Global fitting of line intensities of acetylene molecule in the infrared using the effective operator approach

Journal of Molecular Spectroscopy 218 (2003) 180–189 www.elsevier.com/locate/jms

Global fitting of line intensities of acetylene molecule in the infrared using the effective operator approachq V.I. Perevalov,a O.M. Lyulin,a D. Jacquemart,b C. Claveau,b J.-L. Teffo,b,* V. Dana,b J.-Y. Mandin,b and A. Valentinb a b

Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, 1, Akademicheskii av., 634055 Tomsk, Russia Laboratoire de Physique Mol
eculaire et Applications, (Unit
e mixte CNRS/Universit
e Pierre et Marie Curie), Case Courrier 76, Universit
e Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France Received 12 June 2002; in revised form 18 November 2002

Abstract The method of effective operators has been applied to the global fitting of line intensities of the acetylene molecule in the middle infrared. Simultaneous fittings of recently observed line intensities in the cold and hot bands lying in the 13.6, 7.8, and 5 lm regions have been performed. The eigenfunctions of the effective Hamiltonian developed for the global treatment of the vibration–rotation line positions of acetylene [O.M. Lyulin, V.I. Perevalov, S.A. Tashkun, J.-L. Teffo, in: Leonid N. Sinitsa (Ed.), 13th Symposium and School on High Resolution Molecular Spectroscopy, Proceedings of SPIE, vol. 4063, 2000, pp. 126–133] have been used in the calculations. The sets of effective dipole moment parameters obtained reproduce the observed line intensities within the experimental accuracy. The importance of l-type resonance, responsible for some large differences between intensities of the same lines in subbands having opposite parities, is exhibited and discussed. Ó 2003 Elsevier Science (USA). All rights reserved. Keywords: Acetylene; Infrared spectroscopy; Line intensities; HITRAN; GEISA

1. Introduction In a series of papers [1–18], the problem of the global modeling of high resolution spectra of the tri-atomic linear molecules CO2 and N2 O within the framework of the method of effective operators has been considered. It has been demonstrated that the suggested models of effective Hamiltonians and respective effective dipole moment operators reproduce and predict line positions and line intensities with an accuracy close to the experimental uncertainties. Recently, our modeling has been extended to the line positions of a four-atomic linear molecule, acetylene [19,20]. The present paper is devoted to the global modeling of line intensities of this molecule. For these purposes we use the eigenfunctions, obtained in [20], of the effective Hamiltonian developed in [19] for the global

treatment of the vibration–rotation line positions of acetylene in its ground electronic state. The effective dipole moment approach for the calculation of linestrengths is reviewed in Section 2. The results of the line intensity fittings are reported in Section 3. 2. Linestrength The absorption line intensity SN 0 J 0 e0 NJ e (in cm1 / molecule cm2 at temperature T in K) of a transition N 0 J 0 e0 NJ e, where N and J are, respectively, the vibrational index and angular momentum quantum number, and e ¼ 1 is the parity, is related to the transition moment squared (or linestrength) WN 0 J 0 e0 NJ e by the well-known equation S N 0 J 0 e0

NJ e ðT Þ

q

Supplementary data for this article is available on ScienceDirect. Corresponding author. Fax: +33-1-44-27-70-33. E-mail address: teff[email protected] (J.-L. Teffo). *

0022-2852/03/$ - see front matter Ó 2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0022-2852(02)00090-5

¼

8p3 CmN 0 J 0 e0 3hc

NJ e

expðhcENJ e =kT Þ QðT Þ

 ½1  expðhcmN 0 J 0 e0

NJ e =kT Þ WN 0 J 0 e0

NJ e ;

ð1Þ

V.I. Perevalov et al. / Journal of Molecular Spectroscopy 218 (2003) 180–189

where c is the speed of light, h is PlanckÕs constant, k is BoltzmannÕs constant, T is the sample temperature in Kelvin, ENJ e is the energy of the lower state, mN 0 J 0 e0 NJ e is the wavenumber of the line, Q is the total internal partition function, and C is the isotopic abundance. Within the framework of the method of effective operators, the linestrength is given by the following expression: X  eff     w 0 0 0 M eff weff 2 WN 0 J 0 e0 NJ e ¼ 3gNJ e NJe

Z

NJ e

MM 0

   X  X ¼ 3gNJ e   MM 0  V1 V2 V3 V4 V5  l4 l5 0

X

J

CNV1eV2 V3 V4 V5 l4 l5

V 0V 0V 0V 0V 0 1 2 3 4 5 l0 l0 4 5

V 0 V 0 V30 V40 V50 l04 l05 

V10 V20 V30 V40 V50 l04 l05 J 0 M 0 K 0 e0 2    eff   M V1 V2 V3 V4 V5 l4 l5 JMKe  : ð2Þ Z   

 J CN10 e02

In this expression, the sum is taken over magnetic quantum numbers M and M 0 of the lower and upper states, respectively, gNJ e is the nuclear statistic weight of the lower state, and J CNV1eV2 V3 V4 V5 l4 l5 are the expansion coefficients of the lower state eigenfunctions of the effective Hamiltonian on the Wang-type harmonic-oscillator rigid-rotor basis functions: X J V1 V2 V3 V4 V5 l4 l5 Weff CN e jV1 V2 V3 V4 V5 l4 l5 JMKei: ð3Þ NJMe ¼ V1 V2 V3 V4 V5 l4 l5 0

V 0 V 0 V 0 V 0 V 0 l0 l0

In the same way J CN10 e02 3 4 5 4 5 stands for the expansion coefficients of the upper state. The definition of Wangtype basis functions is given below: 1 jV1 V2 V3 V4 V5 l4 l5 JMKei ¼ pffiffiffi ðjV1 V2 V3 V4 V5 l4 l5 i 2 jJMK ¼ l4 þ l5 i þ ejV1 V2 V3 V4 V5  l4  l5 i jJM  K ¼ l4  l5 iÞ; jV1 V2 V3 V4 V5 00JM0e ¼ 1i ¼ jV1 V2 V3 V4 V5 00ijJM0i:

ð4Þ ð5Þ

Here jV1 V2 V3 V4 V5 l4 l5 i and jJMKi are the eigenfunctions of the C2 H2 harmonic oscillators and rigid rotor, respectively. The label K ¼ l4 þ l5 in Eq. (4) defining the Wang-type basis functions jV1 V2 V3 V4 V5 l4 l5 JMKei is always positive or zero and, when K ¼ 0 and l4 6¼ 0, l5 6¼ 0, then l4 > 0 in this equation. The component of the effective dipole moment operator in the laboratory-fixed frame, MZeff , is P obtained from that of the dipole moment operator MZ ¼ a kaZ la , where la ða ¼ x; y; zÞ are the dipole moment components in the molecule-fixed frame, by the same unitary transformation ð6Þ M eff ¼ eiS MeiS ;

181

as the effective Hamiltonian is obtained from the vibration–rotation Hamiltonian HVR H eff ¼ eiS HVR eiS :

ð7Þ

In this work we use the eigenfunctions of the effective Hamiltonian suggested in [19] for the global treatment of vibration–rotation energy levels of the acetylene molecule and extended on to the higher-order terms in [20]. These eigenfunctions have been obtained by fitting the parameters of this effective Hamiltonian to the observed line positions of the vibration–rotation transitions involving energy levels below 8000 cm1 . The results of the line position fitting will be published elsewhere [21]. The effective Hamiltonian is based on the assumption [22] of the cluster (polyad) structure of the vibrational energy levels. This clustering arises due to the approximate relations between harmonic frequencies x1  x3  5x4  5x5 ;

ð8Þ

x2  3x4  3x5 :

ð9Þ

Each polyad is made up of the vibrational basis states, the quantum numbers of which fulfill the equation P ¼ 5V1 þ 3V2 þ 5V3 þ V4 þ V5 :

ð10Þ

Thus, the polyad can be labeled with the integer P and the series of bands can be labeled with the difference DP ¼ P 0  P ;

ð11Þ

where P 0 and P are integers numbering the upper and lower polyads, respectively. The vibrational index N labels the vibrational states within the polyad P. Throughout this paper we use a label V1 V2 V3 V4 V5 l4 l5 for the vibrational state, the principal contribution to which is given by the jV1 V2 V3 V4 V5 l4 l5 JKi basis function at J ¼ K ¼ l4 þ l5 . In addition, when K ¼ 0 and l4 6¼ 0; l5 6¼ 0, we use subscripts ‘‘+’’ for Rþ states and ‘‘)’’ for R states. The disadvantage of this label follows from its dependence in some cases on the accuracy of the effective Hamiltonian parameters. This label is convenient for us, however, because it is consistent with the notations of the effective dipole moment parameters (see below). Pl
ıva [23] suggested the label V1 V2 V3 ðV4 V5 Þl for a vibrational state with l ¼ l4 þ l5 , where l, contrary to l4 and l5 , is a rather good quantum number. When two states have the same principal vibrational quantum numbers, the same value of l, and the same symmetry, he used symbols ‘‘I’’ for the upper state and ‘‘II’’ for the lower state. In Table 1 we give the correspondence between Pl
ıvaÕs notations and our own for the bands involved in this work. In a previous paper [24] the following expression for the linestrength of the P 0 N 0 J 0 e0 PNJ e transition was obtained

182

WN 0 J 0 e0

V.I. Perevalov et al. / Journal of Molecular Spectroscopy 218 (2003) 180–189

NJ e

   X  ¼ ð2J þ 1ÞgNJ e   5V þ3V þ5V þV þV ¼P  1 2 l l3 4 5 4 5



X

J

CNV1eV2 V3 V4 V5 l4 l5

5DV1 þ3DV2 þ5DV3 þDV4 þDV5 ¼DP Dl4 Dl5

(

J 0 V1 þDV1 V2 þDV2 V3 þDV3 V4 þDV4 V5 þDV5 l4 þDl4 l5 þDl5 CN 0 e0

Dl4 Dl5 MDV UDJ DK ðJ ; KÞ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dl4 Dl5  fDV ðV ; l4 ; l5 Þð1 þ dl4 ;0 dl5 ;0 þ dl4 þDl4 ;0 dl5 þDl5 ;0  2dl4 ;0 dl5 ;0 dl4 þDl4 ;0 dl5 þDl5 ;0 Þ ! X DV Dl Dl X DV Dl Dl DV Dl4 Dl5 4 5 4 5  1þ ji Vi þ ai ð2li þ Dli Þ þ FDJ DK ðJ ; KÞ i

i¼4;5

2l4 þDl4 2l5 þDl5 þ e0 MDV UDJ ½2ðl4 þl5 ÞþDl4 þDl5 ðJ ; KÞ

 ð1  dl4 þDl4 ;0 dl5 þDl5 ;0 Þ 1 þ

X

jDV i

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2l þDl Þð2l5 þDl5 Þ fDV 4 4 ðV ; l4 ; l5 Þð1  dl4 ;0 dl5 ;0 Þ

2l4 þDl4 2l5 þDl5

Vi þ

i

aDV i

2l4 þDl4 2l5 þDl5

Dli

i¼4;5

 !)2   2l4 þDl4 2l5 þDl5 þ DV FDJ ðJ ; KÞ : ½2ðl4 þl5 ÞþDl4 þDl5

 

ð12Þ

For the sake of simplicity we omit here as well as below the indices P and P 0 . The functions UDJDK ðJ ; KÞ ¼ ð1Þ1þDJ UDJ DK ðJ ; KÞ in Eq. (12) for DK ¼ 0; 1 coincide with the Clebsh–Gordon coefficients UDJ DK ðJ ; KÞ ¼ ð1DKJKjJ þ DJK þ DKÞ;

X

ð13Þ

and for DK ¼ 2 they are given by the following equations:

U12 ðJ ; KÞ ¼ ð1  1JKjJ þ 1K  1Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðJ  KÞðJ  K þ 3Þ;

ð14Þ

U02 ðJ ; KÞ ¼ ð1  1JKjJK  1Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðJ  K  1ÞðJ  K þ 2Þ;

ð15Þ

U12 ðJ ; KÞ ¼ ð1  1JKjJ  1K  1Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðJ  K  2ÞðJ  K þ 1Þ: DV

Table 1 Correspondence between Pl
ıvaÕs and present notations [23] for the bands involved in this work Present notations

PlivaÕs notations

m15

m15 2m05  m15 2m25  m15 ðm4 þ m5 Þ0þ  m14 ðm4 þ m5 Þ0  m14 ðm4 þ m5 Þ2  m14 ðm4 þ m5 Þ0þ ðm4 þ m5 Þ0 3m15 ð2m4 þ m5 Þ1 I ð2m4 þ m5 Þ1 II ð3m4 þ m5 Þ0þ  m14 ð3m4 þ m5 Þ0  m14 ð3m4 þ m5 Þ2 I  m14 ð3m4 þ m5 Þ2 II  m14 m2 þ m15  m14 ðm4 þ 3m5 Þ0þ  m14 ðm4 þ 3m5 Þ0  m14 ðm4 þ 3m5 Þ2 I  m14 ðm4 þ 3m5 Þ2 II  m14 m2 þ m14  m15 ð2m4 þ 2m5 Þ0þ II  m15 ð2m4 þ 2m5 Þ0  m15 4m05  m15 4m25  m15

2m05  m15 2m25  m15 1 ðm14 þ m1 5 Þþ  m4 1 1 ðm4 þ m5 Þ  m14 m14 þ m15  m14 ðm14 þ m1 5 Þþ ðm14 þ m1 5 Þ 3m15 2m04 þ m15 2m25 þ m1 5 1 ð3m14 þ m1 5 Þþ  m4 1 ð3m14 þ m1 Þ  m 5  4 3m14 þ m15  m14 1 3m34 þ m1 5  m4 m2 þ m15  m14 1 ðm14 þ 3m1 5 Þþ  m4 1 ðm14 þ 3m1 5 Þ  m4 m14 þ 3m15  m14 3 1 m1 4 þ 3m5  m4 m2 þ m14  m15 1 ð2m24 þ 2m2 5 Þþ  m5 1 ð2m24 þ 2m2 Þ  m 5  5 4m05  m15 4m25  m15

ð16Þ Dl4 Dl5 FDJ DK ðJ; KÞ

The Herman–Wallis type functions ¼ DV Dl4 Dl5 FDJ DK ðJ ; KÞ for DK ¼ 0; 1 are listed below. They coincide with those used for triatomic linear molecules [5–7,9], except for the particular case: DK ¼ 0, Dl4 6¼ 0, Dl5 6¼ 0. In the case of DK ¼ 1 these functions are: Q-branch: DV

1 DV Dl4 Dl5 Dl4 Dl5 FDJ ð2KDK þ 1Þ DK ðJ ; KÞ ¼  bJ 2  DV Dl4 Dl5 þ dJQ J ðJ þ 1Þ  K 2

 DK  DK K þ : 2

ð17Þ

P- and R-branches:

1 DV Dl4 Dl5 DV Dl4 Dl5 FDJ DK ðJ ; KÞ ¼  dJQ  dJDV Dl4 Dl5 4

1 Dl4 Dl5 DV Dl4 Dl5  bDV þ dJQ J 2 DV Dl4 Dl5 2 K  ð2KDK þ 1Þ  dJQ Dl4 Dl5 þ bDV m þ dJDV Dl4 Dl5 m2 J



1 DV Dl4 Dl5 þ dJQ :  dJDV Dl4 Dl5 m KDK þ 2

ð18Þ

V.I. Perevalov et al. / Journal of Molecular Spectroscopy 218 (2003) 180–189

Here m ¼ J ; 0; J þ 1 for P-, Q-, and R-branches, respectively. In the case DK ¼ 0, Dl4 ¼ 0, and Dl5 ¼ 0 the formula is again the same as in the case of linear triatomic molecules DV

Dl4 Dl5 DV Dl4 Dl5 FDJ m þ dJDV Dl4 Dl5 DK¼0 ðJ ; KÞ ¼ bJ    J ðJ þ 1Þ þ m  K 2 :

ð19Þ

In the particular case l4 ¼ l5 ¼ 0, Q-branches are absent. The case DK ¼ 0, Dl4 6¼ 0, and Dl5 6¼ 0 is specific of four-atomic linear molecules. Two possibilities have to be considered: (i) K ¼ 0, (ii) K 6¼ 0. (i) K ¼ 0 Dl4 Dl5 In this case, the function DV FDJDK¼0 ðJ ; KÞ is given by Eq. (19) for P- and R-branches. Q-branches are activated by vibration–rotation interactions appearing one order of magnitude further than the terms giving rise to P- and R-branches. Therefore the following expression for the respective matrix element qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dl4 Dl5 DV Dl4 Dl5 Dl4 Dl5 MDV bJQ ðV ; l4 ; l5 Þ J ðJ þ 1Þ ð20Þ fDV is to be substituted for the expression in brackets of Eq. (12). For example, this is the case for the ðm4 þ m5 ÞðRþ uÞ and ðm4 þ m5 ÞðR Þ bands of C H discussed by Watson 2 2 u [25]. (ii) K 6¼ 0 Dl4 Dl5 In this case the function DV FDJ DK ðJ ; KÞ is again given by Eq. (19) for P- and R-branches, but for Q-branches one has ! Dl4 Dl5 bDV JQ DV Dl4 Dl5 DV Dl4 Dl5 FDJ DK ðJ ; KÞ ¼ ½J ðJ þ 1Þ  K 2 : þ dJ K ð21Þ Dl4 Dl5 parameter has be emphasized that the bDV JQ Dl4 Dl5 order of magnitude as the bDV parameter. J

It should the same Therefore, in this particular case, a very strong depenDl4 Dl5 dence of the DV FDJ DK ðJ ; KÞ function on the angular momentum quantum number J is present. Dl4 Dl5 Dl4 Dl5 The functions fDV ðV ; l4 ; l5 Þ ¼ fDV ðV ; l4 ; l5 Þ involved into Eq. (12) can be obtained as products of the single mode functions presented in Appendix A. The factors with combinations of Kronecker symbols appear in Eq. (12) because of the use of Wang-type basis functions. The parameters of the matrix elements of the effective dipole moment operaDl4 Dl5 Dl4 Dl5 Dl4 Dl5 Dl4 Dl5 tor MDV ¼ MDV , jDV ¼ jDV ði ¼ 1; i i DV Dl4 Dl5 DV Dl4 Dl5 Dl4 Dl5 ¼ ai ði ¼ 4; 5Þ, bDV 2; 3; 4; 5Þ, ai J Dl4 Dl5 DV Dl4 Dl5 ¼ bDV , dJDV Dl4 Dl5 ¼ dJDV Dl4 Dl5 , dJQ ¼ J DV Dl4 Dl5 DV Dl4 Dl5 DV Dl4 Dl5 and bJQ ¼ bJQ , involved in dJQ Eqs. (12) and (17)–(21), describe simultaneously the line intensities of hot and cold bands belonging to the same series of transitions that are determined by the value of DP . Within the framework of this semi-

183

Table 2 Selection rules in absorption and emission Vibrational Dm5 -odd (Dl5 ¼ 1; 3; . . .), DV3 -even Dm5 -even (Dl5 ¼ 0; 2; 4; . . .), DV3 -odd Vibrational–rotational D1h point group þ$ g$u SO(3) group DJ

e $ e0

DJ ¼ 0 DJ ¼ 1

1 $ 1  1$1 1 $ 1

Table 3 Nuclear statistic weights for C2 H2 Symmetry type

Nuclear statistic weight

 Rþ g ; Ru þ ; R R g u

1 3

empirical approach, these parameters are fitted to the observed line intensities. They can then be used for the prediction of the line intensities of the hot bands and for the prediction of the intensities of lines with high values of the quantum number J. There are two terms inside the brackets of Eq. (12). Dl4 Dl5 and They involve the leading parameters MDV 2l4 þDl4 2l5 þDl5 MDV , respectively. In most cases, the second parameter is several orders of magnitude smaller than the first one. However, there are cases when both parameters have the same order of magnitude. These cases will be discussed in Section 3. It should be emphasized that the second term in Eq. (12) contributes opposite signs to the intensities of e $ e and f $ f (or f e and e f ) transitions. The absorption and emission selection rules and the nuclear statistic weights are gathered in Tables 2 and 3, respectively. The correspondence between symmetry labels used in these tables and vibration–rotation quantum numbers are given by the following equations:  1 ! Rþ ; J eð1Þ ¼ 1 ! R ; and ð1Þ

V3 þV5

 ¼

1 ! Rg ; 1 ! Ru :

3. Least-square fittings Using the parameters defined above, we have performed least-square fittings of the recently published line

184

V.I. Perevalov et al. / Journal of Molecular Spectroscopy 218 (2003) 180–189

intensities [26–30] in three wavenumber regions corresponding to three series of transitions: DP ¼ 1; 2; 3. The aim of the fitting is to demonstrate the efficiency of the suggested approach. Therefore we have not taken into account at this stage less extensive line intensity measurements published earlier [31–33]. The values of the expansion coefficients J CNV1eV2 V3 V4 V5 l4 l5 of the eigenfunctions have been obtained from the global fitting of the effective Hamiltonian parameters to the observed line positions of the vibration–rotation transitions involving energy levels below 8000 cm1 [21]. The partition function QðT Þ is taken from [34]. The value of isotopic abundance is C ¼ 1 because we used the observed line intensities recalculated for pure 12 C2 H2 , except for the data from [26]. The aim of the fitting procedure is to minimize the value of the dimensionless weighted standard deviation v, defined according to the usual formula vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uPN S obs S calc 2 u i i t i¼1 di v¼ ; ð22Þ ðN  nÞ Siobs

Sicalc

where and are, respectively, observed and calculated values of the intensity for the ith line; di ¼ Siobs ri =100%, ri is the measurement error of ith line given as a percentage, N is the number of fitted line intensities, and n is the number of adjusted parameters. In order to characterize the quality of a fit, it is sometimes more convenient to use the root mean square (RMS) deviation defined according to the equation vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP obs calc 2 S S u N t i¼1 i S obsi i RMS ¼  100%: ð23Þ N The third statistical characteristic, which is used in this paper, is the value of the mean residual (MR) for a given band. The MR is defined according to the equation MR ¼

N 1 X Siobs  Sicalc  100%; N i¼1 Siobs

ð24Þ

where N is the number of fitted line intensities for a given band. 3.1. DP ¼ 1 series The line intensities of six bands m15 , 2m05  m15 , 2m25  m15 , 1 1 þ m1 ðm14 þ m1 and m14 þ m15  m14 , 5 Þþ  m4 , 5 Þ  m4 measured from FTS at LPMA in Paris [27,28], have ðm14

been used in the fitting. The declared absolute accuracy of the line intensity determination for both cold and hot bands is 5% [27,28]. The line intensities of the hot bands were weighted according to their absolute accuracy ri ¼ 5%, but in the case of the cold m15 band we used ri ¼ 3%. The reason for this choice is to enhance the statistical weight of the cold band in the fit in order to get a more reliable determination of the leading M parameter. The results of the global line intensity fit for this series of transitions are presented in Table 4. The values of v ¼ 0:82 and of RMS ¼ 3:6% show that the fit has been achieved within the experimental accuracy. The values of the fitted effective dipole moment parameters are given in Table 5. Table 6 presents the statistics of the fit for each band. The comparison of calculated line intensities of the m15 band with those observed is also given in Fig. 1. Taking into account the relation between the effective dipole moment parameter M0001 0 0 1 and the dipole moment derivative l5 : 1 1 olx 1 oly M0001 0 0 1 ¼ l5 ¼ ¼ ; 2 2 oq5a 2 oq5b

ð25Þ

where lx and ly are the dipole moment components perpendicular to the molecular axis, and q5a and q5b are the dimensionless normal coordinates associated with the degenerate vibration m5 , we obtained the following value for the dipole moment derivative: l5 ¼ 0:313 debye. Our calculated line intensities have been compared with those presented in the HITRAN data base for the same bands [35]. The latter were calculated using the rotationless transition moment and Herman–Wallis coefficients obtained from band by band reductions of the observed data reported in [27,28]. This comparison exhibits some non-typical behavior of the residuals for the Q-branch of the 2m25  m15 band (see Fig. 2). The residuals are very small for Qf e lines but they reach 100% for Qe f lines. The reason is the following: no intensity of Qe f lines has been measured in [28]. To calculate the intensities of the Qe f lines of the 2m25  m15 band in [35], 2 only the rotationless transition moment squared jRDV 0 j , determined from the intensities of the lines of R- and Pbranches and from intensities of Qf e lines, has been used. However, contrary to the upper states of Qf e transitions, the upper states of Qe f transitions are in very strong l-type resonance with the 2m05 state. Thus very large Herman–Wallis coefficients are needed for the

Table 4 Summary of the line intensity fits DP series

Number of lines

Number of bands

Jmax

v

RMS (%)

Number of adjusted parameters

1 2 3

430 136 522

6 2 15

38 35 35

0.82 1.01 1.00

3.6 4.4 4.7

4 3 18

V.I. Perevalov et al. / Journal of Molecular Spectroscopy 218 (2003) 180–189

185

Table 5 Effective dipole moment parameters Parametera

DV1

DV2

DV3

DP ¼ 1 M j5 bJ dJ

0 0 0 0

0 0 0 0

DP ¼ 2 M bJ M

0 0 0

DP ¼ 3 M j4 bJ M a4 bJ dJ dJQ M j4 bJ dJ dJQ M M M M M

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

a b

DV4

DV5

0 0 0 0

0 0 0 0

0 0 0

0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Value

Order

0.1564(2)b )1.4(2) )0.73(5) 0.46(3)

102 103 104

)1 )1 1

0.2691(3) )1.22(6) 0.406(4)

101 103 104

1 1 1 )1 )1 )1 )1 )1 1 1 1 1 1 )1 )1 )1 )3 3

0.5863(9) 2.5(3) )1.78(8) 0.161(3) 42.1(8) )20.0(4) )9.8(3) 7.3(6) 0.622(2) )4.6(5) )4.8(1) 2.90(9) -0.90(19) 1.858(6) 0.944(4) )0.318(9) )0.51(5) )0.49(2)

103 102 103 103 102 103 104 104 103 102 103 104 104 103 103 104 105 104

Dl4

Dl5

1 1 1 1

0 0 0 0

1 1 1 1

1 1 1

1 1 1

1 1 1

0 0 0 2 2 2 2 2 2 2 2 2 2 1 )1 0 0 2

3 3 3 1 1 1 1 1 1 1 1 1 1 )1 1 3 3 1

0 0 0 2 2 2 2 2 0 0 0 0 0 1 1 2 2 )2

The parameters M are given in Debye, while the other parameters are dimensionless. The numbers in parentheses are one standard deviation in units of the last digit.

correct calculation of the intensities of Qe f lines. No Herman–Wallis factor has been used for the calculation of these line intensities in [35]. In our approach, the ltype resonances are automatically taken into account in the corresponding wavefunctions. 3.2. DP ¼ 2 series The line intensities of allowed ðm14 þ m1 5 Þþ and forbidden m14 þ m15 bands measured in [26] together with the line intensities of ðm14 þ m1 5 Þþ band measured in [29] have been fitted simultaneously. The isotopic abundance C ¼ 0:977828 and C ¼ 1 were used for the data from [26] and [29], respectively. The data have been weighted in accordance with the declared mean absolute accuracy of the line intensity determination: ri ¼ 2% in [26] and ri ¼ 5% in [29]. Because of very large residuals between observed and calculated values presented in Table 3 of [26], the line intensities of Q-branch of the forbidden m14 þ m15 band have been weighted taking ri ¼ 7%. The results of the global line intensity fit for this series of transitions are presented in Table 4. The values of the fitted effective dipole moment parameters are given in Table 5 and the statistics of the fit for each band are presented in Table 6. Here again, the experimental ac-

curacy of the fit has been achieved (v ¼ 1:04). The residuals between our calculated line intensities for the ðm14 þ m1 5 Þþ band and those observed in [26] and [29] are plotted in Figs. 3 and 4, respectively. The residuals between our calculated and observed [26] line intensities for the forbidden m14 þ m15 band are plotted in Fig. 5. As one can see from these figures, the residuals for the ðm14 þ m1 5 Þþ band are close to the experimental uncertainty, but in the case of the Q-branch of the forbidden m14 þ m15 band, the residuals reach 24%. It should be mentioned that similar calculations performed in [26] yielded the same large residuals for some of the Q lines of this band. 3.3. DP ¼ 3 series The intensities of 535 lines of 15 cold and hot bands observed in [29,30] in the 5 lm region have been fitted simultaneously with the help of 18 parameters of the effective dipole moment operator. All but two bands 1 observed in this region, the ð2m24 þ 2m2 5 Þ  m5 and 0 2 1 2m4 þ 2m5  m5 bands, have been included into the fit. It is worth noting that only one line for the first band and only three lines for the second have been observed. In 1 addition one Q line of the ð3m14 þ m1 5 Þþ  m4 band has

186

V.I. Perevalov et al. / Journal of Molecular Spectroscopy 218 (2003) 180–189

Table 6 Band statistics Jmax

N (%)

MR (%)

RMS

Ref.

0 1 1 0 0 0

38 32 30 27 31 28

77 66 80 55 54 99

0.6 -0.2 -0.6 1.3 )2.2 -0.5

3.7 3.7 2.6 2.9 3.6 4.3

27 28 28 28 28 28

0 0 0 0

0 0 0 0

35 35 29 27

51 40 14 10

)1.3 0.3 )0.3 6.9

3.6 1.8 2.8 11.6

29 26 26 ðP  RÞ 26 ðQÞ

0 0 0 1 1 1 1 1 1 1 1 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 1 1 1

35 25 32 13 27 11 21 20 26 20 27 21 21 27 26

59 29 46 11 36 5 44 22 38 41 45 52 15 31 61

)0.2 0.4 )1.1 )5.8 3.2 2.2 )0.1 3.4 2.1 )2.6 )2.2 )0.2 )0.3 -0.1 0.3

1.5 3.5 2.5 8.3 5.9 9.5 3.4 4.6 5.7 5.9 6.7 4.8 6.9 2.7 3.4

29 29 29 30 30 30 30 30 30 30 30 30 30 30 30

Upper state

Lower state

V10 V20 V30 V40 V50 l04 l05

V1 V2 V3 V4 V5 l4 l5

DP ¼ 1 series 00001 0 1 00002 0 0 00002 0 2 (00011 1-1)þ ð000111  1Þ 00011 1 1

00000 00001 00001 00010 00010 00010

0 0 0 1 1 1

Dp ¼ 2 00011 00011 00011 00011

00000 00000 00000 00000 00000 00000 00000 00010 00010 00010 00010 00010 00010 00010 00010 00001 00001 00001 00001

series 1-1 1-1 11 11

DP series 00003 0 1 00021 0 1 00021 2-1 ð000311-1Þ 00031 3-1 00031 1 1 01001 0 1 (00013 1-1)þ ð000131-1Þ 00013 1 1 00013-1 3 01010 1 0 (00022 2-2)þ 00004 0 0 00004 0 2

Jmax is the maximum value of the rotational quantum number in the file of observed data for a given band, N is the number of observed line intensities for a given band, RMS (%) is the root mean square of the residuals for a given band (Eq. (23)), MR (%) is the mean value of the residuals for a given band (Eq. (24)). See text for details.

Fig. 1. Residuals between observed [27] and our calculated line intensities for the m5 band of 12 C2 H2 .

Fig. 2. Comparison of HITRAN [35] with our calculated line intensities for the Q-branch of the 2m25  m15 band of 12 C2 H2 .

also been excluded. The mean absolute accuracy of the line intensity measurements reported in the above references is 5%. As for the DP ¼ 1 series, we have

weighted the line intensities of cold bands with ri ¼ 3% and those of hot bands with ri ¼ 5%. The results of the global line intensity fit for this series of transitions are

V.I. Perevalov et al. / Journal of Molecular Spectroscopy 218 (2003) 180–189

187

Fig. 3. Residuals between observed [29] and our calculated line in12 tensities for the ðm14 þ m1 C2 H2 . 5 Þþ band of

presented in Table 4. The values of v ¼ 1:00 and of RMS ¼ 4:7% show that the experimental accuracy has been achieved. The values of the fitted effective dipole moment parameters are given in Table 5. Table 6 presents the statistics of the fit for each band. As examples, the residuals between observed and calculated line intensities for the 3m15 cold band and m2 þ m14  m15 hot band are plotted in Figs. 6 and 7, respectively. We have found large values for the a4 and bJ parameters of the DV4 ¼ 2, DV5 ¼ 1, Dl4 ¼ 2, and Dl5 ¼ 1 matrix element, compared with the conventional ones. This could be partly explained by an accidentally small value for the leading parameter of the 3 matrix element M0201 debye. It can 0 2 1 ¼ 0:161ð3Þ  10 be seen from Table 5 that the other parameters which appear in the same order of perturbation theory have values several times larger:

Fig. 4. Residuals between observed [26] and our calculated line in12 tensities for the ðm14 þ m1 C2 H2 . 5 Þþ band of

Fig. 6. Residuals between observed [29] and our calculated line intensities for the 3m15 band of 12 C2 H2 .

Fig. 5. Residuals between observed [26] and our calculated line intensities for the forbidden m14 þ m15 band of 12 C2 H2 .

Fig. 7. Residuals between observed [30] and our calculated line intensities for the m2 þ m14  m15 band of 12 C2 H2 .

188

V.I. Perevalov et al. / Journal of Molecular Spectroscopy 218 (2003) 180–189

M00010 0 3 ¼ 0:5863ð9Þ  103 debye; M00010 2 1 ¼ 0:622ð2Þ  103 debye; M01110 1 1 ¼ 1:858ð6Þ  103 debye; M01110 1 1 ¼ 0:944ð4Þ  103 debye: The case of the DP ¼ 3 series of transitions gives examples of the importance of the second term inside the brackets of Eq. (12). The first example concerns the 1 3 1 1 ð3m14 þ m1 5 Þþ  m4 and 3m4 þ m5  m4 bands. Their strengths are mainly described by the leading parameters M00010 2 1 and M02 01 0 2 1 , respectively, which appear at the same order in perturbation theory. But the second parameter M02 01 0 2 1 also contributes to the strength of the first band through the second term inside the brackets of 2 3 2 3 Eq. (12). The parameters M0201 0 0 3 , M0 0 0 0 3 , and M0 0 0 2 1 are other examples of the contribution of this second term inside the brackets of Eq. (12). The results of our line intensity calculation show that, without these parameters, it is impossible to account for some large differences between experimental intensities of the same lines in subbands having opposite parities. 4. Conclusion In this paper, the method of effective operators has been developed for the simultaneous fitting of the line intensities of cold and hot bands in four-atomic linear molecules. This method has been applied to the global fitting of the line intensities of acetylene in three wavenumber regions: 13.6, 7.8, and 5 lm. In all cases the calculations have achieved the experimental accuracy. The importance of l-type resonance, both in the eigenfunctions of the effective Hamiltonian and in the effective dipole moment operator, has been evidenced. These resonances are responsible for some large differences between intensities of the same transitions in subbands having opposite parities. The fitted sets of effective dipole moment parameters, together with the set of effective Hamiltonian parameters to be reported [21], allow us to extend and improve the C2 H2 line intensities of the HITRAN databank [35] in the same spectral regions. The list of observed and calculated line intensities is available upon request. It has been deposited with the editorial office of the journal. We plan to extend our calculations in the near future to other spectral regions with the intention of generating a high temperature databank for acetylene. Acknowledgments The authors are indebted to CNRS and RFBR PICS grant 01-05-22002. O.M. Lyulin is also indebted to INTAS grant YSF 01/1-24.

Appendix A. Matrix elements of elementary vibrational and rotational operators in the case of four-atomic linear molecules Nondegenerate vibrations    pffiffiffiffiffiffiffiffiffiffiffiffi   V i þ 1; Vi þ 1aþ i Vi ¼ hVi  1jai jVi i ¼

pffiffiffiffi Vi :

Here aþ i and ai are the creation and annihilation operators of vibrational quanta with the frequency xi , where i ¼ 1; 2; 3 numbers nondegenerate vibrations. Degenerate vibrations D E pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Vt þ 1lt  1jðtÞ Aþ V t  lt þ 2;  jVt lt ¼  D

E pffiffiffiffiffiffiffiffiffiffiffiffiffi Vt  1lt  1jðtÞ A jV l ¼  V t  lt ; t t 

where t ¼ 4; 5 numbers degenerate vibrations. The ladder operators are defined by the following equations: ðtÞ

þ þ Aþ  ¼ ata  atb ;

ðtÞ

A  ¼ ata  atb ;

where a and b are components of double degenerate vibrations. Components of the angular momentum operator pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hJK  1jJ jJKi ¼ ðJ  KÞðJ  K þ 1Þ: The phases of vibration and rotation basis functions are chosen according to [36]. Dl4 Dl5 Functions fDV ðV1 ; V2 ; V3 ; V4 ; V5 ; l4 ; l5 Þ 1 DV2 DV3 DV4 DV5

These functions have the following symmetry property: Dl4 Dl5 fDV ðV1 ; V2 ; V3 ; V4 ; V5 ; l4 ; l5 Þ 1 DV2 DV3 DV4 DV5 Dl4 Dl5 ðV1 ; V2 ; V3 ; V4 ; V5 ; l4 ; l5 Þ: ¼ fDV 1 DV2 DV3 DV4 DV5

They are products of elementary functions for each vibrational mode. The latter are given by the following expressions:    E pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D DVi   fDVi ðVi Þ ¼ Vi þ DVi  aþ Vi i sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðVi þ 1ÞðVi þ 2Þ    ðVi þ DVi Þ ; |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} DVi

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi     i Vi fDVi ðVi Þ ¼ Vi  DVi aDV i sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ Vi ðVi  1Þ    ðVi  DVi þ 1Þ ; |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} DVi

where i ¼ 1; 2; 3.

V.I. Perevalov et al. / Journal of Molecular Spectroscopy 218 (2003) 180–189

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dlt ðVt ; lt Þ fDV t ¼ ð1Þ

ð1=2ÞðDVt Dlt Þ

D

Vt þ DVt lt  Dlt

E  ð1=2ÞðDVt Dlt Þ  þ ð1=2ÞðDVt Dlt Þ j Aþ A jV l t t þ  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fð1=2ÞðDVt Dlt Þg fð1=2ÞðDVt Dlt Þg ¼ ðVt þ lt þ 2Þ ; ðVt  lt þ 2Þ qffiffiffiffiffiffiffiffiffiffi Dlt ðVt ; lt Þ fDV t ¼ ð1Þ

ð1=2ÞðDVt Dlt Þ

D

Vt  DVt lt  Dlt

E  ð1=2ÞðDVt Dlt Þ   ð1=2ÞðDVt Dlt Þ j A A jV l t t þ  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðVt þ lt Þfð1=2ÞðDVt Dlt Þg ðVt  lt Þfð1=2ÞðDVt Dlt Þg ; qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D E  þ  ð1=2ÞDlt ð1=2ÞDlt Dlt ðV ; l Þ ¼ ð1Þ V l j A A jV l fDV þ Dl t t t t t t t ¼0 þ þ t qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fð1=2ÞDlt g fð1=2ÞDlt g ¼ ðVt þ lt þ 2Þ ; ðVt  lt Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D E  þ  ð1=2ÞDlt ð1=2ÞDlt Dlt ðV ; l Þ ¼ ð1Þ V l j A A jV l fDV  Dl t t t t t t t   t ¼0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fð1=2ÞDlt g fð1=2ÞDlt g ¼ ðVt  lt þ 2Þ ; ðVt þ lt Þ where t ¼ 4; 5. In the above expressions the following notations are used: xfng ¼ xðx þ 2Þ    ½x þ 2ðn  1Þ ; n > 0; |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} n

xfng ¼ xðx  2Þ    ½x  2ðn  1Þ ; n > 0: |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} n

References [1] J.-L. Teffo, O.N. Sulakshina, V.I. Perevalov, J. Mol. Spectrosc. 156 (1992) 48–64. [2] J.-L. Teffo, V.I. Perevalov, O.M. Lyulin, J. Mol. Spectrosc. 168 (1994) 390–403. [3] V.I. Perevalov, E.I. Lobodenko, O.M. Lyulin, J.-L. Teffo, J. Mol. Spectrosc. 171 (1995) 435–452. [4] O.M. Lyulin, V.I. Perevalov, J.-L. Teffo, J. Mol. Spectrosc. 174 (1995) 566–580. [5] O.M. Lyulin, V.I. Perevalov, J.-L. Teffo, J. Mol. Spectrosc. 180 (1996) 72–74. [6] V.I. Perevalov, J.-L. Teffo, O.M. Lyulin, E.I. Lobodenko, O.N. Sulakshina, S.A. Tashkun, V.l.G. Tyuterev, Atmos. Oceanic Opt. 10 (1997) 474–489. [7] J.-L. Teffo, O.M. Lyulin, V.I. Perevalov, E.I. Lobodenko, J. Mol. Spectrosc. 187 (1998) 28–41. [8] S.A. Tashkun, V.I. Perevalov, J.-L. Teffo, L.S. Rothman, Vl.G. Tyuterev, J. Quantum Spectrosc. Radiat. Transfer 60 (1998) 785–801. [9] S.A. Tashkun, V.I. Perevalov, J.-L. Teffo, Vl.G. Tyuterev, J. Quantum Spectrosc. Radiat. Transfer 62 (1998) 571–598.

189

[10] S.A. Tashkun, V.I. Perevalov, J.-L. Teffo, M. Lecoutre, T.R. Huet, A. Campargue, D. Bailly, M.P. Esplin, J. Mol. Spectrosc. 200 (2000) 162–176. [11] D. Bailly, S.A. Tashkun, V.I. Perevalov, J.-L. Teffo, P. Arcas, J. Mol. Spectrosc. 190 (1998) 1–6. [12] D. Bailly, S.A. Tashkun, V.I. Perevalov, J.-L. Teffo, P. Arcas, J. Mol. Spectrosc. 197 (1999) 114–119. [13] A. Campargue, D. Bailly, J.-L. Teffo, S.A. Tashkun, V.I. Perevalov, J. Mol. Spectrosc. 193 (1999) 204–212. [14] J.-L. Teffo, C. Claveau, Q. Kou, G. Guelachvili, A. Ubelmann, V.I. Perevalov, S.A. Tashkun, J. Mol. Spectrosc. 201 (2000) 249–255. [15] L. Daumont, J. Vander Auwera, J.-L. Teffo, V.I. Perevalov, S.A. Tashkun, J. Mol. Spectrosc. 208 (2001) 281–291. [16] A. Campargue, G. Weirauch, S.A. Tashkun, V.I. Perevalov, J.-L. Teffo, J. Mol. Spectrosc. 209 (2001) 198–206. [17] S.A. Tashkun, V.I. Perevalov, J.-L. Teffo, J. Mol. Spectrosc. 210 (2001) 137–145. [18] L. Daumont, C. Claveau, M.-R. Debacker-Barilly, A. Hamdouni, L. R
egalia-Jarlot, J.-L. Teffo, S.A. Tashkun, V.I. Perevalov, J. Quantum Spectrosc. Radiat. Transfer 72 (2002) 37–55. [19] V.I. Perevalov, E.I. Lobodenko, J.-L. Teffo, Reduced effective Hamiltonian for global fitting of C2 H2 rovibrational lines, in: 12th Symposium and School on High Resolution Molecular Spectroscopy, Proc. SPIE 3090 (1997) 143–149. [20] O.M. Lyulin, V.I. Perevalov, S.A. Tashkun, J.-L. Teffo, Global fitting of the vibrational–rotational line positions of acetylene molecule, in: 13th Symposium and School on High Resolution Molecular Spectroscopy, Proc. SPIE 4063 (2000) 126–133. [21] O.M. Lyulin, V.I. Perevalov, and J.-L. Teffo, to be published. [22] M. Abbouti Temsamani, M. Herman, J. Chem. Phys. 102 (1995) 6371–6384. [23] J. Pl
ıva, J. Mol. Spectrosc. 44 (1998) 145–164. [24] V.I. Perevalov, O.M. Lyulin, J.-L. Teffo, Atmos. Oceanic Opt. 14 (2001) 730–738. [25] J.K.G. Watson, J. Mol. Spectrosc. 188 (1998) 78–84. [26] J. Vander Auwera, J. Mol. Spectrosc. 201 (2000) 143–150. [27] J.-Y. Mandin, V. Dana, C. Claveau, J. Quantum Spectrosc. Radiat. Transfer 67 (2000) 429–446. [28] D. Jacquemart, C. Claveau, J.-Y. Mandin, V. Dana, J. Quantum Spectrosc. Radiat. Transfer 69 (2001) 81–101. [29] D. Jacquemart, J.-Y. Mandin, V. Dana, L. R
egalia-Jarlot, X. Thomas, P. Von der Heyden, J. Quantum Spectrosc. Radiat. Transfer 75 (2002) 397–422. [30] D. Jacquemart, J.-Y. Mandin, V. Dana, L. R
egalia-Jarlot, J.-J. Plateaux, D. D
ecatoire, L.S. Rothman, J. Quantum Spectrosc. Radiat. Transfer 76 (2003) 237–267. [31] J.R. Podolske, M. Loewenstein, P. Varanasi, J. Mol. Spectrosc. 107 (1984) 241–249. [32] M. Weber, W.E. Blass, J.-L. Salanave, J. Quantum Spectrosc. Radiat. Transfer 42 (1989) 437–443. [33] M. Weber, W.E. Blass, G.W. Halsey, J.J. Hillman, J. Mol. Spectrosc. 165 (1994) 107–123. [34] R.R. Gamache, R.L. Hawkins, L.S. Rothman, J. Mol. Spectrosc. 142 (1990) 205–219. [35] L.S. Rothman, A. Barbe, D.C. Benner, L.R. Brown, C. CamyPeyret, M.R. Carleer, K.V. Chance, C. Clerbaux, V. Dana, V.M. Devi, A. Fayt, J.-M. Flaud, R.R. Gamache, A. Goldman, D. Jacquemart, K.W. Jucks, W.J. Lafferty, J.-Y. Mandin, S.T. Massie, D. Newnham, A. Perrin, C.P. Rinsland, J. Schroeder, K. Smith, M.A.H. Smith, R.A. Toth, J. Vander Auwera, P. Varanasi, K. Yoshino, The HITRAN Molecular Spectroscopic Database: 2001 Edition, J. Quantum Spectrosc. Radiat. Transfer (to be published). [36] V.I. Perevalov, O.N. Sulakshina, J.-L. Teffo, J. Mol. Spectrosc. 155 (1992) 433–435.