First high resolution ro–vibrational analysis of C2HD3 in the region of the ν12 band

Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

Contents lists available at ScienceDirect

Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt

First high resolution ro–vibrational analysis of C2 HD3 in the region of the ν 12 band O.N. Ulenikov a,∗, O.V. Gromova a, E.S. Bekhtereva a, N.V. Kashirina a, C. Sydow b, M. Schiller b, T. Blinzer b, S. Bauerecker b,& a b

Research School of High-Energy Physics, National Research Tomsk Polytechnic University, Tomsk, 634050, Russia Institut für Physikalische und Theoretische Chemie, Technische Universität Braunschweig, Braunschweig, D - 38106, Germany

a r t i c l e

i n f o

Article history: Received 24 May 2018 Revised 4 July 2018 Accepted 4 July 2018 Available online 5 July 2018 Keywords: C2 HD3 ethylene High-resolution spectra Spectroscopic parameters

a b s t r a c t The high-resolution infrared spectra of C2 HD3 ethylene was analyzed for the first time in the region of 1230–1340 cm−1 , where the strong ν 12 band is located. The 1748 transitions with the maximum values of the upper quantum numbers J max. = 43 and Kamax. = 14 were assigned to the ν 12 band. The 14 transitions have been assigned to the 2ν 10 band whose appearance is caused by the strong resonance interaction with the ν 12 one. For description of the assigned transitions (upper ro-vibrational energy levels), the effective Hamiltonian was used which takes resonance interactions between the vibrational state (v12 = 1 ) and three other closely located states, (v10 = 2 ), (v7 = v10 = 1 ) and (v4 = v10 = 1 ) into account. A set of 70 spectroscopic parameters obtained from a weighted least square fit reproduces the initial experimental data (593 upper energy values, 1762 transitions) with the drms = 1.3 ×10−3 cm−1 . Finally, the strengths of 106 ro–vibrational lines of the ν 12 band were roughly estimated. © 2018 Elsevier Ltd. All rights reserved.

1. Introduction Ethylene is an important chemical species in many fields such as synthetic and analytical chemistry, astrophysics and astrobiology, laser techniques and planetology, etc. Ethylene is a naturally occurring compound in ambient air that affects atmospheric chemistry and the global climate. Due to its high reactivity towards hydroxyl (OH) radicals, ethylene plays a significant role in tropospheric chemistry and ozone generation, Ref. [1]. Ethylene is one of the most relevant substances of study in astrophysics, [2–13]. It acts as a hormone in plants and its role in plant biochemistry, physiology, mammals metabolism, and ecology is the subject of extensive research (see, e.g., [14]). Ethylene is also important as a prototype example in the development of our understanding of relating spectra, dynamics, and potential hypersurfaces of many organic molecules. Therefore, over the years numerous both theoretical and laboratory spectroscopic studies of the ethylene molecule and its different isotopologues have been performed. Without having the opportunity to refer all the “ethylene” studies, we mention here only a few of them, namely, studies which have been per-

∗

Corresponding authors. Corresponding author for experimental issues. E-mail addresses: [email protected] (O.N. Ulenikov), [email protected] (S. Bauerecker). &

https://doi.org/10.1016/j.jqsrt.2018.07.002 0022-4073/© 2018 Elsevier Ltd. All rights reserved.

formed during the last ten years (see Refs. [15–54] and references cited therein). The subject of the present study is the ν 12 band of the C2 HD3 species. Earlier the high resolution spectra of C2 HD3 have been discussed only in a few papers, Refs. [55–63]. The first three papers are devoted to the theoretical ab initio estimations of the intramolecular force field parameters, and estimations of the fundamental band centers of the C2 HD3 molecule can be found there. In the fourth, Ref. [58], the local mode model (see, e.g., Refs. [64– 68]) is applied for analysis of the CH and CD stretching vibrational manifolds of C2 H3 D and C2 HD3 . In a set of papers by Tan with co– authors, Refs. [59–63], the high resolution spectra of the ν 8 and 2ν 8 bands of 12 C2 HD3 and 13 C2 HD3 are discussed. In this paper we present the results of the first analysis of the high resolution Fourier transformed spectra of 12 C2 HD3 in the region of 1230–1340 cm−1 where the ν 12 band is located. The experimental details are given in Section 2. Section 3 presents briefly the theoretical background of our study. A description of the experimental spectra and assignment of transitions are given in Section 4. Section 5 is devoted to the analysis of the ro–vibrational energy structure of the (v12 = 1 ) vibrational state and discussion. Estimation of individual line strengths is discussed in Section 6.

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

87

Table 1 Experimental setup for the regions 1060–2050 cm−1 of the infrared spectrum of C2 HD3 . Spectr.

Resolution /cm−1

No. of scans

Detector

Beamsplitter

Opt. pathlength/m

Aperture /mm

Temp. /o C

Pressure /Pa

Calibr. gas

I II

0.0021 0.0021

350 300

MCT MCT

KBr KBr

4 24

1.3 1.3

25 ± 1 25 ± 1

100 500

H2 O, N2 O H2 O, N2 O

2. Experimental details In the Braunschweig infrared laboratory two spectra in the 1060–2050 cm−1 region have been recorded using an IFS120HR Fourier transform infrared spectrometer (FTIR) combined with a stainless steel White cell with a base length of one meter and a maximum path–length of up to 50 m. A Globar IR source, a KBr beamsplitter, a mercury–cadmium–telluride (MCT) semiconductor detector have been used. The sample C2 HD3 was generated in our laboratory via the exchange reaction between ethylene C2 D4 and hydrogen H2 on a nickel–wire catalyst which was electrically heated to the temperature range of 120–180°C similar as described in Ref. [69]. From this experiment it is clear that the seven isotopologues, C2 H4 , C2 H3 D, C2 H2 D2 , C2 HD3 and C2 D4 , occur while the C2 H2 D2 still splits into the –cis, –trans and –as variants. To get an optimum output of C2 HD3 and a favorable concentration–ratio combination with the “neighbor isotopologues” C2 H2 D2 and C2 D4 with minimized spectral overlap, an analysis of the distribution of the five isotopologue categories dependent on the ratio of deuterium to hydrogen atoms in the gas phase of the system was performed with the following approach: each ethylene molecule has eight possibilities for its four H and D atoms to change atoms with H2 , D2 and HD molecules in the gas phase. In equilibrium the net inflows and outflows from the neighboring isotopologue categories are zero and therefore five balance equations can be formed. Together with the additional general balance equation for the portions of the categories being unity in sum, six equations form an overdetermined linear equation system for the five isotopologue categories which can be solved depending on the H/D atom ratio in the system. As the result, the maximum concentration forms out as a flat maximum with about 42.2 % for the C2 HD3 portion (0.4 % for C2 H4 , 4.7 % for C2 H3 D, 21.1 % for C2 H2 D2 and 31.6 % for C2 D4 ) at an atom ratio of c(D)/c(H) = 3. With this atom ratio we created the mixture of isotopologues over about five hours in the heated system with the nickel wire which we used for the spectra recording. The distribution of isotopologues was checked on the one hand by the band intensities in the transmission spectra and on the other hand generally by a dynamic simulation being both in accordance with the analytical result. The fact that the bond strengths are slightly different for H and D atoms has been neglected in our calculations. For detailed optical and recording parameters see Table 1; the optical resolution was 0.0021 cm−1 for both spectra, the number of scans was 350 and 300 resulting in measuring durations of 17.5 and 15 hours, the optical path-length was 4 m for both spectra and the sample gas pressure was 100 and 500 Pa to get lines with stronger and weaker line intensities. The sample temperature was (25 ± 1)° C. The spectral resolution at 1300 cm−1 was mainly dominated by Doppler broadening of 0.0029 cm−1 for both spectra. The pressure broadening was 0.0 0 02 and 0.0 01 cm−1 for the used sample pressures of 100 and 500 Pa. This means that it has a secondary contribution to the total line widths which can be computed by the root sum square approximation of a convolution of Doppler, pressure and instrumental line widths resulting in 0.0032 and 0.0034 cm−1 for the two pressures which is in accordance with the experimental results. The spectra were calibrated with N2 O and H2 O lines which occur in the sample as an impu-

α

Fig. 1. Axes definitions used in the present work for the C2 HD3 molecule (for comparison, the “mother” C2 H4 molecule is also shown at the bottom part of the figure). The notations of axes refer to the definition of the A−reduction and Ir representation of the Watson effective Hamiltonian. The angle α = 4.37o indicates the angle between the Z axis and the C=C bond, and it is the angle of a turn of the “mother” molecular–fixed coordinate system to the C2 HD3 molecular–fixed coordinate system.

rity of small concentration. For optimization of data recording and line calibration we used data and procedures described in Refs. [34,70,71]. 3. Theoretical background and the Hamiltonian model 3.1. General information The C2 HD3 molecule is an asymmetric top with the value of the asymmetry parameter κ = (2B − A − C )/(A − C )  −0.885 and with the symmetry isomorphic to the Cs point symmetry group (see Fig. 1). For convenience of the reader, the symmetry properties of C2 HD3 are shown in Table 2: the list of irreducible representations and table of characters of the Cs symmetry group are shown in columns 1 - 3; symmetries of vibrational coordinates, qλ (see also Fig. 2), rotational operators Jα , and direction cosines kzα are shown in column 4 and 5. Column 6 presents types of rotational operators Jα and direction cosines kzα , which correspond to the Ir representation (see, e.g., Refs. [72–74]) in asymmetric top molecules.

88

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

Fig. 2. Normal vibrational coordinates of the C2 HD3 molecule (Cs symmetry group).

Table 2 Symmetry types and characters of irreducible representations of the Cs group (application to C2 HD3 ). Repr. 1

E 2

σ (xy)

A

1

1

A 

1

−1

3

Vibr. 4

Rot. 5

Rot.(Ir ) 6

q1 , q2 , q3 , q5 , q6 , q9 , q10 , q11 , q12 q4 , q7 , q8

Jz , kzz

Jy , kzy

Jx , kzx Jy , kzz

Jx , kzx Jz , kzz

As it follows from column 6 of Table 2 (see, also e.g., Refs. [75– 78]), there are two types of vibrational bands which are allowed in absorption: (1) the hybrid bands (both the a−type and b−type transitions are allowed) with the selection rules J = 0, ±1 and Ka = any, Kc = odd; and (2) the c−type bands with the selection rules J = 0, ±1 and Ka = odd, Kc = even. To choose which type of selection rules is applied to a concrete absorption band, one should consider that (1) the selection rules are determined by unequal-to-zero matrix elements of the kzα values: kzx , kzy and kzz are responsible for the appearance of the b−, c− and a−type transitions (bands); (2) the following rule (see, e.g., Ref. [77,79]) is valid: the type of a vibrational band (a−, b−, or c−) for an asymmetric top (Cs symmetry) molecule is determined by the symmetry (kzα ) = A  γ v1  γ v2 , where  (kzα ) is the symmetry of kzα (see column 6 of Table 2), γ v1 and γ v2 are the symmetries of the lower and upper vibrational states, respectively, and  denotes a direct product. In our case of the C2 HD3 molecule, γ v1 is A (ground vibrational state). As a consequence, (A  ← A ) are the bands of the c−type, and (A ← A ) are hybrid bands. For that reason, the ν 12 (A ) bands can be identified as a hybrid band with allowed transition of both a− and b−types. As mentioned in the introduction, in the further analysis we also took into account the bands 2ν 10 (A ), ν7 + ν10 (A ) and ν4 + ν10 (A ). The band 2ν 10 (A ) is also the hybrid band, and ν7 + ν10 (A ) and ν4 + ν10 (A ) are the c−type bands. 3.2. Estimation of the band centers As the preliminary analysis showed, the rotational structure of the ν 12 band is strongly perturbed by the 2ν 10 band. In this case, it is important to estimate the value of the 2ν 10 band center within

accuracy of, at least, 4–5 cm−1 because the worse accuracy of estimation can lead to physically unsuitable values of spectroscopic parameters in the further fit procedure (even in spite of the fact of correct assignment of transitions). In principle, the center of the 2ν 10 band can be estimated if one knows the center of the fundamental band ν 10 in accordance with a simple approximate formula:

2ν10 = 2 × ν10 + 2x10,10 ,

(1)

where x10, 10 is a small anharmonicity coefficient. The problem is that the ν 10 band is extremely weak and overlapped by the considerably stronger ν 7 band. In consequence, the determination of the experimental value of the ν 10 band center is a complicated problem. In such situation, one can use results of ab initio predictions (see e.g., Refs. [55–57]). Unfortunately, ab initio values of the ν 10 band center significantly differ from each other ( ∼ 610 cm−1 , 631.7 cm−1 , 625.6 cm−1 ), and their use in Eq. (1) will lead to large uncertainty in the value of the 2ν 10 band center (especially, if one takes into account the fact that the x10, 10 coefficient is unknown). To solve the problem, we made an analysis of the centers of the bands ν 10 , 2ν 10 and of the values of x10, 10 coefficients for the set of molecules C2 H4 , C2 H3 D, CH2 =CD2 , C2 H2 D2 −cis, C2 H2 D2 −trans, C2 HD3 , and C2 D4 . As the analysis showed (see second and third lines of Table 3), the mean differences, ν 10 , between ab initio−estimated (second and third lines) and experimental values (first line) of the ν 10 band centers of the species C2 H4 , C2 H3 D, CH2 =CD2 , C2 H2 D2 −cis, C2 H2 D2 −trans, and C2 D4 are close to 3.7 cm−1 (mean difference between experimental values from the first line and corresponding values from Ref. [57]) and -1.5 cm−1 (mean difference between experimental values from the first line and corresponding values from Ref. [56]). This gave us the possibility to estimate the mean “experimental” value of the center of the ν 10 band of the C2 HD3 species as 629.75 cm−1 (the mean value of 629.3 and 630.2 cm−1 in column 7, fourth line) taking into account ab initio calculated values 625.6 cm−1 and 631.7 cm−1 in column 7. As the next step, the values of the x10, 10 coefficients for some isotopologues have been estimated. To make this, we used in Eq. (1) experimental values of the ν 10 and 2ν 10 band centers of some isotopic species known from the literature (corresponding values are shown in the fifth line of Table 3). The experimental values of the 2ν 10 band centers which can be found in the literature are: 1372.0 cm−1 for CH2 =CD2 , Ref. [45]; 1330.6 cm−1 for C2 H2 D2 −cis, Ref. [51]; and 1191.3 cm−1 for C2 D4 (our preliminary result of the experimental spectra analysis). After that, data from the first and fifth lines can be used in Eq. (1) for estima-

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

89

Table 3 Centers of the bands ν 10 and 2ν 10 of different ethylene isotopologuesa) . C2 H 4

C2 H 3 D

CH2 =CD2

C2 H2 D2 −cis

C2 H2 D2 −trans

C2 HD3

C2 D4

1

2

3

4

5

6

7

8

exp. ν10 calc. ν10 , [57] ν 10 calc. ν10 , [56] ν 10 estim. ν10 (C2 HD3 )

825. 9b) 821.7 4.2 827.2 −1.3

732. 0c) 728.2 3.7 729.7 2.3

exp. 2ν10 x10, 10 xestim. 10,10 estim. 2ν10 a) b) c) d) e) f) g) h) i) j)

684. 6d) 680.9 3.7 685.8 −1.2

662.8e) 659.5 3.3 665.4 −2.6

1372.0h) 2.5

1.4

673.5f) 669.4 4.1 675.8 −2.3

593.3g) 590.0 3.3 596.6 −3.3

625.6 3.7 631.7 1.5 629.3 630.2

1330.6i)

1191.3j) 2.3 2.1 1263.7

Dimension of all values in Table 2 is cm–1 . From Ref. [33]. From Ref. [80]. From Ref. [52]. From Ref. [54]. From Ref. [81]. From Ref. [53]. From Ref. [45]. From Ref. [51]. From our preliminary analysis. Table 4 Spectroscopic parameters of a few vibrational states of the C2 HD3 molecule (in cm−1 )a . Parameter

Groundb

(v10 = 2 )

(v12 = 1 )

(v7 = v10 = 1 )

(v4 = v10 = 1 )

1

2

3

4

5

6

1260.545(15) 2 .75728(16) 0 .760770(65) 0 .61373(11) 3 .1568 0 .34767 0 .09472 0 .5023 0 .024149

1288.56379(22) 2 .855095(10) 0 .7871513(46) 0 .6131671(33) 1 .314(64) 0 .3124(66) 0 .07256(98) 0 .5023 0 .024149

1330.33(21) 2 .7793(56) 0 .79539(96) 0 .62988(28) 3 .1568 0 .34767 0 .09472 0 .5023 0 .024149

1364.77(19) 2 .84029(66) 0 .78739(35) 0 .632525(21) 3 .1568 0 .34767 0 .09472 0 .5023 0 .024149

E A B C

2 0 0 3 0 0 0 0

K × 105 JK × 105 J × 105 δ K × 105 δ J × 105

.8446778 .78580090 .61415904 .1568 .34767 .09472 .5023 .024149

a Values in parentheses are 1σ standard errors. Values of parameters presented without parentheses have been constrained to the values of corresponding parameters of the ground vibrational state. b Reproduced from Ref. [47].

Table 5 Statistical information for a few bands of the C2 HD3 molecule. a) Ntr

Nlc )

md1)

md2)

md3)

Band

Center/cm−1

1

2

3

4

5

6

7

8

9

10

11

2ν 10

1260.488 1288.62088

16 43

10 14

14 1748

0.4 1.5

8 585

100.0 78.9

0.0 14.9

0.0 7.0

0.5 1.3

ν 12

Jmax

Kamax

b) dtr rms

dlrms

e)

a)

Ntr is the number of assigned transitions. b) Here dtr rms is a root mean square deviation for Ntr transitions of the band (in 10−3 cm−1 ). c) Nl is the number of obtained upper-state energies. d) Here mi = ni /Nl × 100 % (i = 1, 2, 3); n1 , n2 , and n3 are the numbers of upper-state energies for which the differences δ = E exp − E calc satisfy the conditions δ ≤ 1 × 10−3 cm−1 , 1 × 10−3 cm−1 < δ ≤ 2 × 10−3 cm−1 , and δ > 2 × 10−3 cm−1 , respectively. e) Here dlrms is a root mean square deviation for Nl energy levels of the upper state (in 10−3 cm−1 ).

tion of the x10,10 −coefficient values. One can see, that three values of x10,10 −coefficients obtained by this way, are close to each other and positive. As earlier, we estimated a mean value of the x10,10 −coefficients taking into account these three individual values (obtained mean value equals to 2.1 cm−1 and is presented in column 7, seventh line). Finally, the estimated value of the 2ν 10 band center is 1263.7 cm−1 . Analogously, the initial values of the ν7 + ν10 and ν4 + ν10 band centers can be estimated.

cussed in the literature (see, e.g., Refs. [72,82]). For that reason we mention here only part of the Hamiltonian which is responsible for the states considered in the present study (taking into account the Cs symmetry of the C2 HD3 molecule). In its general form, the effective Hamiltonian can be written as

3.3. Effective Hamiltonian model

where the summation is taken from 1 to 4 for both v and v˜ , which represent the four above discussed vibrational states: |1 = (v12 = 1, A ), |2 = (v10 = 2, A ), |3 = (v7 = v10 = 1, A ) and |4 = (v4 = v10 = 1, A ).

The effective Hamiltonian of an asymmetric top molecule which is used for theoretical analysis of experimental data have been dis-

H vib.−rot. =



|v v˜ |H vv˜ ,

(2)

v,v˜

90

Table 6 Ro-vibrational term values for the (v12 = 1 ) vibrational state of the C2 HD3 molecule (in cm−1 )a ) . J

E



2

3

4

1

0 0 1 1 0 1 1 2 2 0 1 1 2 2 3 3 0 1 1 2 2 3 3 4 4 0 1 1 2 2 3 3 4 4 5 5 0 1 1 2 2 3 3 4 4 5 5 6 6 0

0 1 1 0 2 2 1 1 0 3 3 2 2 1 1 0 4 4 3 3 2 2 1 1 0 5 5 4 4 3 3 2 2 1 1 0 6 6 5 5 4 4 3 3 2 2 1 1 0 7

1288.6207 1290.0219 1292.0917 1292.2659 1292.8138 1294.7197 1295.2427 1301.4516 1301.4621 1296.9755 1298.6557 1299.7008 1305.6552 1305.7076 1316.4449 1316.4449 1302.4772 1303.8919 1305.6318 1311.2519 1311.4076 1322.0696 1322.0718 1337.1469 1337.1469 1309.2830 1310.4202 1313.0230 1318.2345 1318.5905 1329.1071 1329.1193 1344.1763 1344.1763 1363.5596 1363.5596 1317.3569 1318.2304 1321.8574 1326.5944 1327.2832 1337.5622 1337.5954 1352.6195 1352.6201 1371.9936 1371.9936 1395.6808 1395.6808 1326.6695

0.2 0.1 0.2 0.2 0.1 0.3 0.1 0.1 0.2 0.2 0.2 0.2 0.1 0.7 0.7 0.4 0.1 0.1 0.3 0.1 0.6 0.6 0.6 0.6 0.3 0.2 0.1 0.1 0.1 0.9 0.2 0.4 0.4 0.2 0.2 0.3 0.1 0.4 0.2 0.2 0.5 0.5 0.6 0.6 0.2 0.2 0.1 0.1 0.2

−0.2 −0.2 0.1 0.0 −0.3 −0.1 0.0 0.5 0.5 −0.3 0.1 −0.3 0.4 0.2 1.0 0.6 −0.2 0.0 −0.6 0.3 0.1 0.6 0.1 1.4 1.3 −0.2 0.1 −0.8 0.1 0.0 −0.3 0.8 0.9 0.8 1.0 1.0 −0.3 0.0 −0.4 0.0 −0.1 0.2 0.2 0.9 0.3 0.7 0.7 0.1 0.1 −0.3

7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10

J



δ

2

3

4

1

1362.4815 1381.8398 1381.8398 1405.5199 1405.5199 1433.5069 1433.5069 1337.2018 1337.6591 1343.7577 1347.4032 1349.2589 1358.7246 1358.9023 1373.7616 1373.7678 1393.1011 1393.1011 1416.7701 1416.7701 1444.7522 1444.7522 1477.0328 1477.0328 1348.9441 1349.2598 1356.7590 1359.8275 1362.5412 1371.4299 1371.7757 1386.4689 1386.4844 1405.7811 1405.7811 1429.4336 1429.4336 1457.4077 1457.4077 1489.7112 1489.7112 1526.2531 1526.2531 1361.8953 1362.1080 1371.0763 1373.5803 1377.3330 1385.5451 1386.1633

0.5 0.3 0.3 0.1 0.1 0.1 0.1 0.2 0.1 0.2 0.2 0.2 0.3 0.1 0.3 0.2 0.3 0.3 0.1 0.1 0.3 0.3

0.3 0.5 0.5 −0.1 −0.1 −0.8 −0.8 −0.1 0.0 −0.9 −0.1 −0.8 0.1 0.3 0.6 0.7 0.3 0.2 −0.2 −0.2 −1.0 −1.0 −1.0 −1.0 −0.1 0.0 −0.6 −0.1 −0.8 0.2 0.2 0.5 0.1 0.5 0.2 −0.2 −0.2 −0.9 −0.9 −0.9 −0.9 −0.3 −0.3 0.0 0.0 −0.3 −0.1 −0.9 0.2 −0.1

10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

Ka

Kc

E

4 5 5 6 6 7 7 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 0 1 1 2 2 3 3

3 3 2 2 1 1 0 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 10 10 9 9 8 8 7

0.1 0.1 0.4 0.2 0.1 0.1 0.1 0.3 0.4 0.5 0.5 0.1 0.1 0.2 0.2 0.2 0.2 0.3 0.3 0.1 0.1 0.3 0.1 0.2 0.1 0.2

J



δ

Ka

Kc

E 2

3

4

1

7 7 8 8 9 9 10 10 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9

4 3 3 2 2 1 1 0 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3

1471.4745 1471.4745 1503.7710 1503.7710 1540.2915 1540.2915 1581.1605 1581.1605 1376.0571 1376.1979 1386.6695 1388.6476 1393.6093 1401.0623 1402.0883 1416.1755 1416.2526 1435.4115 1435.4137 1459.0109 1459.0109 1486.9548 1486.9548 1519.2374 1519.2374 1555.7345 1555.7345 1596.6042 1596.6042 1641.7466 1641.7466 1391.4330 1391.5253 1403.5022 1405.0156 1411.3392 1417.9710 1419.4720 1433.1799 1433.3312 1452.3699 1452.3767 1475.9310 1475.9310 1503.8512 1503.8512 1536.1151 1536.1151 1572.5793 1572.5793

0.2 0.2 0.1 0.1 0.2 0.2

−0.7 −0.7 −0.3 −0.3 0.1 0.1 0.9 0.9 0.0 0.0 −0.7 −0.1 −0.8 0.2 0.1 0.3 0.0 0.7 0.2 −0.3 −0.4 −0.6 −0.6 0.2 0.2 −0.1 −0.1 −0.3 −0.3 1.3 1.3 0.0 0.0 −0.5 0.0 −0.4 0.1 0.9 0.1 −0.3 0.3 0.4 −0.2 −0.4 −0.3 −0.3 0.5 0.5 −0.4 −0.4

13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14

0.2 0.1 0.2 0.3 0.2 0.1 0.2 0.4 1.1 1.1 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.9 0.9

0.1 0.1 0.1 0.3 0.3 0.1 0.4 0.3 0.5 0.3 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.2 0.2

J



δ

Ka

Kc

E 2

3

4

0 1 1 2 2 3 3 4 4 5 5 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12

13 13 12 12 11 11 10 10 9 9 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3

1408.0264 1408.0868 1421.5472 1422.6710 1430.4861 1436.2580 1438.6910 1451.6196 1451.8985 1470.7635 1470.7785 1494.2767 1522.1662 1522.1662 1554.4066 1554.4066 1590.8135 1590.8135 1631.7188 1631.7188 1676.8488 1676.8488 1726.2502 1726.2502 1779.9144 1779.9144 1425.8412 1425.8829 1440.7888 1441.6017 1451.0084 1455.9067 1459.3207 1471.4926 1471.9771 1490.5966 1490.6281 1514.0511 1514.0517 1541.9023 1541.9023 1574.1144 1574.1144 1610.3893 1610.3893 1651.3890 1651.3890 1696.5128 1696.5128 1745.9051

0.1 0.3 0.2 0.2 0.5 0.3 0.4 0.2 0.1 0.1 0.5 0.3 0.2 0.2 0.2 0.2

−0.1 0.1 −0.3 0.1 0.0 0.3 −0.6 0.2 0.1 0.1 0.0 −0.6 0.2 0.2 0.3 0.3 −0.5 −0.5 −0.1 −0.1 0.0 0.0 0.3 0.3 −0.6 −0.6 0.4 0.0 0.0 0.1 0.0 0.1 −0.2 0.0 0.0 −0.1 0.1 0.6 0.6 0.6 0.6 0.1 0.1 −0.4 −0.4 0.0 0.0 −0.3 −0.3 −0.3

0.1 0.1 0.1 0.1

0.3 0.3 0.2 0.3 0.2 0.1 0.3 0.3 0.1 0.2 0.1 0.1 0.2 1.1 1.1 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2 0.2

(continued on next page)

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

Kc

1 0 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 7

δ

Ka

Table 6 (continued) J

Ka

Kc

1 1 2 2 3 3 4 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12

7 6 5 5 4 4 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 16 16 15 15 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4



δ

J

2

3

4

1

1327.3131 1336.3212 1337.5045 1347.4350 1347.5170 1362.4800 1461.7983 1472.8620 1476.90 0 0 1481.5082 1492.7942 1493.5943 1511.8731 1511.9329 1535.2595 1535.2595 1563.0628 1563.0628 1595.2407 1595.2407 1631.8982 1631.8982 1672.4676 1672.4676 1717.5863 1717.5863 1766.9688 1766.9688 1820.6096 1820.6096 1465.1048 1465.1414 1482.8494 1483.2557 1496.0 0 0 0 1499.2220 1505.2203 1515.5180 1516.7771 1534.5962 1534.7119 1557.9033 1557.9098 1585.6510 1585.6510 1617.7884 1617.7884 1654.3458 1654.3458 1694.9523 1694.9523 1740.0699 1740.0699 1789.4413 1789.4413

0.1 0.2 0.6 0.1 0.3 0.7 0.0 0.1 0.0 0.2 0.2 0.1 0.2 0.2 1.7 1.7 0.3 0.3 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.3 0.4 0.6 0.3 0.1 0.3 0.2 0.2 0.3 0.3 0.4 0.4 0.4 0.4 0.2 0.2 0.3 0.3 0.2 0.2 0.1 0.1

−0.1 0.0 0.1 0.5 0.4 0.9 0.1 0.4 0.0 0.3 −0.2 0.0 −0.2 −1.9 1.3 −1.2 1.2 1.2 −0.3 −0.3 −0.2 −0.2 0.2 0.2 −0.3 −0.3 −0.3 −0.3 −0.1 −0.1 1.0 0.0 0.1 −0.3 0.5 0.1 0.1 −0.1 −0.7 −0.2 0.5 −0.4 0.7 2.3 2.1 −0.3 −0.3 −0.4 −0.4 0.3 0.3 −0.2 −0.2 −0.5 −0.5

10 10 10 10 10 10 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 19

Ka

4 4 5 5 6 6 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 11 11 12 12 13 13 0

Kc

7 6 6 5 5 4 15 15 14 14 13 13 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 5 4 18 18 17 17 16 16 15 15 14 14 13 13 12 12 11 11 10 10 9 8 7 7 6 6 5 19

E



δ

J

2

3

4

1

1400.6056 1400.6425 1419.8834 1419.8834 1443.5130 1443.5130 1520.3802 1522.8640 1530.4218 1539.6539 1541.5469 1558.7676 1558.9735 1581.9898 1582.0030 1609.6681 1609.6681 1641.7572 1641.7572 1678.2560 1678.2560 1718.7631 1718.7631 1763.9646 1763.9646 1813.3241 1813.3241 1866.9347 1866.9347 1509.2877 1509.2991 1529.5808 1529.7627 1545.9654 1547.8252 1557.0703 1565.1897 1567.9144 1584.3880 1584.7400 1607.5227 1607.5488 1635.1246 1635.1246 1667.1539 1667.1539 1703.6020 1703.6020 1789.2708 1789.2708 1838.6178 1838.6178 1892.2108 1892.2108 1533.2215

0.4 0.4 0.9 0.9 0.3 0.3 0.3 0.2 0.2 0.3 0.1 0.7 0.2 0.1 0.6 2.3 2.3 1.5 1.5 0.2 0.2 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2

0.2 0.4 0.8 −0.5 −0.2 −0.2 0.1 0.0 0.6 −0.3 −0.2 −0.5 0.2 −0.2 0.8 1.5 1.0 −2.5 −2.5 −0.3 −0.3 0.7 0.7 0.5 0.5 −0.4 −0.4 0.8 0.8 0.0 0.3 −2.6 −1.4 0.9 0.0 0.5 −0.6 0.0 −0.8 0.1 −0.3 1.7 5.8 4.8 −2.9 −2.9 0.0 0.0 1.9 1.9 −0.4 −0.4 1.2 1.2 0.3

12 12 12 12 12 12 19 19 19 19 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 21 21 21 21 21 21 21 21 21 21 21 21

0.4 0.4 0.3 0.5 0.2 0.4 0.4 0.2 0.1 0.2 0.2 1.2 1.2 0.4 0.4 0.2 0.2 0.3 0.3 0.3 0.3 0.7 0.7 0.8

Ka

10 10 11 11 12 12 5 5 6 6 8 8 9 9 11 11 12 12 13 13 0 1 1 2 2 3 3 4 4 5 5 6 6 8 8 9 9 11 11 12 12 13 13 0 1 1 2 2 3 3 4 4 5 5 6

Kc

3 2 2 1 1 0 15 14 14 13 12 11 11 10 9 8 8 7 7 6 20 20 19 19 18 18 17 17 16 16 15 15 14 13 12 12 11 10 9 9 8 8 7 21 21 20 20 19 19 18 18 17 17 16 15

E



δ

J

2

3

4

1

1613.4576 1613.4576 1658.5935 1658.5935 1708.0040 1708.0040 1611.4559 1612.0346 1634.5056 1634.5530 1693.9796 1693.9796 1730.3772 1730.3772 1815.9875 1815.9875 1865.3234 1865.3234 1918.8961 1918.8961 1558.3742 1558.3767 1581.3170 1581.3962 1600.6733 1601.6624 1614.5184 1620.4025 1625.5723 1639.9671 1640.8839 1662.9451 1663.0293 1722.2372 1722.2372 1758.5807 1758.5807 1844.1082 1844.1082 1893.4416 1893.4416 1946.9926 1946.9926 1584.7507 1584.7507 1608.9767 1609.0585 1629.7860 1630.4915 1645.2174 1650.0457 1656.6582 1669.9145 1671.3152 1692.9869

0.2 0.2 0.3 0.3 0.7 0.7 0.3 0.2 0.2 1.0 0.2 0.2 0.2 0.2 0.9 0.9 0.3 0.3 0.3 0.3 0.6 0.5 0.4 0.1 0.2

0.1 0.1 0.4 0.4 2.2 2.2 −1.1 0.1 −0.8 1.2 −3.0 −3.0 0.5 0.5 3.5 3.5 −0.6 −0.6 0.4 0.4 0.0 0.0 0.4 0.1 0.4 1.9 0.0 −2.1 0.5 −1.6 0.3 1.2 0.4 −3.2 −3.0 1.1 1.1 0.3 0.3 −1.0 −1.0 −0.3 −0.3 0.0 −0.8 0.6 −0.3 0.4 1.3 −0.3 −4.1 −0.5 −2.8 0.2 2.8

14 14 14 15 15 15 21 21 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 24 24 24 24 24 24 24 24 24 24 24 24 24

0.3 0.2 0.1 0.3 0.4 0.5 0.1 0.5 0.5 0.2 0.2

0.2 0.2 0.2 0.2 1.1 1.1 0.2 0.3 0.2 0.3 0.3 0.3 0.1 0.5 0.1 0.2

Ka

12 13 13 0 1 1 13 13 0 1 1 2 2 3 3 4 4 5 6 8 8 9 9 12 12 13 13 0 1 1 2 2 3 3 4 4 5 8 9 9 12 12 0 1 1 2 2 3 3 4 8 8 9 9 12

Kc

2 2 1 15 15 14 9 8 22 22 21 21 20 20 19 19 18 17 16 15 14 14 13 11 10 10 9 23 23 22 22 21 21 20 20 19 18 16 14 15 11 12 24 24 23 23 22 22 21 21 17 16 16 15 13

E



δ

2

3

4

1745.9051 1799.5586 1799.5586 1444.8794 1444.9677 1461.2217 1976.50 0 0 1976.50 0 0 1612.3499 1612.3499 1637.7197 1637.8480 1660.0766 1660.5703 1677.1648 1681.0342 1689.3030 1703.3535 1724.4421 1783.0623 1783.0623 1819.2763 1819.2763 1953.9173 1953.9173 2007.4193 2007.4193 1641.1728 1641.1728 1667.90 0 0 1667.9333 1691.5519 1691.8918 1710.3280 1713.3298 1723.4337 1737.0148 1815.6369 1851.7725 1851.7725 1986.2701 1986.2701 1671.2190 1671.2190 1699.2208 1699.2383 1724.2192 1724.4488 1744.6552 1746.9322 1849.6580 1849.6580 1885.7077 1885.7077 2020.0391

0.2 0.1 0.1 0.1 0.6 0.1 0.3 0.3 0.7 0.7 0.4 0.1

−0.3 −0.5 −0.5 −0.2 2.1 0.1 −1.1 −1.1 0.4 −0.4 −1.8 0.2 0.3 −0.2 −2.6 3.5 −0.6 0.2 0.1 −1.7 −2.8 0.9 0.9 −0.1 −0.1 1.1 1.1 0.3 −0.2 0.0 0.1 0.2 −0.1 4.0 −0.8 −2.8 0.5 −0.6 −0.3 −0.3 0.0 0.0 0.0 −0.2 −0.2 −0.1 0.2 −0.4 0.0 −1.3 0.8 −0.6 1.0 0.9 3.4

0.4 0.2 0.2 0.2 0.2 0.4 1.1 1.1 0.4 0.0 0.5 0.5 0.3 0.3 0.3 0.3

0.1 0.4 0.2 0.3 0.2 0.1 0.2 0.3 0.3 0.2 0.2 0.3 0.3 0.2 0.1 0.3 0.3 0.1 0.3 2.1 2.1 0.4 0.4

91

(continued on next page)

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

7 7 7 7 7 7 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16

E

92

Table 6 (continued) J

Ka

Kc

1 13 13 14 14 0 1 1 2 3 3 4 5 5 8 8 9 9 0 1 1 2 2 3 3 4 5 7 8 8 0 1 1 2 3 3 4 5 8 0 1 1 2

4 3 3 2 17 17 16 16 23 22 22 21 20 18 17 17 16 26 26 25 25 24 24 23 23 22 19 19 18 27 27 26 26 25 24 24 23 19 28 28 27 27



δ

J

2

3

4

1

1843.0681 1843.0681 1900.9064 1900.9064 1486.5942 1486.7620 1505.6868 1505.9927 1758.2398 1780.1414 1781.8255 1803.8661 1809.1714 1885.1286 1885.1321 1921.0793 1921.0793 1734.9814 1734.9814 1765.5080 1765.5138 1793.1579 1793.2753 1816.7776 1817.9949 1840.8138 1891.0270 1922.0550 1922.0618 1768.6970 1768.6970 1800.4807 1800.4807 1829.4349 1854.5672 1855.4302 1879.1124 1960.4536 1803.6349 1803.6349 1836.6728 1836.6728

0.3 0.3 0.2 0.2 0.1 0.4 0.3 0.3 0.5 0.2 0.5 0.4 0.2 0.4 0.3 0.5 0.5 0.2 0.2

0.5 0.5 0.2 0.2 0.4 −1.1 −0.6 −1.7 −0.4 −0.5 −1.3 4.3 1.7 1.0 0.6 −0.7 −1.0 0.0 0.0 0.7 0.3 0.5 3.2 −0.4 −1.9 2.3 5.4 0.3 0.9 0.0 0.0 0.9 −2.8 −0.4 0.4 −1.6 1.0 1.0 −0.1 −0.1 0.0 0.0

19 19 19 19 19 19 19 19 28 28 28 28 28 29 29 29 29 29 29 29 29 29 30 30 30 30 30 30 30 30 30 31 31 31 31 31 31 31 31 32 32

0.4 0.2 0.3 0.2 0.5 0.5 0.3 0.2 0.3 0.3 1.1 1.1 0.2 0.1 0.2 0.1 0.5 0.2 0.2 2.1 2.1

Ka

1 1 2 2 3 3 4 4 2 3 3 4 5 0 1 1 2 2 3 3 4 5 0 1 1 2 2 3 3 4 5 0 1 1 2 2 3 3 5 0 1

Kc

19 18 18 17 17 16 16 15 26 26 25 25 24 29 29 28 28 27 27 26 26 25 30 30 29 29 28 28 27 27 26 31 31 30 30 29 29 28 27 32 32

E



δ

J

2

3

4

1

1533.2255 1554.8662 1554.9795 1572.7331 1574.0988 1585.1189 1592.1111 1595.8496 1866.8148 1866.9096 1893.5179 1894.1187 1918.7429 1839.7954 1839.7954 1874.0867 1874.0867 1905.5504 1905.5955 1933.6408 1934.0511 1959.6869 1877.1772 1877.1772 1912.7195 1912.7204 1945.4721 1945.4988 1974.9446 1975.2198 2001.9289 1915.7810 1915.7810 1952.5738 1952.5738 1986.6034 1986.6201 2017.4387 2045.4505 1955.6060 1955.6060

0.9 0.4 0.1 0.2 0.7 0.4 0.2 0.2 0.0 0.2 0.9 0.2 0.4 0.1 0.1 1.0 1.0 0.4 0.5 0.3 0.4 0.3 0.4 0.4 0.4 0.3 0.2 0.3 0.5 0.4 0.3 0.2 0.2 0.5 0.5 0.5 0.5 0.3

−0.4 0.4 −0.1 0.5 0.8 0.4 −1.4 1.1 4.0 −1.7 0.6 −0.4 −0.2 0.2 0.2 0.3 −1.2 −0.2 −1.7 −0.9 −0.5 −1.2 −0.1 −0.1 −0.4 −1.0 −0.7 −1.1 0.4 2.1 1.0 0.0 0.0 −1.1 −1.1 −0.6 −0.6 −1.2 0.2 0.1 0.1

21 21 21 21 21 21 21 21 32 32 32 32 32 33 33 33 33 33 33 33 33 34 34 34 34 34 34 34 34 35 35 35 35 35 35 35 36 36 36 36 36

0.4 0.4

Ka

8 8 9 9 11 11 12 12 1 2 2 3 3 0 1 1 2 2 3 3 4 0 1 1 2 2 3 3 4 0 1 1 2 2 3 4 0 1 1 2 2

Kc

14 13 13 12 11 10 10 9 31 31 30 30 29 33 33 32 32 31 31 30 30 34 34 31 31 30 30 33 29 35 35 34 34 33 32 32 36 36 35 35 34

E



δ

J

2

3

4

1

1751.9305 1751.9305 1788.2132 1788.2132 1873.6363 1873.6363 1922.9732 1922.9732 1993.6486 1993.6486 2028.9492 2028.9594 2061.1382 1996.6518 1996.6518 2035.9431 2035.9431 2072.5106 2072.5172 2106.0435 2106.1176 2038.9179 2038.9179 2079.4571 2079.4571 2117.2915 2117.2915 2151.9057 2152.1122 2082.4041 2082.4041 2124.1903 2124.1903 2163.2841 2199.3119 2199.3864 2127.1102 2127.1102 2170.1422 2170.1422 2210.4937

0.6 0.6 0.1 0.1 0.2 0.2 0.2 0.2 0.3 0.3 0.4 0.3 0.2 0.3 0.3 0.3 0.3 1.3 1.1 0.5

−2.8 −2.4 1.4 1.4 1.9 1.9 −0.9 −0.9 −0.7 −0.7 0.0 −0.3 0.6 0.2 0.2 −0.4 −0.4 0.3 0.3 0.6 −3.3 0.1 0.1 −0.1 −0.1 −0.5 −0.5 −1.1 −1.6 −1.0 −1.0 1.8 1.7 −1.2 2.2 −1.5 −0.1 −0.1 0.6 0.5 0.3

24 24 24 25 25 25 25 25 36 36 36 37 37 37 37 37 37 38 38 38 38 38 38 39 39 39 39 39 40 40 40 40 41 41 41 42 42 42 42 43 43

0.3 0.3 0.2 0.2 2.0 2.0 0.6 0.5 0.5 0.4 0.4 1.1 1.1 0.2 0.2 0.3 0.3 0.2

Ka

12 13 13 0 1 1 2 2 3 3 4 0 1 1 2 2 3 0 1 1 2 2 3 0 1 1 2 3 0 1 1 2 0 1 1 0 1 1 2 0 1

Kc

12 12 11 25 25 24 24 23 34 33 33 37 35 34 36 33 35 38 38 37 37 36 36 39 39 38 38 37 40 40 39 39 41 41 40 42 42 41 41 43 43

E



δ

2

3

4

2020.0391 2073.4933 2073.4933 1702.4887 1702.4887 1731.7549 1731.7549 1758.0857 2210.4957 2247.8328 2247.8706 2173.0357 2173.0357 2217.3112 2217.3112 2258.9208 2258.9222 2220.1803 2220.1803 2265.6998 2265.6998 2308.5646 2308.5646 2268.5426 2268.5426 2315.3050 2315.3050 2359.4234 2318.1240 2318.1240 2366.1279 2366.1279 2368.9220 2368.9220 2418.1662 2420.9365 2420.9365 2471.4199 2471.4199 2474.1687 2474.1687

0.3 0.3 0.2 0.2 0.4 0.4 0.1 0.3 0.4 0.4 0.5 0.5 1.3 1.3 0.6 0.2 1.0 1.0 0.5 0.5 0.6 0.6 0.2 0.2 0.6 0.6 0.4 0.5 0.5 0.3 0.3 0.6 0.6 0.6 0.3 0.3 0.2 0.2

3.4 −0.5 −0.5 0.0 −0.2 0.1 −0.1 0.4 0.7 3.3 2.8 −0.1 −0.1 −0.5 −0.5 −0.2 0.2 0.2 0.2 0.1 0.1 0.4 −0.2 −0.4 −0.4 −0.3 −0.3 0.4 0.2 0.2 0.0 0.0 −0.1 −0.1 −0.1 −0.8 −0.8 0.0 0.0 −0.1 −0.1

a) In Table 6,  is the experimental uncertainty of the energy value, equal to one standard error in units of 10−3 cm−1 ; δ is the difference Eexp. -Ecalc. , also in units of 10−3 cm−1 . When the -value is absent, the corresponding energy level was determined from the single transition and was not used in the fit.

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

16 16 16 16 17 17 17 17 25 25 25 25 25 25 25 25 25 26 26 26 26 26 26 26 26 26 26 26 26 27 27 27 27 27 27 27 27 27 28 28 28 28

E

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

93

Table 7 Transitions belonging to the 2ν 10 band of C2 HD3 . Band

Upper

Lower

J

Ka

Kc

J

K

a

K

Line position (cm

1 2ν 10

12

2 5

7

2ν 10

17

2

15

2ν 10

14

10

d

2ν 10

15

10

d

2ν 10

16

10

d

11 12 13 16 18 16 18 13 14 15 15 16 15 17

3 3 3 3 0 0 1 1 9 9 9 9 9 9 9

8 10 10 16 18 16 18 d d d d d d d

4 1306.5195 1290.6230 1270.0366 1309.7890 1265.5729 1309.7725 1265.5672 1309.9352 1290.2716 1269.1955 1289.4127 1266.9229 1311.4874 1265.0918

c

−1

)

Transmittance

Upper energy −1

(%)

(cm

)

5 82.9 97.1 81.7 87.0 91.0 93.8 94.4 90.6 90.4 91.0 91.7 93.0 95.7 97.1

6 1419.7461 1419.7472 1419.7465 1486.3710 1486.3710 1486.3697 1486.3711 1610.9897 1610.9898 1610.9898 1631.2069 1631.2071 1653.2816 1653.2817

Mean value (cm

−1

)

δa (10−3 cm−1 )

7 1419.7466

8 −0.7

1486.3707

0.7

1610.9898

0.3

1631.2070

0.0

1653.2817

-0.5

δ = (Eexp. -Ecalc. )(in units of 10−3 cm−1 ) is the difference between the experimental value of upper energy from column 7 and corresponding value calculated with the parameters from Tables 3 and 7.

a

Any diagonal block Hvv , Eq. (2), describes unperturbed rotational structure of the vibrational state |v and has a form of reduced effective Hamiltonian in the A−reduction and Ir representation (see, e.g., Ref. [72]):

1 1 1 2 H vv = E v + [Av − (Bv + C v )]Jz2 + (Bv + C v )J 2 + (Bv − C v )Jxy 2 2 2 2 2 −vK Jz4 − vJK Jz2 J 2 − vJ J 4 − δKv [Jz2 , Jxy ]+ − 2δJv J 2 Jxy v J 4 J 2 + H v J 2 J 4 + H v J 6 + [J 2 , hv J 4 +HKv Jz6 + HKJ z xy JK z J K z

+hvJK J 2 Jz2 + hvJ J 4 ]+ + LvK Jz8 + LvK K J Jz6 J 2 + LvJK Jz4 J 4 2 v J 2 J 4 + l v J 4 J 2 + l v J 6 ] + ..., +LvKJJ Jz2 J 6 + LvJ J 8 + [Jxy , lKv Jz6 + lKJ + z z JK J

Fig. 3. Survey spectrum of C2 HD3 in the region of the ν 12 band. Experimental conditions: sample pressure is 100 Pa, absorption path length is 4 m; room temperature; number of scans is 350.

2 = J 2 − J 2 ; [..., ...] denotes anticommutators; Av , Bv , and where Jxy + x y Cv are the effective rotational constants connected with the vibrational state (v), and the other parameters are the different order centrifugal distortion coefficients. Nondiagonal blocks H vv˜ (v = v˜ )

Fig. 4. Detail of the high resolution experimental spectrum of C2 HD3 in the Q-branch region of the ν 12 band. For experimental conditions see Fig. 3.

94

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99 Table 8 Mixing coefficients b(vv,J,Ka Kc ) which indicate a power of the borrowing of line intensities from the strong ν 12 band to the weak bands 2ν 10 and ν4 + ν10 . 1

2

3

4

5

6

Vib. state

J

Ka

Kc

EJKa Kc

) b((... v =2 )

) b((... v =1 )

) b((... v =v

(v10 = 2 ) (v12 = 1 ) (v10 = 2 ) (v12 = 1 ) (v10 = 2 ) (v12 = 1 ) (v10 = 2 ) (v12 = 1 ) (v10 = 2 ) (v12 = 1 )

12 12 17 17 14 14 15 15 16 16

5 3 2 1 10 9 10 9 10 9

7 9 15 17 d d’ d d’ d d’

1419.7466 1419.7466 1486.3707 1486.7620 1610.9898 1610.3893 1631.2070 1631.8982 1653.2817 1654.3458

0.534 0.465 0.590 0.407 0.658 0.330 0.695 0.297 0.864 0.129

0.466 0.535 0.410 0.593 0.332 0.667 0.300 0.699 0.130 0.869

0.00 0.00 0.00 0.00 0.010 0.003 0.005 0.004 0.006 0.002

10

12

7 7

10 =1

)

) b((... v =v 4

10 =1

)

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Table 9 Fermi and Coriolis interaction parameters for a few vibrational states of C2 HD3 obtained from the fit (incm−1 )a . Parameter

Value

Parameter

Value

Parameter

Value

1, 2

F0 1, 2 FKK × 104 1, 2 FKJJ × 107 1, 2 FKKJxy × 109 1, 2 1y C

1.266(68) 0.984(11) 0.171(12) 0.321(18) −0.09386(89)

1, 2

0.02305(45) −0.1409(81) 0.38214(83) −0.1842(66) 0.174(25)

1, 2

FJ × 102 1, 2 FKKJ × 107 1, 2 FKKxy × 106

0.3613(25) 0.441(48) −0.379(14)

−0.597(26)

1,2 1y CJJ × 107 1,2 1y CKJJ × 109 1,2 2y CKK × 106 1,2 2y CJJJ × 1011 1,3 1z CK 1,3 1z CKJ × 104 1, 3 2z 2

0.180(16)

1,2 1y CJ × 104 1,2 1y CK K K × 107 1,2 2y CK × 104 1,2 2y CKJ × 107

0.280(10)

1,2 1y CKK × 105 1,2 1y CK K J × 107 1,2 2y CJ × 105 1,2 2y CJJ × 108 1, 3 1z

−0.588(32) 0.0207(25) −0.2332(62) 0.590(23)

1,3 1z CJ × 102 1,3 1z CK K J × 107 1,3 2z CK K K × 108

C

1,3 1z CKK × 103 1,3 1z CKJJ × 107 1,3 2z CK K J × 108 1,3 2x CJ × 104 2,3 2x CJ × 105 2,4 1x CJ × 103 2,4 1x CJJ × 106 2, 4 2x 2

C × 10

2,4 2x CKJ × 106 2,4 2x CK K J × 109

−0.1174(59) −0.434(51) 0.9954(72) −0.469(66) −0.1180(12) −0.184(17) −0.2331(66) 0.1323(94) 0.346(20) −0.1951(78) 0.1990(69) −0.634(41) −0.2632(62) 0.988(29)

FK 1, 2 FKJ × 104 1, 2 Fxy × 102 1, 2 FKJJxy × 1010 1,2 1y CK × 103

C × 10

2,4 1x CKK × 105 2,4 1x CK K J × 107 2,4 2x CJ × 104 2,4 2x CJJ × 107 2,4 2x CKJJ × 109

0.1271(53) 0.507(25)

−0.347(46) −0.131(19) 0.101(19) −0.102(15) 0.1424(44)

2,4 1x CKJ × 105 2,4 1x CKJJ × 108 2,4 2x CKK × 106 2,4 2x CK K K × 108

0.477(23) −0.242(22) −0.409(38) 0.2932(28) 0.726(56) 0.379(31)

0.590(15) −0.421(13) 0.428(22) −0.173(12)

describe different kinds of resonance interactions between vibrational states. In our case, four types of interaction operators should be taken into account:

and

(1) Operators H 12 = H 21 or H 34 = H 43 , which connect the vibrational states |1 = (v12 = 1, A ) and |2 = (v10 = 2, A ) or |3 = (v7 = v10 = 1, A ) and |4 = (v4 = v10 = 1, A ), are the (Fermi + C–type Coriolis) operator and has the form:

In Eqs. (4)–(7) it is denoted

v,v˜ H v,v˜ = HFv,v˜ + HCy ,

(3)

where

HFv,v˜ = v,v˜ F0 + v,v˜ FK Jz2 + v,v˜ FJ J 2 + v,v˜ FKK Jz4 + v,v˜ FKJ Jz2 J 2 + v,v˜ FJJ J 4 + ... +v,v˜ Fxy (Jx2 − Jy2 ) + v,v˜ FKxy [Jz2 , (Jx2 − Jy2 )]+ and

HCy = iJy H(v1,v˜y ) + H(v1,v˜y ) iJy + [Jx , Jz ]+ H(v2,v˜y ) + H(v2,v˜y ) [Jx , Jz ]+ ... 31+

41+

32+

(4) +

(2) Operators H 13 = H , H 14 = H , H 23 = H , and H 24 = H 42 are (A + B )−type Coriolis interaction operators which connect the vibrational states |1 = (v12 = 1, A ) and |2 = (v10 = 2, A ) with the vibrational states |3 = (v7 = v10 = 1, A ) and |4 = (v4 = v10 = 1, A ). They have the form v,v˜ v,v˜ H v,v˜ = HCz + HCx ,

(5)

where v,v˜ HCz = iJz H(v1,v˜z ) + [Jx , Jy ]+ H(v2,v˜z ) + H(v2,v˜z ) [Jx , Jy ]+ ...

H(vi,αv˜ ) =

(7)

1 vv˜ (iα ) vv˜ (iα ) 2 1 vv˜ (iα ) 2 vv˜ (iα ) 4 vv˜ (iα ) 2 2 C + CK Jz + CJ J + CKK Jz + CKJ Jz J 2 2 1 + vv˜ CJJ(iα ) J 4 + vv˜ CK(iKαK) Jz6 + vv˜ CK(iKαJ) Jz4 J 2 2 1 ( iα ) 2 4 v + v˜ CKJJ Jz J + vv˜ CJ(JiJα ) J 6 + ..., (8) 2

and α = x, y, z. 4. Description of the spectrum and assignment of transitions

+ v,v˜ FJxy J 2 (Jx2 − Jy2 ) + ... v,v˜

v,v˜ HCx = iJx H(v1,v˜x ) + H(v1,v˜x ) iJx + [Jy , Jz ]+ H(v2,v˜x ) + H(v2,v˜x ) [Jy , Jz ]+ ...

(6)

The survey spectrum in the region of 1230–1340 cm−1 , where the ν 12 band of C2 HD3 is located, is shown in Fig. 3. One can see clearly pronounced the Q−, as well the P − and R−branches. As an illustration of the quality of the experimental spectrum, the upper part of Fig. 4 shows a small part of the high resolution spectrum in the region of the Q-branch. A few sets of transitions of the Q QK (J )−type (K = 4 − 13) are marked in Fig. 4. One can see strong enough perturbation of the Q Q10 (J) set of transitions and a very strong perturbation of the Q Q9 (J) set of transitions which are caused by pronounced resonance interactions between ro–vibrational structures of the (v12 = 1 ) and (v10 = 2 ) vibrational states.

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

95

Table 10 List of transitions with an experimentally obtained individual line strengths. Wavenumber 1

J 2

Ka

1259.0863 1259.4832 1259.5679 1259.5679 1260.5898 1260.8159 1260.8159 1260.8699 1261.0926 1262.0625 1262.0625 1263.5430 1263.6663 1264.6306 1264.9956 1265.0722 1265.8540 1266.4328 1266.4809 1267.1150 1267.8642 1267.8906 1268.4178 1269.5477 1270.7842 1271.1468 1271.9315 1272.5674 1274.0203 1274.4266 1274.5136 1274.9280 1274.9280 1275.5002 1275.6628 1275.7627 1276.3311 1276.3311 1277.0 0 05 1277.0164 1277.7328 1277.7328 1278.0941 1278.2761 1278.4450 1278.5114 1279.3172 1279.5431 1279.8502 1280.5575 1280.8184 1281.2792 1281.5150 1281.8256 1282.1026 1283.3955 1284.1902 1284.6965 1285.8325 1286.0046 1289.2932 1289.2932 1289.3320 1289.3320 1289.5093 1289.5093 1289.6290 1289.6290 1289.6533 1289.6533 1289.6711 1289.6711

20 20 22 22 19 21 21 19 19 20 20 17 17 16 16 16 15 15 15 14 14 14 13 14 13 11 11 10 9 9 10 9 9 8 9 9 8 8 7 8 7 7 7 7 6 6 6 6 5 5 5 4 4 4 4 3 2 2 1 1 7 7 9 9 8 8 12 12 13 13 14 14

5 5 0 1 5 0 1 5 2 0 1 5 5 2 5 5 2 5 5 2 5 5 2 1 1 2 1 2 2 1 1 5 5 2 0 1 5 5 2 1 5 5 0 1 1 2 0 1 1 0 1 1 2 0 1 1 1 1 0 1 7 7 7 7 8 8 8 8 8 8 9 9

Kc 15 16 22 22 14 21 21 15 17 20 20 12 13 14 11 12 13 10 11 12 9 10 11 14 13 9 10 8 7 8 10 4 5 6 9 9 3 4 5 8 2 3 7 7 5 4 6 6 4 5 5 3 2 4 4 3 1 2 1 1 0 1 2 3 0 1 4 5 5 6 6 5

J 3

Ka

21 21 23 23 20 22 22 20 20 21 21 18 18 17 17 17 16 16 16 15 15 15 14 15 14 12 12 11 10 10 11 10 10 9 10 10 9 9 8 9 8 8 8 8 7 7 7 7 6 6 6 5 5 5 5 4 3 3 2 2 7 7 9 9 8 8 12 12 13 13 14 14

5 5 0 1 5 0 1 5 2 0 1 5 5 2 5 5 2 5 5 2 5 5 2 1 1 2 1 2 2 1 1 5 5 2 0 1 5 5 2 1 5 5 0 1 1 2 0 1 1 0 1 1 2 0 1 1 1 1 0 1 7 7 7 7 8 8 8 8 8 8 9 9

Kc

δ tr. a 4

16 17 23 23 15 22 22 16 18 21 21 13 14 15 12 13 14 11 12 13 10 11 12 15 14 10 11 9 8 9 11 5 6 7 10 10 4 5 6 9 3 4 8 8 6 5 7 7 5 6 6 4 3 5 5 4 2 3 2 2 1 0 3 2 1 0 5 4 6 5 5 6

4 −18 −6 −1 3 4 12 −11 7 7 −5 1 −5 8 4 −3 5 −19 −1 0 0 −1 −3 3 2 −9 −7 −10 −9 −11 0 8 2 −8 −3 0 6 4 −6 −1 8 7 −4 −1 −9 −3 −5 −1 −8 −5 0 −6 3 −5 0 0 −1 −1 −1 1 −8 −8 −10 −10 −12 −12 6 6 6 6 −4 −4

δ str. d

Transm.b 5

SνN (exp. )c 6

SνN (calc. )c 7

78.1 78.5 60.6

.2746E−21 .2808E−21 .5705E−21

.2255E−21 .2267E−21 .5969E−21

17.9 19.3 −4.6

77.1 58.2

.2857E−21 .6131E−21

.2468E−21 .6509E−21

13.6 −6.2

77.7 73.1 57.4

.2859E−21 .3128E−21 .6651E−21

.2477E−21 .3097E−21 .7004E−21

13.4 1.0 −5.3

75.1 75.3 67.7 73.3 74.6 66.6 72.9 73.3 64.6 72.7 72.7 64.1 66.8 63.9 64.1 63.8 64.6 65.6 64.0 65.1 60.1

.3041E−21 .3089E−21 .4718E−21 .3309E−21 .3236E−21 .4641E−21 .3213E−21 .3218E−21 .4832E−21 .3812E−21 .3418E−21 .4755E−21 .4113E−21 .4970E−21 .5080E−21 .4666E−21 .4666E−21 .4503E−21 .4633E−21 .4686E−21 .5989E−21

.2858E−21 .2862E−21 .3886E−21 .3021E−21 .3023E−21 .4113E−21 .3153E−21 .3154E−21 .4304E−21 .3245E−21 .3246E−21 .4458E−21 .4897E−21 .5100E−21 .4592E−21 .4795E−21 .4560E−21 .4446E−21 .4661E−21 .5063E−21 .5648E−21

6.0 7.3 17.6 8.7 6.6 11.4 1.9 2.0 10.9 14.9 5.0 6.2 −19.1 −2.6 9.6 −2.8 2.3 1.3 −0.6 −8.1 5.7

66.9 66.0 64.5 62.3

.4653E−21 .4726E−21 .4548E−21 .4901E−21

.4251E−21 .4775E−21 .4913E−21 .5007E−21

8.6 −1.0 −8.0 −2.2

69.1 66.2 67.8

.3988E−21 .4625E−21 .4109E−21

.3964E−21 .4686E−21 .4166E−21

0.6 −1.3 −1.4

67.2 68.3 70.1 71.1 70.1 69.8 72.5 73.0 73.0 76.4 79.1 75.7 75.4 80.7 85.1 85.4 87.8 91.5 45.3

.4058E−21 .3743E−21 .3896E−21 .3587E−21 .3862E−21 .3594E−21 .3548E−21 .3152E−21 .3410E−21 .2812E−21 .2512E−21 .3008E−21 .2874E−21 .2252E−21 .1738E−21 .1693E−21 .1192E−21 .9493E−22 .9201E−21

.4312E−21 .4385E−21 .3904E−21 .3508E−21 .4065E−21 .4008E−21 .3423E−21 .3642E−21 .3557E−21 .2994E−21 .2556E−21 .3157E−21 .3035E−21 .2444E−21 .1770E−21 .1779E−21 .1369E−21 .1018E−21 .9083E−21

−6.3 −17.1 −0.2 2.2 −5.2 −11.5 3.5 −15.6 −4.3 −6.5 −1.7 −4.9 −5.6 −8.5 −1.8 −5.1 −14.9 −7.3 1.3

57.4

.6700E−21

.6351E−21

5.2

47.6

.8535E−21

.8482E−21

0.6

68.0

.4300E−21

.4203E−21

2.3

69.4

.4357E−21

.3578E−21

17.9

80.5

.2190E−21

.2200E−21

−.5

8

(continued on next page)

96

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99 Table 10 (continued)

a) b) c) d)

Wavenumber 1

J 2

Ka

1290.7054 1290.7054 1290.7260 1290.7260 1290.7504 1290.7504 1290.8066 1290.8066 1290.8386 1290.8386 1293.8687 1294.1285 1295.1600 1295.4353 1295.8695 1296.4410 1296.7054 1297.7115 1297.9442 1298.6357 1298.9719 1299.1620 1300.2229 1300.3457 1300.4872 1301.1366 1301.4653 1301.5720 1302.0378 1302.7009 1302.7758 1303.9309 1305.0884 1305.1570 1305.1898 1306.3830 1306.5738 1307.6150 1307.6652 1308.0232 1308.7936 1308.8056 1313.6296 1313.6296 1314.8342 1314.8342 1316.0369 1316.0369

12 12 13 13 14 14 16 16 17 17 4 4 5 5 5 6 6 7 7 7 8 8 9 8 8 9 10 10 9 11 11 12 11 13 13 14 12 15 15 13 16 16 20 20 21 21 22 22

12 12 12 12 12 12 12 12 12 12 1 0 1 0 2 1 0 1 0 3 1 0 1 1 2 2 1 0 2 1 0 1 2 1 0 1 2 0 1 2 0 1 0 1 0 1 0 1

Kc

0 1 1 2 2 3 4 5 5 6 4 4 5 5 3 6 6 7 7 5 8 8 9 7 6 8 10 10 7 11 11 12 9 13 13 14 10 15 15 11 16 16 20 20 21 21 22 22

J 3

Ka

12 12 13 13 14 14 16 16 17 17 3 3 4 4 4 5 5 6 6 6 7 7 8 7 7 8 9 9 8 10 10 11 10 12 12 13 11 14 14 12 15 15 19 19 20 20 21 21

12 12 12 12 12 12 12 12 12 12 1 0 1 0 2 1 0 1 0 3 1 0 1 1 2 2 1 0 2 1 0 1 2 1 0 1 2 0 1 2 0 1 0 1 0 1 0 1

Kc

δ tr. a 4

1 0 2 1 3 2 5 4 6 5 3 3 4 4 2 5 5 6 6 4 7 7 8 6 5 7 9 9 6 10 10 11 8 12 12 13 9 14 14 10 15 15 19 19 20 20 21 21

22 22 3 3 −2 −2 −5 −5 −5 −5 −1 −5 1 −5 0 0 −5 −1 −5 6 0 −3 1 −10 −8 −2 0 −2 −9 1 −1 2 −9 2 −1 4 −4 −3 24 −5 11 −3 −5 5 −3 19 −11 2

δ str. d

Transm.b 5

SνN (exp. )c 6

SνN (calc. )c 7

68.9

.5104E−21

.4276E−21

16.2

72.2

.3698E−21

.3624E−21

2.0

73.8

.3659E−21

.3066E−21

16.2

81.2

.2192E−21

.2180E−21

0.5

83.0

.2011E−21

.1830E−21

9.0

80.5 79.3 75.3 75.5 80.2 72.9 73.4 70.7 70.0 75.5 68.5 68.8 64.7 71.1 71.1 68.7 64.7 65.2 69.9 64.6 64.4 64.2 68.1 63.7 63.3 63.8 67.2 69.6 72.4 69.8 79.5 79.1 52.8

.2383E−21 .2446E−21 .2958E−21 .2955E−21 .2249E−21 .3294E−21 .3272E−21 .3629E−21 .3917E−21 .2724E−21 .4186E−21 .4304E−21 .4641E−21 .3988E−21 .3684E−21 .3770E−21 .4617E−21 .4877E−21 .3806E−21 .4702E−21 .4787E−21 .5007E−21 .4373E−21 .4929E−21 .5681E−21 .4747E−21 .4592E−21 .4003E−21 .4016E−21 .4199E−21 .2913E−21 .2456E−21 .7772E−21

.2464E−21 .2637E−21 .3066E−21 .3194E−21 .2591E−21 .3601E−21 .3691E−21 .4065E−21 .4125E−21 .3092E−21 .4454E−21 .4495E−21 .4767E−21 .4328E−21 .4059E−21 .4377E−21 .5007E−21 .5023E−21 .4365E−21 .5169E−21 .5181E−21 .5258E−21 .4714E−21 .5271E−21 .5279E−21 .5124E−21 .4763E−21 .3814E−21 .3291E−21 .4739E−21 .2651E−21 .2666E−21 .7833E−21

−3.4 −7.8 −3.7 −8.1 −15.2 −9.3 −12.8 −12.0 −5.3 −13.5 −6.4 −4.4 −2.7 −8.5 −10.2 −16.1 −8.4 −3.0 −14.7 −9.9 −8.2 −5.0 −7.8 −6.9 7.1 −8.0 −3.7 4.7 18.0 −12.9 9.0 −8.6 −0.8

53.2

.8576E−21

.7354E−21

14.3

56.0

.7313E−21

.6805E−21

6.9

8

The δ tr. is (νexp. − νcalc. ) in 10−4 cm−1 . Transmittance in per cent. The line strength, SνNi , in cm−1 /(molec. · cm−2 ). The δ str. is a difference (

SνN

exp.

i

−SνN

SνN

exp.

calc.

i

) in per cent.

i

The assignment of the transitions was made with the Ground State Combination Differences method. In this case, the rotational energies of the ground vibrational state have been calculated with the parameters from Ref. [47] (for convenience of the reader, ground state parameters from [47] are reproduced in column 2 of Table 4). As the result of assignment, 1748 transitions with the maximum values of upper quantum numbers, J max. = 43 and Kamax. = 14 have been assigned to the ν 12 band (the complete list of all transitions assigned in the experimental spectrum is presented in the Supplementary Material section of this paper; see also statistical information in Table 5). On that basis, 585 ro–vibrational energy levels of the (v12 = 1 ) vibrational state were determined (they are presented in column 2 of Table 6 together with their experimental uncertainties ; the latter are shown in column 3 of Table 6). The presence of strong interactions between the (v12 = 1 ) state, on the one hand, and the states (v10 = 2 ), (v7 = v = 1 ), on

the other hand, allowed us to definitely assign a few transitions of the band 2ν 10 ν4 + ν10 . The results can be seen in Table 7. One can see positions of assigned lines (columns 4 of Table 7), values of upper ro–vibrational energy levels determined from individual line positions (columns 6), and mean values of upper energy levels in columns 7. To give the reader an impression of the power of resonance interactions, Table 8 illustrates the borrowing of line intensities from the strong ν 12 band to the considerably weaker 2ν 10 and ν4 + ν10 bands (upper ro-vibrational states of transitions from Table 7 are considered). Columns 4–7 of (v,J,K K ) Table 8 show values of coefficients bv a c which just indicate the

effect of resonance interactions.1) For example, as one can see from the first lines of Table 8, ro-vibrational states [(v10 = 2 ), 12 5 7] and [(v12 = 1 ), 12 3 9] have values in the columns 4 and 5 being very close to each other. This means that about 50% per cent of in-

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

tensity is borrowed by the state [(v10 = 2 ), 12 5 7] from the state [(v12 = 1 ), 12 3 9], etc. 5. Fit of parameters and discussion The 593 ro–vibrational energy values of the states (v12 = 1 ), (v10 = 2 ) were used as input data in a weighted least square fit with the aim to determine rotational, centrifugal distortion, and resonance interaction parameters. As the preliminary analysis showed, correctness of a fit strongly depends on the initial values of the model parameters. In the present analysis, the initial values of the rotational parameters and centrifugal distortion coefficients have been taken to be equal values of corresponding parameters of the ground vibrational state. Initial values of the vibrational energies have been taken from estimations discussed in Section 3.2. Results of the fit are presented in columns 3–6 of Table 4 and in Table 9 (values in parentheses are 1σ statistical confidence intervals). Parameters presented without confidence intervals have been constrained to their initial values. In this case, following the strategy of our preceding studies (see, e.g., Ref. [33]) we preferred to vary only the largest parameters of diagonal blocks, Hvv , keeping higher order centrifugal coefficient values to be constrained to the values of the ground state corresponding coefficients. It is important that in the frame of this strategy, parameters of resonance interactions get a considerable influence on the ro–vibrational energy values concerning high order centrifugal distortion coefficients. In particular, in the present analysis the fit of parameters /δ (even the parameters δ K and δ J of the (v12 = 1 ) vibrational state) leads to such values of their confidence intervals which are comparable or close to the absolute values of the parameters themselves (at the same time, the value of drms of the fit is not changed). For that reason, it is physically suitable to constrain the values of such /δ parameters to the values of the corresponding parameters of the ground vibrational state. The drms −value of the present fit (drms = 1.3 × 10−3 cm−1 ) is about three times larger than estimated experimental error in line positions. In principle, it is a more than satisfactory result, but we believe that the situation can be improved considerably by one of the following ways (it is impossible to realize both of them at the moment): (a) by assignment of transitions with low values of quantum numbers J and Ka belonging to the 2ν 10 , ν7 + ν10 and ν4 + ν10 bands, and/or (b) by more correct theoretical prediction of the values of the band centers and of the main rotational and resonance interaction parameters. The latter is especially important because of the presence of numerous interactions between all four discussed vibrational states. To illustrate the correctness of the analysis, column 4 of Table 6 and columns 8 of Table 7 present differences δ between “experimental” energy values and such calculated with the parameters from Tables 4 and 9. Analogously, column 5 of Supplementary Material shows corresponding δ −value for the line positions.

97

much better accuracy and may be more useful than the absolute results. A line strengths analysis of 106 lines (see Table 10) of the ν 12 band (nonsaturated unblended not very weak lines with J max. = 22 and Kamax. = 12) was made on the basis of the fit of their shapes with the Voigt profile model (see, e.g., Ref. [83–87]). When the only main effective dipole moment parameter μ1z is used (notations of the dipole moment parameters in this section correspond the notations from Ref. [77]), the result is μ z 1 = 2.603(12 ) × 10−2 D, which provides the drms = 10.3% for 106 lines used in the fit. The value in parentheses of the μ1z parameter is the 1σ statistical confidence interval; the drms value was obtained in accordance with the formula



drms =



exp. calc. SνN − SνN 1 100 × i Nexp. i n Sνi

2 1/2

.

(9)

i

The value n in Eq. (9) is the number of line strengths used in the fit. It is necessary to mention that the obtained value of the μ1z parameter leads to such a situation when the difference exp .

(SνPi

calc.

− SνPi

) is changed slowly (from −7 × 10−4 to +16 × 10−4

cm−2 atm−1 )

with increasing quantum number J. If one also considers the second effective dipole moment parameter, μ4z , the drms does improve considerably (it is changed from 10.3% to 9.0%), exp . calc. but this provides a rather uniform value of (SνPi − SνPi ) among all 106 initial experimental line strengths. The mentioned values obtained from the fit are: μ1z = 2.602(11 ) × 10−2 D and μ4z = −4.11(90 ) × 10−5 D. Columns 6, 7, and 8 of Table 10 presents valexp. calc. ues of the experimental, SνNi , and calculated, SνNi , line strengths and their difference, (

SνN

exp.

i

−SνN

exp. SνN i

calc.

i

) in per cent, respectively.

7. Conclusion We performed an analysis of the high resolution IR spectra of C2 HD3 in the region of the ν 12 band, 1230 - 1340 cm−1 . The 1748 transitions with the maximum values of the upper quantum numbers J max. = 43 and Kamax. = 14 were assigned to the ν 12 band. Additionally, 14 transitions have been assigned to the 2ν 10 band which appearance is caused by the strong resonance interactions of this band with the ν 12 band. For a further theoretical analysis of the results, the effective Hamiltonian was used which takes into account resonance interactions between the vibrational states (v12 = 1 ), (v10 = 2 ), (v7 = v10 = 1 ) and (v4 = v10 = 1 ). A set of 70 spectroscopic parameters obtained from a weighted least square fit reproduces the initial experimental data (593 upper energy values, 1762 transitions) with the drms = 1.3 ×10−3 cm−1 . 8. Footnotes (v,J,Ka Kc )

(1) The bv

coefficients are determined as

  (v,JK K ) 2 b(vv,J,Ka Kc ) = a(v,J,Kaa Kcc ) , a ,K c K

( v,JK K )

6. Line strengths estimation As described in Section 2, the generation technique of C2 HD3 in our experiment provides the maximum concentration of C2 HD3 in the sample as about 42%. This percentage has not a high accuracy as, e.g., the different exchange probabilities of H and D have not been considered. So we give a final estimate for the accuracy of the line strengths derived in the following with an error ± 20%. Note that the relative line strengths in the present study have a

where the a(v,J,Ka Kc ) −values are known coefficients of real functions a c of the ro-vibrational states:

[v, JKa Kc ] =

  (v,JK K ) a(v,J,Kaa Kcc ) | v|JKa Kc .  v Ka ,Kc

Acknowledgments The work was funded by the Tomsk Polytechnic University Competitiveness Enhancement Program, project 203/2018 and by

98

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99

the Deutsche Forschungsgemeinschaft (grants BA 2176/4-1, BA 2176/4-2, and BA 2176/5-1). Part of the work was supported by RFBR according to the research project No 18-02-00819 A. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jqsrt.2018.07.002. References [1] Abele FB, Heggetad H. Ethylene: an urban air pollutant. J Air Pollut Control Assoc 1973;23:517–21. [2] Betz L. Ethylene in IRC.10216. Astrophys J 1981;244:L103–5. [3] Cernicharo J, Heras AM, Tielens APJ, Guelin M, Dartois E, LBFM W, et al. Methylpolyynes and small hydrocarbons in CRL 618. Astrophys J 2001;546:L127–30. [4] Kostiuk T, Romani P, Espenak F, Livengood TA, Goldstein J. Temperature and abundances in the jovian auroral stratosphere 2. eyhylene as aprobe of the microbar region. J Geophys Res 1993;98:18823–30. [5] Griffith CA, Bézard B, Greathouse TK, Kelly DM, Lacy JH, Noll K. Thermal infrared imagining spectroscopy of shoemaker-levy 9 impact sities: spatial and vertical distributions of NH3 , C2 H4 , and 10 μm dust emission. Icarus 1997;128:275–93. [6] Bézard B, Moses JL, Lacy J, Greathouse T, Richter M, Griffith C. Detection of ethylene (C2 H4 ) on jupiter and saturn in non-auroral regions. Bull Am Astron Soc 2001;33:1079. [7] Schulz B, Encrenaz T, Bézard B, Romani P, Lellouch E, Atreya S. Detection of C2 H4 in neptube fom ISO/PHTS observations. Astron Astrophys 1999;350:L13–17. [8] Saslaw WC, Wildey R. On the chemistry of jupiter’s upper atmosphere. Icarus 1967;7:85–93. [9] Coustenis A, Achterberg RK, Conrath BJ, Jennings DE, Marten A, Gautier D, et al. The composition of titan’s stratosphere from cassini CIRS midinfrared spectra. Icarus 2007;189:35–62. [10] Kunde VG, Aikin AC, Hanel RA, Jennings DE, Maguire WC, Samuelson R. C2 H4 , HC3 N and C2 N2 in titan’s atmosphere. Nature 1981;292:686–8. [11] Bar-Nun A, Podolak M. The photochemistry of hydrocarbons in titan’s atmosphere. Icarus 1979;38:115–22. [12] Coustenis A, Salama A, Schulz B, Ott S, Lellouch E, Th E, et al. Titan’s atmosphere from ISO mid-infrared spectroscopy. Icarus 2003;161:383–403. [13] Vervack J, Sandel BR, Strobel D. New perspectives on titan’s upper atmosphere from a reanalysis of the voyager 1 UVS solar occultations. Icarus 2004;170:91–112. [14] Wang F, Cui X, Sun Y, Dong C-H. Ethylene signaling and regulation in plant growth and stress responses. Plant Cell Rep 2013;32:1099–109. [15] Rotger M, Boudon V, Auwera J. Line positions and intensities in the ν 12 band of ethylene near 1450 cm−1 : an experimental and theoretical study. J Quant Spectrosc Radiat Transfer 2008;109:952–62. [16] Goh KL, Tan TL, Ong PP, Teo H. High–resolution FTIR spectroscopy of the ν 11 and ν2 + ν7 bands of ethylene-d4 . Mol Phys 2009;98:583–7. [17] Ulenikov ON, Onopenko GA, Bekhtereva ES, Petrova TM, Solodov AM, Solodov AA. High resolution study of the ν5 + ν12 band of C2 H4 . Mol Phys 2010;108:637–47. [18] J-M F, Lafferty WJ, Sams R, Malathy Devi V. High resolution analysis of the ethylene−1 −13 C spectrum in the 8.4 − 14.3 − μm region. J Mol Spectrosc 2010;259:39–45. [19] Tan TL, Lebron GB. High–resolution infrared analysis of the ν 7 band of cis–ethylene–d2 (cis–C2 H2 D2 ). J Mol Spectrosc 2010;261:87–90. [20] Lebron GB, Tan TL. High–resolution FTIR measurement and analysis of the ν 3 band of C2 H3 D. J Mol Spectrosc 2010;261:119–23. [21] Tan TL, Lebron GB. The high–resolution FTIR spectrum of the ν 6 band of C2 H3 D. J Mol Spectrosc 2010;263:160–5. [22] LMA G, Boudon V, Loëte M, Rotger M, Bourgeois MT, Didriche K, et al. High–resolution spectroscopy and preliminary global analysis of C–H stretching vibrations of C2 H4 in the 30 0 0 and 60 0 0 cm−1 regions. J Quant Spectrosc Radiat 2010;111:2265–78. [23] Lafferty W.J., Flaud J-M, Kwabia Tchana F. The high–resolution infrared spectrum of ethylene in the 1800-2350 cm−1 spectral region. Mol Phys 2011;109:2501–2510. [24] Lebron GB, Tan TL. Improved rovibrational constants for the ν 12 band of C2 H3 D. J Mol Spectrosc 2011;265:55–7. [25] Tan TL, Gabona MG, Lebron GB. The ν 12 band of C2 D4 . J Mol Spectrosc 2011;266:113–15. [26] J-M F, Lafferty WJ, Malathy Devi V, Sams RL, Benner CD. Absolute line intensities and self–broadened half–width coefficients in the ethylene−1 −13 C bands in the 700–1190 cm−1 region. J Mol Spectrosc 2011;267:3–12. [27] Lebron GB, Tan TL. The high–resolution FTIR spectrum of the ν4 + ν8 band of trans C2 –ethylene (trans– C2 H2 D2 ). J Mol Spectrosc 2012;271:44–9. [28] Tan TL, Gabona MG. Analysis of the coriolis interaction between ν 6 and ν 4 bands of ethylene–cis–d2 (cis–C2 H2 D2 ) by high–resolution FTIR spectroscopy. J Mol Spectrosc 2012;272:51–4.

[29] Tan TL, Gabona MG. High–resolution FTIR spectroscopic analysis of the coriolis interaction in the ν7 + ν8 band of ethylene–cis–d2 (cis–C2 H2 D2 ). J Mol Spectrosc 2012;275:5–8. [30] Cartera S, Bowman JM, Handy NC. Multimode calculations of rovibrational energies of C2 H4 and C2 D4 . Mol Phys 2012;110:775–81. [31] Lebron GB, Tan TL. Integrated band intensities of ethylene (12 C2 H4 ) by fourier transform infrared spectroscopy. J Mol Spectrosc 2012;282:1–5. [32] Ben Hassen A, Kwabia Tchana F, J-M F, Lafferty WJ, Landsheere X, Aroui H. Absolute line intensities for ethylene from 1800 to 2350 cm−1 . J Mol Spectrosc 2012;282:30–3. [33] Ulenikov ON, Gromova OV, YuS A, V-M H. High resolution spectroscopic study of C2 H4 : Re–analysis of the ground state and ν 4 , ν 7 , ν 10 , and ν 12 vibrational bands. J Quant Spectrosc Radiat Transfer 2013;118:14–25. [34] Rothman LS, Gordon IE, Babikov Y, Barbe A, Chris Benner D, Bernath PF, et al. The HITRAN 2012 molecular spectroscopic database. J Quant Spectrosc Radiat Transfer 2013;130:4–50. [35] Ba YA, Wenger C, Surleau R, Boudon V, Rotger M, Daumont L, et al. MecaSDa and ECaSDa: methane and ethene calculated spectroscopic databases fort he virtual atomic and molecular data center. J Quant Spectrosc Radiat Transfer 2013;130:62–8. [36] Ballandras A, Cirtog M, Lorono MA, Bourgeois MT, Rotger M, Bermejo D, et al. High–resolution stimulated raman spectroscopy and analysis of the ν 2 and ν 3 bands of C2 H4 . J Raman Spectrosc 2013;44:1033–8. [37] Lebron GB, Tan TL. High–resolution fourier transform infrared spectrum of the ν 11 band of ethylene (12 C2 H4 ). J Mol Spectrosc 2013;288:11–13. [38] Vander Auwera J, Fayt A, Tudorie M, Rotger M, Boudon V, Franco B, Mahieu E. Self–broadening coefficients and improved line intensities for the ν 7 band of ethylene near 10.5 mm, and impact on ethylene retrievals from jungfraujoch solar spectra. J Quant Spectrosc Radiat Transfer 2014;148:177–85. [39] Tan TL, Gabona MG, DRT A, Godfrey PD, McNaughton D. Rovibrational constants of the ground and v12 =1 states of C2 D4 by high–resolution synchrotron FTIR spectroscopy. J Mol Spectrosc 2014;303:42–5. [40] Gabona MG, Tan TL, Woo JQ. High–resolution FTIR analysis and rotational constants for the ν 12 band of ethylene−1−13 C (13 C12 CH4 ). J Mol Spectrosc 2014;305:22–4. [41] Ulenikov ON, Gromova OV, Bekhtereva ES, Onopenko GA, YuS A, Gericke KH, Bauerecker S, Horneman VM. High resolution FTIR study of the ν7 + ν10 − ν10 and ν10 + ν12 − ν10 “hot” bands of C2 H4 . J Quant Spectrosc Radiat Transfer 2014;149:318–33. [42] Gabona MG, Tan TL. Coriolis interaction of the ν2 + ν12 band with ν2 + ν10 of cis–C2 H2 D2 by high resolution FTIR spectroscopy. J Mol Spectrosc 2014;299:31–4. [43] Gabona MG, Tan TL. Improved ground state and v12 = 1 state rovibrational constants for ethylene−13 C2 (13 C2 H4 ). J Mol Spectrosc 2014;299:35–7. [44] Ulenikov ON, Gromova OV, Bekhtereva ES, Maul C, Bauerecker S, Gabona MG, Tan TL. High resolution ro-vibrational analysis of interacting bands ν 4 , ν 7 , ν 10 , and ν 12 of 13 C2 H4 . J Quant Spectrosc Radiat Transfer 2015;151:224–38. [45] Ulenikov ON, Gromova OV, Bekhtereva ES, Berezkin KB, Sklyarova EA, Maul C, Gericke KH, Bauerecker S. Study of the high resolution FTIR spectrum of CH2 =CD2 in the region of 1300 – 1450 cm−1 : the ν 12 (a1 ) and 2ν 10 (a1 ) bands. J Quant Spectrosc Radiat Transfer 2015;161:180–96. [46] Ulenikov ON, Gromova OV, Bekhtereva ES, Kashirina NV, Bauerecker S, V-M H. Precise ro-vibrational analysis of molecular bands forbidden in absorption: the ν8 + ν10 band of the 12 C2 H4 molecule. J Mol Spectrosc 2015;313:4–13. [47] Ng LL, Tan TL, Gabona MG, Godfrey PD, McNaughton D. High–resolution FTIR spectroscopy of ethylene-d3 (C2 HD3 ): rovibrational constants for the ground state and the v8 = 1 state. J Mol Spectrosc 2015;316:79–83. [48] Tan TL, Gabona MG, Godfrey PD, McNaughton D. Rovibrational analysis of the ethylene isotopologue 13 C2 D4 by high–resolution fourier transform infrared spectroscopy. J Mol Spectrosc 2015;307:40–3. [49] Tan TL, Ng LL, Gabona MG. The hybrid a/b type ν 12 band of transethylene–1,2d2 by high–resolution fourier transform infrared spectroscopy. J Mol Spectrosc 2015;312:6–12. [50] Tan TL, Gabona MG, Wong A, DRT A, McNaughton D. The coriolis–interacting ν 6 and ν 4 bands of ethylene–cis–1,2–d2 (cis–C2 H2 D2 ) by high-resolution synchrotron fourier transform infrared (FTIR) spectroscopy. J Mol Spectrosc 2016;329:8–12. [51] Ulenikov ON, Gromova OV, Bekhtereva ES, Konov IA, Chertavskikh YV, Maul C, Bauerecker S. Re–analysis of the high resolution FTIR spectrum of C2 H2 D2 −cis in the region of 1280-1400 cm−1 . J Quant Spectrosc Radiat Transfer 2016;170:69–82. [52] Ulenikov ON, Gromova OV, Bekhtereva ES, Berezkin KB, Kashirina Tan TL, Sydow C, Maul C, Bauerecker S. Study of interactionsin polyatomic molecules on the basis of highly accuexperimental data: Set of strongly interacting bands ν 10 (B1 ), ν 7 (B2 ), ν 4 (A2 ), ν 8 (B2 ), ν 3 (A1 ), and ν 6 (B1 ) of CH2 =CD2 . J Quant Spectrosc Radiat Transfer 2016;180:14–28. [53] Ulenikov ON, Gromova OV, Bekhtereva ES, Fomchenko AL, Zhang F, Sydow C, Maul C, Bauerecker S. High resolution analysis of C2 D4 in the region of 600 1150cm−1 . J Quant Spectrosc Radiat Transfer 2016;182:55–70. [54] Ng LL, Tan TL, Wong A, DRT A, McNaughton D. High–resolution synchrotron FTIR spectroscopic analysis of the coriolis interaction between the v10 = 1 and v8 = 1 states of ethylene–cis–1,2–d2 . Mol Phys 2016;114:2798–807. [55] Duncan JL, McKean DC, Mallinson PD. Infrared crystal spectra of C2 H4 , C2 D4 , and as–C2 H2 D2 and the general harmonic force field of ethylene. J Mol Spectrosc 1973;45:221–46.

O.N. Ulenikov et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 218 (2018) 86–99 [56] Duncan JL, Hamilton E. An improved general harmonic force field for ethylene. J Mol Struct 1981;76:65–80. [57] JML M, Lee TJ, Taylor PR, Francois JP. The anharmonic force field of ethylene, C2 H4 , by means of accurate ab initio calculations. J Chem Phys 1995;103:2589–602. [58] Duncan JL, Ferguson AM, Goodlad ST. Local mode interpretation of the CH and CD stretching vibrational manifolds of isotopic ethylenes, C2 H3 D and C2 HD3 . Spectrochim Acta 1993;49A:149–60. [59] Tan TL, Lebron GB. Rovibrational constants for the ground state and ν8 = 1 state of ethylene–d3 (C2 HD3 ) by high–resolution FTIR spectroscopy. J Mol Spectrosc 2011;269:109–12. [60] Ng LL, Tan TL, Gabona MG, Godfrey PD, McNaughton D. High–resolution FTIR spectroscopy of ethylene–d3 (C2 HD3 ): Rovibrational constants for the ground state and the v8 = 1 state. J Mol Spectrosc 2015;316:79–83. [61] Ng LL, Tan TL. Rovibrational constants of the ground state and v8 = 1 state of 13 C2 HD3 by high-resolution FTIR spectroscopy. J Mol Spectrosc 2016;324:6–11. [62] Ng LL, Tan TL, Akasyah L, Wong A, DRT A, McNaughton D. The ν8 = 1 band of C2 HD3 by high–resolution synchrotron FTIR spectroscopy: Coriolis interactions between the v8 = 1 and v6 = 1 states. J Mol Spectrosc 2017;340:29–35. [63] Ng LL, Tan TL, Chia AH. First analysis of the hybrid a/b−type 2ν 8 band of C2 HD3 and the coriolis interactions with the ν3 + ν4 = 1 band by high-resolution FTIR spectroscopy. J Mol Spectrosc 2018;344:27–33. [64] Child MS, Lawton RT. Local and normal vibrational states: a harmonically coupled anharmonic-oscillator model. J Chem SocFaraday Discuss 1981;71:273–85. [65] Child MS, Halonen LL. Overtone frequencies and intensities in the local mode picture. Adv Chem Phys 1984;57:1–58. [66] Mills IM, Robiette AG. On the relationship of normal modes to local modes in molecular vibrations. Mol Phys 1985;56:743–65. [67] Mills IM, Mompean FJ. Local modes and x, k relations in ethene and propadiene. Chem Phys Lett 1986;124:425–31. [68] Duncan JL, Mills IM. Local mode and normal mode interpretations of the CH and CD stretching vibrational manifolds of 1,1–dideuteroethene. Chem Phys Lett 1988;145:347–53. [69] Twigg GH, Rideal EK. The exchange reaction between ethylene and deuterium on a nickel catalyst. Proc Roy Soc A 1939;179we a:55–69. [70] High-Resolution Fouriertrans Form Infrared Spectroscopy. Handbook of high–resolution spectroscopy.2. Chichester, NY: John Wiley & Sons, Ltd; 2011. p. 965–1019. [71] Maki AG, Wells JS. Wavenumber calibration tables from heterodyne frequency measurements (version 1.3). National institute of standards and technology; 1998. Gaithersburg, MD.

99

[72] JKG W. Determination of centrifugal distortion coefficients of asymmetric-top molecules. J Chem Phys 1967;46:1935–49. [73] Ulenikov ON, S-M H, Bekhtereva ES, Onopenko GA, Wang X-H, He S-G, Zheng J-J, Zhu Q-S. High–resolution fourier transform spectrum of HDO in the region 6140–7040 cm−1 . J Mol Spectrosc 2001;208:224–35. [74] S-M H, Ulenikov ON, Onopenko GA, Bekhtereva ES, He S-G, Wang X-H, Lin H, Zhu Q-S. High–resolution study of strongly interacting vibrational bands of HDO in the region 760 0–810 0 −1 . J Mol Spectrosc 20 0 0;203:228–34. [75] Herzberg G. Molecular spectra and molecular structure, infrared and Raman spectra of polyatomic molecules, 2. New York: van Nostrand; 1945. [76] Papousek D, Aliev MR. Molecular vibrational-rotational spectra. Amsterdam: Elsevier; 1982. [77] Flaud JM, Camy-Peyret C. Vibration-rotation intensities in h2 o-type molecules application to the 2ν 2 , ν 1 , and ν 3 bands of H16 2 O. J Mol Spectrosc 1975;55:278–310. [78] Lafferty WJ, Flaud J-M, Kwabia Tchana F. The high-resolution infrared spectrum of ethylene in the 1800–2350 cm−1 spectral region. Mol Phys 2011;109:2501– 2510. [79] Saveliev VN, Ulenikov ON. Calculation of vibration–rotation line intensities of polyatomic molecules based on the formalism of irreducible tensorial sets. J Phys B 1987;20:67–83. [80] Herbin P, Blanquet G, Valentin A. Vibration–rotation analysis of C2 H3 D from 725 to 1170 cm−1 . J Mol Spectrosc 1988;127:390–9. [81] Hegelund F, Nicolaisen FM. Coriolis perturbations in the ν 10 , ν 7 , ν 4 , ν 12 band system of trans–d2–ethylene. J Mol Spectrosc 1986;116:214–27. [82] Ulenikov ON. On the determination of the reduced rotational operator for polyatomic molecules. J Mol Spectrosc 1986;119:144–52. [83] Humlicek J. Optimized computation of the voigt and complex probability functions. J Quant Spectrosc Radiat Transfer 1982;27(4):437–44. [84] Armstrong BH. Spectrum line profiles: the voigt function. J Quant Spectrosc Radtat Transfer 1967;7:61–88. [85] Lether FG, Wenston PR. The numerical computation of the voigt function by a corrected midpoint quadrature rule. J Comput Appl Math 1991;34:75–92. [86] Berman PR. Speed–dependent collisional width and shift parameters in spectral profiles. J Quant Spectrosc Radiat Transfer 1972;12:1331–42. [87] Pickett HM. Effects of velocity averaging on the shapes of absorption lines. J Chem Phys 1980;73:6090–4.