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Analysis of the Comet-Tail (A2Πi–X2Σ+) Bands of 13C16O+
Journal of Molecular Spectroscopy 214, 117–123 (2002) doi:10.1006/jmsp.2002.8595
Analysis of the Comet-Tail (A2 Πi –X 2 Σ+ ) Bands of 13 C16 O+ R. K¸epa,∗ A. Kocan,∗ M. Ostrowska,∗ I. Piotrowska-Domagala,∗ Z. Jakubek,† and M. Zachwieja† ∗ Atomic and Molecular Physics Laboratory, Institute of Physics, University of Rzesz´ow, 35-310 Rzesz´ow, Poland; and †Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada K1A OR6 Received October 29, 2001; in revised form May 16, 2002
In the electronic emission spectrum of the isotopic carbon monoxide ion 13 C16 O+ molecule, seven bands of the comet-tail (A2 i –X 2 + ) system have been recorded and analyzed. The spin splitting in most observed lines of the bands 1–0, 2–0, 3–0, 4–0, 5–0, 2–1, and 7–1 comprising over 1900 lines has been recorded under high resolution by using conventional spectroscopy. The rotational analysis of bands has been performed by nonlinear least-squares procedures and by means of effective Hamiltonians of Brown et al., the rovibronic structure parameters have been obtained. As a result of multistaged and merged analysis of the currently obtained bands of the A–X system and of the bands of the B–X system obtained earlier the state of information about the energy structure has been significantly enlarged for the A state and enlarged and improved for the X state. Also RKR potential curves have been calculated for both states and Franck–Condon factors as well as r -centroids of the comet-tail system C 2002 Elsevier Science (USA) of 13 C16 O+ . INTRODUCTION
Laboratory studies of the spectrum and the energy structure of the molecular ion CO+ are especially stimulating because of the important role which it plays in astrophysics. The occurrence of this molecular ion in the atmospheres of planets, the sun and stars, and in comet tails and interstellar space provides, however, possibilities of diagnosing physical conditions and physical– chemical processes occurring in these objects. There is also an increased interest in this molecule due to the role it plays on the Earth in monitoring combustion processes and in environmental research. The bibliography and tabulations of the spectroscopic information dealing with the four electronic states, X 2 + , A2 i , B 2 + , and C 2 r , and the four observed band systems, namely, the comet-tail (A2 i –X 2 + ), the Baldet–Johnson (B 2 + –A2 i ), the first-negative (B 2 + –X 2 + ), and the Marchand–D’Incan–Janin (C 2 r –A2 i ) systems of this molecule, have been collected in several monographs (1–3) and by Haridass et al. (4). The comet-tail system, being one of the most comprehensive band systems of this molecule, has been explored the most extensively in the most abundant isotopomer 12 C16 O+ (1, 4–11). There have been fewer works, which were concerned with a smaller number of bands, devoted to the study of this system in the other isotopomers of CO+ . Asundi et al. (12) and Dhumwad et al. (13) recorded under low resolution several bands of this system and analyzed isotopic shifts of bandheads in 13 C16 O+ and 12 C18 O+ , respectively. Rotational analysis of the 2–0, 3–0, 4–0, and 0–2 bands of the 12 C18 O+ molecule was performed by Supplementary data for this article are available on IDEAL (http://www. idealibrary.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://msa.lib.ohio-state.edu/jmsa hp.htm). 117
Vujisi´c and Pesi´c (10), as well as for the 1–0, 2–0, 3–0, 4–0, and 2–1 bands of 14 C16 O+ by Jakubek et al. (14), and for nine bands, v –0, v = 1 to 5, 1–1, 2–1, 0–1, and 0–2 bands of the 13 C18 O+ isotopomer by Prasad and Reddy (15). It is surprising that in spite of an easy availability of the 13 C isotope, its relatively high abundance in space, and a large deficiency of molecular constants for the 13 C16 O+ molecule, the studies of the A–X system performed so far in this isotopomer have been fragmentary and incomplete. Brown et al. (16) recorded under moderate resolution and analyzed 124 lines of the 0–0 band by using an ion-beam laser spectroscopy technique. Vujisi´c et al. (17) photographed and analyzed 99 lines of the 2–0 band. Carrington et al. (18) by means of a high-velocity ion-beam technique measured and analyzed 22 fine and hyperfine components belonging to the 0–0 and 1–0 band lines. In the present work we present the results of high-resolution observations and modern analysis of seven bands v –0, v = 1 to 5, 2–1, and 7–1 of the comet-tail system in the 13 C16 O+ molecule. The objective of this paper is to complete, unify, and improve the spectroscopic and quantum-mechanical information related both to the first excited −A2 i electronic state and the whole energy structure of 13 C16 O+ . EXPERIMENTAL DETAILS
As a source of the emission spectrum of the comet-tail bands, just as in our earlier investigations of the spectra of the CO+ molecule (14, 19, 20) an air-cooled hollow-cathode discharge tube was used. The tube was filled with carbon monoxide enriched with carbon 13 C with about 90% concentration of the 13 C isotope and at a pressure of 0.1 kPa. The tube was supplied by a standard 500-V D.C. generator; mean current was about 50 mA. This permitted us to limit the temperature of the source and to limit the width of the spectrum lines, which for the resolved lines 0022-2852/02 $35.00 C 2002 Elsevier Science (USA)
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FIG. 1. Microdensitometer trace and the rotational assignments of the R21 and R22 /Q21 and Q22 /P21 bandhead regions in the spectrum of the 2–0 band of the Comet-Tail system of 13 C16 O+ .
was about 0.12–0.14 cm−1 . The spectra of the bands were photographed in the 6th and 7th orders of a 2-m plane grating Ebert spectrograph PGS-2, equipped with a 651-grooves/mm grating with a total of 45 600 grooves, and blazed at 1.0 µm. The theoretical resolving power and approximate observed resolving power varied from 270 000 to 320 000, and the reciprocal linear dispersion varied from 0.041 to 0.067 nm/mm. The exposure time of the 7 selected bands of this system located in the region ˚ on ORWO WU-2 spectral plates varied from of 3530–4640 A 2 to 7 h, depending on band intensity. Thorium emission lines (21) obtained from several orders from a water-cooled hollowcathode tube were used as wavelength standards. The relative position of the lines was measured on an automatic comparator assembled in our laboratory. The position on the plate was controlled interferometrically, whereas the profile of lines was measured photoelectrically point by point. The positions of the line centers were calculated by means of an interactive graphic computer program using the least-squares procedure and assuming Gaussian profiles for the lines. The precision of the wavenumbers of the single and resolved molecular lines was considered to be in the range of 0.005–0.010 cm−1 , whereas for the lines not completely resolved or blended (marked by an asterisk) it was estimated to be 0.020–0.040 cm−1 . In Fig. 1 is shown a part of the microdensitometer trace of the R21 and R22 /Q 21 and Q 22 /P21 bandhead regions in the spectrum of the 2–0 band. In Table 1 are presented observed wavenumbers of the 2–0 band,
whereas the wavenumbers of bands 1–0, 2–0, 3–0, 4–0, 5–0, 2–1, and 7–1 are deposited in the Electronic Depository of the Supplementary Material of the journal. Additional information about observed bands is collected in Table 2. RESULTS
Description of the Band System The comet-tail system in the CO+ molecule spectrum is a result of transitions between the first excited A2 i and the ground X 2 + states. The A state is inverted with a 13-electron structure and values of constants typical of this group of molecules. It also shows changes in the modes of coupling of intramolecular angular momenta, from Hund’s case (a), at a low quantum J number, to Hund’s case (b), at high J values. On the other hand, the lower X state belongs to Hund’s case (b). Consequently, each band of this transition resolves into two subbands, 2 1/2 –2 + and 2 3/2 –2 + , and in the transition spectrum 12 branches appear which are identified as R21ee , R22 f f , Q 21 f e , Q 22e f , P21ee , P22 f f , R11ee , R12 f f , Q 11 f e , Q 12e f , P11ee , and P12 f f . The scheme of this transition is well known as well as the parity of levels indicated in the e/f notation, as proposed by Brown et al. (22). Because the spin–rotation interaction constant in the lower state is small (γ X ≈ 9 · 10−3 cm−1 ), the following pairs of branches, R22 f f and Q 21 f e ; Q 22e f and P21ee ; Q 11 f e and R12 f e as well as P11ee and Q 12e f can overlap partially or completely.
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ANALYSIS OF COMET-TAIL BANDS
TABLE 1 Observed Wavenumbers (in cm−1 ) and Rotational Assignments for the 2–0 Band of the Comet-Tail (A2 Πi − X2 Σ+ ) System in the 13 C16 O+ Moleculea J
R21ee
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5
23458.396(23) 23462.069(12) 23464.957(−4) 23467.097(10) 23468.425(−2) 23468.688(0) 23468.777(10) 23467.769(7) 23465.970(−5) 23463.407(4) 23460.038(−8) 23455.901(−1) 23450.987(15) 23445.253(−1) 23438.701∗ 23431.460(11) 23423.365(5) 23414.502(22) 23404.808(4) 23394.308(−27) 23383.066(−5) 23371.005(−4) 23358.150(1) 23344.527∗ 23330.056(24) 23314.791(20)
R22 f f 23454.597(12) 23453.733(−16) 23452.113(−17) 23449.707(−26) 23446.518∗ 23442.563∗ 23437.804∗ 23432.275∗ 23425.966∗ 23418.861∗ 23410.976∗ 23402.385(5) 23392.946(17) 23382.720(10) 23371.682(19) 23359.818(−28) 23347.229(−11) 23333.838(−4) 23319.610∗ 23304.675(10) 23288.858(−28) 23272.315(4) 23254.952(11) 23236.772(0) 23217.804(1) 23198.032(−5) 23177.465(−5) 23156.100(0) 23133.927(−1) 23110.791∗ 23087.172(1) 23062.583(−3)
J
R11ee
R12 f f
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5
23333.483∗ 23336.968(0) 23339.599∗ 23341.452(2) 23342.395(−22) 23342.517(−19) 23341.809(5) 23340.219(−5) 23337.785(−10) 23334.514(−4) 23330.391(−1) 23325.421(2) 23319.610(12) 23312.933(3) 23305.415(−1) 23297.036(−19) 23287.847(−1) 23277.800(4) 23266.895(−4) 23255.153(−4) 23242.566(−6) 23229.138(−5) 23214.863(−7) 23199.749(−5) 23183.792(−4) 23167.005(8) 3149.353(−2) 23130.889(17) 23111.557(9) 23091.384(1)
23329.689(−12) 23329.462(−1) 23328.358(−18) 23326.418(−23) 23323.624∗ 23319.980∗ 23315.491∗ 23310.158∗ 23303.972∗ 23296.970∗ 23289.139(−13) 23280.428(−9) 23270.866(−11) 23260.451(−21) 23249.199(−24) 23237.141(10) 23224.199(5) 23210.434(9) 23195.816(20) 23180.345(11) 23164.041(10) 23146.899(10) 23128.917(11) 23109.962∗ 23090.430(6) 23069.923(−3) 23048.558(−12) 23026.163∗ 23003.148∗
a ∗
Q 21 f e
23454.597(23) 23453.733(15) 23452.113(22) 23449.707(22) 23446.518(21) 23442.563∗ 23437.804∗ 23432.275∗ 23425.966∗ 23418.861∗ 23410.976∗ 23402.285(23) 23392.836(18) 23382.594(18) 23371.522(3) 23359.725(10) 23347.070(−9) 23333.679(8) 23319.463(−9) 23304.479(1) 23288.700(9) 23272.102(−5) 23254.746(19) 23236.546(−4) 23217.565(−9) 23197.801(3) 23177.231(10) 23155.833(−11)
Q 11 f e 23329.689(2) 23329.462(21) 23328.358(12) 23326.418(16) 23323.624(15) 23319.980(11) 23315.491(11) 23310.158(15) 23303.972(13) 23296.970∗ 23289.054(3) 23280.331(3) 23270.762(3) 23260.347(1) 23249.085(−4) 23236.983(−4) 23224.034(−9) 23210.259(4) 23195.621(−5) 23180.160(4) 23163.843(−1) 23146.691(−2) 23128.700(−1) 23109.873(2) 23090.197(−5) 23069.691(−4) 23048.286∗ 23026.162(−7) 23003.146(−4) 22979.293(−3) 22955.768∗ 22929.122(11) 22902.719(−1) 22875.477(−19)
Q 22e f 23450.155(3) 23447.093(−9) 23443.264(−7) 23438.665(3) 23433.258(−15) 23427.100(−4) 23420.138(−18) 23412.414(−12) 23403.902(−15) 23394.610(−17) 23384.540(−14) 23373.686(−13) 23362.048(−13) 23349.635(−4) 23336.431(−2) 23322.446(4) 23307.644(−21) 23292.100(−2) 23275.753(2) 23258.619(8) 23240.673(−9) 23221.961(−2) 23202.453(0) 23182.153(1) 23161.061(4) 23139.134∗ 23116.490(3) 23093.013(4) 23068.731(−5) 23043.680(16) 23017.804(9) 22991.125(−2) 22963.650(−9) 22935.380(−10) 22906.332(11) Q 12e f 23325.411∗ 23322.264∗ 23318.174(−9) 23313.324(−11) 23307.644(5) 23301.072(−24) 23293.665(−19) 23285.439(−16) 23276.316(−13) 23266.407∗ 23255.600∗ 23243.988∗ 23231.518∗ 23218.281(16) 23204.123(14) 23189.121(10) 23173.254(−17) 23156.565(−24) 23139.048(−19) 23120.692(−14) 23101.493(−11) 23081.453(−12) 23060.590(3) 23038.880(8) 23016.320(−2) 22992.906(−18) 22968.709(−4) 22943.726(19) 22917.758(−9)
Figures in parentheses denote observed minus calculated values in units of the last quoted digit. The lines marked by asterisk are less accurate and not used in the evaluation of molecular constants. C 2002 Elsevier Science (USA)
P21ee
P22 f f
23450.155(16) 23447.093(13) 23443.264(23) 23438.665∗ 23433.258∗ 23427.100∗ 23420.138∗ 23414.412∗ 23403.902∗ 23394.610∗ 23384.402∗ 23373.572(−15) 23361.960(17) 23349.518(5) 23336.316(17) 23322.264(14)∗ 23307.551∗ 23291.924(−16) 23275.581(0) 23258.426(−7) 23240.475(−20) 23221.772(4) 23202.245(−4) 23181.940(1) 23160.839(3) 23138.916(−22) 23116.273(25) 23092.769(5) 23068.541∗ 23043.290∗ 23017.566(15)
23442.563∗ 23435.863(19) 23428.270(5) 23419.906(0) 23410.745(−24) 23400.854(1) 23390.177(20) 23378.682(−1) 23366.423(−4) 23353.400(8) 23339.599(22) 23324.986(6) 23309.604(2) 23293.451(9) 23276.501(3) 23258.782(11) 23240.255(−6) 23220.960(−5) 23200.882(−3) 23180.148∗ 23158.365(1) 23135.918(−5) 23112.695(2) 23088.665(−9) 23063.865(0) 23038.270(3) 23011.867(−9) 22984.676(−17) 22956.718(0) 22927.956(7) 22898.379(−6)
P11ee
P12 f f
23325.411∗ 23322.264∗ 23318.174∗ 23313.324∗ 23307.644∗ 23301.072∗ 23293.665∗ 23285.439∗ 23276.316∗ 23266.407∗ 23255.600∗ 23243.988∗ 23231.518∗ 23218.193∗ 23203.963(−11) 23188.963(−4) 23173.128(9) 23156.440(11) 23138.916(19) 23120.531(4) 23101.321(4) 23081.261(−7) 23060.590∗ 23038.672(13) 23016.100(1) 22992.709(5) 22968.481(7) 22943.422(13) 22917.540∗ 22890.779(1)
23317.927∗ 23310.940∗ 23303.205∗ 23294.529(−6) 23285.083(4) 23274.777(0) 23263.624(−6) 23251.633(−1) 23238.779(−15) 23225.097(−12) 23210.264∗ 23195.208(−1) 23178.994(−1) 23161.936(−2) 23145.758∗ 23125.301(−4) 23105.706(−23) 23085.309(−5) 23064.063(1) 23041.977(4) 23019.041(−7) 22995.287(−2)
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TABLE 2 Summary of Observations and Analyses of the Comet-Tail System (A2 Πi –X 2 Σ+ ) of the 13 C16 O+ Molecule Band heads (in cm−1 )
Band 1–0
2–0
3–0
4–0
5–0
2–1
7–1
21994.43 21979.22 21867.79 21854.12
R21 R22 /Q 21 R11 Q 11 /R12
23468.99 23469.05c 23454.60 23454.65c 23342.52 23342.54c 23329.69 23329.73c
R21
Band origina (in cm−1 )
Total number of lines
Jmax
σ f · 102b (in cm−1 )
21914.4663(17)
294
32.5
1.03
23390.0235(15) 23390.65(5)c
232 99c
34.5 18.5c
0.95 8.9c
24839.8860(13)
305
32.5
0.79
26264.1619(12)
365
35.5
0.88
27662.9857(17)
309
35.5
1.10
21254.1531(22)
289
30.5
1.33
28247.2904(38)
123
21.5
1.63
R22 /Q 21 R11 Q 11 /R12
24917.89 24904.39 24791.67 24779.54
R21 R22 /Q 21 R11 Q 11 /R12
26341.23 26328.52 26215.37 26203.78
R21 R22 /Q 21 R11 Q 11 /R12
27739.35 27727.29 27613.54 27602.52
R21 R22 /Q 21 R11 Q 11 /R12
21333.66 21318.85 21207.21 21193.83
R21 R22 /Q 21 R11 Q 11 /R12
28321.37 28310.31 28198.13 28187.92
R21 R22 /Q 21 R11 Q 11 /R12
a
Values from final merging (3); uncertainties in parentheses represent one standard deviation in units of the last quoted digit. Standard deviation of the fit for the individual band analysis. c After Vujsi´ c et al. (17). b
TABLE 3 Rotational Structure Constants (in cm−1 ) for the A2 Πi State of the 13 C16 O+ Moleculea v
Bv
Dv · 106
−Av
−A Dv · 104
1
1.491856(19) 1.491849(27)b 1.473764(16) 1.4783(1)c 1.455632(16) 1.437477(16) 1.419417(18) 1.38.3261(70)
5.949(19) 5.976(27)b 6.027(12) 2.0(3)c 6.053(12) 6.0611(97) 5.999(15) 6.028(23)
121.9842(29) 121.988(3)b 121.8792(20) 122.02(1)c 121.7984(20) 121.7556(19) 121.8401(28) 119.4710(61)
1.757(94) 1.459(49)b 1.412(49) — 1.284(52) 1.071(38) 1.397(79) 6.96(53)
2 3 4 5 7 a
pv · 102 1.115(24) 1.218(14)b 1.194(13) −1.01(4)c 1.067(14) 0.853(12) 0.644(22) 4.04(11)
Uncertainties in parentheses are one standard deviation in units of the last quoted digit. After Jakubek (23). c After Vujisi´ c et al. (17). b
C 2002 Elsevier Science (USA)
−qv · 104 1.98(12) 1.851(53)b 2.039(66) −1.6(4)c 2.209(79) 1.929(51) 2.53(15) 2.40(15)
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ANALYSIS OF COMET-TAIL BANDS
TABLE 4 Rotational Structure Constants (in cm−1 ) for the X 2 Σ+ State in the 13 C16 O+ Moleculea v
Bv
Dv · 106
γ · 103
0
1.880830(15) 1.880797(51)b 1.8868(22)c 1.88126(52)d 1.8860(1)e 1.863007(18) 1.863024(60)b 1.8616(7)c 1.845087(31) 1.845158(43)b 1.8439(5)c 1.827211(33) 1.827131(45)b 1.809202(32) 1.809333(50)b 1.791230(41) 1.791383(82)b
5.7275(84) 5.717(26)b 4.9(32)c 8.31(109)d 23(4)e 5.722(11) 5.734(30)b 5.2(10)c 5.707(17) 5.733(24)b 4.85(48)c 5.720(18) 5.713(26)b 5.698(21) 5.797(33)b 5.74(11) 5.876(55)b
[8.700] [12.8]b [8.686]c [0]d 9.2(1)e [8.649] [12.8]b [8.686]c [8.575] [12.8]b [8.686]c [8.480] [12.8]b [8.363] [12.8] [8.223] [12.8]b
1
2
3 4 5
a Uncertainties in parentheses are one standard deviation in units of the last quoted digit. Values in square brackets were fixed during the fits. b After K¸ edzierski et al. (19). c After Misra et al. (24). d After Brown et al. (16). e After Vujisi´ c et al. (17).
Calculation of Constants The preliminary rotational analysis of the bands observed for the first time, i.e., the identification of the bands and branches and J -numbering of the lines, was performed directly using the earlier obtained information about both A2 i (16, 17, 23) and X 2 + (19, 24) states of this transition and by performing a simulation calculus of lines for each band. The corresponding constants necessary for the above calculations have been obtained by isotopic recalculating of equilibrium molecular contants of the A (11, 20) and X (11, 25) states obtained earlier for the 12 C16 O+ molecule. The final analysis and the calculation of constants were performed in many stages via a nonlinear least-squares procedure and by means of effective Hamiltonians proposed by Brown et al. (26). The matrix elements, the definition of molecular constants, and their physical meaning were taken from the work of Amiot et al. (27). Considering the real TABLE 6 Vibrational Levels and RKR Turning Points for the A2 Πi and X 2 Σ+ States of the 13 C16 O+ Moleculea A2 i v=0 v=1
TABLE 5 Equilibrium Molecular Constants (in cm−1 ) for the A2 Πi and X 2 Σ+ States of the 13 C16 O+ Moleculea
v=3
X 2+
Te we we x e we ye · 102
A2 i
This work
20731.476(23) 1527.318(23) 13.0015(68) 2.019(65)
2164.8130(46) 14.4703(25) −0.303(33)
Be αe · 102 γe · 106
1.519092(73) 1.8152(42) 5.02(57)
De · 106 β De · 108
5.940(39) 2.90(11)
Ae α Ae · 101 β Ae · 102
−122.207(16) 1.71(11) −1.57(17)
A De · 104 α A De · 105
1.952(99) 1.97(27)
pe · 102 α pe · 103
1.665(61) −1.80(16)
qe · 104 αqe · 105
−1.702(64) −1.45(21)
1.889732(25) 1.7785(26) −24.1(51) 5.7305(42) −0.59(17)
v=2
Kdzierski et al. (19)
2164.925(60) 14.521(24) 0.33(27) 1.889714(34) 1.7750(27) 24.2(47) 5.721(22) 1.70(73)
v=4 v=5 v=6 v=7 v=8 v=9 v = 10
a Uncertainties in parentheses represent one standard deviation in units of the last quoted digit.
G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax re
760.584 1.19191 1.30328 2261.965 1.15800 1.35226 3737.524 1.13648 1.38909 5187.383 1.12001 1.42110 6611.663 1.10647 1.45041 8010.486 1.09489 1.47800 9383.971 1.08476 1.50441 10732.241 1.07572 1.52997 12055.42 1.0676 1.5549 13353.62 1.0601 1.5794 14627.0 1.053 1.604 1.24387
X 2+ 1078.867 1.07123 1.16470 3214.729 1.04209 1.20488 5321.624 1.02339 1.23476 7399.533 1.00897 1.26051 9448.437 0.99704 1.28394 11468.319 0.98679 1.30585 13459.16 0.9778 1.3267 15420.94 0.9697 1.3468 17353.6 0.962 1.366
1.11523
❛ a G(v) values are in cm−1 , r values are in A; Y = 0.173 cm−1 for the A2 00 i and Y00 = 0.078 cm−1 for the X 2 + .
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TABLE 7 Franck–Condon Factors and r -Centroids for the Comet-Tail Band System in the 13 C16 O+ Moleculea v \v
0
1
2
3
4
5
0
3.9462 E-2 1.1782 1.0797 E-1 1.1616 1.6229 E-1 1.1459 1.7801 E-1 1.1308 1.5973 E-1 1.1165 1.2467 E-1 1.1027 8.7902 E-2 1.0896 5.7427 E-2 1.0770 3.540 E-2 1.065 2.086 E-2 1.053 1.19 E-2 1.04
1.4455 E-1 1.2018 1.9158 E-1 1.1841 1.0420 E-1 1.1669 1.7679 E-2 1.1485 2.7679 E-3 1.1483 3.6831 E-2 1.1261 7.5115 E-2 1.1114 9.3720 E-2 1.0979 9.124 E-2 1.085 7.616 E-2 1.073 5.72 E-2 1.06
2.4425 E-1 1.2262 8.8062 E-2 1.2064 1.1858 E-3 1.2108 6.6602 E-2 1.1767 9.6407 E-2 1.1597 5.4382 E-2 1.1434 9.2704 E-3 1.1252 1.8856 E-3 1.1312 2.372 E-2 1.108 5.051 E-2 1.094 6.66 E-2 1.08
2.5263 E-1 1.2515 8.7246 E-6 1.5041 1.0126 E-1 1.2160 7.5927 E-2 1.1969 2.5901 E-3 1.1681 2.5449 E-2 1.1708 6.7778 E-2 1.1532 6.1249 E-2 1.1376 2.586 E-2 1.122 2.137 E-3 1.099 3.87 E-3 1.11
1.7927 E-1 1.2780 8.2422 E-2 1.2614 9.0786 E-2 1.2380 1.4171 E-3 1.2430 7.1122 E-2 1.2067 6.2579 E-2 1.1884 6.6120 E-3 1.1658 1.0419 E-2 1.1666 4.618 E-2 1.148 5.614 E-2 1.132 3.54 E-2 1.12
9.3324 E-2 1.3057 1.9051 E-1 1.2871 1.3686 E-3 1.2247 8.9696 E-2 1.2472 4.2557 E-2 1.2256 4.3768 E-3 1.2232 5.7241 E-2 1.1980 5.2000 E-2 1.1807 8.795 E-3 1.161 4.142 E-3 1.164 3.12 E-2 1.14
1 2 3 4 5 6 7 8 9 10
a
❛ The upper and lower entries for each band are the Franck–Condon factors and r -centroids (in A), respectively.
precision of the determined wavenumbers of lines and the fact that the highest observed value of J is Jmax = 40.5, in the first stage of this calculation, in individual band-by-band analysis, only the parameters Bv , Dv , Av , A Dv , pv , and qv for the A2 i state, and Bv , Dv , and γv as well as the ν0 -band origin for the X 2 + -state were statistically significant for reproducing of the lines in all observed bands. In the second stage the calculation of constants was performed by a least-squares merge fit of the observed bands, proposed by Albritton et al. (28) and Coxon (29). As a result of this calculation (Merging 1) including the 7 bands of the A–X system it was possible to determine 49 molecular constants comprising the v = 1–5 and 7 levels of the A state and v = 0 and 1 of the X state. Considering the fact that the levels of the X state were observed and analyzed in our laboratory earlier and in a larger number in the B–X transition, and taking into account the enlargement and completeness of the information about the A–X transition, in the following stage of the calculation of constants a merged fitting (Merging 2) was performed of the A–X system bands and the currently reanalyzed 0–0, 0–1, 0–2, 0–3, 1–2, 1–3, 1–4, 1–5, and 2–4 bands belonging to the B–X system (19). However, as a result of the changing resolving power of the spectrograph, from band to band, and the changing γ constant, deciding about the spin structure split of band lines of the A–X system and the changing of the difference of the γ − γ constants for the B–X band system, different ranges of band branches were recorded with a resolved spin structure of
lines. Subsequently, the calculated values of the spin–rotation interaction constants of the X state differed significantly. Therefore, in the final stage the calculation of constants (Merging 3) was performed with fixed γv -constants in the X 2 + state. Fixed γv values were used which were obtained after isotopic recalculation to the 13 C16 O+ molecule of the γe , αγe , and βγe equilibrium constants which were derived earlier for the X state of the 12 16 + C O molecule (25). The estimated variance of this merging σ M2 is 1.14, the number of the calculated constants n is 73, and the number of degrees of freedom f M is 44. Table 3 presents the constant values derived for the A2 i state, and Table 4 presents the X 2 + state. In order to determine the equilibrium molecular constants, the obtained individual constant values were developed into power series of the argument (v + 12 ). By making use of the calculation based on the weighted least-squares method it was possible to determine the equilibrium molecular constants for both states, which are listed in Table 5. On the basis of these constants the RKR potential curve parameters for both the A and X states were calculated. Also the Franck–Condon factors and r -centroids for the A–X transition were calculated. The results are collected in Tables 6 and 7, respectively. DISCUSSION AND CONCLUSION
The present work provides a comprehensive and modern analysis of 7 bands and over 1900 lines of the so far fragmentarily observed and investigated comet-tail system in the
C 2002 Elsevier Science (USA)
ANALYSIS OF COMET-TAIL BANDS
C16 O+ molecule. The use of conventional high resolution made it possible both to observe the 12 branches, i.e., the complete spectrum of the 2 –2 + transition, and to resolve and record the doublets of lines characteristic of this transition, main branch/satellite branch, R22 (J )/Q 21 (J + 1), Q 22 (J )/ P21 (J + 1), P11 (J )/Q 12 (J − 1), and Q 11 (J )/R12 (J − 1), in most of the observed bands. The fitting of the spectral lines to the parameters of the commonly used Hamiltonians of Brown et al. (26) made it possible both to unify the information about the excited A2 i and the ground X 2 + states and to perform a global analysis comprising the remaining transitions and states in the 13 C16 O+ molecule. The results of this phase of research will be published in Ref. (30). Also a multistage and merged procedure of the calculation of molecular constants comprising the currently observed 7 bands of the A–X system and the earlier recorded and now reanalyzed 9 bands of the B–X system (19) made it possible to perform a complete characteristic of the A state and to enlarge and improve the information about the X state. This made it possible to derive for the first time the equilibrium molecular constants for the A state and more precise constants for the X state. By making use of these constants, the RKR potential curve parameters for both A and X states and Franck–Condon factors and r -centroids for the A–X transition were calculated for 13 C16 O+ . We believe that the present results extend and improve the information about the spectrum and energy structure of this 13 C16 O+ isotopic molecule which is present on the Earth and in space. 13
ACKNOWLEDGMENTS The authors thank Urszula Domin for excellent and creative technical support. This work was partially supported by the State Committee for Scientific Research (KBN) and the University of Rzesz´ow. One of the authors M. Z. is an award holder of the NATO Science Fellowship Program.
REFERENCES 1. P. H. Krupenie, “The Band Spectrum of Carbon Monoxide.” National Standard Reference Data Series, Natl. Bur. Stand., 5, 1966. 2. B. Rosen, “Spectroscopic Data Relative to Diatomic Molecules.” Pergamon, New York, 1970.
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3. K. P. Huber and G. Herzberg, “Molecular Spectra and Molecular Structure. Vol. IV. Constants of Diatomic Molecules.” Van Nostrand, New York, 1979; Russian translation, “Konstanty Dvuhatomnych Molekul.” Mir, Moscow, 1984. 4. C. Haridass, C. V. V. Prasad, and S. P. Reddy, Astrophys. J. 388, 669–677 (1992). 5. K. N. Rao, Astrophys. J. 111, 306–313 (1950). 6. H. Gagnaire and J. P. Goure, Can. J. Phys. 54, 2111–2117 (1976). 7. D. H. Katayama and J. A. Welsh, J. Chem. Phys. 75, 4224–4230 (1981). 8. J. A. Coxon and S. G. Foster, J. Mol. Spectrosc. 93, 117–130 (1982). 9. R. D. Brown, R. G. Dittman, and D. C. McGilvery, J. Mol. Spectrosc. 104, 337–342 (1984). 10. B. R. Vujisi´c and D. S. Pesi´c, J. Mol. Spectrosc. 128, 334–349 (1988). 11. C. Haridass, C. V. V. Prasad, and S. P. Reddy, J. Mol. Spectrosc. 199, 180–187 (2000). 12. R. K. Asundi, R. K. Dhumwad, and A. B. Patwardhan, J. Mol. Spectrosc. 34, 528–532 (1970). 13. R. K. Dhumwad, A. B. Patwardhan, and V. T. Kulkarni, J. Mol. Spectrosc. 78, 341–343 (1979). 14. Z. Jakubek, R. K¸epa, and J. D. Janji´c, J. Mol. Spectrosc. 125, 43–53 (1987). 15. C. V. V. Prasad and S. P. Reddy, J. Chem. Phys. 90, 3010–3014 (1989). 16. R. D. Brown, R. G. Dittman, D. C. McGilvery, and P. D. Godfrey, J. Mol. Spectrosc. 101, 61–70 (1983). 17. B. R. Vujisi´c, D. S. Pesi´c, S. Weniger, and D. Rakotoarijimy, Indian J. Pure Appl. Phys. 18, 370–372 (1980). 18. A. Carrington, D. R. J. Milverton, and P. J. Sarre, Mol. Phys. 35, 1505–1521 (1978). 19. J. K¸edzierski, R. K¸epa, Z. Malak, and M. Rytel, J. Mol. Spectrosc. 162, 55–61 (1993). 20. Z. Bembenek, U. Domin, R. K¸epa, K. Porada, M. Rytel, M. Zachwieja, Z. Jakubek, and J. D. Janji´c, J. Mol. Spectrosc. 165, 205–218 (1994). 21. B. A. Palmer and R. Engleman, Jr., “Atlas of the Thorium Spectrum.” Los Alamos National Laboratory, Los Alamos, NM, unpublished. 22. J. M. Brown, J. T. Hougen, K. P. Huber, J. W. C. Johns, I. Kopp, H. LefebvreBrion, A. J. Merer, D. A. Ramsay, J. Rostas, and R. N. Zare, J. Mol. Spectrosc. 55, 500–503 (1975). 23. Z. Jakubek, J. Mol. Spectrosc. 131, 207–214 (1988). 24. P. Misra, D. W. Ferguson, K. N. Rao, E. Williams, Jr., and C. W. Mathews, J. Mol. Spectrosc. 125, 54–65 (1987). 25. M. Bogey, C. Demuynck, and J. L. Destombes, J. Chem. Phys. 79, 4704– 4707 (1983). 26. J. M. Brown, E. A. Colbourn, J. K. G. Watson, and F. D. Wayne, J. Mol. Spectrosc. 74, 294–318 (1979). 27. C. Amiot, J. P. Maillard, and J. Chauville, J. Mol. Spectrosc. 87, 196–218 (1981). 28. D. L. Albritton, A. L. Schmeltekopf, and R. N. Zare, J. Mol. Spectrosc. 67, 132–156 (1977). 29. J. A. Coxon, J. Mol. Spectrosc. 72, 252–263 (1978). 30. R. K¸epa, Z. Malak, W. Szajna, and M. Zachwieja, to be published.
C 2002 Elsevier Science (USA)
Analysis of the Comet-Tail (A2 Πi –X 2 Σ+ ) Bands of 13 C16 O+ R. K¸epa,∗ A. Kocan,∗ M. Ostrowska,∗ I. Piotrowska-Domagala,∗ Z. Jakubek,† and M. Zachwieja† ∗ Atomic and Molecular Physics Laboratory, Institute of Physics, University of Rzesz´ow, 35-310 Rzesz´ow, Poland; and †Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada K1A OR6 Received October 29, 2001; in revised form May 16, 2002
In the electronic emission spectrum of the isotopic carbon monoxide ion 13 C16 O+ molecule, seven bands of the comet-tail (A2 i –X 2 + ) system have been recorded and analyzed. The spin splitting in most observed lines of the bands 1–0, 2–0, 3–0, 4–0, 5–0, 2–1, and 7–1 comprising over 1900 lines has been recorded under high resolution by using conventional spectroscopy. The rotational analysis of bands has been performed by nonlinear least-squares procedures and by means of effective Hamiltonians of Brown et al., the rovibronic structure parameters have been obtained. As a result of multistaged and merged analysis of the currently obtained bands of the A–X system and of the bands of the B–X system obtained earlier the state of information about the energy structure has been significantly enlarged for the A state and enlarged and improved for the X state. Also RKR potential curves have been calculated for both states and Franck–Condon factors as well as r -centroids of the comet-tail system C 2002 Elsevier Science (USA) of 13 C16 O+ . INTRODUCTION
Laboratory studies of the spectrum and the energy structure of the molecular ion CO+ are especially stimulating because of the important role which it plays in astrophysics. The occurrence of this molecular ion in the atmospheres of planets, the sun and stars, and in comet tails and interstellar space provides, however, possibilities of diagnosing physical conditions and physical– chemical processes occurring in these objects. There is also an increased interest in this molecule due to the role it plays on the Earth in monitoring combustion processes and in environmental research. The bibliography and tabulations of the spectroscopic information dealing with the four electronic states, X 2 + , A2 i , B 2 + , and C 2 r , and the four observed band systems, namely, the comet-tail (A2 i –X 2 + ), the Baldet–Johnson (B 2 + –A2 i ), the first-negative (B 2 + –X 2 + ), and the Marchand–D’Incan–Janin (C 2 r –A2 i ) systems of this molecule, have been collected in several monographs (1–3) and by Haridass et al. (4). The comet-tail system, being one of the most comprehensive band systems of this molecule, has been explored the most extensively in the most abundant isotopomer 12 C16 O+ (1, 4–11). There have been fewer works, which were concerned with a smaller number of bands, devoted to the study of this system in the other isotopomers of CO+ . Asundi et al. (12) and Dhumwad et al. (13) recorded under low resolution several bands of this system and analyzed isotopic shifts of bandheads in 13 C16 O+ and 12 C18 O+ , respectively. Rotational analysis of the 2–0, 3–0, 4–0, and 0–2 bands of the 12 C18 O+ molecule was performed by Supplementary data for this article are available on IDEAL (http://www. idealibrary.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://msa.lib.ohio-state.edu/jmsa hp.htm). 117
Vujisi´c and Pesi´c (10), as well as for the 1–0, 2–0, 3–0, 4–0, and 2–1 bands of 14 C16 O+ by Jakubek et al. (14), and for nine bands, v –0, v = 1 to 5, 1–1, 2–1, 0–1, and 0–2 bands of the 13 C18 O+ isotopomer by Prasad and Reddy (15). It is surprising that in spite of an easy availability of the 13 C isotope, its relatively high abundance in space, and a large deficiency of molecular constants for the 13 C16 O+ molecule, the studies of the A–X system performed so far in this isotopomer have been fragmentary and incomplete. Brown et al. (16) recorded under moderate resolution and analyzed 124 lines of the 0–0 band by using an ion-beam laser spectroscopy technique. Vujisi´c et al. (17) photographed and analyzed 99 lines of the 2–0 band. Carrington et al. (18) by means of a high-velocity ion-beam technique measured and analyzed 22 fine and hyperfine components belonging to the 0–0 and 1–0 band lines. In the present work we present the results of high-resolution observations and modern analysis of seven bands v –0, v = 1 to 5, 2–1, and 7–1 of the comet-tail system in the 13 C16 O+ molecule. The objective of this paper is to complete, unify, and improve the spectroscopic and quantum-mechanical information related both to the first excited −A2 i electronic state and the whole energy structure of 13 C16 O+ . EXPERIMENTAL DETAILS
As a source of the emission spectrum of the comet-tail bands, just as in our earlier investigations of the spectra of the CO+ molecule (14, 19, 20) an air-cooled hollow-cathode discharge tube was used. The tube was filled with carbon monoxide enriched with carbon 13 C with about 90% concentration of the 13 C isotope and at a pressure of 0.1 kPa. The tube was supplied by a standard 500-V D.C. generator; mean current was about 50 mA. This permitted us to limit the temperature of the source and to limit the width of the spectrum lines, which for the resolved lines 0022-2852/02 $35.00 C 2002 Elsevier Science (USA)
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KE¸ PA ET AL.
FIG. 1. Microdensitometer trace and the rotational assignments of the R21 and R22 /Q21 and Q22 /P21 bandhead regions in the spectrum of the 2–0 band of the Comet-Tail system of 13 C16 O+ .
was about 0.12–0.14 cm−1 . The spectra of the bands were photographed in the 6th and 7th orders of a 2-m plane grating Ebert spectrograph PGS-2, equipped with a 651-grooves/mm grating with a total of 45 600 grooves, and blazed at 1.0 µm. The theoretical resolving power and approximate observed resolving power varied from 270 000 to 320 000, and the reciprocal linear dispersion varied from 0.041 to 0.067 nm/mm. The exposure time of the 7 selected bands of this system located in the region ˚ on ORWO WU-2 spectral plates varied from of 3530–4640 A 2 to 7 h, depending on band intensity. Thorium emission lines (21) obtained from several orders from a water-cooled hollowcathode tube were used as wavelength standards. The relative position of the lines was measured on an automatic comparator assembled in our laboratory. The position on the plate was controlled interferometrically, whereas the profile of lines was measured photoelectrically point by point. The positions of the line centers were calculated by means of an interactive graphic computer program using the least-squares procedure and assuming Gaussian profiles for the lines. The precision of the wavenumbers of the single and resolved molecular lines was considered to be in the range of 0.005–0.010 cm−1 , whereas for the lines not completely resolved or blended (marked by an asterisk) it was estimated to be 0.020–0.040 cm−1 . In Fig. 1 is shown a part of the microdensitometer trace of the R21 and R22 /Q 21 and Q 22 /P21 bandhead regions in the spectrum of the 2–0 band. In Table 1 are presented observed wavenumbers of the 2–0 band,
whereas the wavenumbers of bands 1–0, 2–0, 3–0, 4–0, 5–0, 2–1, and 7–1 are deposited in the Electronic Depository of the Supplementary Material of the journal. Additional information about observed bands is collected in Table 2. RESULTS
Description of the Band System The comet-tail system in the CO+ molecule spectrum is a result of transitions between the first excited A2 i and the ground X 2 + states. The A state is inverted with a 13-electron structure and values of constants typical of this group of molecules. It also shows changes in the modes of coupling of intramolecular angular momenta, from Hund’s case (a), at a low quantum J number, to Hund’s case (b), at high J values. On the other hand, the lower X state belongs to Hund’s case (b). Consequently, each band of this transition resolves into two subbands, 2 1/2 –2 + and 2 3/2 –2 + , and in the transition spectrum 12 branches appear which are identified as R21ee , R22 f f , Q 21 f e , Q 22e f , P21ee , P22 f f , R11ee , R12 f f , Q 11 f e , Q 12e f , P11ee , and P12 f f . The scheme of this transition is well known as well as the parity of levels indicated in the e/f notation, as proposed by Brown et al. (22). Because the spin–rotation interaction constant in the lower state is small (γ X ≈ 9 · 10−3 cm−1 ), the following pairs of branches, R22 f f and Q 21 f e ; Q 22e f and P21ee ; Q 11 f e and R12 f e as well as P11ee and Q 12e f can overlap partially or completely.
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ANALYSIS OF COMET-TAIL BANDS
TABLE 1 Observed Wavenumbers (in cm−1 ) and Rotational Assignments for the 2–0 Band of the Comet-Tail (A2 Πi − X2 Σ+ ) System in the 13 C16 O+ Moleculea J
R21ee
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5
23458.396(23) 23462.069(12) 23464.957(−4) 23467.097(10) 23468.425(−2) 23468.688(0) 23468.777(10) 23467.769(7) 23465.970(−5) 23463.407(4) 23460.038(−8) 23455.901(−1) 23450.987(15) 23445.253(−1) 23438.701∗ 23431.460(11) 23423.365(5) 23414.502(22) 23404.808(4) 23394.308(−27) 23383.066(−5) 23371.005(−4) 23358.150(1) 23344.527∗ 23330.056(24) 23314.791(20)
R22 f f 23454.597(12) 23453.733(−16) 23452.113(−17) 23449.707(−26) 23446.518∗ 23442.563∗ 23437.804∗ 23432.275∗ 23425.966∗ 23418.861∗ 23410.976∗ 23402.385(5) 23392.946(17) 23382.720(10) 23371.682(19) 23359.818(−28) 23347.229(−11) 23333.838(−4) 23319.610∗ 23304.675(10) 23288.858(−28) 23272.315(4) 23254.952(11) 23236.772(0) 23217.804(1) 23198.032(−5) 23177.465(−5) 23156.100(0) 23133.927(−1) 23110.791∗ 23087.172(1) 23062.583(−3)
J
R11ee
R12 f f
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5
23333.483∗ 23336.968(0) 23339.599∗ 23341.452(2) 23342.395(−22) 23342.517(−19) 23341.809(5) 23340.219(−5) 23337.785(−10) 23334.514(−4) 23330.391(−1) 23325.421(2) 23319.610(12) 23312.933(3) 23305.415(−1) 23297.036(−19) 23287.847(−1) 23277.800(4) 23266.895(−4) 23255.153(−4) 23242.566(−6) 23229.138(−5) 23214.863(−7) 23199.749(−5) 23183.792(−4) 23167.005(8) 3149.353(−2) 23130.889(17) 23111.557(9) 23091.384(1)
23329.689(−12) 23329.462(−1) 23328.358(−18) 23326.418(−23) 23323.624∗ 23319.980∗ 23315.491∗ 23310.158∗ 23303.972∗ 23296.970∗ 23289.139(−13) 23280.428(−9) 23270.866(−11) 23260.451(−21) 23249.199(−24) 23237.141(10) 23224.199(5) 23210.434(9) 23195.816(20) 23180.345(11) 23164.041(10) 23146.899(10) 23128.917(11) 23109.962∗ 23090.430(6) 23069.923(−3) 23048.558(−12) 23026.163∗ 23003.148∗
a ∗
Q 21 f e
23454.597(23) 23453.733(15) 23452.113(22) 23449.707(22) 23446.518(21) 23442.563∗ 23437.804∗ 23432.275∗ 23425.966∗ 23418.861∗ 23410.976∗ 23402.285(23) 23392.836(18) 23382.594(18) 23371.522(3) 23359.725(10) 23347.070(−9) 23333.679(8) 23319.463(−9) 23304.479(1) 23288.700(9) 23272.102(−5) 23254.746(19) 23236.546(−4) 23217.565(−9) 23197.801(3) 23177.231(10) 23155.833(−11)
Q 11 f e 23329.689(2) 23329.462(21) 23328.358(12) 23326.418(16) 23323.624(15) 23319.980(11) 23315.491(11) 23310.158(15) 23303.972(13) 23296.970∗ 23289.054(3) 23280.331(3) 23270.762(3) 23260.347(1) 23249.085(−4) 23236.983(−4) 23224.034(−9) 23210.259(4) 23195.621(−5) 23180.160(4) 23163.843(−1) 23146.691(−2) 23128.700(−1) 23109.873(2) 23090.197(−5) 23069.691(−4) 23048.286∗ 23026.162(−7) 23003.146(−4) 22979.293(−3) 22955.768∗ 22929.122(11) 22902.719(−1) 22875.477(−19)
Q 22e f 23450.155(3) 23447.093(−9) 23443.264(−7) 23438.665(3) 23433.258(−15) 23427.100(−4) 23420.138(−18) 23412.414(−12) 23403.902(−15) 23394.610(−17) 23384.540(−14) 23373.686(−13) 23362.048(−13) 23349.635(−4) 23336.431(−2) 23322.446(4) 23307.644(−21) 23292.100(−2) 23275.753(2) 23258.619(8) 23240.673(−9) 23221.961(−2) 23202.453(0) 23182.153(1) 23161.061(4) 23139.134∗ 23116.490(3) 23093.013(4) 23068.731(−5) 23043.680(16) 23017.804(9) 22991.125(−2) 22963.650(−9) 22935.380(−10) 22906.332(11) Q 12e f 23325.411∗ 23322.264∗ 23318.174(−9) 23313.324(−11) 23307.644(5) 23301.072(−24) 23293.665(−19) 23285.439(−16) 23276.316(−13) 23266.407∗ 23255.600∗ 23243.988∗ 23231.518∗ 23218.281(16) 23204.123(14) 23189.121(10) 23173.254(−17) 23156.565(−24) 23139.048(−19) 23120.692(−14) 23101.493(−11) 23081.453(−12) 23060.590(3) 23038.880(8) 23016.320(−2) 22992.906(−18) 22968.709(−4) 22943.726(19) 22917.758(−9)
Figures in parentheses denote observed minus calculated values in units of the last quoted digit. The lines marked by asterisk are less accurate and not used in the evaluation of molecular constants. C 2002 Elsevier Science (USA)
P21ee
P22 f f
23450.155(16) 23447.093(13) 23443.264(23) 23438.665∗ 23433.258∗ 23427.100∗ 23420.138∗ 23414.412∗ 23403.902∗ 23394.610∗ 23384.402∗ 23373.572(−15) 23361.960(17) 23349.518(5) 23336.316(17) 23322.264(14)∗ 23307.551∗ 23291.924(−16) 23275.581(0) 23258.426(−7) 23240.475(−20) 23221.772(4) 23202.245(−4) 23181.940(1) 23160.839(3) 23138.916(−22) 23116.273(25) 23092.769(5) 23068.541∗ 23043.290∗ 23017.566(15)
23442.563∗ 23435.863(19) 23428.270(5) 23419.906(0) 23410.745(−24) 23400.854(1) 23390.177(20) 23378.682(−1) 23366.423(−4) 23353.400(8) 23339.599(22) 23324.986(6) 23309.604(2) 23293.451(9) 23276.501(3) 23258.782(11) 23240.255(−6) 23220.960(−5) 23200.882(−3) 23180.148∗ 23158.365(1) 23135.918(−5) 23112.695(2) 23088.665(−9) 23063.865(0) 23038.270(3) 23011.867(−9) 22984.676(−17) 22956.718(0) 22927.956(7) 22898.379(−6)
P11ee
P12 f f
23325.411∗ 23322.264∗ 23318.174∗ 23313.324∗ 23307.644∗ 23301.072∗ 23293.665∗ 23285.439∗ 23276.316∗ 23266.407∗ 23255.600∗ 23243.988∗ 23231.518∗ 23218.193∗ 23203.963(−11) 23188.963(−4) 23173.128(9) 23156.440(11) 23138.916(19) 23120.531(4) 23101.321(4) 23081.261(−7) 23060.590∗ 23038.672(13) 23016.100(1) 22992.709(5) 22968.481(7) 22943.422(13) 22917.540∗ 22890.779(1)
23317.927∗ 23310.940∗ 23303.205∗ 23294.529(−6) 23285.083(4) 23274.777(0) 23263.624(−6) 23251.633(−1) 23238.779(−15) 23225.097(−12) 23210.264∗ 23195.208(−1) 23178.994(−1) 23161.936(−2) 23145.758∗ 23125.301(−4) 23105.706(−23) 23085.309(−5) 23064.063(1) 23041.977(4) 23019.041(−7) 22995.287(−2)
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TABLE 2 Summary of Observations and Analyses of the Comet-Tail System (A2 Πi –X 2 Σ+ ) of the 13 C16 O+ Molecule Band heads (in cm−1 )
Band 1–0
2–0
3–0
4–0
5–0
2–1
7–1
21994.43 21979.22 21867.79 21854.12
R21 R22 /Q 21 R11 Q 11 /R12
23468.99 23469.05c 23454.60 23454.65c 23342.52 23342.54c 23329.69 23329.73c
R21
Band origina (in cm−1 )
Total number of lines
Jmax
σ f · 102b (in cm−1 )
21914.4663(17)
294
32.5
1.03
23390.0235(15) 23390.65(5)c
232 99c
34.5 18.5c
0.95 8.9c
24839.8860(13)
305
32.5
0.79
26264.1619(12)
365
35.5
0.88
27662.9857(17)
309
35.5
1.10
21254.1531(22)
289
30.5
1.33
28247.2904(38)
123
21.5
1.63
R22 /Q 21 R11 Q 11 /R12
24917.89 24904.39 24791.67 24779.54
R21 R22 /Q 21 R11 Q 11 /R12
26341.23 26328.52 26215.37 26203.78
R21 R22 /Q 21 R11 Q 11 /R12
27739.35 27727.29 27613.54 27602.52
R21 R22 /Q 21 R11 Q 11 /R12
21333.66 21318.85 21207.21 21193.83
R21 R22 /Q 21 R11 Q 11 /R12
28321.37 28310.31 28198.13 28187.92
R21 R22 /Q 21 R11 Q 11 /R12
a
Values from final merging (3); uncertainties in parentheses represent one standard deviation in units of the last quoted digit. Standard deviation of the fit for the individual band analysis. c After Vujsi´ c et al. (17). b
TABLE 3 Rotational Structure Constants (in cm−1 ) for the A2 Πi State of the 13 C16 O+ Moleculea v
Bv
Dv · 106
−Av
−A Dv · 104
1
1.491856(19) 1.491849(27)b 1.473764(16) 1.4783(1)c 1.455632(16) 1.437477(16) 1.419417(18) 1.38.3261(70)
5.949(19) 5.976(27)b 6.027(12) 2.0(3)c 6.053(12) 6.0611(97) 5.999(15) 6.028(23)
121.9842(29) 121.988(3)b 121.8792(20) 122.02(1)c 121.7984(20) 121.7556(19) 121.8401(28) 119.4710(61)
1.757(94) 1.459(49)b 1.412(49) — 1.284(52) 1.071(38) 1.397(79) 6.96(53)
2 3 4 5 7 a
pv · 102 1.115(24) 1.218(14)b 1.194(13) −1.01(4)c 1.067(14) 0.853(12) 0.644(22) 4.04(11)
Uncertainties in parentheses are one standard deviation in units of the last quoted digit. After Jakubek (23). c After Vujisi´ c et al. (17). b
C 2002 Elsevier Science (USA)
−qv · 104 1.98(12) 1.851(53)b 2.039(66) −1.6(4)c 2.209(79) 1.929(51) 2.53(15) 2.40(15)
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ANALYSIS OF COMET-TAIL BANDS
TABLE 4 Rotational Structure Constants (in cm−1 ) for the X 2 Σ+ State in the 13 C16 O+ Moleculea v
Bv
Dv · 106
γ · 103
0
1.880830(15) 1.880797(51)b 1.8868(22)c 1.88126(52)d 1.8860(1)e 1.863007(18) 1.863024(60)b 1.8616(7)c 1.845087(31) 1.845158(43)b 1.8439(5)c 1.827211(33) 1.827131(45)b 1.809202(32) 1.809333(50)b 1.791230(41) 1.791383(82)b
5.7275(84) 5.717(26)b 4.9(32)c 8.31(109)d 23(4)e 5.722(11) 5.734(30)b 5.2(10)c 5.707(17) 5.733(24)b 4.85(48)c 5.720(18) 5.713(26)b 5.698(21) 5.797(33)b 5.74(11) 5.876(55)b
[8.700] [12.8]b [8.686]c [0]d 9.2(1)e [8.649] [12.8]b [8.686]c [8.575] [12.8]b [8.686]c [8.480] [12.8]b [8.363] [12.8] [8.223] [12.8]b
1
2
3 4 5
a Uncertainties in parentheses are one standard deviation in units of the last quoted digit. Values in square brackets were fixed during the fits. b After K¸ edzierski et al. (19). c After Misra et al. (24). d After Brown et al. (16). e After Vujisi´ c et al. (17).
Calculation of Constants The preliminary rotational analysis of the bands observed for the first time, i.e., the identification of the bands and branches and J -numbering of the lines, was performed directly using the earlier obtained information about both A2 i (16, 17, 23) and X 2 + (19, 24) states of this transition and by performing a simulation calculus of lines for each band. The corresponding constants necessary for the above calculations have been obtained by isotopic recalculating of equilibrium molecular contants of the A (11, 20) and X (11, 25) states obtained earlier for the 12 C16 O+ molecule. The final analysis and the calculation of constants were performed in many stages via a nonlinear least-squares procedure and by means of effective Hamiltonians proposed by Brown et al. (26). The matrix elements, the definition of molecular constants, and their physical meaning were taken from the work of Amiot et al. (27). Considering the real TABLE 6 Vibrational Levels and RKR Turning Points for the A2 Πi and X 2 Σ+ States of the 13 C16 O+ Moleculea A2 i v=0 v=1
TABLE 5 Equilibrium Molecular Constants (in cm−1 ) for the A2 Πi and X 2 Σ+ States of the 13 C16 O+ Moleculea
v=3
X 2+
Te we we x e we ye · 102
A2 i
This work
20731.476(23) 1527.318(23) 13.0015(68) 2.019(65)
2164.8130(46) 14.4703(25) −0.303(33)
Be αe · 102 γe · 106
1.519092(73) 1.8152(42) 5.02(57)
De · 106 β De · 108
5.940(39) 2.90(11)
Ae α Ae · 101 β Ae · 102
−122.207(16) 1.71(11) −1.57(17)
A De · 104 α A De · 105
1.952(99) 1.97(27)
pe · 102 α pe · 103
1.665(61) −1.80(16)
qe · 104 αqe · 105
−1.702(64) −1.45(21)
1.889732(25) 1.7785(26) −24.1(51) 5.7305(42) −0.59(17)
v=2
Kdzierski et al. (19)
2164.925(60) 14.521(24) 0.33(27) 1.889714(34) 1.7750(27) 24.2(47) 5.721(22) 1.70(73)
v=4 v=5 v=6 v=7 v=8 v=9 v = 10
a Uncertainties in parentheses represent one standard deviation in units of the last quoted digit.
G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax G(v) + Y00 rmin rmax re
760.584 1.19191 1.30328 2261.965 1.15800 1.35226 3737.524 1.13648 1.38909 5187.383 1.12001 1.42110 6611.663 1.10647 1.45041 8010.486 1.09489 1.47800 9383.971 1.08476 1.50441 10732.241 1.07572 1.52997 12055.42 1.0676 1.5549 13353.62 1.0601 1.5794 14627.0 1.053 1.604 1.24387
X 2+ 1078.867 1.07123 1.16470 3214.729 1.04209 1.20488 5321.624 1.02339 1.23476 7399.533 1.00897 1.26051 9448.437 0.99704 1.28394 11468.319 0.98679 1.30585 13459.16 0.9778 1.3267 15420.94 0.9697 1.3468 17353.6 0.962 1.366
1.11523
❛ a G(v) values are in cm−1 , r values are in A; Y = 0.173 cm−1 for the A2 00 i and Y00 = 0.078 cm−1 for the X 2 + .
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KE¸ PA ET AL.
TABLE 7 Franck–Condon Factors and r -Centroids for the Comet-Tail Band System in the 13 C16 O+ Moleculea v \v
0
1
2
3
4
5
0
3.9462 E-2 1.1782 1.0797 E-1 1.1616 1.6229 E-1 1.1459 1.7801 E-1 1.1308 1.5973 E-1 1.1165 1.2467 E-1 1.1027 8.7902 E-2 1.0896 5.7427 E-2 1.0770 3.540 E-2 1.065 2.086 E-2 1.053 1.19 E-2 1.04
1.4455 E-1 1.2018 1.9158 E-1 1.1841 1.0420 E-1 1.1669 1.7679 E-2 1.1485 2.7679 E-3 1.1483 3.6831 E-2 1.1261 7.5115 E-2 1.1114 9.3720 E-2 1.0979 9.124 E-2 1.085 7.616 E-2 1.073 5.72 E-2 1.06
2.4425 E-1 1.2262 8.8062 E-2 1.2064 1.1858 E-3 1.2108 6.6602 E-2 1.1767 9.6407 E-2 1.1597 5.4382 E-2 1.1434 9.2704 E-3 1.1252 1.8856 E-3 1.1312 2.372 E-2 1.108 5.051 E-2 1.094 6.66 E-2 1.08
2.5263 E-1 1.2515 8.7246 E-6 1.5041 1.0126 E-1 1.2160 7.5927 E-2 1.1969 2.5901 E-3 1.1681 2.5449 E-2 1.1708 6.7778 E-2 1.1532 6.1249 E-2 1.1376 2.586 E-2 1.122 2.137 E-3 1.099 3.87 E-3 1.11
1.7927 E-1 1.2780 8.2422 E-2 1.2614 9.0786 E-2 1.2380 1.4171 E-3 1.2430 7.1122 E-2 1.2067 6.2579 E-2 1.1884 6.6120 E-3 1.1658 1.0419 E-2 1.1666 4.618 E-2 1.148 5.614 E-2 1.132 3.54 E-2 1.12
9.3324 E-2 1.3057 1.9051 E-1 1.2871 1.3686 E-3 1.2247 8.9696 E-2 1.2472 4.2557 E-2 1.2256 4.3768 E-3 1.2232 5.7241 E-2 1.1980 5.2000 E-2 1.1807 8.795 E-3 1.161 4.142 E-3 1.164 3.12 E-2 1.14
1 2 3 4 5 6 7 8 9 10
a
❛ The upper and lower entries for each band are the Franck–Condon factors and r -centroids (in A), respectively.
precision of the determined wavenumbers of lines and the fact that the highest observed value of J is Jmax = 40.5, in the first stage of this calculation, in individual band-by-band analysis, only the parameters Bv , Dv , Av , A Dv , pv , and qv for the A2 i state, and Bv , Dv , and γv as well as the ν0 -band origin for the X 2 + -state were statistically significant for reproducing of the lines in all observed bands. In the second stage the calculation of constants was performed by a least-squares merge fit of the observed bands, proposed by Albritton et al. (28) and Coxon (29). As a result of this calculation (Merging 1) including the 7 bands of the A–X system it was possible to determine 49 molecular constants comprising the v = 1–5 and 7 levels of the A state and v = 0 and 1 of the X state. Considering the fact that the levels of the X state were observed and analyzed in our laboratory earlier and in a larger number in the B–X transition, and taking into account the enlargement and completeness of the information about the A–X transition, in the following stage of the calculation of constants a merged fitting (Merging 2) was performed of the A–X system bands and the currently reanalyzed 0–0, 0–1, 0–2, 0–3, 1–2, 1–3, 1–4, 1–5, and 2–4 bands belonging to the B–X system (19). However, as a result of the changing resolving power of the spectrograph, from band to band, and the changing γ constant, deciding about the spin structure split of band lines of the A–X system and the changing of the difference of the γ − γ constants for the B–X band system, different ranges of band branches were recorded with a resolved spin structure of
lines. Subsequently, the calculated values of the spin–rotation interaction constants of the X state differed significantly. Therefore, in the final stage the calculation of constants (Merging 3) was performed with fixed γv -constants in the X 2 + state. Fixed γv values were used which were obtained after isotopic recalculation to the 13 C16 O+ molecule of the γe , αγe , and βγe equilibrium constants which were derived earlier for the X state of the 12 16 + C O molecule (25). The estimated variance of this merging σ M2 is 1.14, the number of the calculated constants n is 73, and the number of degrees of freedom f M is 44. Table 3 presents the constant values derived for the A2 i state, and Table 4 presents the X 2 + state. In order to determine the equilibrium molecular constants, the obtained individual constant values were developed into power series of the argument (v + 12 ). By making use of the calculation based on the weighted least-squares method it was possible to determine the equilibrium molecular constants for both states, which are listed in Table 5. On the basis of these constants the RKR potential curve parameters for both the A and X states were calculated. Also the Franck–Condon factors and r -centroids for the A–X transition were calculated. The results are collected in Tables 6 and 7, respectively. DISCUSSION AND CONCLUSION
The present work provides a comprehensive and modern analysis of 7 bands and over 1900 lines of the so far fragmentarily observed and investigated comet-tail system in the
C 2002 Elsevier Science (USA)
ANALYSIS OF COMET-TAIL BANDS
C16 O+ molecule. The use of conventional high resolution made it possible both to observe the 12 branches, i.e., the complete spectrum of the 2 –2 + transition, and to resolve and record the doublets of lines characteristic of this transition, main branch/satellite branch, R22 (J )/Q 21 (J + 1), Q 22 (J )/ P21 (J + 1), P11 (J )/Q 12 (J − 1), and Q 11 (J )/R12 (J − 1), in most of the observed bands. The fitting of the spectral lines to the parameters of the commonly used Hamiltonians of Brown et al. (26) made it possible both to unify the information about the excited A2 i and the ground X 2 + states and to perform a global analysis comprising the remaining transitions and states in the 13 C16 O+ molecule. The results of this phase of research will be published in Ref. (30). Also a multistage and merged procedure of the calculation of molecular constants comprising the currently observed 7 bands of the A–X system and the earlier recorded and now reanalyzed 9 bands of the B–X system (19) made it possible to perform a complete characteristic of the A state and to enlarge and improve the information about the X state. This made it possible to derive for the first time the equilibrium molecular constants for the A state and more precise constants for the X state. By making use of these constants, the RKR potential curve parameters for both A and X states and Franck–Condon factors and r -centroids for the A–X transition were calculated for 13 C16 O+ . We believe that the present results extend and improve the information about the spectrum and energy structure of this 13 C16 O+ isotopic molecule which is present on the Earth and in space. 13
ACKNOWLEDGMENTS The authors thank Urszula Domin for excellent and creative technical support. This work was partially supported by the State Committee for Scientific Research (KBN) and the University of Rzesz´ow. One of the authors M. Z. is an award holder of the NATO Science Fellowship Program.
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C 2002 Elsevier Science (USA)