Near infrared spectroscopy of carbon dioxide I. 16O12C16O line positions

Journal of Molecular Spectroscopy 228 (2004) 329–354 www.elsevier.com/locate/jms

Near infrared spectroscopy of carbon dioxide I. line positions

16

O12C16O

Charles E. Millera,b,* and Linda R. Brownb b

a Department of Chemistry, Haverford College, Haverford, PA 19041-1392, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109-8099, USA

Received 19 August 2003; in revised form 3 November 2003 Available online 18 March 2004

Abstract High-resolution near-infrared (4000–9000 cm
1 ) spectra of carbon dioxide have been recorded using the McMath–Pierce Fourier transform spectrometer at the Kitt Peak National Solar Observatory. Some 2500 observed positions have been used to determine spectroscopic constants for 53 different vibrational states of the 16 O12 C16 O isotopologue, including eight vibrational states for which laboratory spectra have not previously been reported. Calibration by simultaneous use of CO near 4200 cm
1 and C2 H2 near 6500 cm
1 provides absolute line position accuracies of 6.0  10
5 cm
1 (RMS) for strong, isolated transitions throughout the observed range. Fits with RMS errors <3.8  10
5 cm
1 have been obtained for the 20013 00001, 20012 00001, and 20011 00001 bands, RMS errors <6  10
5 cm
1 have been obtained for the 30014 00001, 30013 00001, 30012 00001, and 00031 00001 bands, and RMS errors <5  10
4 cm
1 for even the weakest fitted bands. This work reduces CO2 near-infrared line position uncertainties by a factor of 10 or more compared to the 2000 HITRAN line list, which has not been modified since the comprehensive work of Rothman et al. [J. Quant. Spectrosc. Rad. Transfer 48 (1992) 537]. The new line list satisfies the line position accuracies required for the next generation of CO2 remote sensing instruments, improves the capability of solar-viewing spectrometers to retrieve precise column CO2 measurements, and provides a secondary frequency standard in the near-infrared. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Calibration standards; Carbon dioxide; Near-infrared; Positions

1. Introduction The importance of carbon dioxide (CO2 ) in determining the radiative properties of the EarthÕs atmosphere was first recognized by Arrhenius [1] at the end of the 19th century. More recently, CO2 has been recognized as the principal anthropogenic driver of climate change. The Third Assessment Report from the Intergovernmental Panel on Climate Change stressed the need for improved characterization of atmospheric CO2 to forecast future climate change scenarios [2]. Numerous surface, suborbital and satellite assets will be deployed during the next decades in an intensive effort to answer the fundamental science questions surrounding atmospheric CO2 and its link to climate change [3]. High-resolution near infrared * Corresponding author. Fax: 1-818-354-0966. E-mail address: [email protected] (C.E. Miller).

0022-2852/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2003.11.001

(NIR, 4000–10,000 cm
1 ) remote sensing provides an excellent method for measuring the total column abundance and vertical profiles of atmospheric CO2 from ground-based [4], airborne [5,6], and space-based platforms [7–13]. Observational system simulation experiments have demonstrated that remote sensing techniques must obtain column CO2 measurements with a precision of 1 part in 370 (0.3%) to enable synthesis inversion and data assimilation models to characterize carbon sources and sinks on regional scales [8–10]. Wallace and Livingston first demonstrated the ability to use ground-based high-resolution NIR spectra for remote sensing of column CO2 by recording solar spectra in the 4000–10,000 cm
1 region at 0.014 cm
1 resolution using the McMath–Pierce FTS at the Kitt Peak National Solar Observatory [4]. They showed that precise measurements of total column CO2 could be obtained by ratioing CO2 abundances determined from

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the 30012 ! 00001 band (m0 ¼ 6348 cm
1 ) by the total 3
column O2 abundance determined from the 1 Dg Rg
1 band (m0 ¼ 7882 cm ). This work proved that groundbased high-resolution NIR spectra could yield reliable column CO2 retrievals but that more accurate line parameters (positions, intensities, and pressure broadening coefficients) were required. Yang et al. [14] recently reanalyzed these Kitt Peak solar spectra using a more sophisticated retrieval algorithm and updated spectroscopic parameters [15]. They demonstrated an impressive 0.5% measurement precision in retrieved values of total column CO2 . The retrieval errors were dominated by deficiencies in the spectroscopic parameters, as can be seen in the retrieval residuals in Fig. 1. This led Yang et al. [14] to conclude that solar viewing Fourier transform spectrometry (FTS) could be used to validate future space-based CO2 column observations; however, such FTS measurements will require knowledge of the CO2 line-by-line parameters with an accuracy not available from the 2000 HITRAN database [15]. For CO2 line positions, uncertainties less than 5  10
4 cm
1 are required to reduce the residuals in Fig. 1. The 16 O12 C16 O isotopologue is a symmetric D1h form of carbon dioxide with two equivalent 16 O bosons and zero spin statistical weights for odd-J rotational levels of the ground vibrational state. Vibrational transitions involving excitation of an odd number of quanta in the m3 antisymmetric stretching mode inverts the spin statistical weights, resulting in zero weights for even-J rotational levels. Therefore, transitions originating from the ground vibrational state are missing every other rotational line. Vibrational transitions originating from states involving excitation of the m2 bending mode give rise to both e and f transition sequences due to l-type doubling. These bands are characterized by the occurrence of doublets for low to moderate J rotational values and the presence of a Q-branch. In addition,

Fig. 1. Retrieval of atmospheric CO2 from the 30013 00001 and 30012 00001 bands [14]. Lower panel: solar spectrum (symbols) with optimized fit (lines). Upper panel: fit residuals. Systematic inadequacies in the CO2 line parameters are observed in the fitting residuals.

transitions to symmetric vibrations from the ground state are forbidden by symmetry; these include m1 and even overtones of the other two fundamentals (2m2 , 4m2 , 2m3 , etc.). Following the convention used in HITRAN, vibrational states in this paper are identified as m1 m2 l2 m3 n, where l is the value of the l-type doubling and n shows the nth component in states linked by rovibrational interaction. For example, under this scheme the ground state is 00001, m1 2 yields 01101e and 01101f and m3 is 00011. For the Fermi dyad [m1 , 2m02 ]I;II , m1 is denoted as 10001 and 2m02 is 10002. Fig. 2 gives examples of the two schemes for labeling of vibrational levels. Inspection of the 2000 HITRAN database revealed that the CO2 line parameters had not been revised since the comprehensive review of carbon dioxide spectroscopy reported by Rothman et al. [16], hereafter referred to as R92. At that time the goal for NIR line position uncertainties was 0.001 cm
1 for the strongest bands. The carbon dioxide line parameters were predicted via the direct numerical diagonalization (DND) method [17], and then bands were recomputed if good experimental data were available. Line positions for the NIR bands were determined from the laboratory measurements of Maillard et al. [18] and Arcas et al. [19] recorded in the early 1980s. Many weaker bands were not observed in the laboratory, and the recommended spectroscopic parameters were taken from MandinÕs spectra of Venus recorded in 1977 [20]. In the last decade, there has been relatively little experimental work on CO2 line positions in the 4300– 8500 cm
1 range. Positions observed with Fourier transform spectrometers have been reported at 5300 cm
1 by Giver et al. [21], at 6950 cm
1 by VanderAuwera et al. [22] and from 7000 to 8500 cm
1 by Teffo

Fig. 2. Energy level diagram showing the frequency chain used to determine the spectroscopic constants for the 00001 state. The narrow arrows represent absolute frequency measurements from CO2 lasers. The broad arrows linking the 00001, 00011, and 00021 states indicate that infrared measurements of the line positions were used. HITRAN and conventional normal mode designations are given for each vibrational state.

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

et al. [23]. Chou et al. [24] used a diode laser to measure lines near 6500 cm
1 . The extensive analysis of CO2 emission spectra in the 3.0, 4.5, and 15 lm regions performed by Bailly and coworkers [25–38] merits special mention. Although these high-resolution FTS experiments did not probe NIR transitions directly, they did provide spectroscopic constants for many of the upper vibrational states involved in NIR transitions. Bailly performed a global fit to all of the emission spectra [33] which demonstrated the high quality of that data. Other global assessments of 16 O12 C16 O rotation-vibration line positions providing information on the NIR transitions include those of Tashkun et al. [39], Zuniga et al. [40], and Aguir et al. [41]. Motivated by the need for a CO2 spectral database with sufficient accuracy to support 0.3% precision retrievals of atmospheric CO2 from the space-based and ground-based observations to be made by the orbiting carbon observatory (OCO) [42] and for the North American Carbon Program [3], we are undertaking a systematic reinvestigation of the NIR spectrum of carbon dioxide up to 8500 cm
1 . Here we report spectroscopic constants and line positions for the 16 O12 C16 O isotopologue with RMS fitting residuals less than Table 1 Summary of experimental parametersa Spectrum

Path (m)

CO2 pressure (Torr)

Integration (h)

1 2 3 CO + C2 H2 (all scans)

25 97 241 2.4

2.0 2.0 7.0 1.1 Torr CO + 0.5 Torr C2 H2

2.6 2.6 10.3

a All spectra recorded with resolution ¼ 0.012 cm
1 , pass ¼ 3600–8400 cm
1 and T ¼ 295 K.

band-

331

4  10
5 cm
1 for strong bands and RMS residuals less than 3  10
4 cm
1 for most of the weaker bands. This reduces NIR CO2 line position uncertainties by a factor of 10 or more compared to the 2000 HITRAN database [15] or the Tashkun et al. [39,43] Carbon Dioxide Spectroscopic Database. The new data and analysis satisfy the line position accuracies required for the next generation of CO2 remote sensing instruments, improve the capability of solar-viewing spectrometers to retrieve precise column CO2 measurements, and provide selfconsistent secondary frequency standards in the NIR.

2. Experimental Spectra were recorded with the McMath–Pierce FTS at the Kitt Peak National Solar Observatory using a pair of liquid nitrogen cooled InSb detectors and the multi-pass absorption cell with a 6 m base path length. High signal-to-noise spectra were recorded between 4000 and 8500 cm
1 with a resolution of 0.012 cm
1 . Spectra were integrated for several hours, as indicated in Table 1. The three scans used in the spectral analysis were taken using pressure-path length combinations of 2.0 Torr and 25 m, 2 Torr and 97 m, and 7 Torr and 241 m. Calibration spectra of the (2–0) band of CO at 4200 cm
1 [44] and the (m1 þ m3 ) band of C2 H2 at 6500 cm
1 [45–47] were recorded simultaneously by placing a 2.4 m quartz cell containing 0.5 Torr of C2 H2 and 1.1 Torr of CO in the beam path while recording the CO2 spectrum in the multipass cell. Fig. 3 displays the 4000–5200 cm
1 portion of Spectrum #2. Samples of CO2 , CO, and C2 H2 were used as received. Line centers were obtained by peak finding on the apodized and interpolated spectra.

Fig. 3. Survey spectrum of the 2 lm region: P ¼ 2:06 Torr, L ¼ 97 m, T ¼ 295 K. CO calibration gas absorption is observed at 4250 cm
1 . The CO2 (2m1 þ m3 ) Fermi triad and associated hot bands are observed in the 4700–5200 cm
1 region. The band centered near 4050 cm
1 is due to C2 H2 .

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One major goal of this work was to produce a CO2 NIR spectral database with an accuracy comparable to that currently achieved for high quality mid-infrared analyses, i.e., 5  10
5 cm
1 or better. This mandated the use of low gas pressures since previous studies [48– 55] showed that CO2 transitions in the NIR experience large, negative pressure-induced frequency shifts with strong dependencies on J and DJ . Ideally, line positions should be acquired from spectra with pressures of 2 Torr or less. For example, line shifts at 2 Torr for the 00031 00001 band (m0 ¼ 6972 cm
1 ) will be d <
3:5  10
5 cm
1 , assuming a pressure shift coefficient b ¼
0:014 cm
1 atm
1 [48]. The pressure shift under these conditions is within a factor of two of the expected calibration uncertainty and should have minimal effect on the line positions. It is crucial to use the minimum possible pressures for these experiments since even pressures as low as 5 Torr will induce measurable line position shifts ()1  10
4 cm
1 ). The situation is compounded for high-J transitions since they experience larger pressure shifts than low-J transitions [48,49,51– 53,56]. The excellent characterization of the McMath–Pierce FTS instrumental line shape (ILS) and the ability to generate spectra with line position measurement precisions of 2  10
5 cm
1 enabled us to determine accurate CO2 NIR line positions. Spectral calibration was performed by identifying the CO and C2 H2 peak positions in each spectrum and then minimizing the differences between these positions and their absolute wavenumbers using a constant multiplicative factor for the entire spectrum. This calibration procedure produced RMS uncertainties of 1.8–2.0  10
5 cm
1 for strong, unblended CO and C2 H2 lines in the corrected spectra. Possible pressureinduced frequency shifts caused by the CO/C2 H2 mixture in the calibration gas cell were considered by assuming self-broadened shifts of each molecule [44,47]. Our best estimate is that the shifts on the calibration lines would be no larger than 2.0  10
5 cm
1 . Experimental uncertainties of 2.0  10
5 cm
1 were therefore assigned to all strong, unblended CO2 absorption features in the 4300– 6500 cm
1 range. For bands above 6500 cm
1 the uncertainty of the positions depends on the size of the uncertainty in the correction factor. For example, at 8100 cm
1 , the calibration could have degraded to the extent that the uncertainty of the positions is 2.5  10
4 cm
1 . The positions for weaker lines (<20% absorbance) were assigned larger experimental uncertainties based on the absorption strengths. A number of hot bands originating from the m1 2 or 2 2m2 vibrational states were measured as well. To obtain better rotational constants for those transitions, we re1 2 1 fitted the m12 or 2m2 2 levels using m2 and (2m2
m2 ) positions obtained from one FTS spectrum recorded from 500 to 1400 cm
1 at 0.0056 cm
1 resolution with As-doped Si detectors. The CO2 sample was 0.15 Torr in

a 0.25 m cell, and a second cell (1.5 m path) containing 0.5 Torr of OCS was included for the calibration of the wavenumber scale [57].

3. Results and analysis Following R92, the energy levels for each vibrational state were characterized by the spectroscopic constants Gv , Bv , Dv , and Hv . Transitions in the observed ‘‘cold’’ and ‘‘hot’’ bands often involved the same vibrational energy, and these were constrained to have the same spectroscopic constants. States with vibrational energies below 4600 cm
1 were fitted using data from the literature to determine the best parameters for the range of J values observed in the NIR transitions; these parameters were then held fixed in the fitting of the NIR transitions. Vibrational states involving one quantum of excitation in the m2 bending mode were constrained to have degenerate vibrational energies while the rotational and distortion constants were fit independently. Vibrational states involving two quanta of m2 excitation were constrained to have degenerate vibrational energies and Be ¼ Bf while the distortion constants were fitted independently. All fitting was performed using PickettÕs SPFIT program suite [58]. The spectroscopic constants determined in this work are presented in Table 2 along with the RMS fitting residuals. Examples of individual fits are presented in Appendix A. Below we present extensive comparisons of our fitting parameters with the constants reported in R92 [16]; however, this comparison is greatly hindered by the lack of parameter uncertainties or other statistical figures of merit in R92. We encourage the inclusion of such detailed information in future updates to the CO2 database. All absorption band strengths (Sv0 ) listed will be taken from R92 and given in units of cm/molecule  10
22 at 296 K. 3.1. The ground (00001) and low-lying symmetric and anti-symmetric stretching (10002, 10001, 00011, 10011, 10012, and 00021) vibrational states It became clear during the analysis of our new spectra that fixing the spectroscopic constants of the ground and other low-lying vibrational states to the R92 values did not yield optimal fits for the near-IR transitions. While a global refitting of all available 16 O12 C16 O data was beyond the scope of the present work, we found it necessary to perform a limited refitting of these vibrational states to reproduce our observed spectra within their experimental uncertainties. In the analysis presented below, reported line positions and uncertainties were collected from the referenced sources and refit in an effort to define the optimal set of lower state constants for fitting the NIR line positions.

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

333

Table 2 16 12 16 O C O spectroscopic constants from this worka

gs 01101e 01101f 10002b 02201e 02201f 10001b 11101e 11101f 00011b 01111e 01111f 10012 02211e 02211f 10011 00021 20013 20012 20011 01121e 01121f 21113e 21113f 21112e 21112f 21111e 21111f 30014 22213e 22213f 30013 22212e 22212f 30012 22211e 22211f 30011 31114e 31114f 31113e 31113f 00031 31112e 31112f 31111e 31111f 40014 40013 01131e 01131f 40012 10032 10031 a

Gv

Bv

Dv (10
6 )

Hv (10
12 )

Jmax

RMS

0.0000 667.3798265(45) 667.3798265(45) 1285.4081123(117) 1335.1313992(77) 1335.1313992(77) 1388.1840918(117) 2076.8558926(61) 2076.8558926(61) 2349.1426834(117) 3004.0123018(59) 3004.0123018(59) 3612.8406918(112) 3659.2721361(96) 3659.2721361(96) 3714.7818358(112) 4673.3253699(112) 4853.6231494(56) 4977.8346548(63) 5099.6601778(56) 5315.7131296(46) 5315.7131296(46) 5475.0739725(61) 5475.0739725(61) 5632.7648793(45) 5632.7648793(45) 5790.5755924(41) 5790.5755924(41) 6075.9795926(59) 6103.6833711(249) 6103.6833711(249) 6227.9165633(63) 6288.4945688(265) 6288.4945688(265) 6347.8509516(62) 6474.5332996(242) 6474.5332996(242) 6503.0796493(67) 6688.1742308(49) 6688.1742308(49) 6863.5558537(49) 6863.5558537(49) 6972.5771967(55) 7023.6743697(50) 7023.6743697(50) 7203.8252608(57) 7203.8252608(57) 7460.5210678(76) 7593.6894017(62) 7602.5138313(40) 7602.5138313(40) 7734.4477160(74) 8192.5506286(57) 8293.9516352(57)

0.390218949(36) 0.390639109(15) 0.391254698(20) 0.390482292(1) 0.391666762(32) 0.391666762(32) 0.390188916(1) 0.390409731(16) 0.391334089(20) 0.387141391(1) 0.387592610(17) 0.388190370(21) 0.387503193(1) 0.388636164(34) 0.388636164(34) 0.387063180(1) 0.384066147(1) 0.388197666(16) 0.386533591(22) 0.387499640(17) 0.384547434(10) 0.385128989(26) perturbed 0.389436362(17) 0.387010716(20) 0.388113837(20) 0.387406695(13) 0.388620339(13) 0.388906062(21) 0.389419640(107) 0.389419640(107) 0.386711288(28) 0.388474297(86) 0.388474297(86) 0.386455031(28) 0.388638779(104) 0.388638779(104) 0.387976550(25) 0.388539345(23) 0.390257710(20) 0.386922123(26) 0.388334558(28) 0.380993189(15) 0.386749452(28) 0.388118581(26) 0.387592140(27) 0.389154226(30) 0.387351941(29) 0.385578470(18) 0.381503745(17) 0.382068868(20) 0.386961162(30) 0.381559893(18) 0.380805392(17)

0.1334088(186) 0.1353930(122) 0.1361606(170) 0.15715707(50) 0.137366(33) 0.138125(32) 0.11494271(50) 0.1258970(112) 0.1212784(148) 0.13302614(50) 0.1348447(118) 0.1358403(163) 0.15758093(118) 0.135944(32) 0.1375157(309) 0.11428791(102) 0.13270177(96) 0.1816938(101) 0.1363761(178) 0.0965755(114) 0.1341937(38) 0.1361785(250) perturbed 0.1757534(106) 0.1290972(182) 0.1322737(174) 0.1133083(84) 0.1065744(88) 0.2128206(179) 0.128011(103) 0.168368(107) 0.1717973(290) 0.146990(60) 0.145724(80) 0.0982331(293) 0.146486(100) 0.114388(102) 0.0748839(214) 0.1707217(186) 0.1918125(137) 0.1352391(292) 0.148623(34) 0.1322653 (85) 0.1199782(297) 0.1162874(281) 0.0975645(202) 0.0943452(240) 0.2007863(206) 0.1120656(97) 0.1327666(136) 0.1345867(201) 0.0922856(237) 0.1572557(110) 0.1125702(94)

0.01918(250) 0.02967(260) 0.0304(38) 0.233398(141) )0.3765(78) 0.0738(80) 0.186596(141) 0.09043(273) 0.0844(35) 0.014118(141) 0.03089(240) 0.0332(34) 0.22663(38) )0.3588(70) 0.0679(72) 0.195754(240) 0.015008(214) 0.56286(171) 0.8467(38) 0.40949(204)

76 79 72 69 62 61 69 55 54 77 80 73 55 63 62 55 76 65 57 65 55 56

4.40  10
5 4.90  10
5 4.90  10
5 4.40  10
5 4.90  10
5 4.90  10
5 4.40  10
5 4.90  10
5 4.90  10
5 4.40  10
5 4.90  10
5 4.90  10
5 4.40  10
5 4.90  10
5 4.90  10
5 4.40  10
5 4.40  10
5 3.30  10
5 4.70  10
5 3.60  10
5 1.80  10
4 1.80  10
4

65 56 57 66 65 57 53 52 51 64 53 51 52 53 55 38 41 50 47 69 50 51 38 37 39 45 60 55 37 45 45

1.33  10
4 1.74  10
4 1.74  10
4 2.06  10
4 2.06  10
4 5.70  10
5 6.30  10
4 6.30  10
4 4.40  10
5 1.39  10
3 1.39  10
3 4.50  10
5 3.34  10
4 3.34  10
4 2.13  10
4 2.77  10
4 2.77  10
4 1.87  10
4 1.87  10
4 5.80  10
5 2.41  10
4 2.41  10
4 5.50  10
4 5.50  10
4 4.30  10
4 3.58  10
4 3.21  10
4 3.21  10
4 1.37  10
3 2.95  10
4 2.90  10
4

0.2461(58) perturbed 0.21457(177) )0.6157(42) )0.5033(39) 0.28240(143) 0.04702(151) 1.5457(40) )1.7789(263) 1.3696(284) 1.0973(78) 2.1932(103) 0.4979(206) 0.5755(79) )0.6688(258) 0.4084(274) 0.8315(50)

)1.9323(84) )1.1221(104) )0.0255(130) 0.5340(82) 0.4251(78)

)0.30948(281) )0.1324(49)

All values in cm
1 . 1r errors given in units of the least significant digit. L10002 ¼
0:9928ð131Þ  10
18 ; L10001 ¼ 0:5663ð131Þ  10
18 ; L00011 ¼ 0:0697ð131Þ  10
18 .

b

Absolute frequencies of the 10 lm CO2 laser band transitions 00011 ! 10001 and 00011 ! 10002 have been measured with precisions of a few kHz (<1.0  10
7 cm
1 ) [59]. These measurements provide an ideal frequency standard for infrared spectral analysis since the

laser band transition frequencies have essentially zero uncertainty on the scale of infrared measurements. Infrared absorption measurements of the strong 00011 00001 fundamental at 4.3 lm [60] can be used to link the ground state to the laser band states. Thus, we

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C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

leverage the absolute frequency measurements of the laser bands to determine accurate ground state constants in a simultaneous fit of the 00011 ! 10001, 00011 ! 10002, and 00011 00001 transitions. Ideally, one would verify the self-consistency of the energy levels defined by the spectroscopic constants by including 10002 00001 and 10001 00001 line positions in the fit to complete the energy level loops, but these bands are not infrared active for the 16 O12 C16 O isotopologue. However, absolute frequencies have been measured for the 00021 ! 10011 laser transitions at 10.3 lm [61] and 10011 ! 00001 laser transitions at 3 lm [62]. These absolute frequencies, combined with the 00021 ! 00011 infrared emission spectrum measured at 4.3 lm by Bailly et al. [26], can be used to create the closed energy level loop shown in Fig. 2. The constants given in Table 2 for the 00001, 10002, 10001, 00011, 10012, 10011, and 00021 vibrational states were determined by fitting 395 transitions that combined the laser [59,61,62] and infrared [26,60] measurements. The infrared line positions were corrected by a factor of 0.999999817 as recommended by the IUPAC evaluation for infrared frequency standards [63,64]. The laser band frequencies were included for transitions up to J 0 ¼ 69 and assigned the uncertainties tabulated in [59,61,62], typically < 7  10
7 cm
1 (20 kHz). The 00011 00001 infrared transitions were sampled up to J 0 ¼ 77 and were given uncertainties of 1.2  10
4 cm
1 [60] while the 00021 ! 00011 line positions were sampled up to J 0 ¼ 76 and were assigned uncertainties of 2  10
5 cm
1 [26]. This fit yielded a RMS error of 4.4  10
5 cm
1 and an average error of +1.3  10
5 cm
1 with all of the significant residuals contributed by the infrared transitions. Fitting only the 00011 00001 infrared data with the laser transitions yielded a RMS error of 8  10
6 cm
1 ; fitting only the 00021 ! 00011 infrared data with the laser transitions yielded a RMS error of 1.0  10
5 cm
1 . The significantly larger RMS errors associated with the combined fit reflect simultaneous constraints on the 00011 and 00021 vibrational origins not present when only one set of infrared data was included. This fit also more accurately reflects the uncertainties in the infrared data. In fact, the fit tended to shift the calculated 00011 00001 transitions to the limit of their listed uncertainties. This increased the RMS error and caused the non-zero average error. There is clearly a need to recalibrate 00011 00001 line positions to obtain absolute wavenumbers of the 00011 and 00021 vibrational energies with uncertainties of 2  10
5 cm
1 . The vibrational energy differences between the states involved in laser transitions were determined with kHz accuracy (<5  10
8 cm
1 ) while the absolute values of the vibrational state energies were determined entirely from the infrared data: the G10002 , G10001 , and G00011 were all determined with an uncertainty of 1.2  10
5 cm
1

while G10012 , G10011 , and G00021 were all determined with an uncertainty of 1.1  10
5 cm
1 . The vibrational energies in the present work are systematically 1.0  10
4 cm
1 lower than the R92 values. This discrepancy can not be due solely to the application of the IUPAC correction factor to the infrared data. For example, this factor would scale the R92 G00011 from 2349.14291 to 2349.14248 cm
1 , a decrease of 4.3  10
4 cm
1 or a factor of four larger than the observed difference. The G00021 value determined in the present work, 4673.3253699(112) cm
1 , is virtually identical to the 4673.325363(7) cm
1 value determined by Chou et al. [61]. The Chou et al. [61] analysis included uncorrected 00021 ! 00011 positions from Bailly et al. [26] to provide spectral information from 46 < J < 92 for the 00021 state; however, the Chou et al. fit did not include any 00011 00001 lines. The present rotational and distortion constants B00001 , D00001 , and H00001 are similar to those reported in R92, Bailly [33] and Chou et al. [61]. The results are compared in Table 3. The largest difference is in H00001 with the present value a factor of two larger than that in R92, although the values agree within the 3r uncertainty. Octic distortion constants (Lm ) were required to fit the 10001, 10002, and 00011 states. The rotational and distortion constants determined for those states are identical to those reported by Maki et al. [59] within fitting uncertainty. The inclusion of L00001 produced no significant improvement in the RMS error and increased the uncertainty in D00001 and H00001 ; L00001 was therefore omitted from the final fit. The 00001 state spectroscopic constants determined from the present analysis represent the most accurate values available for low to moderate J rotational levels (J  70). They are able to reproduce the reported 00011 00001 line positions within experimental uncertainty for transitions up to J ¼ 140. However, the high-J 00011 00001 line positions [65,66] have significantly larger uncertainties (4  10
4 cm
1 ) than the Guelachvilli data (1.2  10
4 cm
1 ) [60] and produced RMS fitting errors a factor of 40 larger than the present fit. Incorporating the laser band frequencies reported by Bernard et al. [67] exhibited no significant difference from the present results. The Maki et al. laser band data [59] were chosen for the present work because they reported a larger range of J -values. In subsequent fitting the spectroscopic constants for the 00001, 10002, and 10001 states were fixed to the values determined in this limited fit. 3.2. The excited bending states (01101, 02201, 01111, and 11102) We also found that hotband fits using the R92 constants for the 01101 and 02201 vibrational states did not yield optimal fits for the NIR transitions. We therefore undertook a limited redetermination of spectroscopic

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

335

Table 3 Comparison of 00001, 00011, and 00021 spectroscopic constantsa Gv

Bv

Dv (10
6 )

Hv (10
12 )

Ref.

00001 0.0000 0.0000 0.0000 0.0000

0.39021889 0.3902188929(200) 0.3902189560(192) 0.390218949(36)

0.133338 0.13335361(600) 0.1333746(60) 0.1334088(186)

0.0077 0.011095(600) 0.01330(52) 0.01918(250)

[16] [33] [61] This work

0.132998 0.132924(31) 0.13302488(100) 0.13302616(54) 0.13302614(50)

0.0096

2349.1426834(117)

0.38714135 0.38714137(19) 0.3871413903(20) 0.387141391429(404) 0.387141391(1)

[16] [60] [33] [59]e This workf

00021 4673.32546 4673.325416(10)d 4673.325363(7) 4673.3253699(112)

0.38406605 0.3840661605(50) 0.38406614758(353) 0.384066147(1)

0.132645 0.13269976(200) 0.132702228(2370) 0.13270177(96)

00011 2349.14291 2349.142830(12)b 2349.142835(10)c

0.014192(200) 0.014125(255) 0.014118(141) 0.0066 0.01453845(29945) 0.015008(214)

[16] [33] [61] This work

a

All values in cm
1 . 1r errors given in units of the least significant digit. Ref. [60] G00011 uncorrected ¼ 2349.14326(12). c Ref. [33] G00011 uncorrected ¼ 2349.143265(10). d Ref. [33] G00021 uncorrected ¼ 4673.326266(10). e Ref. [59] L00011 ¼ 0:0690ð384Þ  10
18 . f L00011 ¼ 0:0697ð131Þ  10
18 . b

parameters for the 01101 and 02201 states by leveraging the absolute frequency measurements of CO2 laser hot bands with the highest quality infrared data in much the same manner as the 00001 state constants were reevaluated. The laser hot band transition frequencies reported by Petersen et al. [68] for the 01111 ! 11101 and 01111 ! 11102 transitions were used to determine the rotational and distortion constants for these three states. The accuracy of these measurements was linked to the 01101 state via the 01111 ! 01101 infrared emission

measurements of Bailly et al. [26] corrected by a factor 0.999999817. Positions of 01101 00001 and 02201 01101 obtained by Brown and calibrated to the OCS transitions in the 800–1100 cm
1 range [57] were used. Corrected line positions for the 02211 ! 02201 band [26] were also included. The ground state constants were fixed to the values in Table 2. All transitions were weighted according to their reported measurement uncertainties and fitted simultaneously. The fitted spectroscopic parameters are compared in Tables 4 and 5.

Table 4 Comparison of 01101 and 02201 spectroscopic constantsa Gv

Bv

Dv (10
6 )

01101e 667.37996 667.379568(10) 667.3798265(45)

0.39063900 0.3906390147(200) 0.390639109(15)

0.135295 0.13529529(900) 0.1353930(122)

0.0099 0.010513(1000) 0.02967(260)

[16] [33] This work

01101f 667.37996 667.379568(10) 667.3798265(45)

0.39125465 0.3912546491(200) 0.391254698(20)

0.136088 0.13607120(900) 0.1361606(170)

0.0149 0.013775(900) 0.0304(38)

[16] [33] This work

02201e 1335.13161 1335.130885(20) 1335.1313992(77)

0.39166676 0.3916667451(300) 0.391666762(32)

0.137452 0.13731967(2000) 0.137366(33)

)0.3605 )0.399352(2000) )0.3765(78)

[16] [33] This Work

02201f 1335.13161 1335.130885(20) 1335.1313992(77)

0.39166676 0.3916667451(300) 0.391666762(32)

0.138022 0.13798556(2000) 0.138125(32)

0.0148 0.010606(2000) 0.0738(80)

[16] [33] This work

a

All values in cm
1 . 1r errors given in units of the least significant digit.

Hv (10
12 )

Ref.

336

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

Table 5 Comparison of 01111 and 02211 spectroscopic constantsa Bv

Dv (10
6 )

0.38759250 0.3875925554(200) 0.3875924319 0.387592610(17)

0.134768 0.13475559(900) 0.1347047 0.1348447(118)

3004.0123018(59)

0.38819027 0.3881903142(200) 0.3881900710 0.388190370(21)

0.135761 0.13573344(900) 0.1356077 0.1358403(163)

02211e 3659.27229 3659.272038(23)c 3659.2721361(96)

0.38863604 0.3886361312(300) 0.388636164(34)

0.136021 0.13585971(2000) 0.135944(32)

)0.3407(70) )0.389540(2000) )0.3588(70)

[16] [33] This work

02211f 3659.27229 3659.272038(23)c 3659.2721361(96)

0.38863604 0.3886361312(300) 0.388636164(34)

0.137396 0.13737327(2000) 0.1375157(309)

0.0173 0.011832(2000) 0.0679(72)

[16] [33] This work

Gv 01111e 3004.01227 3004.012306(10)b 3004.0123018(59) 01111f 3004.01227 3004.012306(10)b

Hv (10
12 ) 0.0149 0.013(1) 0.03089(240) 0.0172 0.014(1) 0.0332(34)

Ref. [16] [33] [68] This work [16] [33] [68] This work

Note. Bailly 0nn01 stack has equal and opposite offset to the 000n1 stack, such that for the hotband transitions the values are in good agreement with R92 and this work using no correction term. It is unclear what correction term should be applied for the 01101 region. a All values in cm
1 . 1r errors given in units of the least significant digits. b Bailly 01111 ! 01101 uncorrected ¼ 2336.632738(2); corrected 01111 + uncorrected 01101 ¼ 3004.011878(10). c Bailly 02211 ! 02201 uncorrected ¼ 2324.141153(3); corrected 02211 + uncorrected 02201 ¼ 3659.271613.

The RMS fitting error to 437 line positions in the combined fit of excited v2 states was 4.9  10
5 cm
1 with the majority of the error coming from the 01101 00001 and 02201 01101 transitions. Fits to just the 01101 00001 and 02201 01101 transitions yield a RMS error of 5.8  10
5 cm
1 . This fit lacks the closed loops that were used to constrain the vibrational energies in the ground state fit, yet the accuracy of the laser frequency measurements has been effectively transferred to the 01101 and 02201 constants. This procedure enabled us to determine the Hv constants, and the parameter uncertainties were reduced 10% compared to previous determinations [33]. The small discrepancies in the distortion constants are most likely a result of the truncated range of J -values used in the present analysis and would be reduced by fitting available data with J > 70. However, we sought the most accurate possible constants for the range of J -values sampled in the NIR spectra, and the results presented here for 01101 and 02201 have the benefit of combining laser and IR work with a common calibration standard. In the fits discussed below, the spectroscopic constants for the 01101 and 02201 states are fixed to the values determined in this limited fit. 3.3. The 2.0 lm region: Fermi triads 2001n, 2111n, and 2221n As seen in Fig. 3, the spectrum between 4700 and 5200 cm
1 is dominated by the [4m02 þ m3 , m1 þ 2m02 þ m3 ,

2m1 þ m3 ] Fermi triad corresponding to the 20013 00001 (m0 ¼ 4853:6 cm
1 ), 20012 00001 (m0 ¼ 4977:8 cm
1 ) and 20011 00001 (m0 ¼ 5099:6 cm
1 ) bands. Also observed in this region are the associated hot band transitions originating from excited bending levels, e.g., 21113 01101 and 22213 02201, as well as the 01121 00001 combination band. The R92 line positions for the 2001n 00001, 2111n 01101 and 01121 00001 transitions are based on the work of Arcas et al. [19]. R92 line positions for the 22213 02201 and 22211 02201 transitions are calculated using the spectroscopic parameters derived from Venusian spectra recorded by Mandin [20] while the 22212 02201 line positions have been computed with DND spectroscopic constants. The 20012 00001 (Sv0 ¼ 347:5) band is sufficiently intense that Spectrum #1 (details in Table 1) provided excellent line position data through J 00 ¼ 56 while the weaker 20013 00001 (Sv0 ¼ 78:1) and 20011 00001 (Sv0 ¼ 109) bands were better fitted using Spectrum #2. RMS errors were 3.3  10
5 , 4.7  10
5 , and 3.6  10
5 cm
1 for the 20013 00001, 20012 00001, and 20011 00001 bands, respectively. The comparison of spectroscopic constants in Table 6 shows that Arcas et al. obtained RMS errors of 9.9  10
5 , 10.9  10
5 , and 5.0  10
5 cm
1 for fits to these same bands [19]. The constants presented in Table 2 also predict accurate line positions for higher J transitions. For example, the constants for the 20011 00001 band determined by fitting transitions up to J 00 ¼ 64 were used to identify

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

337

Table 6 Comparison of 20013, 20012, and 20011 spectroscopic constantsa Gv

Bv

Dv (10
6 )

Hv (10
12 )

20013 4853.62341 4853.6233840(78) 4853.623142(81) 4853.6233 4853.6231496(56)

0.38819761 0.388198213(23) 0.3881980(2) 0.38820041 0.388197640(16)

0.181675 0.182064(16) 0.1821(2) 0.181357 0.1817135(101)

0.5612 0.5888(27) 0.64(3) 0.5165 0.56653(171)

Variational 3.3  10
5

[16] [19] [33] [41] This work

20012 4977.83500 4977.8350073(82) 4977.8333 4977.8346548(63)

0.38653399 0.386534401(25) 0.38653996 0.386533591(22)

0.136836 0.137052(17) 0.138047 0.1363761(178)

0.9598 0.9518(29) 1.1488 0.8467(38)

10.9  10
5 Variational 4.7  10
5

[16] [19] [41] This work

20011 5099.66050 5099.6604976(38) 5099.660190(69) 5099.6606 5099.6601778(56)

0.38749949 0.387499973(12) 0.3874984(1) 0.38750337 0.387499640(17)

0.096452 0.096724(9) 0.09524(4) 0.096407 0.0965755(114)

0.3901 0.3938(17)

5.0  10
5

0.3749 0.40949(204)

Variational 3.6  10
5

a

RMS

9.9  10
5

Ref.

[16] [19] [33] [41] This work

All values in cm
1 . 1r errors given in units of the least significant digits.

transitions up to P ð76Þ and Rð76Þ in Spectrum #2. All predictions were within 0.001 cm
1 of the observed line positions, and further assignments were limited only by the vanishing intensity of J 00 > 76 transitions. The spectroscopic constants determined in the present study are compared with those from previous studies in Table 6. The Gv values from the Arcas et al. fits [19], and thus the R92 values, are systematically 2  10
4 cm
1 higher than the present values, and the difference is most likely due to changes in the calibration standards, given the good overall agreement between the rotational and distortion constants. However, the direct comparison of 20011 00001 line positions given in Fig. 4 shows that the discrepancies between our line positions and those of Arcas et al. diverge asymmetrically for high-J transitions. The R92 line positions also exhibit systematic differences from our predictions, but the standard deviation of the line position differences is only 2.2  10
5 cm
1 after compensating for the 2.9  10
4 cm
1 offset. We note that the R92 rotational and distortion constants for the 20013, 20012, and 20011 states were determined from fits to four to six different vibrational transitions, presumably including the moderately strong hot bands in the 3000–4000 cm
1 region [69]. We conclude that absolute wavenumber accuracies on the order of a few times 10
5 cm
1 are possible for the 2001n 00001 transitions given accurate calibration standards and high quality measurements. The hot band transitions 21113 01101 (Sv0 ¼ 7:85), 21112 01101 (Sv0 ¼ 23:5) and 21111 01101 (Sv0 ¼ 10:1) are readily apparent in Fig. 3: they have twice the line density of the 2001n 00001 transitions and lesser absorption depths. Fits to the hot bands yielded RMS errors <2  10
4 cm
1 for all of the e- and f -components with the exception of 21113e. The perturbation of this

Fig. 4. A comparison of the predicted line positions for the 20011 00001 band at 5100 cm
1 expressed as differences relative to the present work (MB). Upper panel: R92: Rothman et al. [16]. Arcas: Arcas et al. [19]. Lower panel: Bailly: [33]. Aguir: Aguir et al. [41].

state is known and has been discussed by Arcas et al. [19] and Bailly et al. [36]. Since it is not possible to provide an accurate description of the 21113e 01101e line positions using the simple spectroscopic parameters Gv , Bv ,

338

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

Dv , and Hv , detailed reinvestigation of this problem is deferred for the future. The accuracy of the fits for these bands is limited by the signal-to-noise of the high-J lines. The hot band vibrational energies are compared in Table 7. The Gv values reported for Arcas et al. [19] are calculated from G0
Bl2 for consistent comparison. We note that Arcas et al. fit the vibrational origins for the e and f components of each upper state independently. The vibrational origins were not constrained to be degenerate although the fitted origins of the transitions are reproduced within 1  10
4 cm
1 [19]. The Gv values from Arcas et al. are again systematically higher than the present Gv values, but the differences are not uniform and range from +5 to +11  10
4 cm
1 . The R92 G21113 and G21112 values are based on hot band data for the 21113 01101 and 21112 01101 bands [19], but the R92 G21113 and G21112 are 2 to 10  10
4 cm
1 lower than the Arcas et al. G21113 and G21112 values. The source of this difference is not obvious. R92 determined G21111 from a fit to two different vibrational bands which explains its difference from the Arcas et al. results. The R92 Gv values agree better with our results, but G21113 and G21111 are still 4  10
4 cm
1 higher. The G21112 values agree within 2  10
5 cm
1 ; we believe this accuracy is possible over the whole region considered

given the current calibration standards. The reason for the very good agreement of G21112 values may be due to the fact that this is the strongest of the 2111n Fermi triad and thus yields the highest signal-to-noise measurements. It was also possible to calculate G21111 from the results of Bailly and coworkers [33,37]. It is 5  10
4 cm
1 higher than our result, similar to the R92 value, which we consider reasonable agreement given the fact that it was derived from a sequence of six emission transitions and has an estimated 3r uncertainty of 2  10
4 cm
1 . Comparison of the rotational and distortion constants in Table 7 shows reasonable consistency. Most notably the H21112e and H21112f distortion constants were determined to be negative in the present work and by Arcas et al. [19]. Differences in predicted line positions from the present work and the R92 line list are plotted in Fig. 5 for the 21111e 01101e and 21111f 01101f bands. A )4  10
4 cm
1 offset in the vibrational origins is clearly seen for each band. The more interesting point is that the standard deviation of the 21111e 01101e line positions is about a factor of two smaller than the standard deviation of the 21111f 01101f line positions. Furthermore, the deviations between the two line lists behave very differently for J > 40 with the

Table 7 Comparison of 21113, 21112, and 21111 spectroscopic constantsa Gv

Bv

Dv (10
6 )

21113e 5475.07444

0.38815515

0.161

0.38943597 0.389436634(120) 0.3894336(7) 0.389436362(17)

0.175365 0.175838(110) 0.1742(1) 0.1757534(106)

0.38701311 0.387011137(63) 0.387010735(2000) 0.387010716(20)

0.131657 0.129455(61) 0.1314(4) 0.1290972(182)

5632.7648793(45)

0.38811592 0.388114641(89) 0.388117(2) 0.388113837(20)

0.134365 0.132861(82) 0.1338(3) 0.1322737(174)

21111e 5790.57598 5790.576672(26) 5790.576084(69) 5790.5755924(41)

0.38740648 0.387407051(100) 0.387405061(700) 0.387406695(13)

0.113096 0.113474(90) 0.1114(1) 0.1133083(84)

21111f 5790.57598 5790.576119(26) 5790.576084(69) 5790.5755924(41)

0.38862059 0.388 621241(79) 0.3886173(7) 0.388620339(13)

0.106749 0.106987(66) 0.1051(1) 0.1065744(88)

21113f 5475.07444 5475.074571(30) 5475.0739725(61) 21112e 5632.76490 5632.765981(22) 5632.7648793(45) 21112f 5632.76490 5632.765383(22)

a

All values in cm
1 . 1r errors given in units of the least significant digit.

Hv (10
12 )

0.141(28) 0.21457(177)

)0.593(14) )0.6157(42)

)0.433(19) )0.5033(39) 0.2383 0.253(20) 0.28240(143) 0.0819 0.042(14) 0.04702(151)

RMS

Ref.

perturbed

[16]

2.0  10
4 1.4  10
4 1.33  10
4

[16] [19] [37] This work

1.6  10
4 2.8  10
4 1.74  10
4

[16] [19] [37] This work

2.4  10
4 2.4  10
4 1.7  10
4

[16] [19] [37] This work

2.1  10
4 1.6  10
4 2.06  10
4

[16] [19] [37] This work

1.6  10
4 1.5  10
4 2.06  10
4

[16] [19] [37] This work

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

Fig. 5. A comparison of the predicted line positions for the 21111 01101 band at 5123 cm
1 expressed as differences relative to the present work (MB). R92: Rothman et al. [16]. Note the distinct behavior of the e- and f -components at large m values.

21111e 01101e differences becoming positive while the 21111f 01101f differences become increasingly negative. This demonstrates that the e and f components of transitions with l 6¼ 0 must be compared individually. The hot band transitions 22213 02201 (Sv0 ¼ 0:344), 22212 02201 (Sv0 ¼ 0:851), and 22211 02201 (Sv0 ¼ 0:422) were initially identified in Spectrum #3 using pre-

339

dictions based on the Mandin Venusian analysis [20]. Initial assignments could be made for J 00 6 10 transitions by shifting the band origins by up to 8  10
3 cm
1 , but assignments of higher J transitions could not be made with confidence. Subsequent assignments were made by iteratively fitting the assigned lines, generating more accurate predictions for higher-J transitions, and including new lines in the line list. In this manner assignments were made for transitions through J 00 ¼ 50 for the e- and f components of each band. The line positions reported in Appendix A are the first high-resolution laboratory measurements for these bands. The 22213 02201 and 22211 02201 bands were fitted with RMS errors of 6.3  10
4 and 3.3  10
4 cm
1 , respectively, but the fit to the 22212 02201 band yielded an RMS error of 1.3  10
3 cm
1 , perhaps indicating the presence of a weak perturbation in this band. We note that R92 adopted the Mandin constants for 22213 and 22211 but reported DND constants for the 22212 state. Table 8 compares the fitted spectroscopic constants from the present study to those reported by Mandin [20] and R92. The large differences in the Gv values is not surprising given the difficulties in calibrating the Venusian spectra. The very large 3.80  10
2 cm
1 discrepancy in G22212 suggests possible complications in identifying unblended lines in the Venusian spectra. In Fig. 6A the plot of differences between the present and R92 line positions reveals that the

Table 8 Comparison of 22213, 22212, and 22211 spectroscopic constantsa Gv

Bv

Dv (10
6 )

Hv (10
12 )

RMS

Ref

22213e 6103.686 6103.6853(7) 6103.6833711(249)

0.38948235 0.38948235(6390) 0.389419640(107)

0.298 0.29781(5000) 0.128011(103)

)1.7789(263)

5.91  10
3 6.30  10
4

[16] [20] This work

22213f 6103.686 6103.6818(7) 6103.6833711(249)

0.38939756 0.38939756(940) 0.389419640(107)

0.158 0.15853(380) 0.168368(107)

1.3696(284)

1.12  10
3 6.30  10
4

[16] [20] This work

22212e 6288.5325 6288.4971(6) 6288.4945688(265)

0.38851273 0.38848603(180) 0.388474297(86)

0.156510 0.156510 0.145724(80)

0.2030 0.14358(90) 0.4979(206)

DND 1.17  10
3 1.388  10
3

[16] [20] This work

22212f 6228.5325 6288.5021(36) 6288.4945688(265)

0.38846264 0.38845182(900) 0.388474297(86)

0.138597 0.11400(480) 0.146 990(60)

0.1637

DND 1.17  10
3 1.388  10
3

[16] [20] This work

22211e 6474.534 6474.5343(4) 6474.5332996(242)

0.38864364 0.38865498(160) 0.388638779(104)

0.1498 0.14931(50) 0.146486(100)

)0.6688(258)

2.28  10
3 3.34  10
4

[16] [20] This work

22211f 6474.534 6474.5304(4) 6474.5332996(242)

0.38864364 0.38867401(750) 0.388638779(104)

0.125 0.12452(240) 0.114388(102)

0.4084(274)

10.2  10
3 3.34  10
4

[16] [20] This work

a


1

All values in cm . 1r errors given in units of the least significant digit.

2.1932(103)

340

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

Fig. 6. A comparison of the predicted line positions for the 22211 02201 band at 5169 cm
1 expressed as differences relative to the present work (MB). R92: Rothman et al. [16]. Note the markedly worse agreement for the f -components results for jmj > 20. (B) provides an expanded view of the plot for small m values.

R92 characterization of the e- and f -components are very divergent: the R92 line positions for 22211e 02201e agree much better with the present results than for 22211f 02201f . However, the expanded view for jmj < 40 shown in Fig. 6B demonstrates that even the R92 predictions for 22211e 02201e generate differences that are a factor of 10 or more larger than those shown in Fig. 5 for the 21111e 01101e band. Fig. 7 is a comparison for the 22212e 02201e and 22212f 02201f bands. The Mandin predictions for 22212e 02201e are seen to be relatively good for jmj < 20 although the 22212f 02201f predictions are poor and asymmetrically DJ -dependent. The DND predictions of R92 also display poor agreement with our line positions and once again the situation is worse for the 22212f 02201f predictions. Additionally, we observed the 01121 00001 band (Sv0 ¼ 0:168) in the 5300 cm
1 region and fitted 68 transitions for J 00 6 54 with a RMS error of 1.80  10
4 cm
1 . Available constants are compared in Table 9. Arcas et al. [19] also analyzed this band, and Bailly et al. [33] determined spectroscopic constants for the 01121 state from the 01121 ! 01111 [26] and 01121 ! 00021 [33] emission spectra. Recently, Giver et al. [21] reported estimated zero pressure line positions for the 01121 00001 band but did not report spec-

troscopic constants. We fitted their line positions and show the resulting parameters in Table 9. Also included in Table 9 are the 01121e constants predicted from the variational calculations of Aguir et al. [41]. The present fit obtained statistically significant value for H01121f but not for H01121e . The experimental constants, with the exception of the Arcas et al. G01121e [19], provide excellent agreement for the positions for the 01121e 00001 P - and R-branch transitions (Fig. 8A) and the 01121f 00001 Q-branch transitions (Fig. 8B). The consistency among the different line position predictions is especially good for the J 00 < 40 Q-branch lines (01121f 00001) with all predictions falling within 2  10
4 cm
1 of the present line positions. There are larger and more varied differences for the 01121e 00001 line positions, particularly for the Arcas et al. positions. 3.4. The 1.6 lm region: Fermi tetrads 3001n and 3111n A primary motivation for our work has been to provide accurate NIR line parameters for the remote sensing of CO2 in the atmosphere. The four moderately strong bands of the [3m1 þ m3 , 6m02 þ m3 ] Fermi tetrad in the 6000– 6600 cm
1 range, 30014 00001 (m0 ¼ 6075:9 cm
1 ), 30013 00001 (m0 ¼ 6227:9 cm
1 ), 30012 00001 (m0 ¼

Fig. 7. A comparison of the predicted line positions for the 22212 02201 band at 4953 cm-1 expressed as differences relative to the present work (MB). (A) R92: DND calculations from Rothman et al. [16]. (B) Mandin: parameters derived from Venusian FT spectra [20].

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

341

Table 9 Comparison of 01121 spectroscopic constantsa Gv

Bv

Dv (10
6 )

01121e 5315.71327 5315.7177 5315.713993(15) 5315.713144(11) 5315.7132902(244) 5315.7131296(46)

0.38454736 0.38454846 0.38454672(51) 0.38454754(2) 0.384547662(73) 0.384547434(10)

0.134194 0.134098 0.13401(31) 0.13426(1) 0.134297(37) 0.1341937(38)

01121f 5315.71327 5315.713351(17) 5315.713144(11) 5315.7132902(244) 5315.7131296(46)

0.38512822 0.38512941(47) 0.38512854(2) 0.385128517(71) 0.385128989(26)

0.135306 0.13602(24) 0.135427(9) 0.135422(33) 0.1361785(250)

Hv (10
12 )

RMS

Variational 4.8  10
4 0.014(1) 2.6  10
4 1.8  10
4

4.1  10
4 0.014(1) 0.2461(58)

2.6  10
4 1.8  10
4

Ref. [16] [41] [19] [33] [21] This work [16] [19] [33] [21] This work

Ref. [33] Gv determined from 01121 ! 01111 + 01111 ! 01101 + 01101 ! 00001 correcting m3 by 0.999999817 and adding 0.0003 cm
1 to the m2 transition. a All values in cm
1 . 1r errors given in units of the least significant digit.

Fig. 8. A comparison of the predicted line positions for the 01121 00001 band at 5316 cm
1 expressed as differences relative to the present work (MB). R92: Rothman et al. [16]. Arcas: Arcas et al. [19]. Bailly: [33]. Giver: Giver et al. [21]. (A) Differences for the 01121e lines observed in the P - and R-branches. (B) Differences for the 01121f lines observed in the Q-branch.

6347:8 cm
1 ) and 30011 00001 (m0 ¼ 6503:0 cm
1 ), and their associated hot bands, e.g., 31113 01101, are shown in Fig. 9. R92 calculates line positions for the 3001n 00001 transitions based on the work of Maillard et al. [18]. R92 lists no line position reference for any of the 3111n 01101 transitions, although Mandin [20] reported spectroscopic constants for all four transitions observed in Venusian spectra, and Maillard et al. [18] obtained line positions and constants for the 31113 01101 and 31112 01101 bands. No high-resolution laboratory measurements of the line positions for the 31114 01101 and 31111 01101 bands were previously made. The 30013 00001 (Sv0 ¼ 4:52) and 30012 00001 0 (Sv ¼ 4:54) bands are sufficiently intense that Spectrum #2 provided excellent line position data. The line list for each band included 51 transitions with J 00 6 50 and produced RMS errors of 4.4  10
5 and 4.5  10
5 cm
1 for 30013 00001 and 30012 00001, respectively. This demonstrates that the high quality of the spectra and the calibration extend through the 6500 cm
1 region. Fits extending the J -range for each band from

Fig. 9. Survey spectrum of the 1.6 lm region: P ¼ 2:06 Torr, L ¼ 97 m, T ¼ 295 K. Strong absorptions due to the C2 H2 calibration gas are observed at 6500 cm
1 . The CO2 (3m1 þ m3 ) Fermi tetrad and associated hot bands are observed in the 6000–6550 cm
1 region.

J 0 ¼ 51 to J 0 ¼ 65 were possible using the Spectrum #3; however, these spectra yielded RMS errors that were up to a factor of 1.8 larger and had band origins that were

342

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

Table 10 Comparison of 30014, 30013, 30012, and 30011 spectroscopic constantsa Gv

Bv

Dv (10
6 )

Hv (10
12 )

RMS

Ref.

30014 6075.98035 6075.983723(32) 6075.9795926(59)

0.38890584 0.38890619(12) 0.388906062(21)

0.212621 0.21285(10) 0.2128206(179)

1.5255 1.528(22) 1.5457(40)

21.2  10
5 5.7  10
5

[16] [18] This work

30013 6227.91706 6227.920444(21) 6227.9165633(63)

0.38671097 0.38671123(7) 0.386711288(28)

0.171434 0.17153(5) 0.1717973(290)

0.9966 0.966(10) 1.0973(78)

14.4  10
5 4.4  10
5

[16] [18] This work

30012 6347.85146 6347.854876(26) 6347.8509516(62)

0.38645486 0.38645521(9) 0.386455031(28)

0.098129 0.098 31(7) 0.0982331(293)

0.5609 0.554(13) 0.5755(79)

18.3  10
5 4.5  10
5

[16] [18] This work

30011 6503.08090 6503.083981(37) 6503.07906(13) 6503.0796493(67)

0.38797369 0.38797686(2) 0.38797607(39) 0.387976550(25)

0.071684 0.074 99(15) 0.07450(28) 0.0748839(214)

0.762(39) 0.749(54) 0.8315(50)

a

22.9  10
5 21.3  10
5

[16] [18] [24] This work


1

All values in cm . 1r errors given in units of the least significant digit.

shifted by up to )1.1  10
5 cm
1 , consistent with the expected pressure-induced shift [52,53]. For comparison, Maillard et al. [18] reported RMS errors of 1.4  10
4 and 1.8  10
4 cm
1 for the 30013 00001 and 30012 00001 bands, respectively. The spectroscopic constants determined from our fits are compared in Table 10 to those of Maillard et al. [18], Chou et al. [24] and R92. The Gv values reported by Maillard et al. are systematically 4  10
3 cm
1 higher than our values. A calibration error of this magnitude in the Maillard et al. data had previously been noted by Arcas et al. [19] who found a 3  10
3 cm
1 discrepancy in the Maillard et al. vibrational energy for the 30014 state when observing the 30014 10002 band (m0 ¼ 4790:5 cm
1 ). R92 has corrected for this calibration error. The rotational and distortion constants from each fit show reasonable agreement with the distortion constants from our fits being better determined by a factor of 10–100. In Fig. 10 the differences in present and R92 line positions are shown for 30012 00001, the band which has been the focus of several remote sensing schemes [4,7–10,14,42]. There exists a systematic offset of )5  10
4 cm
1 between the two predictions. An error of this magnitude is within the uncertainty limits defined for the HITRAN 2000 database [15] but will create significant errors in atmospheric CO2 column retrievals [42]. The R92 predictions exhibit a m-dependent deviation from our line positions for jmj > 25. This behavior is most likely due to pressure shifts since Maillard et al. recorded their spectra at pressures from 4 to 60 Torr [18] while the spectrum used in our analysis was recorded at a pressure of only 2 Torr. Despite these differences, we are encouraged by the negligible standard deviations of

Fig. 10. A comparison of the predicted line positions for the 30012 00001 band at 6348 cm
1 expressed as differences relative to the present work (MB). R92: Rothman et al. [16].

the two predictions for corrected jmj < 25 line positions. This supports our conclusion that absolute wavenumbers for the 30012 00001 transitions and the equally intense 30013 00001 transitions can be measured with accuracies of a few times 10
5 cm
1 . The hot band transitions, e.g., 30013 10001 and 30013 10002, were not included in our determination of the spectroscopic constants for the 30013 or 30012 states because they were found to degrade the accuracy of the fits without significantly affecting the values of the constants. The line positions for the hot band transitions were obtained from the Spectrum #3, and the pressure shift effect was observable: a simultaneous modeling of the 30013 10001 (m0 ¼ 4839:7 cm
1 ) and 30013 10002 (m0 ¼ 4942:5 cm
1 ) bands with the 30013, 10002, and

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

10001 constants fixed to the preferred values yielded a RMS error of 4.7  10
4 cm
1 and a systematic deviation of )2.2  10
4 cm
1 . A similar fit for the 30012 10001 (m0 ¼ 4959:6 cm
1 ) and 30012 10002 (m0 ¼ 5060:4 cm
1 ) bands yielded a RMS error of 2.9  10
4 cm
1 and a systematic deviation of )2.0  10
4 cm
1 . We estimated an average pressure shift of )1  10
4 cm
1 for Spectrum #3 relative to Spectrum #2 which is consistent with our results. The weaker 30014 00001 (Sv0 ¼ 0:514) and 30011 00001 (Sv0 ¼ 0:586) bands were analyzed using Spectrum #3. For the 30014 00001, 52 line positions up to J 0 ¼ 57 were reproduced with a RMS error of 5.7  10
5 cm
1 . This is comparable in quality to the 30013 00001 and 30012 00001 results. The 30011 00001 band was analyzed using 49 line positions sampling up to J 0 ¼ 55 but with a significantly worse RMS error, 2.1  10
4 cm
1 , most likely due to overlap from the strong C2 H2 calibration lines in the 6500 cm
1 region (see Fig. 9). For comparison, Maillard et al. [18] reported RMS errors of 2.1  10
4 and 2.3  10
4 cm
1 for the 30014 00001 and 30011 00001 bands, respectively. The Maillard et al. G30014 and G30011 values are again systematically 4  10
3 cm
1 higher than the present values. The 30014 10002 hot band was also identified in Spectrum #3 and fitted with a RMS error of 4.8  10
4 cm
1 . A simultaneous fit to the 30011 10002 and 30011 10001 hot bands yielded a RMS error of 3.3  10
4 cm
1 . Line positions for the 31114 01101 (Sv0 ¼ 0:0665), 31113 01101 (Sv0 ¼ 0:330), 31112 01101 (Sv0 ¼ 0:341) and 31111 01101 (Sv0 ¼ 0:0725) hot bands were determined from Spectrum #3. Fits to the 31113 01101 and 31112 01101 bands yielded RMS errors of 1.9  10
4 and 2.4  10
4 cm
1 , respectively. These results are of similar quality to those obtained for the 30014 00001 and 30011 00001 bands which have similar intensities and similar signal-to-noise ratios for individual transitions. Modeling of the weaker 31114 01101 and 31111 01101 positions are somewhat less accurate, yielding RMS errors of 2.8  10
4 and 5.5  10
4 cm
1 , respectively. The larger errors associated with 31111 01101 are again most likely due to overlap with more intense lines from the C2 H2 calibration gas. The spectroscopic constants for the 31114, 31113, 31112, and 31111 states are compared in Table 11. Maillard et al. [18] and Mandin [20] fit the e- and f -components of these bands independently and obtained independent vibrational origins; in the present analysis, we constrained the vibrational origins to be degenerate as did R92. The statistics of Maillard et al. are similar to ours: their RMS error for 31112 01101 is 3.1  10
4 cm
1 for the e-component and 2.9  10
4 cm
1 for the f component while the RMS errors for the 31113 01101 transitions are 4.1  10
4 cm
1 for the e-component and 2.510
4 cm
1 for the f -component. However, the Mail-

343

lard et al. rotational and distortion constants differ significantly from our constants. In fact, the 31112 01101 line positions predicted by the R92 constants agree better with our line positions (see Fig. 11) although both predictions display significant discrepancies. Accurate knowledge of the line positions for the 3111n 01101 transitions will be critical in remote sensing applications since these lines will overlap with the pressure broadened line shapes of the 3001n 00001 transitions and must be properly modeled to provide remote sensing retrievals with errors less than 0.3% [4,14]. We conclude this section by noting that fits to the 30014 00001, 30013 00001, and 30012 00001 bands have been obtained with accuracies generally achieved for high quality mid-infrared data sets. The absolute wavenumbers of the line positions determined in the present study satisfy the accuracy requirements of remote sensing applications and provide a useful secondary standard for NIR spectroscopic studies. 3.5. The 1.4 lm region: 00031 and 01131 The spectrum in the 7000 cm
1 region is dominated by the 3v3 overtone, 00031 00001 (m0 ¼ 6972:5 cm
1 ), and the accompanying hot band, 01131 01101 (m0 ¼ 6935:1 cm
1 ). The 00031 spectroscopic constants in R92 are based on five different vibrational transitions sampling up to J 0 ¼ 91, and the 01131 constants are from analysis of three different vibrational transitions sampling up to J 0 ¼ 68; however, the 00031 00001 and 01131 01101 line positions in 2000 HITRAN are based on the work of Maillard et al. [18]. For the present study, the spectral features in the 1.4 lm region were analyzed using line positions from Spectrum #3. Fig. 12 provides an overview of the region containing the relatively strong 00031 00001 (Sv0 ¼ 15:8) band and the 01131 01101 (Sv0 ¼ 1:29) hot band. The 00031 00001 band was also readily observed in Spectrum #2; however, the RMS error from the Spectrum #3 fit was lower than that of Spectrum #2 fit (5.8  10
5 vs. 8.7  10
5 cm
1 ) and extended to higher J -values (Jmax ¼ 69 vs. Jmax ¼ 55). Therefore, the Spectrum #3 parameters are reported as our preferred fit with the understanding that the data include a small pressure shift of d 
1:0  10
4 cm
1 from the zero pressure limit [48]. The spectroscopic parameters for the present work are compared to those reported by R92, Maillard et al. [18], and Bailly et al. [26] in Table 12. Vander Auwera et al. [22] reported absolute wavenumbers for the 00031 00001 transitions P ð40Þ–Rð38Þ with an estimated accuracy better than 6  10
5 cm
1 but did not model their line positions. We fitted them and present the results in Table 12. Our G00031 value agrees well with the R92 value, differing by 1.5  10
4 cm
1 . The agreement with the Vander Auwera et al. G00031 value is even better with the difference being comparable to the 3r uncertainty from that fit. The G00031

344

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

Table 11 Comparison of 31114, 31113, 31112, and 31111 spectroscopic constantsa Gv

Bv

Dv (10
6 )

31114e 6688.177 6688.1777(2) 6688.1742308(49)

0.38854452 0.38854452(100) 0.388539345(23)

0.175 0.17495(10) 0.1707217(186)

31114f 6688.177 6688.1778(3) 6688.1742308(49)

0.39025487 0.39025487(6850) 0.390257710(20)

0.191 0.19086(30) 0.1918125(137)

31113e 6863.55646 6863.560625(99) 6863.5590(4) 6863.5558537(49)

0.38692624 0.38692314(57) 0.38693248(7990) 0.386922123(26)

0.141194 0.13547(80) 0.14279(30) 0.1352391(292)

31113f 6863.55646 6863.560534(64) 6863.5591(5) 6863.5558537(49)

0.38833672 0.38833242(45) 0.38833786(8490) 0.388334558(28)

0.151749 0.14402(78) 0.15300(30) 0.148623(34)

31112e 7023.67530 7023.679378(55) 7023.6787(3) 7023.6743697(50)

0.38674989 0.38675003(20) 0.38675146(100) 0.386749452(28)

0.120482 0.11976(14) 0.11863(70) 0.1199782(297)

31112f 7023.67530 7023.679119(55) 7023.6782(4) 7023.6743697(50)

0.38811818 0.38811786(22) 0.38811724(110) 0.388118581(26)

0.115475 0.11503(16) 0.11576(10) 0.1162874(281)

31111e 7203.829 7203.8296(3) 7203.82494(14) 7203.8252608(57)

0.38759651 0.38759651(120) 0.38759448(62) 0.387592140(27)

0.099 0.09947(12) 0.09900(41) 0.0975645(202)

31111f 7203.829 7203.8297(4) 7203.82494(14) 7203.8252608(57)

0.38915188 0.38915188(8470) 0.38915604(59) 0.389154226(30)

0.094 0.09357(30) 0.09536(42) 0.0943452(240)

a

Hv (10
12 )

RMS

Ref.

2.77  10
4

[16] [20] This work

2.77  10
4

[16] [20] This work [16] [18] [20] This work

)2.32(30)

4.10  10
4

)1.9323(84)

1.87  10
4

)3.54(37)

2.49  10
4

)1.1221(104)

1.87  10
4

[16] [18] [20] This work

3.14  10
4 10.70  10
4 2.41  10
4

[16] [18] [20] This work

2.88  10
4 12.60  10
4 2.41  10
4

[16] [18] [20] This work

0.5539

0.5340(82) 0.1717

0.4251(78)

8.60  10
4 5.50  10
4

16.20  10
4 5.50  10
4

[16] [20] [24] This work [16] [20] [24] This work

All values in cm
1 . 1r errors given in units of the least significant digit.

value listed for Bailly et al. [26] has been calculated by summing the corrected [63,64] 00031 ! 00021, 00021 ! 00011, and 00011 ! 00001 vibrational origins. The result is within 3  10
4 cm
1 of our G00031 value. The 4.8  10
3 cm
1 discrepancy in the Maillard et al. G00031 value [18] results from a calibration error as indicated by Arcas et al. [19]. The rotational and distortion constants from R92, Bailly et al. [26] and the Vander Auwera et al. [22] fit show very good agreement with the present results; the agreement with the Maillard et al. constants is significantly worse. Fig. 13A is a graphical comparison of the predicted line positions from several studies with those from the present work. The absolute wavenumbers of the Vander Auwera et al. line positions [22] are in excellent agreement with

those determined from Spectrum #3; the differences in experimentally measured line positions are plotted on an expanded scale in Fig. 13B. A statistical comparison of the common measured lines from that work with our line list yielded an average difference of )2.9  10
5 cm
1 and a RMS difference of 7.9  10
5 cm
1 . This result is consistent with the estimated accuracy of the Vander Auwera et al. data and the RMS fitting error obtained for our line positions. The comparison is also important since the 00031 00001 band lies outside the region bounded by the CO (2–0) and C2 H2 (m1 þ m3 ) calibration standards. This suggests that CO2 NIR line positions can be measured through 7000 cm
1 with absolute accuracies on the order of 10
5 cm
1 using the CO and C2 H2 calibration scheme.

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

345

The fit to the 01131 01101 band included 100 line positions up to J 0 ¼ 60 and produced a RMS error of 3.2  10
4 cm
1 . The spectroscopic parameters for the 01131 state are compared in Table 12. Maillard et al. constants [18] do not agree well with ours or those of R92 or those of Bailly et al. [26]. We were able to determine significant values for the distortion constants H01131e and H01131f in the present study although Bailly et al. [26] did not require these constants to fit their data within experimental uncertainty. 3.6. The 1.3 lm region: (4m1 þ m3 ) Fermi pentad 4001n

Fig. 11. A comparison of the predicted line positions for the 31112 01101 band expressed as differences relative to the present work (MB). R92: Rothman et al. [16]. Maillard: Maillard et al. [18].

Fig. 12. Spectrum of the 1.4 lm region: P ¼ 7:0 Torr, L ¼ 241 m, T ¼ 295 K.Strongabsorptionsduetothe00031 00001(m0 ¼ 6972 cm
1 )and 01131 01101 (m0 ¼ 6939 cm
1 ) are observed. The broad, irregularly spaced absorptions are due to residual water vapor in the optical path.

CO2 absorption in the 7000–8000 cm
1 region is very weak. The principal absorption features belong to the [4m1 þ m3 , 8m02 þ m3 ] Fermi pentad: 40015 00001 (m0 ¼ 7283:9 cm
1 ), 40014 00001 (m0 ¼ 7460:5 cm
1 ), 40013 00001 (m0 ¼ 7593:6 cm
1 ), 40012 00001 (m0 ¼ 7734:4 cm
1 ) and 40011 00001 (m0 ¼ 7920:8 cm
1 ). R92 calculated the line positions for the 4001n 00001 bands based on MandinÕs Venusian spectra [20]. Previous work on these absorptions was limited mostly to determinations of the transition intensities [23,70–72]; there are no reported high-resolution laboratory measurements of the low pressure line positions for these transitions. The 40014 00001 (Sv0 ¼ 0:0469), 40013 00001 0 (Sv ¼ 0:102) and 40012 00001 (Sv0 ¼ 0:0281) bands were identified in Spectrum #3 with transitions observed through J 0 ¼ 39, 45 and 37, respectively, and maximum absorption strengths of 5%. The 40015 00001 (Sv0 ¼ 0:00401) and 40014 00001 (Sv0 ¼ 0:00175) bands were too weak to be observed in the present work. The limited range of observed J -values in these three fits was insufficient to obtain significantly determined Hv0 constants, therefore only the D0v distortion constants were fit. Despite the weakness of these absorptions, reason-

Table 12 Comparison of 00031 and 01131 spectroscopic constantsa Gv

Bv

Dv (10
6 )

00031 6972.57734 6972.581944(62) 6972.577502(13)b 6972.5772967(181) 6972.5771975(55)

0.38099334 0.38099452(26) 0.38099343(7) 0.380993346(69) 0.380993252(15)

0.132399 0.13330(26) 0.13236(2) 0.132380(47) 0.1323620(85)

01131e 7602.51399 7602.51897(11) 7602.514158(15) 7602.5138313(40)

0.38150413 0.38150396(42) 0.3815045(1) 0.381503745(17)

0.133736 0.13360(29) 0.13373(3) 0.1327666(136)

01131f 7602.51399 7602.51825(11) 7602.514158(15) 7602.5138313(40)

0.38206918 0.38207043(45) 0.3820697(1) 0.382068868(20)

0.135007 0.13615(35) 0.13510(3) 0.1345867(201)

a b

All values in cm
1 . 1r errors given in units of the least significant digit. Ref. [18] G00031 uncorrected ¼ 6972.578778(13).

Hv (10
12 ) 0.0128 0.0137(64) 0.013(2) 0.01402(130)

)0.30948(281)

)0.1324(49)

RMS

Ref.

2.4  10
5 5.8  10
5

[16] [18] [26] [22] This work

3.21  10
4

[16] [18] [26] This work

3.21  10
4

[16] [18] [26] This work

19.2  10
5

346

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

Fig. 13. (A) A comparison of the predicted line positions for the 00031 00001 band at 6972 cm
1 expressed as differences relative to the present work (MB). R92: Rothman et al. [16]. Maillard: Maillard et al. [18]. Bailly: Bailly et al. [26]. (B) Differences with respect to the experimentally measured line positions of MB (Spectrum 3) and Vander Auwera: Vander Auwera et al. [22]. Note the change in scale between (A) and (B).

able fits were obtained for the three bands with RMS errors of 4.3  10
4 , 3.6  10
4 , and 1.36  10
3 cm
1 . Table 13 compares the constants determined from the present work with those reported by Mandin [20] and adopted by R92. Our work improves the precision of the band origins for each transition by at least two orders of magnitude and uncovers errors of +5.9  10
3 , +5.6  10
3 , and +0.2  10
3 cm
1 in the Gv values for 40014, 40013 and 40012, respectively, that have propagated from the Mandin work through R92 into HITRAN. The rotational and distortion constants show significantly better agreement, with the constants obtained in the present work providing 2-3 additional significant figures for each value. The differences for the 40013 00001 line positions are compared in Fig. 14. The differences are significant for all m-values and diverge rapidly for jmj > 40. It should be possible to reduce the RMS errors for the line positions of the Fermi pentad bands to 1  10
4 cm
1 by recording longer path spectra with improved signalto-noise.

3.7. The 1.2 lm region: (m1 þ 3m3 ) Fermi dyad 10032 and 10031 The CO2 spectrum near 1.2 lm contains prominent absorptions due to the (m1 þ 3m3 ) dyad: 10032 00001

Fig. 14. A comparison of the predicted line positions for the 40013 00001 band at 7594 cm
1 expressed as differences relative to the present work (MB). R92: Rothman et al. [16].

Table 13 Comparison of 40014, 40013, and 40012 spectroscopic constantsa Gv

Bv

Dv (10
6 )

40014 7460.527 7460.5268(6) 7460.5210678(76)

0.38734776 0.38734776(210) 0.387351941(29)

40013 7593.695 7593.6954(10) 7593.6894017(62) 40012 7734.448 7734.4478(23) 7734.4477160(74) a

Hv (10
12 )

RMS

Ref.

0.199 0.19918(160) 0.2007863(206)

2.02  10
3 4.30  10
4

[16] [20] This work

0.38558301 0.38558301(310) 0.385578470(18)

0.1176 0.11761(220) 0.1120656(97)

3.55  10
3 3.58  10
4

[16] [20] This work

0.38699702 0.38699702(460) 0.386961162(30)

0.1151 0.11509(170) 0.0922856(237)

8.50  10
3 1.37  10
3

[16] [20] This work

All values in cm
1 . 1r errors given in units of the least significant digit.

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

(m0 ¼ 8192:5 cm
1 ) and 10031 00001 (m0 ¼ 8293:9 cm
1 ). Although Mandin observed these transitions in Venusian spectra [20], the R92 line positions for both transitions were apparently calculated based on spectroscopic constants for the 10032 and 10031 states determined from BaillyÕs 4.5 lm emission spectra [28] and not from direct observation of the 1.2 lm transitions. Previous work on these absorptions has focused primarily on determining the band intensities [23,70–72]; there are no reported high-resolution laboratory measurements of the low pressure line positions for the 10032 00001 or 10031 00001 transitions. The 10032 00001 (Sv0 ¼ 0:431) and 10031 00001 0 (Sv ¼ 0:614) bands were identified in Spectrum #3 with rotational transitions observed through J 0 ¼ 45 and 43, respectively, and maximum absorption strengths of 40% as seen in Fig. 15. The integrated band intensities for these bands are at least a factor of 4 larger than the intensity of the nearby 40013 00001 band, the strongest of the [4m1 þ m3 , 8m02 þ m3 ] Fermi pentad bands, and com-

Fig. 15. A survey of the 1.2 lm region: P ¼ 7:0 Torr, L ¼ 241 m, T ¼ 295 K. Moderately strong absorptions due to the 10032 00001 (m0 ¼ 8192 cm
1 ) and 10031 00001 (m0 ¼ 8293 cm
1 ) are observed.

347

parable to the intensities of the 30014 00001 and 30011 00001 bands. The R-branch bandheads in Fig. 15 are seen to occur at J 0 ¼ 43=45 for 10032 00001 and J 0 ¼ 41 for 10031 00001. The overlap of J 0 > 43 transitions with the more intense J 0 < 43 transitions in the bandhead region of each band prevented the assignment of higher J transitions. Fits for these bands yielded RMS errors of 2.90  10
4 and 2.95  10
4 cm
1 and were obtained without Hv0 constants. The quality of the fits is consistent with the RMS errors reported for 30014 00001 and 30011 00001, as would be expected for transitions with similar signal-to-noise characteristics. We also expect slightly larger uncertainties for the 10032 00001 and 10031 00001 transitions due to the fact that the spectral calibration for these bands has been extrapolated 1800 cm
1 from the C2 H2 lines at 6500 cm
1 while the calibration for the 30014 00001 and 30011 00001 bands is interpolated between the CO and C2 H2 calibration standards. Table 14 compares spectroscopic constants for the 10032 and 10031 states. The Gv values given for Bailly [28] have been calculated by adding the 10001 or 10002 Gv value from R92 to the corrected sum of the band centers reported in Table III of [28]; the correction factor [63] was 0.999999817. Also included in Table 14 are the vibrational origins determined by Teffo et al. [23] from an analysis of their low pressure spectrum (5.04 Torr CO2 + 4.025 Torr CO, 40.18 m path length, T ¼ 295 K). The different determinations of the Gv values, with the exception of the Mandin values, agree within 5  10
4 cm
1 and overlap within their respective 3r uncertainties. It is unclear what effect pressure shifting has had on the different determinations, but it most likely has caused each study to underestimate the true value. For example, the vibrational energies reported by Teffo et al. [23] are systematically lower than the other values by 4  10
4 cm
1 and are consistent with pressure shifting that may be exacerbated by the

Table 14 Comparison of 10032 and 10031 spectroscopic constantsa Gv 10032 8192.55067 8192.5584(14) 8192.55079(6) 8192.55016(19) 8192.550172(35) 8192.5506294(57) 10031 8293.95124 8293.9678(37) 8293.95142(6) 8293.95113(13) 8293.951077(37) 8293.9516356(57) a

Bv

Dv (10
6 )

Hv (10
12 )

0.38155873 0.38156454(340) 0.3815600(4)

0.156724 0.16072(220) 0.1577(2)

0.059(38) 0.17(2)

0.381560978(142) 0.381559784(18)

0.157930(104) 0.1572508(110)

0.38080572 0.38080063(65) 0.3808075(3)

0.1275 0.11410(360) 0.1140(2)

0.380806417(152) 0.380805287(17)

0.113167(118) 0.1125688(94)

All values in cm
1 . 1r errors given in units of the least significant digit.

RMS

Ref.

3.43  10
4 2.95  10
4

[16] [20] [28] [23] [23] This work

2.75  10
4 2.90  10
4

[16] [20] [28] [23] [23] This work

0.72(59) 0.25(2)

348

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

4.025 Torr of CO in their sample mixtures. The vibrational energies of the 10032 and 10031 states determined from the present work, G10032 ¼ 8192:55063ð1Þ cm
1 and G10031 ¼ 8293:95164ð1Þ cm
1 , should be pressure shifted less than 1.0  10
4 cm
1 from the absolute wavenumbers for these values. For both 10032 and 10031, the rotational and distortion constants from Bailly and Rossetti [28], R92 and the present work are in good agreement, but the Mandin constants are significantly different. For Bv and Dv , the Bailly and Rossetti and the present values are similar, but the R92 constants differ significantly. A more insightful comparison is given by the differences in the predicted line positions for each band shown in Figs. 16 and 17. The Bailly and Rossetti results for 10032

00001 exhibit an offset of )1.6  10
4 cm
1 from our values, but the agreement between the predictions is otherwise very good, producing a standard deviation of 0.8  10
4 cm
1 . The R92 predictions are significantly worse despite the better agreement between the vibrational origins. The R92 predictions deviate increasingly with increasing J until J  35 and then the differences decrease rapidly. The situation is reversed for the 10031 00001 transitions. In this case the R92 predictions more closely reproduce the present line positions while the Bailly and Rossetti constants yield significantly larger and more varying differences. Nonetheless, we note that none of the differences exceed 1  10
3 cm
1 , the R92 uncertainty for line positions in these bands.

4. Conclusions

Fig. 16. A comparison of the predicted line positions for the 10032 00001 band at 8192 cm
1 expressed as differences relative to the present work (MB). R92: Rothman et al. [16]. Bailly: Bailly and Rossetti [28].

Fig. 17. A comparison of the predicted line positions for the 10031 00001 band at 8293 cm
1 expressed as differences relative to the present work (MB). R92: Rothman et al. [16]. Bailly: Bailly and Rossetti [28].

New near-infrared line positions of the main carbon dioxide isotopologue 16 O12 C16 O have been obtained for 53 different vibrational states with Gv values up to 8400 cm
1 . Fig. 18 is a plot of the energies of vibrational states investigated in this work compared to the vibrational states reported in the comprehensive 1992 review of Rothman et al. [16] that serves as the basis for the 2000 HITRAN database [15]. Fig. 19 presents the differences between the Gv values determined in the present work and those reported by Rothman et al. Most of the Gv differences in the 4000–8000 cm
1 range fall within the 10  10
4 cm
1 uncertainty estimate for HITRAN CO2 transitions in this range; however, the Gv differences are systematically negative and are 10–1000 times larger than the uncertainties on the Gv values determined in the present work. The improved characterization of NIR CO2 spectroscopy has been accomplished through the use of high signal-to-noise, high-resolution spectra and accurate wavenumber calibration at each end of the NIR. In particular, transitions from the ground state to the 20013, 20012, 20011, 30013, 30012, 00031 vibrational

Fig. 18. Energies of the 16 O12 C16 O vibrational states included in the analysis of Rothman et al. (R92) and the present work (MB).

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

Fig. 19. Differences in Gv values determined in the present work (MB) relative to the values reported by Rothman et al. (R92) plotted as a function of Gv . The systematically lower Gv values for vibrational states in the 4000–8000 cm
1 range are due to the improved calibration accuracy in the present work. The dashed lines represent the expected uncertainty of well measured lines in the 2000 HITRAN database for CO2 transitions in the NIR. The uncertainty in the Gv values from the present work is much smaller than the size of the symbols used in the plot.

Fig. 20. Bottom panel: Experimental (symbols) and simulated (solid line) solar spectra in the region of the CO2 30013 00001and 30012 00001 band. Data recorded by Wallace and Livingston (1991) using the McMath–Pierce FTS at Kitt Peak National Solar Observatory. Top panel: Residuals from simulating the experimental spectrum with the 2000 HITRAN database. RMS error ¼ 1.02% (Yang et al., 2002). Middle panel: Simulation residuals using the line positions reported in this work with unpublished intensity data. RMS error ¼ 0.91%.

states have been measured with absolute wavenumber uncertainties less than 6  10
5 cm
1 and are accurate enough to serve as secondary frequency standards. Many additional 16 O12 C16 O NIR transitions have been measured and fitted with uncertainties <5  10
4 cm
1 . Similar studies are underway for other carbon dioxide isotopologues, and we have obtained NIR spectra of 16 13 16 O C O, 16 O12 C18 O, and 16 O12 C17 O, etc. with absolute wavenumber accuracies on the order of 5  10
5 cm
1 . These results will be submitted for the

349

Fig. 21. Bottom panel: Experimental (solid line) and simulated (dashed line) CO2 laboratory spectra in the region of the 20013 00001 band: 30 Torr CO2 and 25 m path Top panel: Residuals from simulating the experimental spectrum with the 2000 HITRAN database. RMS error ¼ 2.75% Middle panel: Simulation residuals using the line positions reported in this work with the unpublished intensity data. RMS error ¼ 0.11%. The remaining residuals are due to small differences in the experimental and simulated intensities.

next revision of the HITRAN database. The present work also indicated that it should be possible to measure carefully calibrated lines of the 16 O12 C16 O v2 and v3 bands with uncertainties better than 2  10
5 cm
1 . The impact of our new spectroscopic parameters on atmospheric remote sensing is shown in Fig. 20. Here the same spectrum as shown in Fig. 1 has been analyzed with our improved CO2 line positions. A comparison of the two plots shows that the fit residuals have been reduced significantly and no longer display systematic deficiencies for high-J transitions. The potential impact in the 2 lm region is even larger, as shown in Fig. 21, where we simulated a laboratory spectrum.

Acknowledgments The authors thank M. Dulick and the National Solar Observatory for use of the McMath–Pierce Fourier transform spectrometer, R. Toth for predicting an interim database used to generate Figs. 20 and 21 and G. Toon for the atmospheric CO2 retrieval figures. The research at the Jet Propulsion Laboratory (JPL), California Institute of Technology was performed under contract with the National Aeronautics and Space Administration. CEM acknowledges support from the Research Corporation.

350

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Appendix A. Observed and calculated line positions (cm
1 ) J0

J 00

20013

Obs

Calc

O)C

J0

J 00

Obs

Calc

O)C

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 46 48 50 52 54 56 58 62 64

4854.39953 4855.94018 4857.46458 4858.97274 4860.46438 4861.93960 4863.39819 4864.84004 4866.26495 4867.67278 4869.06333 4870.43637 4871.79167 4873.12900 4874.44811 4875.74869 4877.03044 4878.29318 4879.53640 4880.75986 4881.96320 4883.14604 4885.44873 4886.56773 4887.66469 4888.73915 4889.79058 4890.81875 4891.82298 4893.75824 4894.68786

4854.39954 4855.94019 4857.46459 4858.97269 4860.46439 4861.93960 4863.39820 4864.84003 4866.26494 4867.67277 4869.06330 4870.43634 4871.79165 4873.12899 4874.44810 4875.74869 4877.03048 4878.29316 4879.53640 4880.75987 4881.96320 4883.14605 4885.44872 4886.56775 4887.66470 4888.73914 4889.79063 4890.81873 4891.82298 4893.75809 4894.68799

)0.00001 )0.00001 )0.00001 0.00005 )0.00002 )0.00001 0.00000 0.00001 0.00001 0.00001 0.00002 0.00003 0.00002 0.00001 0.00001 0.00000 )0.00004 0.00002 0.00000 )0.00001 0.00000 )0.00001 0.00001 )0.00002 )0.00001 0.00001 )0.00006 0.00001 0.00000 0.00015 )0.00013

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

4978.60774 4980.13173 4981.62682 4983.09116 4984.52650 4985.93223 4987.30833 4988.65493 4989.97149 4991.25848 4992.51569 4993.74314 4994.94075 4996.10850 4997.24637 4998.35434 4999.43239 5000.48051 5001.49866

4978.60772 4980.13173 4981.62621 4983.09115 4984.52650 4985.93224 4987.30835 4988.65478 4989.97150 4991.25850 4992.51572 4993.74315 4994.94076 4996.10851 4997.24638 4998.35435 4999.43239 5000.48050 5001.49866

0.00002 0.00000 0.00061* 0.00001 )0.00001 )0.00001 )0.00002 0.00015 )0.00001 )0.00002 )0.00004 )0.00002 )0.00001 )0.00001 )0.00001 )0.00001 0.00000 0.00001 0.00001

00001

1 3 5 7 9 11 13 15

2 4 6 8 10 12 14 16

4852.05822 4850.47715 4848.87995 4847.26655 4845.63698 4843.99116 4842.32901 4840.65045

4852.05824 4850.47717 4848.87995 4847.26657 4845.63700 4843.99116 4842.32901 4840.65044

)0.00001 )0.00002 )0.00001 )0.00003 )0.00002 0.00000 0.00001 0.00001

19 21 23 25 27 29 31 35 37 39 41 43 45 47 49 51 53 55 57 59 63

20 22 24 26 28 30 32 36 38 40 42 44 46 48 50 52 54 56 58 60 64

4837.24363 4835.51509 4833.76964 4832.00705 4830.22711 4828.42968 4826.61450 4822.92983 4821.05986 4819.17102 4817.26314 4815.33576 4813.38868 4811.42150 4809.43381 4807.42535 4805.39563 4803.34672 4801.27155 4799.17562 4794.91507

4837.24362 4835.51510 4833.76963 4832.00703 4830.22712 4828.42968 4826.61448 4822.92983 4821.05985 4819.17106 4817.26314 4815.33580 4813.38869 4811.42148 4809.43382 4807.42534 4805.39566 4803.34440 4801.27117 4799.17557 4794.91556

0.00001 )0.00001 0.00001 0.00002 )0.00001 0.00000 0.00002 0.00000 0.00001 )0.00003 0.00000 )0.00004 )0.00001 0.00002 0.00000 0.00001 )0.00003 0.00232* 0.00038* 0.00005 )0.00049*

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 47 49 51 53 55 57 59 63 65

4976.26641 4974.66871 4973.04158 4971.38504 4969.69910 4967.98381 4966.23916 4964.46519 4962.66191 4960.82935 4958.96752 4957.07644 4955.15614 4953.20664 4951.22796 4949.22014 4947.18320 4945.11717

0.00001 0.00002 )0.00001 )0.00058* )0.00001 )0.00001 )0.00001 )0.00002 )0.00003 0.00000 )0.00038* )0.00001 )0.00002 0.00002 )0.00001 0.00001 0.00001 0.00000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

20012 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

00001 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

4976.26642 4974.66873 4973.04157 4971.38446 4969.69909 4967.98380 4966.23915 4964.46517 4962.66189 4960.82935 4958.96714 4957.07642 4955.15612 4953.20666 4951.22795 4949.22015 4947.18320 4945.11717

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

351

Appendix A (continued) J0

J 00

Obs

Calc

O)C

J0

J 00

Obs

Calc

O)C

37 39 41 43 45 47 49 51 53 55

38 40 42 44 46 48 50 52 54 56

4943.02116 4940.89803 4938.74503 4936.56311 4934.35256 4932.11282 4929.84460 4927.54786 4925.22247 4922.86906

4943.02211 4940.89804 4938.74502 4936.56311 4934.35236 4932.11285 4929.84466 4927.54787 4925.22258 4922.86891

)0.00095* )0.00002 0.00001 )0.00001 0.00020 )0.00004 )0.00006 )0.00001 )0.00011 0.00015

39 41 43 45 47 49 51 53 55 57

38 40 42 44 46 48 50 52 54 56

5002.48686 5003.44510 5004.37337 5005.27165 5006.14009 5006.97855 5007.78722 5008.56700 5009.31511 5010.03453

5002.48685 5003.44508 5004.37336 5005.27169 5006.14009 5006.97859 5007.78724 5008.56607 5009.31514 5010.03453

0.00001 0.00002 0.00001 )0.00004 0.00000 )0.00004 )0.00002 0.00093* )0.00003 0.00000

5098.09387 5096.50583 5094.89612 5093.26478 5091.61189 5089.93754 5088.24182 5086.52485 5084.78676 5083.02769 5081.24781 5079.44727 5077.62629 5075.78505 5073.92378 5072.04272 5070.14211 5068.22223 5066.28336 5064.32580 5062.34987 5060.35591 5058.34427 5056.31533 5054.26948 5052.20712 5050.12870 5048.03466 5045.92547 5043.80162 5041.66364 5039.51205 5037.34742

0.00000 0.00000 )0.00001 )0.00001 0.00001 0.00000 )0.00003 )0.00001 )0.00008 )0.00001 )0.00001 0.00000 0.00001 0.00012 )0.00001 )0.00001 0.00000 )0.00001 )0.00001 )0.00003 )0.00002 )0.00004 )0.00002 0.00001 0.00011 )0.00001 0.00004 0.00004 0.00000 )0.00009 )0.00002 0.00004 )0.00232*

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

5100.43518 5101.96885 5103.48075 5104.97090 5106.43933 5107.88598 5109.31100 5110.71444 5112.09634 5113.45697 5114.79600 5116.11395 5117.41091 5118.68691 5119.94220 5121.17693 5122.39130 5123.58554 5124.75964 5125.91460 5127.04902 5128.16616 5129.26363 5130.34257 5131.40337 5132.44650

5100.43518 5101.96885 5103.48075 5104.97089 5106.43929 5107.88598 5109.31101 5110.71444 5112.09635 5113.45684 5114.79601 5116.11399 5117.41091 5118.68692 5119.94220 5121.17693 5122.39131 5123.58556 5124.75991 5125.91461 5127.04993 5128.16616 5129.26360 5130.34257 5131.40341 5132.44649

0.00000 0.00000 0.00000 0.00001 0.00004 0.00000 )0.00001 0.00000 )0.00001 0.00012 )0.00001 )0.00004 0.00000 )0.00001 0.00000 0.00000 )0.00001 )0.00001 )0.00026* )0.00001 )0.00091* 0.00000 0.00004 0.00001 )0.00004 0.00002

55 57 59 61 63 65

54 56 58 60 62 64

5134.48082 5135.47303 5136.44906 5137.40915 5138.35546 5139.28425

5134.48088 5135.47302 5136.44904 5137.40940 5138.35458 5139.28509

)0.00007 0.00000 0.00002 )0.00025* 0.00088* )0.00084*

6226.34868 6224.75275 6223.12878 6221.47678 6219.79671

0.00011 )0.00006 0.00005 )0.00003 0.00000

1 3 5 7 9 11

0 2 4 6 8 10

6228.69003 6230.21568 6231.71345 6233.18289 6234.62410 6236.03699

6228.68999 6230.21576 6231.71342 6233.18289 6234.62411 6236.03698

0.00005 )0.00008 0.00003 0.00000 )0.00001 0.00001

20011 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65

00001 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66

30013 1 3 5 7 9

5098.09387 5096.50583 5094.89611 5093.26477 5091.61190 5089.93754 5088.24179 5086.52484 5084.78668 5083.02768 5081.24780 5079.44727 5077.62630 5075.78517 5073.92378 5072.04271 5070.14211 5068.22222 5066.28335 5064.32578 5062.34986 5060.35588 5058.34426 5056.31534 5054.26959 5052.20711 5050.12874 5048.03469 5045.92546 5043.80153 5041.66362 5039.51209 5037.34509 00001

2 4 6 8 10

6226.34879 6224.75269 6223.12884 6221.47675 6219.79671

352

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

Appendix A (continued) J0

J 00

Obs

Calc

O)C

J0

J 00

Obs

Calc

O)C

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

6218.08851 6216.35220 6214.58765 6212.79483 6210.97361 6209.12392 6207.24565 6205.33853 6203.40271 6201.43778 6199.44360 6197.42009 6195.36715 6193.28433 6191.17166 6189.02897 6186.85586 6184.65201 6182.41831 6180.15238

6218.08854 6216.35222 6214.58768 6212.79485 6210.97364 6209.12393 6207.24562 6205.33858 6203.40266 6201.43772 6199.44360 6197.42012 6195.36711 6193.28438 6191.17174 6189.02899 6186.85593 6184.65234 6182.41802 6180.15276

)0.00003 )0.00001 )0.00003 )0.00002 )0.00003 )0.00001 0.00003 )0.00005 0.00004 0.00005 0.00000 )0.00003 0.00004 )0.00005 )0.00008 )0.00002 )0.00007 )0.00033* 0.00029* )0.00038*

13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

6237.42140 6238.77733 6240.10441 6241.40276 6242.67214 6243.91234 6245.12323 6246.30456 6247.45616 6248.57785 6249.66934 6250.73051 6251.76100 6252.76054 6253.72913 6254.66615 6255.57172 6256.44503 6257.28679 6258.09567

6237.42141 6238.77727 6240.10445 6241.40279 6242.67215 6243.91235 6245.12321 6246.30455 6247.45615 6248.57782 6249.66933 6250.73045 6251.76094 6252.76057 6253.72907 6254.66619 6255.57168 6256.44527 6257.28671 6258.09571

)0.00001 0.00006 )0.00004 )0.00004 0.00000 )0.00001 0.00002 0.00002 0.00000 0.00003 0.00000 0.00006 0.00005 )0.00003 0.00007 )0.00004 0.00004 )0.00024* 0.00008 )0.00004

30012 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 00031 1 3 5 7

00001 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

6346.28251 6344.68404 6343.05560 6341.39709 6339.70860 6337.99037 6336.24245 6334.46471 6332.65770 6330.82119 6328.95557 6327.06091 6325.13737 6323.18517 6321.20455 6319.19575 6317.15889 6315.09432 6313.00247 6310.88335 6308.73751 6306.56526 6304.36658 6302.14278 6299.89320

6346.28255 6344.68407 6343.05555 6341.39705 6339.70863 6337.99038 6336.24240 6334.46480 6332.65770 6330.82124 6328.95559 6327.06089 6325.13735 6323.18515 6321.20451 6319.19567 6317.15887 6315.09437 6313.00245 6310.88342 6308.73759 6306.56529 6304.36687 6302.14272 6299.89322

)0.00004 )0.00003 0.00005 0.00004 )0.00002 )0.00001 0.00005 )0.00009 0.00000 )0.00005 )0.00002 0.00002 0.00002 0.00002 0.00004 0.00008 0.00003 )0.00005 0.00001 )0.00007 )0.00008 )0.00003 )0.00030* 0.00005 )0.00002

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

6348.62387 6350.14719 6351.64016 6353.10316 6354.53602 6355.93880 6357.31161 6358.65438 6359.96726 6361.25035 6362.50381 6363.72760 6364.92196 6366.08705 6367.22293 6368.32992 6369.40812 6370.45765 6371.47889 6372.47232 6373.43766 6374.37536 6375.28627 6376.16998 6377.02713 6377.85815

6348.62386 6350.14709 6351.64019 6353.10316 6354.53603 6355.93882 6357.31159 6358.65439 6359.96729 6361.25039 6362.50379 6363.72760 6364.92196 6366.08702 6367.22293 6368.32988 6369.40807 6370.45770 6371.47900 6372.47223 6373.43765 6374.37554 6375.28620 6376.16996 6377.02716 6377.85816

0.00001 0.00011 )0.00002 0.00000 0.00000 )0.00003 0.00002 )0.00001 )0.00003 )0.00005 0.00002 )0.00001 )0.00001 0.00003 0.00000 0.00004 0.00005 )0.00005 )0.00011 0.00009 0.00001 )0.00018* 0.00008 0.00002 )0.00003 )0.00001

2 4 6 8

00001 6970.99792 6969.34480 6967.61792 6965.81730

6970.99787 6969.34477 6967.61792 6965.81733

0.00005 0.00002 0.00000 )0.00003

1 3 5 7

0 2 4 6

6973.33923 6974.80781 6976.20253 6977.52345

6973.33918 6974.80779 6976.20255 6977.52344

0.00005 0.00002 )0.00002 0.00000

C.E. Miller, L.R. Brown / Journal of Molecular Spectroscopy 228 (2004) 329–354

353

Appendix A (continued) J0

J 00

Obs

Calc

O)C

J0

J 00

Obs

Calc

O)C

9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 59 61 63 65 67

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 60 62 64 66 68

6963.94303 6961.99511 6959.97348 6957.87820 6955.70949 6953.46712 6951.15102 6948.76215 6946.29894 6943.76264 6941.15291 6938.46982 6935.71334 6932.88364 6929.98059 6927.00430 6923.95477 6920.83211 6917.63624 6914.36728 6911.02518 6907.60992 6904.12195 6900.56091 6893.22094 6889.44029 6885.58717 6881.66224 6877.66393

6963.94305 6961.99509 6959.97349 6957.87827 6955.70946 6953.46709 6951.15120 6948.76180 6946.29893 6943.76262 6941.15290 6938.46980 6935.71336 6932.88360 6929.98056 6927.00426 6923.95475 6920.83206 6917.63622 6914.36726 6911.02522 6907.61013 6904.12204 6900.56096 6893.22002 6889.44023 6885.58761 6881.66219 6877.66401

)0.00002 0.00002 )0.00001 )0.00007 0.00002 0.00002 )0.00018 0.00035* 0.00002 0.00002 0.00002 0.00002 )0.00002 0.00004 0.00003 0.00004 0.00001 0.00005 0.00002 0.00002 )0.00004 )0.00022 )0.00008 )0.00005 0.00092* 0.00006 )0.00044* 0.00005 )0.00008

9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68

6978.77046 6979.94352 6981.04267 6982.06787 6983.01906 6983.89623 6984.69937 6985.42850 6986.08354 6986.66450 6987.17129 6987.60404 6987.96257 6988.24696 6988.45712 6988.59357 6988.64918 6988.64918 6988.55496 6988.39451 6988.15912 6987.84949 6987.46547 6987.00731 6986.47460 6985.86750 6985.18586 6984.43027 6983.60025 6982.69514 6981.71665

6978.77045 6979.94353 6981.04268 6982.06786 6983.01905 6983.89624 6984.69940 6985.42851 6986.08355 6986.66449 6987.17132 6987.60401 6987.96255 6988.24692 6988.45710 6988.59307 6988.65481 6988.64231 6988.55554 6988.39450 6988.15916 6987.84950 6987.46552 6987.00719 6986.47450 6985.86744 6985.18599 6984.43014 6983.59986 6982.69516 6981.71601

0.00002 )0.00001 )0.00001 0.00002 0.00001 )0.00002 )0.00004 )0.00001 0.00000 0.00001 )0.00002 0.00003 0.00002 0.00004 0.00001 0.00050* )0.00563* 0.00687* )0.00058* 0.00001 )0.00003 )0.00001 )0.00005 0.00012 0.00010 0.00005 )0.00013 0.00013 0.00038* )0.00002 0.00064*

Lines marked with an asterisk (*) were not included in the fit.

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