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Global modeling of the 14N216O line positions within the framework of the polyad model of effective Hamiltonian
Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
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Global modeling of the 14N216O line positions within the framework of the polyad model of effective Hamiltonian V.I. Perevalov a,n, S.A. Tashkun a, R.V. Kochanov a, A.-W. Liu b, A. Campargue c a
Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, Academician Zuev Sq. 1, 634021 Tomsk, Russia Hefei National Laboratory for Physical Sciences at Microscale, Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China c Universite´ Grenoble 1/CNRS, UMR5588 LIPhy, Grenoble F-38041, France b
a r t i c l e in f o
abstract
Article history: Received 18 October 2011 Received in revised form 2 December 2011 Accepted 3 December 2011 Available online 17 December 2011
The global modeling of 14N216O line positions in the 0–9700 cm 1 region has been performed using the polyad model of effective Hamiltonian. The effective Hamiltonian parameters were fitted to the line positions collected from an exhaustive review of the literature. A number of lines perturbed by interpolyad resonance interactions were excluded from the fit. The dimensionless weighted standard deviation of the fit is 4.06. The fitted set of 138 effective Hamiltonian parameters allowed reproducing 37,353 measured line positions of 325 bands with an RMS value of 0.00423 cm 1. & 2012 Published by Elsevier Ltd.
Keywords: Nitrous oxide Microwave Infrared Line position Global modeling Effective Hamiltonian
1. Introduction Nitrous oxide, N2O, is a minor constituent of the Earth atmosphere but it plays an important role in atmospheric physics and chemistry. Being a greenhouse gas it contributes to the atmospheric radiation balance. Through the atmospheric chemistry processes N2O participates to the ozone layer depletion. In addition, nitrous oxide is one of the products of the burning of the organic fuels in air. For the calculation of the radiation balance inside an internal-combustion engine or inside a jet propulsion it is necessary to know the high temperature spectrum of this molecule. This spectrum can be calculated theoretically. One of the theoretical approaches is the method of effective operators adopted for the global description of
n
Corresponding author. Tel.: þ 7 3822 491794; fax: þ7 3822 492086. E-mail address: [email protected] (V.I. Perevalov).
0022-4073/$ - see front matter & 2012 Published by Elsevier Ltd. doi:10.1016/j.jqsrt.2011.12.008
the energy levels and transition probabilities inside a given electronic state. We have successfully applied this method to the global modeling of the line positions [1,2] and line intensities [3–7] of the principal isotopologue, 14 N216O, and to the global modeling of the line positions of the rare isotopologues: 14N15N16O [8–10], 15N14N16O [9,10], 15N216O [11], 14N218O [12] and 14N217O [12]. The set of effective Hamiltonian parameters obtained in 1999 for 14N216O [2] allowed us to predict the line positions in a wide spectral range. These predictions were successfully used for the assignment of the spectra recorded by intracavity laser absorption spectroscopy (ICLAS) [13–18], Fourier transform spectroscopy (FTS) [5–7,13,19] and cavity ring down spectroscopy (CRDS) [20–23]. But the set of parameters derived for 14N216O has never been published. Since 1999, the amount of observations has been considerably extended [12–27] in particular from CRDS in the 5800–7900 cm 1 region [20–23]. The aim of this paper is the refinement of the effective
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
Hamiltonian parameters of 14N216O by using the most extensive compilation of line position measurements available to date. 2. Effective Hamiltonian The polyad model of effective Hamiltonian describing globally the 14N216O vibrational–rotational states in the ground electronic state of nitrous oxide has been suggested by Pliva [28] and developed by Teffo and Chedin [29]. In Ref. [1] we elaborated a reduced model of this Hamiltonian which is further described in Refs. [8–12] (see Refs. [8,10] for the notations and definitions). The polyad model of effective Hamiltonian is based on the polyad structure of the 14N216O vibrational states resulting from the approximate relations between harmonic frequencies o3 E2o1 E4o2. This Hamiltonian takes into account in an explicit way all intrapolyad resonance anharmonic and anharmonicþ‘-type interactions up to the sixth order of perturbation theory. The Coriolis interactions are interpolyad interactions within the framework of this model. They are assumed to be accounted for by the effective values of the effective Hamiltonian parameters. For the reader’s convenience we recall below the matrix elements of the effective Hamiltonian. Diagonal matrix element: /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 V 2 ‘2 V 3 JS X g g X g ¼ oi V i þ i þ ij xij V i þ i V j þ j þx‘‘ ‘22 2 2 2 i X gj g g Vk þ k þ y Vi þ i Vj þ ijk ijk 2 2 2 X gi 2 yi‘‘ V i þ þ ‘ 2 2 i X gj g g g Vm þ m Vn þ n þ z Vi þ i Vj þ ijmn ijmn 2 2 2 2 X g g j ‘2 þ z‘‘‘‘ ‘42 þ z Vi þ i Vj þ ij ij‘‘ 2 2 2 ( X g g X g þ Be ai V i þ i þ ij gij V i þ i V j þ j þ g‘‘ ‘22 2 2 2 i g g g þ e Vi þ i Vj þ j Vk þ k ijk ijk 2 2 2 ) X gi 2 ei‘‘ V i þ ‘2 JðJ þ1Þ‘22 þ 2 i ( X g g X g bi V i þ i þ ij Zij V i þ i V j þ j De þ 2 2 2 i ) X
(
X i
di V i þ
) gi ½JðJ þ 1Þ‘22 3 : 2
Matrix elements of anharmonic resonance interactions: /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 1 V 2 þ 2 ‘2 V 3 JS qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ( X g þ DV i ¼ V 1 ½ðV 2 þ2Þ2 ‘22 F e þ Fi V i þ i 2 i X g j þ DV j g þ DV i þ Vj þ F Vi þ i ij ij 2 2 ) þ F ‘‘ ‘22 þ F J ½JðJ þ 1Þ‘22 ,
ð3Þ
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 2 V 2 ‘2 V 3 þ 1 JS ( X ð2Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g þ DV i ¼ ðV 1 1ÞV 1 ðV 3 þ1Þ F ð2Þ Fi Vi þ i e þ 2 i X ð2Þ g j þ DV j g i þ DV i þ Vj þ F Vi þ ij ij 2 2 ) ð2Þ 2 2 þ F ð2Þ ‘‘ ‘ 2 þF J ½JðJ þ 1Þ‘ 2 ,
ð4Þ
V 1 V 2 ‘2 V 3 J Hef f V 1 1 V 2 2 ‘2 V 3 þ 1 J rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ¼ V 1 V 22 ‘22 ðV 3 þ 1Þ (
g i þ DV i F ð3Þ V þ i i 2 i X ð3Þ g j þ DV j g þ DV i þ Vj þ F Vi þ i ij ij 2 2 ) F ð3Þ e þ
X
ð3Þ 2 2 þ F ð3Þ ‘‘ ‘ 2 þF J ½JðJ þ 1Þ‘ 2 ,
ð5Þ
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 V 2 4 ‘2 V 3 þ 1 JS ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðV 3 þ1ÞðV 22 ‘22 Þ½ðV 2 2Þ2 ‘22
( F ð4Þ e þ
X i
) g i þ DV i ð4Þ 2 þF F ð4Þ V þ JðJ þ 1Þ‘ , i 2 J i 2 ð6Þ
/V 1 V 2 ‘2 V 3 J9Hef f V 1 2 V 2 þ4 ‘2 V 3 J qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ V 1 ðV 1 1Þ½ðV 2 þ 2Þ2 ‘22 ½ðV 2 þ 4Þ2 ‘22 ( ) X ð5Þ g i þ DV i ð5Þ 2 F ð5Þ þ F þ F V þ JðJ þ 1Þ‘ , i 2 e J i 2 i ð7Þ
þ Z‘‘ ‘22 ½JðJ þ 1Þ‘22 2 þ He þ
1005
ð1Þ
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 4 V 2 ‘2 V 3 þ 2 JS pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðV 1 3ÞðV 1 2ÞðV 1 1ÞV 1 ðV 3 þ 2ÞðV 3 þ 1Þ ( ) X ð6Þ g i þ DV i ð6Þ 2 þ F þ F V þ JðJ þ 1Þ‘ , F ð6Þ i 2 e J i 2 i ð8Þ
‘-doubling matrix element: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðV 2 7‘2 þ 2ÞðV 2 8 ‘2 Þ½JðJ þ1Þ‘2 ð‘2 71Þ½JðJ þ 1Þð‘2 7 1Þð‘2 7 2Þ ) X gj gi X gi 2 þ Vj þ þ LJ ½JðJ þ 1Þð‘2 7 1Þ : Le þ Li V i þ L Vi þ ij ij 2 2 2 i
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 V 2 ‘2 7 2V 3 JS ¼ (
ð2Þ
1006
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 3 V 2 þ 2 ‘2 V 3 þ 1 JS qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðV 1 2ÞðV 1 1ÞV 1 ½ðV 2 þ 2Þ2 ‘22 ðV 3 þ1Þ ( ) X ð7Þ g i þ DV i ð7Þ 2 , þ F þ F V þ JðJ þ 1Þ‘ F ð7Þ i 2 e J i 2 i ð9Þ /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 3 V 2 2 ‘2 V 3 þ 2 JS qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðV 1 2ÞðV 1 1ÞV 1 ðV 3 þ 1ÞðV 3 þ 2ÞðV 22 ‘22 Þ, ¼ F ð8Þ e
ð10Þ
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 2 V 2 4 ‘2 V 3 þ 2 JS qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðV 1 1ÞV 1 ðV 3 þ 1ÞðV 3 þ 2ÞðV 22 ‘22 Þ½ðV 2 2Þ2 ‘22 ¼ F ð9Þ e ð11Þ /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 þ 1 V 2 6 ‘2 V 3 þ 1 JS qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ F ð10Þ ðV 1 þ 1ÞðV 3 þ 1ÞðV 22 ‘22 Þ½ðV 2 2Þ2 ‘22 ½ðV 2 4Þ2 ‘22 : e ð12Þ Matrix elements interactions:
of
anharmonic þ‘-type
resonance
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 1 V 2 þ2 ‘2 72 V 3 JS ¼ F Le
obtained using different spectroscopic techniques: microwave [33–40], laser heterodyne [41–43,53–57], Fourier transform [19,44–52,58–61,64,66–68], diode laser absorption [65], cavity ring down [20–22,62,63], intracavity laser absorption [16,17,26,69] and emission [24,25]. In Ref. [59] the spectra were recorded at elevated temperatures. The internal consistency between the different experimental sources was checked. The misassigned, misprinted or badly measured lines were revealed and excluded. This checking was done by fitting energy levels to the observed line positions using the fundamental Ritz principle. Details of this approach can be found in Ref. [32]. The following criterion was used for excluding a line from the fit: if the weighted Ritz residual r i-j ¼
nobs i-j ðEi Ej Þ dobs i-j
of a line was greater than 3, the line was deleted from the obs input data file. In the above equation vobs i-j and di-j are measured line position and corresponding uncertainty for
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V 1 ðV 2 7 ‘2 þ2ÞðV 2 7‘2 þ 4Þ½JðJ þ1Þ‘2 ð‘2 7 1Þ½JðJ þ 1Þð‘2 7 1Þð‘2 7 2Þ, ð13Þ
/V 1 V 2 ‘2 V 3 J9H
ef f
9V 1 1 V 2 2 ‘2 72 V 3 þ 1
JS ¼ F eð3ÞL
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V 1 ðV 3 þ 1ÞðV 2 8 ‘2 ÞðV 2 8 ‘2 2Þ½JðJ þ 1Þ‘2 ð‘2 7 1Þ½JðJ þ 1Þð‘2 7 1Þð‘2 7 2Þ,
ð14Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 V 2 4 ‘2 7 2 V 3 þ 1 JS ¼ F ð4ÞL ðV 3 þ 1ÞðV 22 ‘22 ÞðV 2 8 ‘2 2ÞðV 2 8 ‘2 4Þ½JðJ þ 1Þ‘2 ð‘2 7 1Þ½JðJ þ 1Þð‘2 7 1Þð‘2 7 2Þ: e
ð15Þ In the above presented equations, gi is the degeneracy of the vibrational mode i: gi ¼1 for i¼1,3 and gi ¼2 for i¼2. It has been shown that this polyad model of effective Hamiltonian works very well [8–23] except in the cases of interpolyad resonance Coriolis and anharmonic interactions [8–10,14–23]. To take into account these interpolyad resonance interactions we suggested a nonpolyad model of effective Hamiltonian [30,31]. The fitting of the parameters of the nonpolyad model of effective Hamiltonian is under progress. The preliminary results show that this model allows solving the problem of the interpolyad resonance interactions but much work is still needed to achieve a global modeling of all available line positions. We then decided as a first step to publish the set of parameters of the polyad model of effective Hamiltonian because it is widely used but still unpublished. As the mixing between the normal mode ðV 1 V ‘22 V 3 Þ vibrational states can be strong, the triplet {P¼2V1 þ V2 þ4V3, ‘2, i} is used for the labeling of the vibrational states, where the index i increases with the energy. 3. Least-squares fitting The parameters of the effective Hamiltonian have been fitted to the measured line positions collected from the literature [8,9,11,13–26,33–69]. For these purposes a data file of measured line positions was created by gathering all the published line lists from the microwave region up to 9700 cm 1. The characteristics of the involved experimental sources are presented in Table 1. These data were
a transition between an upper state i and a lower state j, Ei and Ej being the Ritz energies (term values). When necessary, a calibration factor was used to correct the observed line positions. The calibration factors included in Table 1 have been obtained in the result of the solution of the Ritz equations (see Ref.[32] for details). The precise microwave and laser heterodyne data were used as reference data. They are marked by symbol 1.0c in column 3 of Table 1. A calibration factor equal to 1.000000000 presented in this column does mean that the respective experimental source does not need the calibration or the calibration factor could not be found using the existing set of data. Some bands were studied by several authors. As a general rule, all the reported position values were included into the fit. Nevertheless, many of the bands studied in Refs. [13,19,68] were later remeasured with a higher accuracy and then not involved into the fit. From the analysis performed in Refs. [14–23] and using the results of the preliminary fits, a number of bands perturbed via interpolyad resonance interactions were identified. The majority of these bands were excluded from the final fit. Nevertheless, the lines of some perturbed bands which are far from the energy levels crossing points were preserved. It was found that beginning with P ¼18 the polyads strongly overlap, i.e. that some vibrational states belonging to different polyads have close energies. As a result of their close vicinity, the majority of the respective observed bands are perturbed via resonance interpolyad interactions. We then
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
Table 1 Spectrum-by-spectrum analysis of the experimental data and statistics of the
1007
14
N216O global line position fit. b
References
Type of spectruma
Wavenumber range (in cm 1)
Calibration factor
Precision (in 10 3 cm 1)
Nfit/Ntot
[33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46,47] [48] [49] [50] [51] [24] [52] [53] [54] [55] [56] [57] [25] [58] [59] [60] [61] [62] [63] [26] [23] [64] [65] [20] [21] [22] [66] [19] [67] [68,13], S2d [68,13], S1d [69] [16] [17]
MW MW MW MW MW MW MW MW HET HET HET FTS FTS FTS FTS FTS FTS FTS EMISSION FTS HET HET HET HET HET EMISSION FTS FTS FTS FTS CRDS CRDS ICLAS CRDS FTS DIODE CRDS CRDS CRDS FTS FTS FTS FTS FTS ICLAS ICLAS ICLAS
20.8–26.1 20.9–24.3 1.6–4.2 12.5–18.5 0.8–2.5 4.1–10.1 50.1–50.2 3.3–10.1 1256–1339 1256–1331 896–1074 542–646 1132–4750 900–2393 1224–4665 554–620 903–1119 3676–7796 2060–2224 1118–1343 4338–4750 1036–1084 1104–1109 1833–1913 1590–1672 896–989 2061–2267 3584–8099 1100–1360 3399–3499 20–48 7788–7797 7783–7789 3900–4090 7647–7919 1831–3192 7515–7797 6001–6885 5906–6833 6759–7066 2098–2231 5313–8955 2308–2605 6700–8727 8837–9620 9362–9420 8836–10,079 9556–9972
1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 0.999999910 1.000000000 1.000000000 0.999999990 1.000000070 0.999999920 1.000000000 1.000000050 0.999999824 1.0c 1.0c 1.0c 1.0c 1.0c 1.000000010 0.999999985 0.999999857 1.000000000 0.999998803 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000 1.000000447 0.999999990 1.000000000 1.000000000 0.999999228 1.000000000 1.000000402 1.000003197 1.000002582 1.000000000 1.000000000 0.999999000
0.00066 0.00066 0.001 0.0017 0.0033 0.0033 0.0066 0.02 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.4 0.4 0.4 0.4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 5.0 5.0 5.0 5.0 5.0 10.0
5/5 59/60 4/4 90/90 3/3 35/35 3/3 15/15 14/14 14/14 129/129 341/355 240/240 2252/2282 3228/3297 236/244 79/79 1287/1367 2566/2670 641/646 39/39 9/9 29/31 8/8 18/18 1855/1860 3068/3241 3297/3314 28 32/32 3/4 8/8 574/583 1581/1667 3638/3660 534/544 4770/5074 2039/2155 1257/1347 439/531 516/1323 148/148 1235/1482 281/316 62/62 339/503 305/423
RMS (in 10 3 cm 1) 0.0009 0.0042 0.0030 0.0058 0.0017 0.1111 0.0258 0.005 0.37 0.10 0.04 0.19 0.17 0.31 0.71 0.16 0.06 0.93 0.69 0.23 0.18 0.09 0.32 0.18 0.34 1.30 1.9 1.4 0.8 0.1 1.1 0.9 1.4 4.3 0.7 3.0 5.5 6.5 5.1 4.0 7.4 2.2 5.5 13.2 13.2 13.9 21.5
a MW, microwave; HET, laser heterodyne; FTS, Fourier transform; EMISSION, emission; CRDS, cavity ring down; ICLAS, intracavity laser absorption; DIODE, diode laser absorption. b Nfit is the number of lines included in the fit, Ntot is the total number of lines in the source. c Reference spectra. d S1—FTS spectrum above 8800 cm 1 and S2—FTS spectrum below 8800 cm 1. Different calibrations were used in the cited references for these spectra.
decided to limit the input data set to the bands with upper vibrational states belonging to polyads with numbers P r17. Table 1 includes for each data source, the total number and the number of lines included in the fit. The list of the P r17 perturbed bands excluded from the fit is given in Table 2. Overall about 7% of lines (perturbed, badly measured and misassigned) in the selected polyad range (Pr17) were excluded from the fit. Note that between 9700 and 15,000 cm 1, a total of 2384 lines of 32 bands with upper vibrational states belonging to
polyads with numbers 18rPr28 were measured but not involved into the fit. Overall, 37 353 line positions were fitted using 138 effective Hamiltonian parameters. The weighted standard deviation is w ¼4.06 and the global root mean squares of the residuals is RMS¼0.00423 cm 1. The fitted set of effective Hamiltonian parameters is presented in Table 3. This set of parameters reproduces the input data set involving transitions from the MW up to 9700 cm 1 with the accuracies close to the experimental uncertainties.
1008
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
Table 2 List of the 14N216O bands (P o17 for upper vibrational state) perturbed by interpolyad resonance interactions. The lines which were excluded from the fit are given in the last column. Banda
Band center (cm 1)b
Interacting states
Jcrossc
Interaction type
Excluded lines e-e: P8-P19, R6-R17 f-f: P13-P25, R11-R23 all P41-P64, R39-R54 P51-P55, R49-R64 e-e: P2-P13, R1-R15 f-f: P6-P31, R4-R29 f-e: Q10-Q12 e-f: Q1-Q18 e-e: P45-P49, R42-R50 e-e: P8-P13, R3-R11 f-f: P7-P35, R6-R30 P31-P50, R29-R52 P11-P21, R9-R19 e-e: P25-P46, R24-R55 f-f: P25-P41, R23-R39 P23, P24 All e-e: P23-P36, R21-R28 f-f: P20-P36, R18-R28 All R26-R36 All All All All
3310-0110 [51]
5029.001
(9 1 8)2(10 2 4)
e: 13; f: 18
Coriolis
0621-0110 4200-0000 2600-0000 5110-0110
6058.668 6192.271 6303.459
(9 1 8)2(10 2 4) (10 0 9)2(11 1 1) (10 0 10)2(11 1 2) (11 1 11)2(12 2 12)
e: 13; f: 18 91 110 e: 10; f: 16
Coriolis Coriolis Coriolis Coriolis
[51] [20] [20] [20]
5110-0110 [20] 0821-0110 [21]
6303.459
(11 1 11)2(12 0 7) (11 1 11) 2(12 2 12)
59 e: 10; f: 16
Coriolis Coriolis
0801-0000 [22] 0333-0330 [20] 1223-0220 [23]
6882.692 6453.897 7710.776
(11 1 11)2(12 0 7) (15 3 2)2(13 3 27) (16 2 7)2(15 1 13)
59 e, f: 15 e, f: 32
Coriolis Anharmonic Coriolis
5400-0000 [19] 1313-0110 [19] 2113-0110 [19]
8810.780 8831.873 8948.507
(14 0 19)2(16 0 3) (17 1 4)2(15 1 19) (17 1 7)2(15 1 20)
25
Anharmonic Anharmonic Anharmonic
d
0912-0000 4401-0000d 5600-0000d 3312-0000d 6400-0000d 7200-0000d
[16] [16] [17] [17] [17] [16]
9517.883 9874.303 9885.108 9975.202 10,062.079
(17 (17 (16 (17 (16 (16
1 1 0 1 0 0
6)2(16 0 17) 6)2(16 0 17) 22)2(18 0 3) 14)2(18 0 3) 23)2(18 0 6) 24)2(18 0 7)
e: 31; f: 25 35 35
62
Coriolis Coriolis Anharmonic Coriolis Anharmonic Anharmonic
a
Labeling according to a cited reference. Approximate value. c Value of J corresponding to an energy level crossing with a perturber. d Labeling according to a principal value of the expansion coefficients of an eigenfunction. The triplets {P, ‘2, i} are used for the labeling of the vibrational states in the respective references. b
The respective RMS value for each involved source is given in the last column of Table 1. In Fig. 1 the plot of the residuals versus wavenumber is presented. As it was expected the residuals increase with the wavenumber. 4. Conclusion The 14N216O line positions collected in the literature has been satisfactory modeled using a polyad model of effective Hamiltonian. This model does not take into account the interpolyad resonance interactions. A number of observed lines (about 2%) belonging to the Pr17 bands perturbed by interpolyad resonance interactions were then excluded from the line position fit. We found that the polyad model of effective Hamiltonian reproduces satisfactory the line positions of the transitions between vibrational states belonging to polyads with Pr17 i.e. up to about 9700 cm 1. As a result, the fit was limited to the bands with Pr17. The set of 138 effective Hamiltonian parameters was fitted to 37,353 observed line positions of 325 bands collected from the literature with dimensionless weighted standard deviation equal to 4.06. The fitted set of parameters reproduces the line positions involved in to the fit with RMS¼ 0.00423 cm 1. The predicted line positions with this set of effective Hamiltonian parameters can be used for the analysis of the experimental spectra even in a larger wavenumber range up to
15,000 cm 1. Fig. 2 shows that for the majority of the observed bands in 9700–15,000 cm 1 region [13,14,68, 70] the residuals between observed and predicted line positions remain small. The global modeling of 14N216O high resolution spectra using nonpolyad model of effective Hamiltonian is under progress. In the cases of the rare isotopologues: 14N15N16O [8–10], 15N14N16O [9,10], 15N216O [11], 14N218O [12] and 14 N217O [12] we have managed to fit all line positions and obtained satisfactory values for the global RMS. These results could be obtained because the set of available line positions is more restricted for the minor isotopologues than for the principal one and limited to 8500 cm 1 in wavenumbers. Even if larger residuals were obtained for the bands perturbed by interpolyad resonance interactions, these perturbations affect very few bands observed for the minor isotopologues. In addition, in the high wavenumber region, only the strongest bands were detected and these strong bands are usually not perturbed by interpolyad resonance interactions It is very interesting to compare the results of the global fits for nitrous oxide molecule to those for carbon dioxide [71–77]. Polyad model of effective Hamiltonian works very well in the case of CO2 molecule because all resonance Coriolis interactions are intrapolyad interactions [78] and due to the higher symmetry, interpolyad resonance anharmonic interactions take place only for
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
Table 3 The effective Hamiltonian parameters for N
Parameter
Diagonal vibrational parameters o1 1 2 o2 3 o3 4 x11 5 x12 6 x13 7 x22 8 x23 9 x33 10 x‘‘ c 11 y111 12 y112 13 y113 14 y122 15 y123 16 y133 17 y222 18 y223 19 y233 20 y333 21 y1‘‘
14
N216O.
Value (cm 1)
1298.2656(57)b 596.3067(14) 2282.2650(58) 5.115(28) 5.43922(62) 22.85(11) 1.12389(12) 14.55799(59) 15.0972(11) 0.594 1.209(18) 0.586(20) 6.98(12) 0.1137(99) 4.152(80) 3.41(15) 0.17496(83) 0.842(12) 0.1444(14) 0.0913(22) 0.3347(99)
Diagonal rotational and vibrational–rotational parameters 43 Be 0.42112438(17) 44 a1 0.190953(12) 45 a2 0.0574713(54) 46 a3 0.3466413(89) 47 g11 0.1410(20) 48 g12 0.0947(11) 49 g13 0.0912(84) 50 g22 0.09268(26) 51 g23 0.31444(35) 52 g33 0.05507(45) 53 g‘‘ 0.04091(22) 54 e111 0.6310((5) 55 e112 0.758(29) 56 e122 0.603(20)
Ordera
N
Parameter
10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
y2‘‘ y3‘‘ z1111 z1112 z1113 z1122 z1123 z1133 z1222 z1223 z1333 z2222 z2223 z2233 z2333 z3333 z11‘‘ z12‘‘ z22‘‘ z23‘‘ z33‘‘
0.16955(83) 0.352(11) 0.025(14) 0.199(17) 0.241(14) 0.165(28) 1.64(13) 13.03(29) 0.0611(78) 0.234(21) 4.42(13) 0.03498(55) 0.1811(62) 0.203(14) 0.0373(20) 0.0900(29) 0.053(19) 0.1473(65) 0.01706(54) 0.1795(61) 0.248(14)
10 1 10 1 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2
10 2 10 2 10 2 10 4 10 4 10 4 10 4 10 4 10 4 10 4 10 6 10 6 10 6
57 58 59 60 61 62 63 64 65 66 67 68 69 70
e123 e133 e222 e223 e333
3.697(84) 0.804(74) 0.0776(35) 0.7864(54) 0.2114(76) 0.172915(22) 0.1697(11) 0.26451(76) 0.048014(63) 1.091(41) 1.846(72) 0.435(14) 1.801(33) 1.69(28)
10 6 10 6 10 6 10 6 10 6 10 6 10 8 10 8 10 8 10 10 10 10 10 10 10 10 10 14
De
b1 b2 b3
Z11 Z13 Z22 Z23 He
Parameters of ‘-doubling matrix element 71 Le 0.196403(11) 72 L1 0.0936(32) 73 L2 0.19356(94) 74 L3 0.3148(11) 75 L11 3.50(14) 76 L12 0.247(98)
10 3 77 L13 10 5 78 L22 5 10 79 L23 10 5 80 L33 10 7 81 LJ 10 7
Parameters of Fermi interaction matrix elements V 1 V 2 ‘2 V 3 J Hef f V 1 1 V 2 þ 2 ‘2 þ D‘2 V 3 J 82 Fe 19.62384(27) 88 F23 83 F1 0.3852(42) 89 F33 84 F2 0.31696(22) 90 F ‘‘ 85 F3 0.0996(82) 91 FJ 2 86 F11 0.457(30) 10 92 F Le 87 F12 0.637(20) 10 2 93 F LJ Parameters of Fermi interaction matrix element /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 2 V 2 ‘2 V 3 þ 1 JS 18.54(24) 100 94 F e ð2Þ 95 1.335(24) 101 F ð2Þ 96 97 98 99
1 F ð2Þ 2 F ð2Þ 3 F ð2Þ 11 F ð2Þ 12
0.314(16)
102
1.288(29)
103
0.217(69) 5.28(19)
10 2 10
104
10 7 10 7 10 7 10 7 10 9
1.362(39) 2.000(73) 0.0569(19) 1.26602(57) 0.8355(22)
10 2 10 2 10 2 10 4 10 5
0.1019(12)
10 9
F ð2Þ 13
26.763(58)
10 2
F ð2Þ 22
0.744(62)
10 2
F ð2Þ 23 F ð2Þ 33 F ð2Þ J
2.76(17)
10 2
7.38(24)
10 2
0.461(16)
10 4
22
0.0893(23)
Ordera
2
1
F ð3Þ 2
Value (cm 1)
2.54(19) 0.872(13) 5.302(84) 2.080(22) 0.2270(15)
Parameters of anharmonic interaction matrix elements /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 1 V 2 2 ‘2 þ D‘2 V 3 þ 1 JS 3.377(44) 111 105 F e ð3Þ F ð3Þ 13 106 0.2028(95) 112 F ð3Þ F ð3Þ 107
1009
113
F ð3Þ 23
0.808(97)
10 2
0.3008(72)
10 2
0.992(27)
10 2
1010
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
Table 3 (continued ) N
Parameter
Value (cm 1)
108
F ð3Þ 3
0.2470(30)
109
F ð3Þ 11 F ð3Þ 12
110
Ordera
N
Parameter
114
F ð3Þ 33
0.781(55)
10
2
115
1.999(44)
10 2
116
F ð3Þ J F ð3ÞL J
Parameters of anharmonic interaction matrix elements /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 V 2 4 ‘2 þ D‘2 V 3 þ 1 JS 0.2388(28) 120 117 F ð4Þ F ð4Þ e 3 118 0.546(53) 10 2 121 F ð4Þ F ð4Þ J 1 119
F ð4Þ 2
Parameters of anharmonic interaction matrix element /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 2 V 2 þ 4 ‘2 V 3 JS 0.785(53) 10 3 125 123 F ð5Þ F ð5Þ 1 3 124 0.571(35) 10 3 126 F ð5Þ F ð5Þ J 2 Parameters of anharmonic interaction matrix element /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 4 V 2 ‘2 V 3 þ 2 JS 0.517(12) 129 127 F ð6Þ F ð6Þ e 2 1 ð6Þ 128 0.2177(62) 10 130 F F ð6Þ 1
J
Parameters of anharmonic interaction matrix element /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 3 V 2 þ 2 ‘2 V 3 þ 1 JS 0.764(41) 10 1 134 131 F ð7Þ F ð7Þ e 3 ð7Þ 132 0.618(36) 10 2 135 F F ð6Þ 1 F ð7Þ 2
133
J
0.332(20)
10
Value (cm 1) 1.47(35) 0.105(43) 0.791(97)
Ordera 10 2 10 5 10 10
2.192(38)
10 2
0.5126(84)
10 5
0.91(23)
10 7
2.491(58)
10 3
0.2477(90)
10 6
0.2251(52)
10 1
0.47(10)
10 6
0.694(54)
10 2
0.431(46)
10 6
2
Parameters of anharmonic interaction matrix elements /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 3 V 2 2 ‘2 V 3 þ 2 JS, /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 2 V 2 4 ‘2 V 3 þ 2 JS and /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 þ 1 V 2 6 ‘2 V 3 þ 1 JS 0.350(17) 136 F ð8Þ e 137 0.2222(42) F ð9Þ
10 1
e
b
Residuals, in 10-3 cm-1
c
F ð10Þ e
0.283(31)
10 3
Order of magnitude of the parameter value. Uncertainties in parentheses represent one standard deviation in units of the last quoted digit. Fixed to the value given in Ref. [29].
60
1.5
40
1.0 Residuals, cm-1
a
138
10 1
20 0 -20
0.5 0.0 -0.5 -1.0
-40 -60 0
2000
4000
6000
8000
10000
-1.5 9000
12000
15000
Wavenumber, cm-1
Wavenumber, cm-1 N216O line positions using the
Fig. 2. Residuals between observed [13,14,68,70] and predicted line positions of 14N216O in the 9700–15,000 cm 1 region.
asymmetric isotopologues. Only a few occurrences of interpolyad resonance perturbations were evidenced, all concerning the asymmetric isotopologues of CO2 molecule [76,79–81].
CAS (China) in the frame of Groupement de Recherche International SAMIA (Spectroscopie d’Absorption des Mole´cules d’Inte´rˆet Atmosphe´rique).
Fig. 1. Residuals of the global fit of the polyad model of effective Hamiltonian.
14
References Acknowledgments This work is jointly supported by RFBR (Russia, Grants N09-05-93105 and N 10-05-91176), CNRS (France) and
[1] Teffo JL, Perevalov VI, Lyulin OM. Reduced effective Hamiltonian for global treatment of rovibrational energy levels of nitrous oxide. Journal of Molecular Spectroscopy 1994;168:390–403. [2] Perevalov V.I., Tashkun S.A., Teffo J.L. Global fitting of rovibrational line positions of nitrous oxide. In: Sixteenth colloquium on high
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
resolution molecular spectroscopy, Dijon (France). 6–10 September 1999, Poster D2, p. 103. Lyulin OM, Perevalov VI, Teffo JL. Effective dipole moment and band intensities of nitrous oxide. Journal of Molecular Spectroscopy 1995;174:566–80. Lyulin OM, Perevalov VI, Teffo JL. Fitting of line intensities using the effective operator approach: the 4 mm region of 14N216O. Journal of Molecular Spectroscopy 1996;180:72–4. Daumont L, Vander Auwera J, Teffo JL, Perevalov VI, Tashkun SA. Line intensity measurements in 14N216O and their treatment using the effective dipole moment approach. I. The 4300 to 5200 cm 1 region. Journal of Molecular Spectroscopy 2001;208:281–91. Daumont L, Claveau C, Debacker-Barilly MR, Hamdouni A, RegaliaJarlot LR, Teffo JL, et al. Line intensities of 14N216O: the 10 mm region revisited. Journal of Quantitative Spectroscopy and Radiative Transfer 2002;72:37–55. Daumont L, Vander Auwera J, Teffo JL, Perevalov VI, Tashkun SA. Line intensity measurements in 14N216O and their treatment using the effective dipole moment approach. II. The 5400–11,000 cm 1 region. Journal of Quantitative Spectroscopy and Radiative Transfer 2007;104:342–56. Ni HY, Song KF, Perevalov VI, Tashkun SA, Liu AW, Wang L, et al. Fourier-transform spectroscopy of 14N15N16O in the 3800– 9000 cm 1 region and global modeling of its absorption spectrum. Journal of Molecular Spectroscopy 2008;248:41–60. Wang CY, Liu AW, Perevalov VI, Tashkun SA, Song KF, Hu SM. Highresolution infrared spectroscopy of 14N15N16O and 15N14N16O in the 1200–3500 cm 1 region. Journal of Molecular Spectroscopy 2009;257: 94–104. Tashkun SA, Perevalov VI, Kochanov RV, Liu AW, Hu SM. Global fittings of 14N15N16O and 15N14N16O vibrational–rotational line positions using the effective Hamiltonian approach. Journal of Quantitative Spectroscopy and Radiative Transfer 2010;111:1089–105. Lyulin OM, Jacquemart D, Lacome N, Tashkun SA, Perevalov VI. Line parameters of 15N216O from Fourier transform measurements in the 5800–7600 cm 1 region and global fitting of line positions from 1000–7600 cm 1. Journal of Quantitative Spectroscopy and Radiative Transfer 2010;111:345–56. Vlasova AV, Perevalov BV, Tashkun SA, Perevalov VI. Global fittings of the line positions of the rare isotopic species of the nitrous oxide molecule. In: Proceedings of the XVth symposium on high- resolution molecular spectroscopy, Nizhny Novgorod, Russia, vol. 6580, SPIE; 2006. p. 658007. Weirauch G, Kachanov AA, Campargue A, Bach M, Herman M, Vander Auwera J. Refined investigation of the overtone spectrum of nitrous oxide. Journal of Molecular Spectroscopy 2000;202:98–106. Campargue A, Weirauch G, Tashkun SA, Perevalov VI, Teffo JL. Overtone spectroscopy of N2O between 10,000 and 12,000 cm 1: a test of the polyad approach. Journal of Molecular Spectroscopy 2001;209:198–206. Bertseva E, Kachanov AA, Campargue A. Intracavity laser absorption spectroscopy of N2O with a vertical external cavity surface emitting laser. Chemical Physics Letters 2002;351:18–26. Ding Y, Perevalov VI, Tashkun SA, Teffo JL, Bertseva E, Campargue A. Weak overtone transitions of N2O around 1.05 mm by ICLASVECSEL. Journal of Molecular Spectroscopy 2003;220:80–6. Bertseva E, Campargue A, Perevalov VI, Tashkun SA. New observations of weak overtone transitions of N2O by ICLAS-VeCSEL near 1.07 mm. Journal of Molecular Spectroscopy 2004;226:196–200. Milloud R, Perevalov VI, Tashkun SA, Campargue A. Rotational analysis of 6n3 and 6n3 þ n2 n2 bands of 14N216O from ICLAS spectra between 12,760 and 12,900 cm 1. Journal of Quantitative Spectroscopy and Radiative Transfer 2011;112:553–7. Wang L, Perevalov VI, Tashkun SA, Gao B, Hao LY, Hu SM. Fourier transform spectroscopy of N2O weak overtone transitions in the 1–2 mm region. Journal of Molecular Spectroscopy 2006;237:129–36. Liu AW, Kassi S, Malara P, Romanini D, Perevalov VI, Tashkun SA, et al. High sensitivity CW-cavity ring down spectroscopy of N2O near 1.5l mm (I). Journal of Molecular Spectroscopy 2007;244: 33–47. Liu AW, Kassi S, Perevalov VI, Tashkun SA, Campargue A. High sensitivity CW-cavity ring down spectroscopy of N2O near 1.5l mm (II). Journal of Molecular Spectroscopy 2007;244:48–62. Liu AW, Kassi S, Perevalov VI, Hu SM, Campargue A. High sensitivity CW-cavity ring down spectroscopy of N2O near 1.5 mm (III). Journal of Molecular Spectroscopy 2009;254:20–7. Liu AW, Kassi S, Perevalov VI, Tashkun SA, Campargue A. High sensitivity CW-Cavity Ring Down Spectroscopy of N2O near 1.28 mm. Journal of Molecular Spectroscopy 2011;267:191–9.
1011
[24] Bailly D, Vervloet M. 14N‘216O in Emission in the 4.5-mm region: ‘ transitions V1V2V3- V1V2(V3-1) occurring between highly excited vibrational states. Journal of Molecular Spectroscopy 2001;209: 207–15. [25] Bailly D, Pirali O, Vervloet M. 14N216O in Emission in the 4.5mm ‘ region: high excitation of the banding mode transitions V1V2V3‘ V1V2(V3-1) with (2V1 þ V2) ¼5 occurring between highly excited vibrational states. Journal of Molecular Spectroscopy 2003;222: 180–90. [26] Herbin H, Picque´ N, Guelachvili G, Sorokin E, Sorokina I. N2O weak lines observed between 3900 and 4050 cm 1 from long path absorption spectra. Journal of Molecular Spectroscopy 2006;238:256–9. [27] Horneman VM. High accurate peak positions for calibration purposes with the lowest fundamental bands n2 of N2O and CO2. Journal of Molecular Spectroscopy 2007;241:45–50. [28] Pliva J. Molecular constants of nitrous oxide, 14N216O. Journal of Molecular Spectroscopy 1968;27:461–88. [29] Teffo JL, Chedin A. Internuclear potential and equilibrium structure of the nitrous oxide molecule from rovibrational data. Journal of Molecular Spectroscopy 1989;135:389–409. [30] Tashkun SA, Perevalov VI, Teffo JL. Global fitting of vibrationrotation line positions of N2O using imterpolyad model of effective Hamiltonian. In: International workshop ‘‘Atmospheric Spectroscopy Applications’’. 25–28 August 2002. p. 41 [Abstracts]. [31] Perevalov VI, Tashkun SA, Lyulin OM, Teffo JL. Global modeling of high-resolution spectra of linear molecules CO2, N2O and C2H2. In: Perrin A, Ben Sari-Zizi N, Demaison J, editors. Remote sensing of atmosphere for environmental security. Springer; 2006. p. 139–59. [32] Tashkun SA, Perevalov VI, Teffo JL, Lecoutre M, Huet TR, Campargue A, et al. 13C16O2: Global treatment of vibrational–rotational spectra and first observation of the 2n1 þ 5n3 and n1 þ2n2 þ 5n3 absorption bands. Journal of Molecular Spectroscopy 2000;200:162–76. [33] Morino I, Fabian M, Takeo H, Yamada KMT. High-J rotational transitions of NNO measured with the NAIR Terahertz Spectrometer. Journal of Molecular Spectroscopy 1997;185:142–6. [34] Morino I, Yamada KMT, Maki AG. Terahertz measurements of rotational transitions in vibrationally excited states of N2O. Journal of Molecular Spectroscopy 1999;196:131–8. [35] Bogey M. Microwave absorption spectroscopy in the n3 states of OCS and N2O through energy transfer from N2*. Journal of Physics B: Atomic and Molecular Physics 1975;11:1934–8. [36] Andreev BA, Burenin AV, Karyakin EN, Krupnov AF, Shapin SM. Submillimeter wave spectrum and molecular constants of N2O. Journal of Molecular Spectroscopy 1976;62:125–48. [37] Lafferty WJ, David R, Lide DR. Rotational constants of excited vibrational states of 14N216O. Journal of Molecular Spectroscopy 1964;14:407–8. [38] Pearson R, Sullivan T, Frenkel L. Microwave spectrum and molecular parameters for 14N216O. Journal of Molecular Spectroscopy 1970;34:440–9. [39] Vanek MD, Jennings DA, Wells JS, Maki AG. Frequency measurements of high-J rotational transitions of OCS and N2O. Journal of Molecular Spectroscopy 1989;138:79–83. [40] Burrus CA, Gordy W. Millimeter and submillimeter wave spectroscopy. Physical Review 1956;101:599–602. [41] Wells JS, Hinz A, Maki AG. Heterodyne frequency measurements on N2O between 1257 and 1340 cm 1. Journal of Molecular Spectroscopy 1985;114:84–96. [42] Hinz A, Wells JS, Maki AG. Heterodyne measurements of hot bands ¨ Physik D and isotopic transitions of N2O near 7.8 mm. Zeitschrift fur 1987;5:351–8. [43] Tachikawa M, Evenson KM, Zink LR, Maki AG. Frequency measurements of 9- and 10-mm N2O laser transitions. IEEE Journal of Quantum Electronics 1996;32:1732–6. [44] Jolma K, Kauppinen J, Horneman VM. Vibration-rotation spectrum of N2O in the region of the lowest fundamental n2. Journal of Molecular Spectroscopy 1983;101:278–84. [45] Brown LR, Toth RA. Comparison of the frequencies of NH3, CO2, H2O, N2O, CO and CH4 as infrared calibration standards. Journal of the Optical Society of America 1985;B2:842–56. [46] Toth RA. Frequencies of N2O in the 1100- to 1440-cm 1 region. Journal of the Optical Society of America 1986;B3:1263–81. [47] Toth RA. N2O vibration-rotation parameters derived from measurements in the 900-1090- and 1580–2380-cm 1 regions. Journal of the Optical Society of America 1987;B4:357–74. [48] Toth RA. Line-frequency measurements and analysis of N2O between 900 and 4700 cm 1. Applied Optics 1991;30:5289–315. [49] Tan TL, Looi EC, Lua KT. Hot-band spectrum of N2O near 589 cm 1. Journal of Molecular Spectroscopy 1992;154:218–22.
1012
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
[50] Barbe A. 1999. Private communication. [51] Toth RA. Line Positions and Strengths of N2O between 3515 and 7800 cm 1. Journal of Molecular Spectroscopy 1999;197:158–87. [52] Guelachvili G. Absolute N2O wavenumbers between 1118 and 1343 cm 1 by Fourier transform spectroscopy. Canadian Journal of Physics 1982;60:1334–47. [53] Pollock CR, Petersen FR, Jennings DA, Wells JS, Maki AG. Absolute frequency measurements of the 0002-0000, 2001-0000, and 12010000 bands of N2O by heterodyne spectroscopy. Journal of Molecular Spectroscopy 1984;107:62–71. [54] Zink LR, Wells JS, Maki AG. Heterodyne frequency measurements on N2O near 1060 cm 1. Journal of Molecular Spectroscopy 1987;123:426–33. [55] Wells JS, Jennings DA, Hinz A, Murray JS, Maki AG. Heterodyne frequency measurements on N2O at 5.3 and 9.0 mm. Journal of the Optical Society of America 1985;B2:857–61. [56] Vanek MD, Schneider M, Wells JS, Maki AG. Heterodyne measurements on N2O near 1635 cm 1. Journal of Molecular Spectroscopy 1989;134:154–8. [57] Maki AG, Wells JS, Vanek MD. Heterodyne frequency measurements on N2O near 930 cm 1. Journal of Molecular Spectroscopy 1989;138:84–8. [58] Amiot C, Guelachvili G. Vibration-rotation bands of 14N216O: 1.2 micron-3.3 micron region. Journal of Molecular Spectroscopy 1974;51:475–91. [59] Esplin MP, Barowy WM, Huppi J, Vanasse GA. High resolution Fourier spectroscopy of nitrous oxide at elevated temperatures. Microchimica Acta 1988;II:403–7. [60] Toth RA. Linelist of N2O parameters from 500 to 7500 cm 1. Available via WEB site SISAM.N2O. [61] Yamada KMT. Pure rotational spectrum of NNO in the far infrared ¨ Naturforschung 1990;45a:837–8. region. Zeitschrift fur [62] He Y, Hippler M, Quack M. High-resolution cavity ring-down absorption spectroscopy of nitrous oxide and chloroform using a nearinfrared cw diode laser. Chemical Physics Letters 1998;289:527–34. [63] Hippler M, Quack M. Cw cavity ring-down infrared absorption spectroscopy in pulsed supersonic jets: nitrous oxide and methane. Chemical Physics Letters 1999;314:273–81. [64] Amiot C, Guelachvili G. Extension of the 106 samples Fourier spectrometry to the Indium Antimonide region: Vibration-rotation bands of 14N216O: 3.3–5.5 mm region. Journal of Molecular Spectroscopy 1976;59:171–90. [65] Oshika H, Toba A, Fujitake M, Ohashi N. Newly observed vibrational bands of N2O in 1.3 mm region. Journal of Molecular Spectroscopy 1999;179:324–5. [66] Farrenq R, Dupre-Maquaire J. Vibrational luminescence of N2O excited by discharge. Rotation–vibration constants. Journal of Molecular Spectroscopy 1974;49:268–79. [67] Krell JM, Sams RL. Vibration-rotation bands of nitrous oxide: 4.1 micron region. Journal of Molecular Spectroscopy 1974;51:492–507. [68] Campargue A, Permogorov, Bach M, Abbouti Temsamani M, Vander Auwera J, Fujii M. Overton spectroscopy in nitrous oxide. Journal of Chemical Physics 1995;103:5931–8.
[69] Garnache A, Campargue A, Kachanov AA, Stoeckel F. Intracavity laser absorption spectroscopy near 9400 cm 1 with a Nd:glass laser: application to 14N216O. Chemical Physics Letters 1998;292:698–704. [70] Campargue A. The near-infrared absorption spectrum of nitrous oxide: analysis of the 5n3 and n1 þ 5n3 clusters. Chemical Physics Letters 1996;259:563–7. [71] Tashkun SA, Perevalov VI, Teffo JL, Rothman LS, Tyuterev VlG. Global Fitting of 12C16O2 vibrational–rotational line positions using the effective Hamiltonian approach. Journal of Quantitative Spectroscopy and Radiative Transfer 1998;60:785–801. [72] Tashkun SA, Perevalov VI, Teffo JL, Lecoutre M, Huet TR, Campargue A, et al. 13C16O2: Global treatment of vibrational–rotational spectra and first observation of the 2n1 þ 5n3 and n1 þ 2n2 þ 5n3 absorption bands. Journal of Molecular Spectroscopy 2000;200:164–75. [73] Tashkun SA, Perevalov VI, Teffo JL. Global fittings of the vibrational–rotational line positions of the 16O12C17O and 16 12 18 O C O isotopic species of carbon dioxide. Journal of Molecular Spectroscopy 2001;210:137–45. [74] Ding Y, Macko P, Romanini D, Perevalov VI, Tashkun SA, Teffo JL, et al. High sensitivity cw-cavity ringdown and Fourier transform absorption spectroscopies of 13CO2. Journal of Molecular Spectroscopy 2004;226:146–60. [75] Majcherova Z, Macko P, Romanini D, Perevalov VI, Tashkun SA, Teffo JL, et al. High-sensitivity CW-cavity ringdown spectroscopy of 12 CO2 near 1.5 mm. Journal of Molecular Spectroscopy 2005;230: 1–21. [76] Perevalov BV, Kassi S, Romanini D, Perevalov VI, Tashkun SA, Campargue A. Global effective Hamiltonians of 16O13C17O and 16 13 18 O C O improved from CW-CRDS observations in the 5900– 7000 cm 1 region. Journal of Molecular Spectroscopy 2007;241: 90–100. [77] Wang L, Perevalov VI, Tashkun SA, Song KF, Hu SM. Fourier transform spectroscopy of 12C18O2 and 16O12C18O in the 3800–8500 cm 1 region and the global modeling of the absorption spectrum of 12 18 C O2. Journal of Molecular Spectroscopy 2008;247:64–75. [78] Teffo JL, Sulakshina ON, Perevalov VI. Effective Hamiltonian for rovibrational energies and line intensities. Journal of Molecular Spectroscopy 1992;156:48–64. [79] Perevalov BV, Kassi S, Perevalov VI, Tashkun SA, Campargue A. High sensitivity CW-Cavity Ring Down Spectroscopy of 12C16O2, 16 12 17 O C O and 16O12C18O between 5851 and 7045 cm 1: line position analysis and critical review of the current databases. Journal of Molecular Spectroscopy 2008;252:143–59. [80] Perevalov BV, Perevalov VI, Campargue A. A (nearly) complete experimental linelist for 13C16O2, 16O13C18O, 16O13C17O, 13C18O2 and 17O13C18O by high-sensitivity CW-CRDS spectroscopy between 5851 and 7045 cm 1. Journal of Quantitative Spectroscopy and Radiative Transfer 2008;109:2437–62. [81] Campargue A, Song KF, Mouton N, Perevalov VI, Kassi S. High sensitivity CW-Cavity Ring Down Spectroscopy of five 13CO2 isotopologues of carbon dioxide in the 1.26–1.44 mm region (I): Line positions. Journal of Quantitative Spectroscopy and Radiative Transfer 2010;111:659–74.
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Global modeling of the 14N216O line positions within the framework of the polyad model of effective Hamiltonian V.I. Perevalov a,n, S.A. Tashkun a, R.V. Kochanov a, A.-W. Liu b, A. Campargue c a
Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, Academician Zuev Sq. 1, 634021 Tomsk, Russia Hefei National Laboratory for Physical Sciences at Microscale, Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China c Universite´ Grenoble 1/CNRS, UMR5588 LIPhy, Grenoble F-38041, France b
a r t i c l e in f o
abstract
Article history: Received 18 October 2011 Received in revised form 2 December 2011 Accepted 3 December 2011 Available online 17 December 2011
The global modeling of 14N216O line positions in the 0–9700 cm 1 region has been performed using the polyad model of effective Hamiltonian. The effective Hamiltonian parameters were fitted to the line positions collected from an exhaustive review of the literature. A number of lines perturbed by interpolyad resonance interactions were excluded from the fit. The dimensionless weighted standard deviation of the fit is 4.06. The fitted set of 138 effective Hamiltonian parameters allowed reproducing 37,353 measured line positions of 325 bands with an RMS value of 0.00423 cm 1. & 2012 Published by Elsevier Ltd.
Keywords: Nitrous oxide Microwave Infrared Line position Global modeling Effective Hamiltonian
1. Introduction Nitrous oxide, N2O, is a minor constituent of the Earth atmosphere but it plays an important role in atmospheric physics and chemistry. Being a greenhouse gas it contributes to the atmospheric radiation balance. Through the atmospheric chemistry processes N2O participates to the ozone layer depletion. In addition, nitrous oxide is one of the products of the burning of the organic fuels in air. For the calculation of the radiation balance inside an internal-combustion engine or inside a jet propulsion it is necessary to know the high temperature spectrum of this molecule. This spectrum can be calculated theoretically. One of the theoretical approaches is the method of effective operators adopted for the global description of
n
Corresponding author. Tel.: þ 7 3822 491794; fax: þ7 3822 492086. E-mail address: [email protected] (V.I. Perevalov).
0022-4073/$ - see front matter & 2012 Published by Elsevier Ltd. doi:10.1016/j.jqsrt.2011.12.008
the energy levels and transition probabilities inside a given electronic state. We have successfully applied this method to the global modeling of the line positions [1,2] and line intensities [3–7] of the principal isotopologue, 14 N216O, and to the global modeling of the line positions of the rare isotopologues: 14N15N16O [8–10], 15N14N16O [9,10], 15N216O [11], 14N218O [12] and 14N217O [12]. The set of effective Hamiltonian parameters obtained in 1999 for 14N216O [2] allowed us to predict the line positions in a wide spectral range. These predictions were successfully used for the assignment of the spectra recorded by intracavity laser absorption spectroscopy (ICLAS) [13–18], Fourier transform spectroscopy (FTS) [5–7,13,19] and cavity ring down spectroscopy (CRDS) [20–23]. But the set of parameters derived for 14N216O has never been published. Since 1999, the amount of observations has been considerably extended [12–27] in particular from CRDS in the 5800–7900 cm 1 region [20–23]. The aim of this paper is the refinement of the effective
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
Hamiltonian parameters of 14N216O by using the most extensive compilation of line position measurements available to date. 2. Effective Hamiltonian The polyad model of effective Hamiltonian describing globally the 14N216O vibrational–rotational states in the ground electronic state of nitrous oxide has been suggested by Pliva [28] and developed by Teffo and Chedin [29]. In Ref. [1] we elaborated a reduced model of this Hamiltonian which is further described in Refs. [8–12] (see Refs. [8,10] for the notations and definitions). The polyad model of effective Hamiltonian is based on the polyad structure of the 14N216O vibrational states resulting from the approximate relations between harmonic frequencies o3 E2o1 E4o2. This Hamiltonian takes into account in an explicit way all intrapolyad resonance anharmonic and anharmonicþ‘-type interactions up to the sixth order of perturbation theory. The Coriolis interactions are interpolyad interactions within the framework of this model. They are assumed to be accounted for by the effective values of the effective Hamiltonian parameters. For the reader’s convenience we recall below the matrix elements of the effective Hamiltonian. Diagonal matrix element: /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 V 2 ‘2 V 3 JS X g g X g ¼ oi V i þ i þ ij xij V i þ i V j þ j þx‘‘ ‘22 2 2 2 i X gj g g Vk þ k þ y Vi þ i Vj þ ijk ijk 2 2 2 X gi 2 yi‘‘ V i þ þ ‘ 2 2 i X gj g g g Vm þ m Vn þ n þ z Vi þ i Vj þ ijmn ijmn 2 2 2 2 X g g j ‘2 þ z‘‘‘‘ ‘42 þ z Vi þ i Vj þ ij ij‘‘ 2 2 2 ( X g g X g þ Be ai V i þ i þ ij gij V i þ i V j þ j þ g‘‘ ‘22 2 2 2 i g g g þ e Vi þ i Vj þ j Vk þ k ijk ijk 2 2 2 ) X gi 2 ei‘‘ V i þ ‘2 JðJ þ1Þ‘22 þ 2 i ( X g g X g bi V i þ i þ ij Zij V i þ i V j þ j De þ 2 2 2 i ) X
(
X i
di V i þ
) gi ½JðJ þ 1Þ‘22 3 : 2
Matrix elements of anharmonic resonance interactions: /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 1 V 2 þ 2 ‘2 V 3 JS qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ( X g þ DV i ¼ V 1 ½ðV 2 þ2Þ2 ‘22 F e þ Fi V i þ i 2 i X g j þ DV j g þ DV i þ Vj þ F Vi þ i ij ij 2 2 ) þ F ‘‘ ‘22 þ F J ½JðJ þ 1Þ‘22 ,
ð3Þ
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 2 V 2 ‘2 V 3 þ 1 JS ( X ð2Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g þ DV i ¼ ðV 1 1ÞV 1 ðV 3 þ1Þ F ð2Þ Fi Vi þ i e þ 2 i X ð2Þ g j þ DV j g i þ DV i þ Vj þ F Vi þ ij ij 2 2 ) ð2Þ 2 2 þ F ð2Þ ‘‘ ‘ 2 þF J ½JðJ þ 1Þ‘ 2 ,
ð4Þ
V 1 V 2 ‘2 V 3 J Hef f V 1 1 V 2 2 ‘2 V 3 þ 1 J rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ¼ V 1 V 22 ‘22 ðV 3 þ 1Þ (
g i þ DV i F ð3Þ V þ i i 2 i X ð3Þ g j þ DV j g þ DV i þ Vj þ F Vi þ i ij ij 2 2 ) F ð3Þ e þ
X
ð3Þ 2 2 þ F ð3Þ ‘‘ ‘ 2 þF J ½JðJ þ 1Þ‘ 2 ,
ð5Þ
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 V 2 4 ‘2 V 3 þ 1 JS ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðV 3 þ1ÞðV 22 ‘22 Þ½ðV 2 2Þ2 ‘22
( F ð4Þ e þ
X i
) g i þ DV i ð4Þ 2 þF F ð4Þ V þ JðJ þ 1Þ‘ , i 2 J i 2 ð6Þ
/V 1 V 2 ‘2 V 3 J9Hef f V 1 2 V 2 þ4 ‘2 V 3 J qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ V 1 ðV 1 1Þ½ðV 2 þ 2Þ2 ‘22 ½ðV 2 þ 4Þ2 ‘22 ( ) X ð5Þ g i þ DV i ð5Þ 2 F ð5Þ þ F þ F V þ JðJ þ 1Þ‘ , i 2 e J i 2 i ð7Þ
þ Z‘‘ ‘22 ½JðJ þ 1Þ‘22 2 þ He þ
1005
ð1Þ
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 4 V 2 ‘2 V 3 þ 2 JS pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðV 1 3ÞðV 1 2ÞðV 1 1ÞV 1 ðV 3 þ 2ÞðV 3 þ 1Þ ( ) X ð6Þ g i þ DV i ð6Þ 2 þ F þ F V þ JðJ þ 1Þ‘ , F ð6Þ i 2 e J i 2 i ð8Þ
‘-doubling matrix element: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðV 2 7‘2 þ 2ÞðV 2 8 ‘2 Þ½JðJ þ1Þ‘2 ð‘2 71Þ½JðJ þ 1Þð‘2 7 1Þð‘2 7 2Þ ) X gj gi X gi 2 þ Vj þ þ LJ ½JðJ þ 1Þð‘2 7 1Þ : Le þ Li V i þ L Vi þ ij ij 2 2 2 i
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 V 2 ‘2 7 2V 3 JS ¼ (
ð2Þ
1006
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 3 V 2 þ 2 ‘2 V 3 þ 1 JS qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðV 1 2ÞðV 1 1ÞV 1 ½ðV 2 þ 2Þ2 ‘22 ðV 3 þ1Þ ( ) X ð7Þ g i þ DV i ð7Þ 2 , þ F þ F V þ JðJ þ 1Þ‘ F ð7Þ i 2 e J i 2 i ð9Þ /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 3 V 2 2 ‘2 V 3 þ 2 JS qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðV 1 2ÞðV 1 1ÞV 1 ðV 3 þ 1ÞðV 3 þ 2ÞðV 22 ‘22 Þ, ¼ F ð8Þ e
ð10Þ
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 2 V 2 4 ‘2 V 3 þ 2 JS qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðV 1 1ÞV 1 ðV 3 þ 1ÞðV 3 þ 2ÞðV 22 ‘22 Þ½ðV 2 2Þ2 ‘22 ¼ F ð9Þ e ð11Þ /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 þ 1 V 2 6 ‘2 V 3 þ 1 JS qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ F ð10Þ ðV 1 þ 1ÞðV 3 þ 1ÞðV 22 ‘22 Þ½ðV 2 2Þ2 ‘22 ½ðV 2 4Þ2 ‘22 : e ð12Þ Matrix elements interactions:
of
anharmonic þ‘-type
resonance
/V 1 V 2 ‘2 V 3 J9Hef f 9V 1 1 V 2 þ2 ‘2 72 V 3 JS ¼ F Le
obtained using different spectroscopic techniques: microwave [33–40], laser heterodyne [41–43,53–57], Fourier transform [19,44–52,58–61,64,66–68], diode laser absorption [65], cavity ring down [20–22,62,63], intracavity laser absorption [16,17,26,69] and emission [24,25]. In Ref. [59] the spectra were recorded at elevated temperatures. The internal consistency between the different experimental sources was checked. The misassigned, misprinted or badly measured lines were revealed and excluded. This checking was done by fitting energy levels to the observed line positions using the fundamental Ritz principle. Details of this approach can be found in Ref. [32]. The following criterion was used for excluding a line from the fit: if the weighted Ritz residual r i-j ¼
nobs i-j ðEi Ej Þ dobs i-j
of a line was greater than 3, the line was deleted from the obs input data file. In the above equation vobs i-j and di-j are measured line position and corresponding uncertainty for
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V 1 ðV 2 7 ‘2 þ2ÞðV 2 7‘2 þ 4Þ½JðJ þ1Þ‘2 ð‘2 7 1Þ½JðJ þ 1Þð‘2 7 1Þð‘2 7 2Þ, ð13Þ
/V 1 V 2 ‘2 V 3 J9H
ef f
9V 1 1 V 2 2 ‘2 72 V 3 þ 1
JS ¼ F eð3ÞL
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V 1 ðV 3 þ 1ÞðV 2 8 ‘2 ÞðV 2 8 ‘2 2Þ½JðJ þ 1Þ‘2 ð‘2 7 1Þ½JðJ þ 1Þð‘2 7 1Þð‘2 7 2Þ,
ð14Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 V 2 4 ‘2 7 2 V 3 þ 1 JS ¼ F ð4ÞL ðV 3 þ 1ÞðV 22 ‘22 ÞðV 2 8 ‘2 2ÞðV 2 8 ‘2 4Þ½JðJ þ 1Þ‘2 ð‘2 7 1Þ½JðJ þ 1Þð‘2 7 1Þð‘2 7 2Þ: e
ð15Þ In the above presented equations, gi is the degeneracy of the vibrational mode i: gi ¼1 for i¼1,3 and gi ¼2 for i¼2. It has been shown that this polyad model of effective Hamiltonian works very well [8–23] except in the cases of interpolyad resonance Coriolis and anharmonic interactions [8–10,14–23]. To take into account these interpolyad resonance interactions we suggested a nonpolyad model of effective Hamiltonian [30,31]. The fitting of the parameters of the nonpolyad model of effective Hamiltonian is under progress. The preliminary results show that this model allows solving the problem of the interpolyad resonance interactions but much work is still needed to achieve a global modeling of all available line positions. We then decided as a first step to publish the set of parameters of the polyad model of effective Hamiltonian because it is widely used but still unpublished. As the mixing between the normal mode ðV 1 V ‘22 V 3 Þ vibrational states can be strong, the triplet {P¼2V1 þ V2 þ4V3, ‘2, i} is used for the labeling of the vibrational states, where the index i increases with the energy. 3. Least-squares fitting The parameters of the effective Hamiltonian have been fitted to the measured line positions collected from the literature [8,9,11,13–26,33–69]. For these purposes a data file of measured line positions was created by gathering all the published line lists from the microwave region up to 9700 cm 1. The characteristics of the involved experimental sources are presented in Table 1. These data were
a transition between an upper state i and a lower state j, Ei and Ej being the Ritz energies (term values). When necessary, a calibration factor was used to correct the observed line positions. The calibration factors included in Table 1 have been obtained in the result of the solution of the Ritz equations (see Ref.[32] for details). The precise microwave and laser heterodyne data were used as reference data. They are marked by symbol 1.0c in column 3 of Table 1. A calibration factor equal to 1.000000000 presented in this column does mean that the respective experimental source does not need the calibration or the calibration factor could not be found using the existing set of data. Some bands were studied by several authors. As a general rule, all the reported position values were included into the fit. Nevertheless, many of the bands studied in Refs. [13,19,68] were later remeasured with a higher accuracy and then not involved into the fit. From the analysis performed in Refs. [14–23] and using the results of the preliminary fits, a number of bands perturbed via interpolyad resonance interactions were identified. The majority of these bands were excluded from the final fit. Nevertheless, the lines of some perturbed bands which are far from the energy levels crossing points were preserved. It was found that beginning with P ¼18 the polyads strongly overlap, i.e. that some vibrational states belonging to different polyads have close energies. As a result of their close vicinity, the majority of the respective observed bands are perturbed via resonance interpolyad interactions. We then
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
Table 1 Spectrum-by-spectrum analysis of the experimental data and statistics of the
1007
14
N216O global line position fit. b
References
Type of spectruma
Wavenumber range (in cm 1)
Calibration factor
Precision (in 10 3 cm 1)
Nfit/Ntot
[33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46,47] [48] [49] [50] [51] [24] [52] [53] [54] [55] [56] [57] [25] [58] [59] [60] [61] [62] [63] [26] [23] [64] [65] [20] [21] [22] [66] [19] [67] [68,13], S2d [68,13], S1d [69] [16] [17]
MW MW MW MW MW MW MW MW HET HET HET FTS FTS FTS FTS FTS FTS FTS EMISSION FTS HET HET HET HET HET EMISSION FTS FTS FTS FTS CRDS CRDS ICLAS CRDS FTS DIODE CRDS CRDS CRDS FTS FTS FTS FTS FTS ICLAS ICLAS ICLAS
20.8–26.1 20.9–24.3 1.6–4.2 12.5–18.5 0.8–2.5 4.1–10.1 50.1–50.2 3.3–10.1 1256–1339 1256–1331 896–1074 542–646 1132–4750 900–2393 1224–4665 554–620 903–1119 3676–7796 2060–2224 1118–1343 4338–4750 1036–1084 1104–1109 1833–1913 1590–1672 896–989 2061–2267 3584–8099 1100–1360 3399–3499 20–48 7788–7797 7783–7789 3900–4090 7647–7919 1831–3192 7515–7797 6001–6885 5906–6833 6759–7066 2098–2231 5313–8955 2308–2605 6700–8727 8837–9620 9362–9420 8836–10,079 9556–9972
1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 1.0c 0.999999910 1.000000000 1.000000000 0.999999990 1.000000070 0.999999920 1.000000000 1.000000050 0.999999824 1.0c 1.0c 1.0c 1.0c 1.0c 1.000000010 0.999999985 0.999999857 1.000000000 0.999998803 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000 1.000000447 0.999999990 1.000000000 1.000000000 0.999999228 1.000000000 1.000000402 1.000003197 1.000002582 1.000000000 1.000000000 0.999999000
0.00066 0.00066 0.001 0.0017 0.0033 0.0033 0.0066 0.02 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.4 0.4 0.4 0.4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 5.0 5.0 5.0 5.0 5.0 10.0
5/5 59/60 4/4 90/90 3/3 35/35 3/3 15/15 14/14 14/14 129/129 341/355 240/240 2252/2282 3228/3297 236/244 79/79 1287/1367 2566/2670 641/646 39/39 9/9 29/31 8/8 18/18 1855/1860 3068/3241 3297/3314 28 32/32 3/4 8/8 574/583 1581/1667 3638/3660 534/544 4770/5074 2039/2155 1257/1347 439/531 516/1323 148/148 1235/1482 281/316 62/62 339/503 305/423
RMS (in 10 3 cm 1) 0.0009 0.0042 0.0030 0.0058 0.0017 0.1111 0.0258 0.005 0.37 0.10 0.04 0.19 0.17 0.31 0.71 0.16 0.06 0.93 0.69 0.23 0.18 0.09 0.32 0.18 0.34 1.30 1.9 1.4 0.8 0.1 1.1 0.9 1.4 4.3 0.7 3.0 5.5 6.5 5.1 4.0 7.4 2.2 5.5 13.2 13.2 13.9 21.5
a MW, microwave; HET, laser heterodyne; FTS, Fourier transform; EMISSION, emission; CRDS, cavity ring down; ICLAS, intracavity laser absorption; DIODE, diode laser absorption. b Nfit is the number of lines included in the fit, Ntot is the total number of lines in the source. c Reference spectra. d S1—FTS spectrum above 8800 cm 1 and S2—FTS spectrum below 8800 cm 1. Different calibrations were used in the cited references for these spectra.
decided to limit the input data set to the bands with upper vibrational states belonging to polyads with numbers P r17. Table 1 includes for each data source, the total number and the number of lines included in the fit. The list of the P r17 perturbed bands excluded from the fit is given in Table 2. Overall about 7% of lines (perturbed, badly measured and misassigned) in the selected polyad range (Pr17) were excluded from the fit. Note that between 9700 and 15,000 cm 1, a total of 2384 lines of 32 bands with upper vibrational states belonging to
polyads with numbers 18rPr28 were measured but not involved into the fit. Overall, 37 353 line positions were fitted using 138 effective Hamiltonian parameters. The weighted standard deviation is w ¼4.06 and the global root mean squares of the residuals is RMS¼0.00423 cm 1. The fitted set of effective Hamiltonian parameters is presented in Table 3. This set of parameters reproduces the input data set involving transitions from the MW up to 9700 cm 1 with the accuracies close to the experimental uncertainties.
1008
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
Table 2 List of the 14N216O bands (P o17 for upper vibrational state) perturbed by interpolyad resonance interactions. The lines which were excluded from the fit are given in the last column. Banda
Band center (cm 1)b
Interacting states
Jcrossc
Interaction type
Excluded lines e-e: P8-P19, R6-R17 f-f: P13-P25, R11-R23 all P41-P64, R39-R54 P51-P55, R49-R64 e-e: P2-P13, R1-R15 f-f: P6-P31, R4-R29 f-e: Q10-Q12 e-f: Q1-Q18 e-e: P45-P49, R42-R50 e-e: P8-P13, R3-R11 f-f: P7-P35, R6-R30 P31-P50, R29-R52 P11-P21, R9-R19 e-e: P25-P46, R24-R55 f-f: P25-P41, R23-R39 P23, P24 All e-e: P23-P36, R21-R28 f-f: P20-P36, R18-R28 All R26-R36 All All All All
3310-0110 [51]
5029.001
(9 1 8)2(10 2 4)
e: 13; f: 18
Coriolis
0621-0110 4200-0000 2600-0000 5110-0110
6058.668 6192.271 6303.459
(9 1 8)2(10 2 4) (10 0 9)2(11 1 1) (10 0 10)2(11 1 2) (11 1 11)2(12 2 12)
e: 13; f: 18 91 110 e: 10; f: 16
Coriolis Coriolis Coriolis Coriolis
[51] [20] [20] [20]
5110-0110 [20] 0821-0110 [21]
6303.459
(11 1 11)2(12 0 7) (11 1 11) 2(12 2 12)
59 e: 10; f: 16
Coriolis Coriolis
0801-0000 [22] 0333-0330 [20] 1223-0220 [23]
6882.692 6453.897 7710.776
(11 1 11)2(12 0 7) (15 3 2)2(13 3 27) (16 2 7)2(15 1 13)
59 e, f: 15 e, f: 32
Coriolis Anharmonic Coriolis
5400-0000 [19] 1313-0110 [19] 2113-0110 [19]
8810.780 8831.873 8948.507
(14 0 19)2(16 0 3) (17 1 4)2(15 1 19) (17 1 7)2(15 1 20)
25
Anharmonic Anharmonic Anharmonic
d
0912-0000 4401-0000d 5600-0000d 3312-0000d 6400-0000d 7200-0000d
[16] [16] [17] [17] [17] [16]
9517.883 9874.303 9885.108 9975.202 10,062.079
(17 (17 (16 (17 (16 (16
1 1 0 1 0 0
6)2(16 0 17) 6)2(16 0 17) 22)2(18 0 3) 14)2(18 0 3) 23)2(18 0 6) 24)2(18 0 7)
e: 31; f: 25 35 35
62
Coriolis Coriolis Anharmonic Coriolis Anharmonic Anharmonic
a
Labeling according to a cited reference. Approximate value. c Value of J corresponding to an energy level crossing with a perturber. d Labeling according to a principal value of the expansion coefficients of an eigenfunction. The triplets {P, ‘2, i} are used for the labeling of the vibrational states in the respective references. b
The respective RMS value for each involved source is given in the last column of Table 1. In Fig. 1 the plot of the residuals versus wavenumber is presented. As it was expected the residuals increase with the wavenumber. 4. Conclusion The 14N216O line positions collected in the literature has been satisfactory modeled using a polyad model of effective Hamiltonian. This model does not take into account the interpolyad resonance interactions. A number of observed lines (about 2%) belonging to the Pr17 bands perturbed by interpolyad resonance interactions were then excluded from the line position fit. We found that the polyad model of effective Hamiltonian reproduces satisfactory the line positions of the transitions between vibrational states belonging to polyads with Pr17 i.e. up to about 9700 cm 1. As a result, the fit was limited to the bands with Pr17. The set of 138 effective Hamiltonian parameters was fitted to 37,353 observed line positions of 325 bands collected from the literature with dimensionless weighted standard deviation equal to 4.06. The fitted set of parameters reproduces the line positions involved in to the fit with RMS¼ 0.00423 cm 1. The predicted line positions with this set of effective Hamiltonian parameters can be used for the analysis of the experimental spectra even in a larger wavenumber range up to
15,000 cm 1. Fig. 2 shows that for the majority of the observed bands in 9700–15,000 cm 1 region [13,14,68, 70] the residuals between observed and predicted line positions remain small. The global modeling of 14N216O high resolution spectra using nonpolyad model of effective Hamiltonian is under progress. In the cases of the rare isotopologues: 14N15N16O [8–10], 15N14N16O [9,10], 15N216O [11], 14N218O [12] and 14 N217O [12] we have managed to fit all line positions and obtained satisfactory values for the global RMS. These results could be obtained because the set of available line positions is more restricted for the minor isotopologues than for the principal one and limited to 8500 cm 1 in wavenumbers. Even if larger residuals were obtained for the bands perturbed by interpolyad resonance interactions, these perturbations affect very few bands observed for the minor isotopologues. In addition, in the high wavenumber region, only the strongest bands were detected and these strong bands are usually not perturbed by interpolyad resonance interactions It is very interesting to compare the results of the global fits for nitrous oxide molecule to those for carbon dioxide [71–77]. Polyad model of effective Hamiltonian works very well in the case of CO2 molecule because all resonance Coriolis interactions are intrapolyad interactions [78] and due to the higher symmetry, interpolyad resonance anharmonic interactions take place only for
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
Table 3 The effective Hamiltonian parameters for N
Parameter
Diagonal vibrational parameters o1 1 2 o2 3 o3 4 x11 5 x12 6 x13 7 x22 8 x23 9 x33 10 x‘‘ c 11 y111 12 y112 13 y113 14 y122 15 y123 16 y133 17 y222 18 y223 19 y233 20 y333 21 y1‘‘
14
N216O.
Value (cm 1)
1298.2656(57)b 596.3067(14) 2282.2650(58) 5.115(28) 5.43922(62) 22.85(11) 1.12389(12) 14.55799(59) 15.0972(11) 0.594 1.209(18) 0.586(20) 6.98(12) 0.1137(99) 4.152(80) 3.41(15) 0.17496(83) 0.842(12) 0.1444(14) 0.0913(22) 0.3347(99)
Diagonal rotational and vibrational–rotational parameters 43 Be 0.42112438(17) 44 a1 0.190953(12) 45 a2 0.0574713(54) 46 a3 0.3466413(89) 47 g11 0.1410(20) 48 g12 0.0947(11) 49 g13 0.0912(84) 50 g22 0.09268(26) 51 g23 0.31444(35) 52 g33 0.05507(45) 53 g‘‘ 0.04091(22) 54 e111 0.6310((5) 55 e112 0.758(29) 56 e122 0.603(20)
Ordera
N
Parameter
10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
y2‘‘ y3‘‘ z1111 z1112 z1113 z1122 z1123 z1133 z1222 z1223 z1333 z2222 z2223 z2233 z2333 z3333 z11‘‘ z12‘‘ z22‘‘ z23‘‘ z33‘‘
0.16955(83) 0.352(11) 0.025(14) 0.199(17) 0.241(14) 0.165(28) 1.64(13) 13.03(29) 0.0611(78) 0.234(21) 4.42(13) 0.03498(55) 0.1811(62) 0.203(14) 0.0373(20) 0.0900(29) 0.053(19) 0.1473(65) 0.01706(54) 0.1795(61) 0.248(14)
10 1 10 1 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2
10 2 10 2 10 2 10 4 10 4 10 4 10 4 10 4 10 4 10 4 10 6 10 6 10 6
57 58 59 60 61 62 63 64 65 66 67 68 69 70
e123 e133 e222 e223 e333
3.697(84) 0.804(74) 0.0776(35) 0.7864(54) 0.2114(76) 0.172915(22) 0.1697(11) 0.26451(76) 0.048014(63) 1.091(41) 1.846(72) 0.435(14) 1.801(33) 1.69(28)
10 6 10 6 10 6 10 6 10 6 10 6 10 8 10 8 10 8 10 10 10 10 10 10 10 10 10 14
De
b1 b2 b3
Z11 Z13 Z22 Z23 He
Parameters of ‘-doubling matrix element 71 Le 0.196403(11) 72 L1 0.0936(32) 73 L2 0.19356(94) 74 L3 0.3148(11) 75 L11 3.50(14) 76 L12 0.247(98)
10 3 77 L13 10 5 78 L22 5 10 79 L23 10 5 80 L33 10 7 81 LJ 10 7
Parameters of Fermi interaction matrix elements V 1 V 2 ‘2 V 3 J Hef f V 1 1 V 2 þ 2 ‘2 þ D‘2 V 3 J 82 Fe 19.62384(27) 88 F23 83 F1 0.3852(42) 89 F33 84 F2 0.31696(22) 90 F ‘‘ 85 F3 0.0996(82) 91 FJ 2 86 F11 0.457(30) 10 92 F Le 87 F12 0.637(20) 10 2 93 F LJ Parameters of Fermi interaction matrix element /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 2 V 2 ‘2 V 3 þ 1 JS 18.54(24) 100 94 F e ð2Þ 95 1.335(24) 101 F ð2Þ 96 97 98 99
1 F ð2Þ 2 F ð2Þ 3 F ð2Þ 11 F ð2Þ 12
0.314(16)
102
1.288(29)
103
0.217(69) 5.28(19)
10 2 10
104
10 7 10 7 10 7 10 7 10 9
1.362(39) 2.000(73) 0.0569(19) 1.26602(57) 0.8355(22)
10 2 10 2 10 2 10 4 10 5
0.1019(12)
10 9
F ð2Þ 13
26.763(58)
10 2
F ð2Þ 22
0.744(62)
10 2
F ð2Þ 23 F ð2Þ 33 F ð2Þ J
2.76(17)
10 2
7.38(24)
10 2
0.461(16)
10 4
22
0.0893(23)
Ordera
2
1
F ð3Þ 2
Value (cm 1)
2.54(19) 0.872(13) 5.302(84) 2.080(22) 0.2270(15)
Parameters of anharmonic interaction matrix elements /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 1 V 2 2 ‘2 þ D‘2 V 3 þ 1 JS 3.377(44) 111 105 F e ð3Þ F ð3Þ 13 106 0.2028(95) 112 F ð3Þ F ð3Þ 107
1009
113
F ð3Þ 23
0.808(97)
10 2
0.3008(72)
10 2
0.992(27)
10 2
1010
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
Table 3 (continued ) N
Parameter
Value (cm 1)
108
F ð3Þ 3
0.2470(30)
109
F ð3Þ 11 F ð3Þ 12
110
Ordera
N
Parameter
114
F ð3Þ 33
0.781(55)
10
2
115
1.999(44)
10 2
116
F ð3Þ J F ð3ÞL J
Parameters of anharmonic interaction matrix elements /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 V 2 4 ‘2 þ D‘2 V 3 þ 1 JS 0.2388(28) 120 117 F ð4Þ F ð4Þ e 3 118 0.546(53) 10 2 121 F ð4Þ F ð4Þ J 1 119
F ð4Þ 2
Parameters of anharmonic interaction matrix element /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 2 V 2 þ 4 ‘2 V 3 JS 0.785(53) 10 3 125 123 F ð5Þ F ð5Þ 1 3 124 0.571(35) 10 3 126 F ð5Þ F ð5Þ J 2 Parameters of anharmonic interaction matrix element /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 4 V 2 ‘2 V 3 þ 2 JS 0.517(12) 129 127 F ð6Þ F ð6Þ e 2 1 ð6Þ 128 0.2177(62) 10 130 F F ð6Þ 1
J
Parameters of anharmonic interaction matrix element /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 3 V 2 þ 2 ‘2 V 3 þ 1 JS 0.764(41) 10 1 134 131 F ð7Þ F ð7Þ e 3 ð7Þ 132 0.618(36) 10 2 135 F F ð6Þ 1 F ð7Þ 2
133
J
0.332(20)
10
Value (cm 1) 1.47(35) 0.105(43) 0.791(97)
Ordera 10 2 10 5 10 10
2.192(38)
10 2
0.5126(84)
10 5
0.91(23)
10 7
2.491(58)
10 3
0.2477(90)
10 6
0.2251(52)
10 1
0.47(10)
10 6
0.694(54)
10 2
0.431(46)
10 6
2
Parameters of anharmonic interaction matrix elements /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 3 V 2 2 ‘2 V 3 þ 2 JS, /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 2 V 2 4 ‘2 V 3 þ 2 JS and /V 1 V 2 ‘2 V 3 J9Hef f 9V 1 þ 1 V 2 6 ‘2 V 3 þ 1 JS 0.350(17) 136 F ð8Þ e 137 0.2222(42) F ð9Þ
10 1
e
b
Residuals, in 10-3 cm-1
c
F ð10Þ e
0.283(31)
10 3
Order of magnitude of the parameter value. Uncertainties in parentheses represent one standard deviation in units of the last quoted digit. Fixed to the value given in Ref. [29].
60
1.5
40
1.0 Residuals, cm-1
a
138
10 1
20 0 -20
0.5 0.0 -0.5 -1.0
-40 -60 0
2000
4000
6000
8000
10000
-1.5 9000
12000
15000
Wavenumber, cm-1
Wavenumber, cm-1 N216O line positions using the
Fig. 2. Residuals between observed [13,14,68,70] and predicted line positions of 14N216O in the 9700–15,000 cm 1 region.
asymmetric isotopologues. Only a few occurrences of interpolyad resonance perturbations were evidenced, all concerning the asymmetric isotopologues of CO2 molecule [76,79–81].
CAS (China) in the frame of Groupement de Recherche International SAMIA (Spectroscopie d’Absorption des Mole´cules d’Inte´rˆet Atmosphe´rique).
Fig. 1. Residuals of the global fit of the polyad model of effective Hamiltonian.
14
References Acknowledgments This work is jointly supported by RFBR (Russia, Grants N09-05-93105 and N 10-05-91176), CNRS (France) and
[1] Teffo JL, Perevalov VI, Lyulin OM. Reduced effective Hamiltonian for global treatment of rovibrational energy levels of nitrous oxide. Journal of Molecular Spectroscopy 1994;168:390–403. [2] Perevalov V.I., Tashkun S.A., Teffo J.L. Global fitting of rovibrational line positions of nitrous oxide. In: Sixteenth colloquium on high
V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
resolution molecular spectroscopy, Dijon (France). 6–10 September 1999, Poster D2, p. 103. Lyulin OM, Perevalov VI, Teffo JL. Effective dipole moment and band intensities of nitrous oxide. Journal of Molecular Spectroscopy 1995;174:566–80. Lyulin OM, Perevalov VI, Teffo JL. Fitting of line intensities using the effective operator approach: the 4 mm region of 14N216O. Journal of Molecular Spectroscopy 1996;180:72–4. Daumont L, Vander Auwera J, Teffo JL, Perevalov VI, Tashkun SA. Line intensity measurements in 14N216O and their treatment using the effective dipole moment approach. I. The 4300 to 5200 cm 1 region. Journal of Molecular Spectroscopy 2001;208:281–91. Daumont L, Claveau C, Debacker-Barilly MR, Hamdouni A, RegaliaJarlot LR, Teffo JL, et al. Line intensities of 14N216O: the 10 mm region revisited. Journal of Quantitative Spectroscopy and Radiative Transfer 2002;72:37–55. Daumont L, Vander Auwera J, Teffo JL, Perevalov VI, Tashkun SA. Line intensity measurements in 14N216O and their treatment using the effective dipole moment approach. II. The 5400–11,000 cm 1 region. Journal of Quantitative Spectroscopy and Radiative Transfer 2007;104:342–56. Ni HY, Song KF, Perevalov VI, Tashkun SA, Liu AW, Wang L, et al. Fourier-transform spectroscopy of 14N15N16O in the 3800– 9000 cm 1 region and global modeling of its absorption spectrum. Journal of Molecular Spectroscopy 2008;248:41–60. Wang CY, Liu AW, Perevalov VI, Tashkun SA, Song KF, Hu SM. Highresolution infrared spectroscopy of 14N15N16O and 15N14N16O in the 1200–3500 cm 1 region. Journal of Molecular Spectroscopy 2009;257: 94–104. Tashkun SA, Perevalov VI, Kochanov RV, Liu AW, Hu SM. Global fittings of 14N15N16O and 15N14N16O vibrational–rotational line positions using the effective Hamiltonian approach. Journal of Quantitative Spectroscopy and Radiative Transfer 2010;111:1089–105. Lyulin OM, Jacquemart D, Lacome N, Tashkun SA, Perevalov VI. Line parameters of 15N216O from Fourier transform measurements in the 5800–7600 cm 1 region and global fitting of line positions from 1000–7600 cm 1. Journal of Quantitative Spectroscopy and Radiative Transfer 2010;111:345–56. Vlasova AV, Perevalov BV, Tashkun SA, Perevalov VI. Global fittings of the line positions of the rare isotopic species of the nitrous oxide molecule. In: Proceedings of the XVth symposium on high- resolution molecular spectroscopy, Nizhny Novgorod, Russia, vol. 6580, SPIE; 2006. p. 658007. Weirauch G, Kachanov AA, Campargue A, Bach M, Herman M, Vander Auwera J. Refined investigation of the overtone spectrum of nitrous oxide. Journal of Molecular Spectroscopy 2000;202:98–106. Campargue A, Weirauch G, Tashkun SA, Perevalov VI, Teffo JL. Overtone spectroscopy of N2O between 10,000 and 12,000 cm 1: a test of the polyad approach. Journal of Molecular Spectroscopy 2001;209:198–206. Bertseva E, Kachanov AA, Campargue A. Intracavity laser absorption spectroscopy of N2O with a vertical external cavity surface emitting laser. Chemical Physics Letters 2002;351:18–26. Ding Y, Perevalov VI, Tashkun SA, Teffo JL, Bertseva E, Campargue A. Weak overtone transitions of N2O around 1.05 mm by ICLASVECSEL. Journal of Molecular Spectroscopy 2003;220:80–6. Bertseva E, Campargue A, Perevalov VI, Tashkun SA. New observations of weak overtone transitions of N2O by ICLAS-VeCSEL near 1.07 mm. Journal of Molecular Spectroscopy 2004;226:196–200. Milloud R, Perevalov VI, Tashkun SA, Campargue A. Rotational analysis of 6n3 and 6n3 þ n2 n2 bands of 14N216O from ICLAS spectra between 12,760 and 12,900 cm 1. Journal of Quantitative Spectroscopy and Radiative Transfer 2011;112:553–7. Wang L, Perevalov VI, Tashkun SA, Gao B, Hao LY, Hu SM. Fourier transform spectroscopy of N2O weak overtone transitions in the 1–2 mm region. Journal of Molecular Spectroscopy 2006;237:129–36. Liu AW, Kassi S, Malara P, Romanini D, Perevalov VI, Tashkun SA, et al. High sensitivity CW-cavity ring down spectroscopy of N2O near 1.5l mm (I). Journal of Molecular Spectroscopy 2007;244: 33–47. Liu AW, Kassi S, Perevalov VI, Tashkun SA, Campargue A. High sensitivity CW-cavity ring down spectroscopy of N2O near 1.5l mm (II). Journal of Molecular Spectroscopy 2007;244:48–62. Liu AW, Kassi S, Perevalov VI, Hu SM, Campargue A. High sensitivity CW-cavity ring down spectroscopy of N2O near 1.5 mm (III). Journal of Molecular Spectroscopy 2009;254:20–7. Liu AW, Kassi S, Perevalov VI, Tashkun SA, Campargue A. High sensitivity CW-Cavity Ring Down Spectroscopy of N2O near 1.28 mm. Journal of Molecular Spectroscopy 2011;267:191–9.
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[24] Bailly D, Vervloet M. 14N‘216O in Emission in the 4.5-mm region: ‘ transitions V1V2V3- V1V2(V3-1) occurring between highly excited vibrational states. Journal of Molecular Spectroscopy 2001;209: 207–15. [25] Bailly D, Pirali O, Vervloet M. 14N216O in Emission in the 4.5mm ‘ region: high excitation of the banding mode transitions V1V2V3‘ V1V2(V3-1) with (2V1 þ V2) ¼5 occurring between highly excited vibrational states. Journal of Molecular Spectroscopy 2003;222: 180–90. [26] Herbin H, Picque´ N, Guelachvili G, Sorokin E, Sorokina I. N2O weak lines observed between 3900 and 4050 cm 1 from long path absorption spectra. Journal of Molecular Spectroscopy 2006;238:256–9. [27] Horneman VM. High accurate peak positions for calibration purposes with the lowest fundamental bands n2 of N2O and CO2. Journal of Molecular Spectroscopy 2007;241:45–50. [28] Pliva J. Molecular constants of nitrous oxide, 14N216O. Journal of Molecular Spectroscopy 1968;27:461–88. [29] Teffo JL, Chedin A. Internuclear potential and equilibrium structure of the nitrous oxide molecule from rovibrational data. Journal of Molecular Spectroscopy 1989;135:389–409. [30] Tashkun SA, Perevalov VI, Teffo JL. Global fitting of vibrationrotation line positions of N2O using imterpolyad model of effective Hamiltonian. In: International workshop ‘‘Atmospheric Spectroscopy Applications’’. 25–28 August 2002. p. 41 [Abstracts]. [31] Perevalov VI, Tashkun SA, Lyulin OM, Teffo JL. Global modeling of high-resolution spectra of linear molecules CO2, N2O and C2H2. In: Perrin A, Ben Sari-Zizi N, Demaison J, editors. Remote sensing of atmosphere for environmental security. Springer; 2006. p. 139–59. [32] Tashkun SA, Perevalov VI, Teffo JL, Lecoutre M, Huet TR, Campargue A, et al. 13C16O2: Global treatment of vibrational–rotational spectra and first observation of the 2n1 þ 5n3 and n1 þ2n2 þ 5n3 absorption bands. Journal of Molecular Spectroscopy 2000;200:162–76. [33] Morino I, Fabian M, Takeo H, Yamada KMT. High-J rotational transitions of NNO measured with the NAIR Terahertz Spectrometer. Journal of Molecular Spectroscopy 1997;185:142–6. [34] Morino I, Yamada KMT, Maki AG. Terahertz measurements of rotational transitions in vibrationally excited states of N2O. Journal of Molecular Spectroscopy 1999;196:131–8. [35] Bogey M. Microwave absorption spectroscopy in the n3 states of OCS and N2O through energy transfer from N2*. Journal of Physics B: Atomic and Molecular Physics 1975;11:1934–8. [36] Andreev BA, Burenin AV, Karyakin EN, Krupnov AF, Shapin SM. Submillimeter wave spectrum and molecular constants of N2O. Journal of Molecular Spectroscopy 1976;62:125–48. [37] Lafferty WJ, David R, Lide DR. Rotational constants of excited vibrational states of 14N216O. Journal of Molecular Spectroscopy 1964;14:407–8. [38] Pearson R, Sullivan T, Frenkel L. Microwave spectrum and molecular parameters for 14N216O. Journal of Molecular Spectroscopy 1970;34:440–9. [39] Vanek MD, Jennings DA, Wells JS, Maki AG. Frequency measurements of high-J rotational transitions of OCS and N2O. Journal of Molecular Spectroscopy 1989;138:79–83. [40] Burrus CA, Gordy W. Millimeter and submillimeter wave spectroscopy. Physical Review 1956;101:599–602. [41] Wells JS, Hinz A, Maki AG. Heterodyne frequency measurements on N2O between 1257 and 1340 cm 1. Journal of Molecular Spectroscopy 1985;114:84–96. [42] Hinz A, Wells JS, Maki AG. Heterodyne measurements of hot bands ¨ Physik D and isotopic transitions of N2O near 7.8 mm. Zeitschrift fur 1987;5:351–8. [43] Tachikawa M, Evenson KM, Zink LR, Maki AG. Frequency measurements of 9- and 10-mm N2O laser transitions. IEEE Journal of Quantum Electronics 1996;32:1732–6. [44] Jolma K, Kauppinen J, Horneman VM. Vibration-rotation spectrum of N2O in the region of the lowest fundamental n2. Journal of Molecular Spectroscopy 1983;101:278–84. [45] Brown LR, Toth RA. Comparison of the frequencies of NH3, CO2, H2O, N2O, CO and CH4 as infrared calibration standards. Journal of the Optical Society of America 1985;B2:842–56. [46] Toth RA. Frequencies of N2O in the 1100- to 1440-cm 1 region. Journal of the Optical Society of America 1986;B3:1263–81. [47] Toth RA. N2O vibration-rotation parameters derived from measurements in the 900-1090- and 1580–2380-cm 1 regions. Journal of the Optical Society of America 1987;B4:357–74. [48] Toth RA. Line-frequency measurements and analysis of N2O between 900 and 4700 cm 1. Applied Optics 1991;30:5289–315. [49] Tan TL, Looi EC, Lua KT. Hot-band spectrum of N2O near 589 cm 1. Journal of Molecular Spectroscopy 1992;154:218–22.
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V.I. Perevalov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 113 (2012) 1004–1012
[50] Barbe A. 1999. Private communication. [51] Toth RA. Line Positions and Strengths of N2O between 3515 and 7800 cm 1. Journal of Molecular Spectroscopy 1999;197:158–87. [52] Guelachvili G. Absolute N2O wavenumbers between 1118 and 1343 cm 1 by Fourier transform spectroscopy. Canadian Journal of Physics 1982;60:1334–47. [53] Pollock CR, Petersen FR, Jennings DA, Wells JS, Maki AG. Absolute frequency measurements of the 0002-0000, 2001-0000, and 12010000 bands of N2O by heterodyne spectroscopy. Journal of Molecular Spectroscopy 1984;107:62–71. [54] Zink LR, Wells JS, Maki AG. Heterodyne frequency measurements on N2O near 1060 cm 1. Journal of Molecular Spectroscopy 1987;123:426–33. [55] Wells JS, Jennings DA, Hinz A, Murray JS, Maki AG. Heterodyne frequency measurements on N2O at 5.3 and 9.0 mm. Journal of the Optical Society of America 1985;B2:857–61. [56] Vanek MD, Schneider M, Wells JS, Maki AG. Heterodyne measurements on N2O near 1635 cm 1. Journal of Molecular Spectroscopy 1989;134:154–8. [57] Maki AG, Wells JS, Vanek MD. Heterodyne frequency measurements on N2O near 930 cm 1. Journal of Molecular Spectroscopy 1989;138:84–8. [58] Amiot C, Guelachvili G. Vibration-rotation bands of 14N216O: 1.2 micron-3.3 micron region. Journal of Molecular Spectroscopy 1974;51:475–91. [59] Esplin MP, Barowy WM, Huppi J, Vanasse GA. High resolution Fourier spectroscopy of nitrous oxide at elevated temperatures. Microchimica Acta 1988;II:403–7. [60] Toth RA. Linelist of N2O parameters from 500 to 7500 cm 1. Available via WEB site SISAM.N2O. [61] Yamada KMT. Pure rotational spectrum of NNO in the far infrared ¨ Naturforschung 1990;45a:837–8. region. Zeitschrift fur [62] He Y, Hippler M, Quack M. High-resolution cavity ring-down absorption spectroscopy of nitrous oxide and chloroform using a nearinfrared cw diode laser. Chemical Physics Letters 1998;289:527–34. [63] Hippler M, Quack M. Cw cavity ring-down infrared absorption spectroscopy in pulsed supersonic jets: nitrous oxide and methane. Chemical Physics Letters 1999;314:273–81. [64] Amiot C, Guelachvili G. Extension of the 106 samples Fourier spectrometry to the Indium Antimonide region: Vibration-rotation bands of 14N216O: 3.3–5.5 mm region. Journal of Molecular Spectroscopy 1976;59:171–90. [65] Oshika H, Toba A, Fujitake M, Ohashi N. Newly observed vibrational bands of N2O in 1.3 mm region. Journal of Molecular Spectroscopy 1999;179:324–5. [66] Farrenq R, Dupre-Maquaire J. Vibrational luminescence of N2O excited by discharge. Rotation–vibration constants. Journal of Molecular Spectroscopy 1974;49:268–79. [67] Krell JM, Sams RL. Vibration-rotation bands of nitrous oxide: 4.1 micron region. Journal of Molecular Spectroscopy 1974;51:492–507. [68] Campargue A, Permogorov, Bach M, Abbouti Temsamani M, Vander Auwera J, Fujii M. Overton spectroscopy in nitrous oxide. Journal of Chemical Physics 1995;103:5931–8.
[69] Garnache A, Campargue A, Kachanov AA, Stoeckel F. Intracavity laser absorption spectroscopy near 9400 cm 1 with a Nd:glass laser: application to 14N216O. Chemical Physics Letters 1998;292:698–704. [70] Campargue A. The near-infrared absorption spectrum of nitrous oxide: analysis of the 5n3 and n1 þ 5n3 clusters. Chemical Physics Letters 1996;259:563–7. [71] Tashkun SA, Perevalov VI, Teffo JL, Rothman LS, Tyuterev VlG. Global Fitting of 12C16O2 vibrational–rotational line positions using the effective Hamiltonian approach. Journal of Quantitative Spectroscopy and Radiative Transfer 1998;60:785–801. [72] Tashkun SA, Perevalov VI, Teffo JL, Lecoutre M, Huet TR, Campargue A, et al. 13C16O2: Global treatment of vibrational–rotational spectra and first observation of the 2n1 þ 5n3 and n1 þ 2n2 þ 5n3 absorption bands. Journal of Molecular Spectroscopy 2000;200:164–75. [73] Tashkun SA, Perevalov VI, Teffo JL. Global fittings of the vibrational–rotational line positions of the 16O12C17O and 16 12 18 O C O isotopic species of carbon dioxide. Journal of Molecular Spectroscopy 2001;210:137–45. [74] Ding Y, Macko P, Romanini D, Perevalov VI, Tashkun SA, Teffo JL, et al. High sensitivity cw-cavity ringdown and Fourier transform absorption spectroscopies of 13CO2. Journal of Molecular Spectroscopy 2004;226:146–60. [75] Majcherova Z, Macko P, Romanini D, Perevalov VI, Tashkun SA, Teffo JL, et al. High-sensitivity CW-cavity ringdown spectroscopy of 12 CO2 near 1.5 mm. Journal of Molecular Spectroscopy 2005;230: 1–21. [76] Perevalov BV, Kassi S, Romanini D, Perevalov VI, Tashkun SA, Campargue A. Global effective Hamiltonians of 16O13C17O and 16 13 18 O C O improved from CW-CRDS observations in the 5900– 7000 cm 1 region. Journal of Molecular Spectroscopy 2007;241: 90–100. [77] Wang L, Perevalov VI, Tashkun SA, Song KF, Hu SM. Fourier transform spectroscopy of 12C18O2 and 16O12C18O in the 3800–8500 cm 1 region and the global modeling of the absorption spectrum of 12 18 C O2. Journal of Molecular Spectroscopy 2008;247:64–75. [78] Teffo JL, Sulakshina ON, Perevalov VI. Effective Hamiltonian for rovibrational energies and line intensities. Journal of Molecular Spectroscopy 1992;156:48–64. [79] Perevalov BV, Kassi S, Perevalov VI, Tashkun SA, Campargue A. High sensitivity CW-Cavity Ring Down Spectroscopy of 12C16O2, 16 12 17 O C O and 16O12C18O between 5851 and 7045 cm 1: line position analysis and critical review of the current databases. Journal of Molecular Spectroscopy 2008;252:143–59. [80] Perevalov BV, Perevalov VI, Campargue A. A (nearly) complete experimental linelist for 13C16O2, 16O13C18O, 16O13C17O, 13C18O2 and 17O13C18O by high-sensitivity CW-CRDS spectroscopy between 5851 and 7045 cm 1. Journal of Quantitative Spectroscopy and Radiative Transfer 2008;109:2437–62. [81] Campargue A, Song KF, Mouton N, Perevalov VI, Kassi S. High sensitivity CW-Cavity Ring Down Spectroscopy of five 13CO2 isotopologues of carbon dioxide in the 1.26–1.44 mm region (I): Line positions. Journal of Quantitative Spectroscopy and Radiative Transfer 2010;111:659–74.