The Microwave and Far Infrared Spectra of Acetaldehyde-d1

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The Microwave and Far Infrared Spectra of Acetaldehyde-d1

Elkeurti, M.; Coudert, L. H.; Medvedev, I. R.; Maeda, A.; De Lucia, F. C.;

McKellar, A. R. W.; Moazzen-Ahmadi, N.; Appadoo, D.; Toumi, S.

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The microwave and far infrared spectra of acetaldehyde-d

1 M. Elkeurti

a,1

, L.H. Coudert

a,*

_{, I.R. Medvedev}

b

_{, A. Maeda}

b

_{, F.C. De Lucia}

b

_{, A.R.W. McKellar}

c

_,

N. Moazzen-Ahmadi

d

, D. Appadoo

e,2

, S. Toumi

f

a_{LISA, UMR 7583 CNRS/Universités Paris Est et Paris Diderot, 94010 Créteil, France} b_{Department of Physics, The Ohio State University, Columbus, OH 43210, USA}

c_{Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ont., Canada K1A 0R6}

d_{Department of Physics and Astronomy, University of Calgary, 2500 University Drive North West, Calgary, Alta., Canada T2N 1N4} e_{Canadian Light Source, 101 Perimeter Road, University of Saskatchewan, Saskatoon, Sask., Canada S7N 0X4}

f_{Laboratoire d’Etude et de Recherche en Instrumentations et Communications d’Annaba (LERICA), Université Mokhtar Badji, B.P. 12, 23000 Annaba, Algeria}

a r t i c l e

i n f o

Article history:

Received 31 May 2010 In revised form 8 July 2010 Available online 30 July 2010

Keywords: CH3COD

Acetaldehyde Internal rotation

Fast scan submillimeter spectroscopic technique

Non-rigid molecule Microwave spectrum Synchrotron radiation

a b s t r a c t

Experimental and theoretical investigations of the microwave and far infrared spectra of CH3COD are

reported. 2883 lines were identified in the far infrared spectrum recorded using the Canadian synchro-tron radiation light source. 1168 lines in

v

_t_{¼ 0 and 700 in}

v

_t_{¼ 1 have been measured in the microwave}

spectrum obtained using the fast scan submillimeter spectroscopic technique. A global analysis of the new data and of already available microwave lines has been carried out and yielded values for 36 rota-tion–torsion parameters. The unitless weighted standard deviation of the fit is 0.9.

1. Introduction

Because of its astrophysical interest and because it was used as a test case for the theoretical models developed to account for internal rotation of a methyl group, the non-rigid acetaldehyde molecule has been the subject of many high resolution investiga-tions. The microwave and far infrared spectra of the normal species have been studied in Refs.[1–7]and a satisfactory understanding of the rotation–torsion energy levels was achieved up to

v

_t_{¼ 4}

in this last reference. The normal species has also been detected a long time ago in the interstellar medium[8–10]. Fewer results, however, are available for symmetrical isotopic variants. The microwave and far infrared spectra of the triply deuterated form CD3COH have been analyzed up to

v

t¼ 1 in Ref.[11]and the

cou-pling between the large amplitude internal rotation and the

hyper-fine quadrupole coupling has been investigated in Ref. [12]. The microwave spectrum of the monodeuterated form CH3COD has

been measured in Ref.[13], but only 60 transitions within

v

_t¼ 0

were reported by the authors.

In this paper experimental and theoretical investigations of the microwave and far infrared (FIR) spectra of CH3COD are reported.

The microwave spectrum was recorded by means of the fast scan submillimeter spectroscopic technique[14,15](FASSST) and 1868 lines within the ground and first excited torsional states were as-signed. The FIR spectrum was measured using the synchrotron radi-ation from the new Canadian Light Source. The very high resolution achieved by this experimental setup allowed us to assign 2883 absorption lines in the fundamental torsional band. An analysis of the new data and of the microwave lines measured in Ref. [13]

was carried out using a rotation–torsion rho axis method (RAM) Hamiltonian[16–20].

2. Experimental

The FASSST microwave spectrum[14,15]used in this work was recorded in the 120–376 GHz range. The data were taken in three segments: 120–188 GHz, 190–260 GHz, and 260–376 GHz. SO2

lines contained in the spectrum were used for frequency calibra-tion. More than 60 thousand transitions were measured. A small

* Corresponding author. Address: Laboratoire Inter-universitaire des Systèmes Atmosphériques, Université Paris 12, 61 Avenue du Général de Gaulle, 94010 Creteil Cedex, France. Fax: +33 1 45 17 15 64.

E-mail addresses: laurent.coudert@lisa.univ-paris12.fr, coudert.laurent@ wanadoo.fr(L.H. Coudert).

1 _{Permanent address: Laboratoire d’Etudes Physico-Chimiques (LEPC), Université}

Tahar Moulay de Saïda, B.P. 138, ENASR, 20002 Saïda, Algeria.

2 _{Present address: Australian Synchrotron Company, 800 Blackburn Road, Clayton,}

Vic. 3168, Australia.

Contents lists available atScienceDirect

Journal of Molecular Spectroscopy

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portion of the spectrum, containing two strong a-type lines, can be seen inFig. 1.

The far infrared spectrum was recorded using synchrotron radi-ation at the Canadian Light Source. The Bruker IFS 125HR Fourier transform spectrometer was fitted with a 6

l

m Ge/mylar beamsp-litter and a liquid-helium cooled Si bolometer detector and oper-ated with an entrance aperture of 2 mm at the full spectral resolution (nominally 0:00096 cm1_{) given by the 9.4 m maximum}

optical path difference. The CH3COD sample at a pressure of

0.30 Torr was contained in a 2 m multiple-traversal gas cell set for a total path of 48 m. The cell was maintained at about 200 K by means of chilled methanol which flowed from a refrigerated bath through copper tubing wrapped around the cell.Fig. 2shows a portion of the spectrum between 118 and 126 cm1_.

3. Assignment

The assignment of the microwave spectrum was initiated by performing a preliminary analysis of the microwave data pub-lished in Ref. [13]. The A and E components of the strong J ¼ 7 6, a-type, Ka¼ 0,

v

_t_{¼ 0 transition were predicted and}

searched for in the FASSST spectrum. Because of their strength, both components could be easily identified andFig. 1shows that they correspond indeed to two prominent features of the experi-mental spectrum. This process was repeated for higher J-values and up to Ka¼ 12. The same procedure was employed for a-type

transitions within

v

_t_{¼ 1 up to K}_a_{¼ 10. At this point, a preliminary}

analysis of the available data was performed which allowed us to obtain sufficiently accurate values of the parameters involved in

Fig. 1. The small portion of the FASSST microwave spectrum between 129 900 and 130 000 MHz can be seen. There is one tick mark every megahertz on the x-axis. The E and A components of the strong a-type 707 606line within the ground torsional state can be seen at 129 931 and 129 947 MHz, respectively. The two weak lines at 129 924 and

129 944 MHz have not been assigned.

Fig. 2. A portion of the FIR spectrum recorded using as a light source the synchrotron radiation from the new Canadian Light Source. Several torsional Q-branches can be observed. Among the strongest ones, the Ka¼ 7 8 involving A-type torsional levels and the Ka¼ 6 7 involving E-type torsional levels near 121 cm1and 124:1 cm1,

respectively.

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the RAM Hamiltonian to start assigning DKa¼ 1 transitions.

These transitions, mostly b-type, could be assigned up to Ka¼ 5

for

v

_t¼ 0 and 1. For transitions involving E-type levels, 44 c-type

lines, which would be forbidden in the rigid-rotator limit, could be assigned.Table 1gives the combination differences obtained for loops involving four transitions characterized by A-type tor-sional levels belonging to

v

_t¼ 1. As combination differences for

all loops are within 0.4 MHz, that is, four times the experimental uncertainty on the transition frequency, we can be fairly confident in the assignment. The same conclusion holds for E-type transi-tions within

v

_t_{¼ 1 and for A- and E-type transitions within}

v

_t_{¼ 0.}

At this point the assignment of the FIR spectrum was fairly straightforward as the upper and lower torsional states were al-ready known. A predicted spectrum was calculated and turned out to be shifted from the experimental one by less than 1 cm1_.

The FIR transitions could then be easily identified from 100 to 180 cm1_{and up to J ¼ 25 and K}

a¼ 11. Below 110 cm1there

re-mains many unassigned lines. They may belong either to the

v

_t_{¼ 2 1 hot band expected to be near 118 cm}1 or to a

v

_t¼ 1 0 torsional band originating from a low lying vibrational

state of a small amplitude vibrational mode such as the

m

10mode

[21].

Table 1

Combination differences for closed microwave loops.a

T1 T2 T3 T4 Db 70;7 60;6 81;8 70;7 71;7 60;6 81;8 71;7 0.092 71;6 61;5 82;7 71;6 72;6 61;5 82;7 72;6 0.182 72;5 62;4 83;6 72;5 73;5 62;4 83;6 73;5 0.237 72;6 62;5 83;5 72;6 73;4 62;5 83;5 73;4 0.106 80;8 70;7 91;9 80;8 81;8 70;7 91;9 81;8 0.198 81;7 71;6 92;8 81;7 82;7 71;6 92;8 82;7 0.064 90;9 80;8 101;10 90;9 91;9 80;8 101;10 91;9 0.029 91;8 81;7 102;9 91;8 92;8 81;7 102;9 92;8 0.072 100;10 90;9 111;11 100;10 101;10 90;9 111;11 101;10 0.150 101;9 91;8 112;10 101;9 102;9 91;8 112;10 102;9 0.067 110;11 100;10 121;12 110;11 111;11 100;10 121;12 111;11 0.090 111;10 101;9 122;11 111;10 112;10 101;9 122;11 112;10 0.040 112;9 102;8 123;10 112;9 113;9 102;8 123;10 113;9 0.186 120;12 110;11 131;13 120;12 121;12 110;11 131;13 121;12 0.011 121;11 111;10 132;12 121;11 122;11 111;10 132;12 122;11 0.085 130;13 120;12 141;14 130;13 131;13 120;12 141;14 131;13 0.019 131;12 121;11 142;13 131;12 132;12 121;11 142;13 132;12 0.105 140;14 130;13 151;15 140;14 141;14 130;13 151;15 141;14 0.308 141;13 131;12 152;14 141;13 142;13 131;12 152;14 142;13 0.044 150;15 140;14 161;16 150;15 151;15 140;14 161;16 151;15 0.164 151;14 141;13 162;15 151;14 152;14 141;13 162;15 152;14 0.004 160;16 150;15 171;17 160;16 161;16 150;15 171;17 161;16 0.101 170;17 160;16 181;18 170;17 171;17 160;16 181;18 171;17 0.206 180;18 170;17 191;19 180;18 181;18 170;17 191;19 181;18 0.082 190;19 180;18 201;20 190;19 191;19 180;18 201;20 191;19 0.096 a _{Closed loops consisting of four transitions in the columns headed T}

1, T2, T3, and

T4, involving A-type rotation–torsion levels inv_t_{¼ 1, are listed. Assignment of the}

transitions in terms of rotational quantum numbers J; Ka, and Kcare given. b _{This column gives the combination difference D ¼ F}

1þ F2 F3 F4, where Fiis

the observed frequency of transition Tiin MHz.

Table 2

Experimental and calculated valuesa_{for the RAM Hamiltonian parameters}

Parameter CH3COH CD3COH CH3COD

Expb _Calc _Expb _Calc _Expb _Calc

F 7.567 7.773 4.907 4.995 6.979 7.158 q 0.329 0.322 0.487 0.481 0.263 0.257 A 1.885 1.876 1.387 1.388 1.494 1.487 B 0.349 0.348 0.294 0.294 0.350 0.349 C 0.303 0.304 0.260 0.261 0.291 0.291 Dab 0.123 0.117 0.093 0.481 0.114 0.108 hRAM 4.55 4.37 4.83 4.73 5.63 5.37 a _{For the CH}

3COH, CD3COH, and CH3COD species, experimental and calculated

values for the kinetic energy parameters appearing in Eq.(1), in cm1_{, and for the}

angle hRAMdefined in Section4, in degrees, are given. b _{Experimental values in this column are from Ref.}_[6]_{for CH}

3COH, from Ref.[11]

for CD3COH, and from the present investigation for CH3COD.

c _{Calculated values in this column were obtained from the structure given in}

Ref.[1].

Table 3

Results of the analysis for each data subset.

Dataa _Reference _Nb _Uncertainty _RMSc _STDd

v_t_{¼ 0, MW} Ref.[13] 60 0.02 MHz 0.03 MHz 1.6 v_t_{¼ 0, MW} This work 1168 0.10 MHz 0.07 MHz 0.7 v_t_{¼ 1, MW} This work 700 0.10 MHz 0.10 MHz 1.0 v_t_{¼ 1 0, FIR} This work 2883 0.00025 cm1 0.00024 cm1 1.0

a_{The data subset is described in this column.}_v

t¼ 0 andv_t_{¼ 1 stand for}

rota-tional transitions within that state.v_t_{¼ 1 0 stands for transitions belonging to}

the fundamental torsional band. MW indicate microwave transitions.

b_{The number of data for each data subset is given in this column. The total}

number of data is 4811.

c _{RMS is the root mean square deviation for each data subset.}

d _{STD is the unitless root mean square weighted deviation for each data subset.}

The unitless weighted standard deviation of the fit is 0.9.

Table 4

Parameters from the fit of the microwave and FIR data of acetaldehyde-d1.

ntra _Operatorb _Parameter _Valuec

220 ð1 cos 3aÞ=2 V3 414.700 523(1400) P2 a F 6.978 660(19) 211 PaJz q 0.262 598 710(930) 202 J2 z A 1.494 272 342(2700) J2 x B 0.350 068 545(1600) J2 y C 0.290 986 936(360) fJx; Jzg Dab 0.113 928 723(7600) 440 P4 a k4 0.423 358(740) 10 3 ð1 cos 6aÞ=2 V6 11.180 182(1400) 431 P3 aJz k3 0.391 373(1500)103 422 P2 aJ2 Gv 5.980 025(78 000) 10 6 P2 aJ2z k2 89.828 617(1 100 000)10 6 2P2 aðJ2x J2yÞ c1 13.103 919(170 000)10 -6 P2 afJx; Jzg Dab 50.535 534(720 000)10 6 sin 3afJx; Jyg Dbc 2.167 380(170 000)103 sin 3afJy; Jzg Dac 1.859 626(29 000)103 ð1 cos 3aÞJ2 Fv 0.331 849(2300)103 ð1 cos 3aÞJ2z k5 14.091 802(4600)10 3 ð1 cos 3aÞðJ2x J2yÞ c2 0.136 037(1200)10 3 ð1 cos 3aÞfJx; Jzg dab 2.960 635(8100)103 413 PaJzJ2 Lv 3.081 115(59 000)10 6 PaJ3z k1 162.615 502(360 000)10 6 PafJz; J2x J 2 yg c4 13.366 456(160 000)10 6 PafJx; J2zg dab 41.007 557(730 000)10 6 404 _J4 z DKK 48.792 943(67 000)10 6 J2J2 z DKJ 2.740 509(30 000)10 6 J4 DJJ 0.259 337(140)106 fJ2z; J2x J2yg dK 1.045 859(26 000)10 6 2J2ðJ2x J2yÞ dJ 0.059 064(70)10 6 642 _P4 aJ2 Mv 18.450 886(1 300 000)10 9 ð1 cos 6aÞJ2 _Nv 63.022 935(1 900 000)10 6 624 P2 aJ4 gv 0.170 699(3900)10 9 ð1 cos 3aÞJ4z fk 1.525 815(20 000) 106 ð1 cos 3aÞfJx; JzgJ2 dabJ 0.029 624(1200)106 ð1 cos 3aÞfJx; J3zg dabK 0.697 851(38 000)106 615 PaJ3zJ2 kv 0.836 176(23 000)10 9 a_{n ¼ t þ r, where n is the total order of the operator, t is the order of the torsional}

part, and r is the order of the rotational part.

b

fA; Bg ¼ AB þ BA. The product of the parameter and operator from a given row yields the term actually used in the RAM rotation–torsion Hamiltonian, except for F;q, and A which occur in the form FðPaqPzÞ2þ AP2z.

c _{Parameters are in cm}1_except_q_{which is unitless. Statistical uncertainties are}

shown as one standard deviation in the same units as the last digit. M. Elkeurti et al. / Journal of Molecular Spectroscopy 263 (2010) 145–149

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4. Theoretical models

The theoretical model used for the analysis of the data is based on the RAM Hamiltonian[16–20]. Defining the angle of internal rotation

a

as in Ref.[20], the exact rotation–torsion RAM Hamilto-nian appropriate for the acetaldehyde molecule can be obtained from Eq. (26) of this reference as:

HRAM¼ FðPa

q

JzÞ 2 þ AJ2zþ BJ 2 xþ CJ 2 yþ DabfJx; Jzg þ Vð

a

Þ ð1Þ

where Jx; Jy, and Jzare the components of the rotational angular

momentum in the molecule-fixed RAM axis system; Pais the

angu-lar momentum conjugated to

a

; Vð

a

Þ is the potential energy func-tion for the internal rotafunc-tion; and F; A; B; C; Dab, and

q

are six

constants. As stressed in Ref.[20], the three constants A; B, and C differ slightly from the usual rotational constants as the RAM axis system is obtained from the principal axis system by a rotation about the y-axis characterized by a small angle denoted hRAM. Using

the structure of acetaldehyde given in Ref.[1], these six constants

Fig. 3. A comparison between observed (upper trace) and calculated (lower trace) spectra for the 139–141 cm1_{range. The calculated spectrum was computed assuming a}

temperature of 200 K and taking Lorentzian line profiles with a half width at half height of 0.0005 cm1_{. The pressure and the length of the absorption cell were adjusted so}

that line intensities in both spectra look similar. In this spectral region, the spectrum contains the Q-branches of the Ka¼ 0 1 and 1 0 torsional bands involving A- and

E-type torsional levels. In the observed spectrum, the lines near 139.8 cm1_{do not belong to the fundamental torsional band.}

Fig. 4. A comparison between observed (upper trace) and calculated (lower trace) spectra from 150 to 158 cm1_{. The temperature and line profiles are the same as for}_{Fig. 3}_.

The pressure and the length of the absorption cell were also adjusted so that line intensities in both spectra look similar. Many torsional Q-branches can be seen in both spectra. Some of the lines which cannot be found in the calculated spectrum belong to water vapor. Such is the case for the strong line near 156:359 cm1_{and for the weaker}

lines near 156.44 and 157:919 cm1_.

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along with the angle hRAMwere calculated for the main isotopic

spe-cies, for the triply deuterated CD3COH, and for the monodeuterated

CH3COD. These calculated values are given inTable 2together with

the experimental ones reported in Ref.[6]for the normal species, in Ref. [11] for CD3COH, and in Table 4 of the present paper for

CH3COD. The agreement is quite satisfactory for the B and C

con-stants. Discrepancies, however, arise for the F and A concon-stants. The Hamiltonian given in Eq.(1)does not allow us to reproduce rotation–torsion energies with spectroscopic accuracy as it does not account for centrifugal distortion effects. Based on the work of Kirtman[16]and on the results of Refs.[18,19], centrifugal dis-tortion rotation–torsion terms are added to the Hamiltonian in Eq.

(1) in order to build the effective rotation–torsion Hamiltonian widely used now in high-resolution spectroscopic investigations of molecules displaying internal rotation. Numerical calculation of the rotation–torsion energy is performed in two steps. In the first step, a so called torsional Hamiltonian is diagonalized in a ba-sis set conba-sisting of free internal rotation functions and this yields torsional energies and wavefunctions characterized by the sym-metric top rotational quantum number k and the torsional quan-tum number

v

_t. In the present investigation, the free internal

rotation functions are chosen so that the matrix of the torsional Hamiltonian is a 21 21 matrix. In the second step, the torsional wavefunctions are used as basis set functions to diagonalize the rotation–torsion Hamiltonian. In this second diagonalization, the

v

_t-values characterizing the torsional wavefunctions ranges from

0 to

v

_{t Max}. The value adopted for

v

_{t Max}in the present investigations

is 9. The rotation–torsion energy levels thus obtained for a given J-valuewerelabeledwiththeirsymmetryspeciesinG6andassigned a

torsional quantum number

v

_t and rotational quantum numbers

J; Ka; Kc. Values for

v

tand Kawere determined by examining their

corresponding rotation–torsion eigenvector. For A-type rotation– torsion energy levels, the value of Kcwas obtained by making sure

that Kcþ

v

_t is even (odd) for levels belonging to the A₁ðA₂Þ

symmetry species. For E-type energy levels, the Kcvalue is chosen

so that, just like in a rigid rotator, the level with Kaþ Kc¼ J þ 1 is

below the one with Kaþ Kc¼ J.

5. Analysis

The microwave and FIR data recorded in the present investiga-tion and the microwave data from Ref.[13]were analyzed calculat-ing the rotation-torsion energy with the theoretical approach outlined in the previous section and using a computer program written by one of the authors. Experimental frequencies and wave-numbers were introduced in a least-squares fit procedure where they were given a weight equal to the inverse of the square of their experimental uncertainty. Unresolved doublets were treated as fol-lows. A doublet consisting of two transitions J0Ka10Kc10 J00Ka100Kc100

and J0Ka20Kc20 J00Ka200Kc200, with calculated frequencies or

wave-numbers F1and F2, respectively, was treated in the analysis as a

single transition with a calculated frequency or wavenumber equal to ðF1þ F2Þ=2.

Altogether 4811 transitions were fitted.Table 3gives for each data subset the number of transitions, the experimental uncer-tainty, the root mean square (RMS) value of the observed minus calculated residuals, and the unitless RMS weighed deviation. For the microwave transitions within

v

_t¼ 1 this last value is larger

than for

v

_t_{¼ 0. This may be due to the fact that, the former}

tran-sitions being weaker than the latter, their experimental frequency is measured less accurately. The unitless weighted standard devia-tion of the analysis is 0.9.Table 4gives the value of the 36 param-eters determined in the analysis as well as their uncertainty.

Supplementary Table S1lists assignments, observed frequencies, and observed minus calculated differences for the 1928 microwave

transitions considered in the analysis. Supplementary Table S2

gives the same results, but for the 2883 FIR transitions. 6. Calculated spectrum and linelist

Using the results in Ref.[22], the values

l

x¼ 1:3205 D and

l

z¼ 2:3940 D were derived for the components of the dipole

mo-ment in the RAM axis system and line intensities were computed. A synthetic spectrum of the fundamental torsional band was calcu-lated up to J ¼ 30 at a temperature of 200 K.Figs. 3 and 4show com-parisons between this spectrum and two different portions of the experimental one. These figures emphasize the satisfactory agree-ment between observed and calculated spectra as all calculated tran-sitions can be found in the experimental spectrum. A linelist to be used for future astronomical high resolution observations was built up to J ¼ 20 and spans the 0–400 GHz region. This list is given in Sup-plementary Table S3and is formatted as the JPL catalog line files[23]. In addition to other informations, line frequencies in MHz, the base 10 logarithm of the line intensities in nm2_{MHz at 300 K, and the line}

assignments can be found. For these calculations, the partition func-tion was estimated to be 43 466 at 200 K and 88 792 at 300 K. Acknowledgments

The Ohio State University authors would like to thank NASA for their support of this work. Some of the research described in this paper was performed at the Canadian Light Source, which is sup-ported by NSERC, NRC, CIHR, and the University of Saskatchewan. This work is also supported by the ANR-08-BLAN-0054 contract. Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, atdoi:10.1016/j.jms.2010.07.005.

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