for the other parity component. Finally, for fit 1, where no explicit perturbation was considered, the centrifugal distortion coefficient obtained is smaller than expected and is effectively zero from the fit. This has been noted previously where a negative value for the distortion coefficient has been reported (9). This can be explained by a homogeneous perturbation with another 3⌸ state at lower energy. In fact there does exist such a state, the k 3 ⌸ valence state (12, 23–25), the v ⫽ 2 level of which lies at 91 959 cm ⫺1 (21), i.e., approximately 118 cm ⫺1 lower in energy than the c 3 ⌸ (v ⫽ 0) state. We note that Berden et al. (25) have correctly reassigned the vibrational numbering of the k state, which has been independently confirmed (26). The vibrational numbering of the k state in studies prior to that work needs incrementing by one unit. Hence a second rotational fit was performed which included explicitly a possible homogeneous interaction with the k 3 ⌸ (v ⫽ 2) state. In the fitting procedure, a 6 ⫻ 6 Hamiltonian matrix with a Hund’s case (a) basis was used with two 3 ⫻ 3 submatrices (19) to represent the c 3 ⌸ (v ⫽ 0) state and the k 3 ⌸ (v ⫽ 2) state, respectively. The rotational levels of the k 3 ⌸ (v ⫽ 2) state were determined using the molecular constants given by Mellinger and Vidal (21). The homogeneous interaction between the two states was represented by including the off-diagonal terms, 具c 3 ⌸ x 兩H兩k 3 ⌸ x 典 ⫽ W, where x ⫽ 0, 1, and 2, in the 6 ⫻ 6 Hamiltonian matrix (6, 27). The ground state was treated as before. The results of the fit are given in the final column of Table 3. By including this interaction we obtained a better fit to the line positions of the c–X (0–0) band and a more realistic value for the centrifugal distortion constant, D. We have also observed a few weak lines emerging from the long wavelength side of the C–X (0–0) absorption band which should be attributable to the k–X (2–0) transition. The main part of the k–X (2–0) band is completely overlapped with the C–X (0–0) band. However, the lines that we have observed present some apparent anomalies which we are currently investigating. We are also planning to reanalyze the 3A band system and the c–b near-infrared band in order to resolve some small discrepancies in the literature concerning the c 3 ⌸ state. CONCLUSION
We have reinvestigated the c 3 ⌸–X 1 ⌺ ⫹ (0–0) absorption band of carbon monoxide taking into account overlap with the allowed C 1 ⌸–X 1 ⌺ ⫹ (0–0) band at lower transition energies. We have identified a new rotational branch corresponding to an S-type branch and extended the analysis to both higher and lower J. An analysis of the band structure and the low J transition lines suggests that the band gains its intensity predominantly as a result of an interaction of the c 3 ⌸ state with a 1 ⫹ ⌺ state, most likely the C 1 ⌺ ⫹ (v ⫽ 0) state. Molecular
Copyright © 2000 by Academic Press
A REINVESTIGATION OF THE c 3 ⌸–X 1 ⌺ ⫹ (0–0) BAND OF CO
constants have been obtained for the c 3 ⌸ state which are in reasonable agreement with those previously published. The apparently anomalous small value for the centrifugal distortion constant is explained by a homogeneous perturbation with the k 3 ⌸ (v ⫽ 2) valence state. ACKNOWLEDGMENTS We are grateful to Dr. Claudina Cossart for use of a densitometer at Orsay and to Maurice Benharrous for technical assistance in the experiments.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
R. Schmid and L. Gero¨, Nature 139, 928 (1937). L. Gero¨, Z. Phys. 109, 210 –215 (1938). S. G. Tilford, J. Chem. Phys. 50, 3126 –3127 (1969). M. L. Ginter and S. G. Tilford, J. Mol. Spectrosc. 31, 292–307 (1969). T. Siwiec-Rytel, J. Mol. Spectrosc. 97, 234 –243 (1983). T. Rytel and M. Rytel, Acta Phys. Hung. 55, 69 – 84 (1984). T. Rytel and M. Rytel, Acta Phys. Hung. 59, 355–369 (1986). R. Hakalla, R. Kepa, M. Rytel, and M. Zachwieja, J. Mol. Spectrosc. 197, 199 –211 (1999). 9. I. Dabrowski, M. Vervloet, and D.-C. Wang, Can. J. Phys. 65, 1171–1177 (1987). 10. P. Klopotek and C. R. Vidal, J. Opt. Soc. Am. B: Opt. Phys. 2, 869 – 876 (1985).
319
11. M. Eidelsberg, J.-Y. Roncin, A. Le Floch, F. Launay, C. Letzelter, and J. Rostas, J. Mol. Spectrosc. 121, 309 –336 (1987). 12. J. Baker and F. Launay, J. Mol. Spectrosc. 165, 75– 87 (1994). 13. W. Ubachs, P. C. Hinnen, P. Hansen, S. Stolte, W. Hogervorst, and P. Cacciani, J. Mol. Spectrosc. 174, 388 –396 (1995). 14. M. Eidelsberg, A. Le Floch, F. Launay, J. Rostas, J-Y. Roncin, and M. Vervloet, unpublished manuscript. 15. D. R. Lide, (Ed.), “CRC Handbook of Chemistry and Physics, 75th ed.,” CRC Press, Boca Raton, FL, 1994. 16. M. Eidelsberg and F. Rostas, Astron. Astrophys. 235, 472– 489 (1990). 17. M. Eidelsberg, J. J. Benayoun, Y. Viala, and F. Rostas, Astron. Astrophys. Suppl. 90, 231–282 (1991). 18. I. Kovacs, “Rotational Structure in the Spectra of Diatomic Molecules,” Hilger, London, 1969. 19. J. M. Brown and A. J. Merer, J. Mol. Spectrosc. 74, 488 – 494 (1979). 20. G. Guelachvili, D. De Villeneuve, R. Farrenq, W. Urban, and J. Verges, J. Mol. Spectrosc. 98, 64 –79 (1983). 21. A. Mellinger and C. R. Vidal, J. Chem. Phys. 101, 104 –110 (1994). 22. C. Amiot, J.-Y. Roncin, and J. Verges, J. Phys. B: At., Mol. Opt. Phys. 19, L19 –L23 (1986). 23. J. Baker, J. L. Lemaire, S. Couris, A. Vient, D. Malmasson, and F. Rostas, Chem. Phys. 178, 569 –579 (1993). 24. J. Baker, J. Mol. Spectrosc. 167, 323–333 (1994). 25. G. Berden, R. T. Jongma, D. Van der Zande, and G. Meijer, J. Chem. Phys. 107, 8303– 8310 (1997). 26. J. Baker and F. Launay, J. Mol. Spectrosc. 203, 196 –199 (2000). 27. H. Lefebvre-Brion and R. W. Field, “Perturbations in the Spectra of Diatomic Molecules,” Academic Press, Orlando, 1986.
Copyright © 2000 by Academic Press