First high-resolution analysis of the ν2+ν6 band of the cis-C2H2D2 isotopologue of ethylene

Journal of Quantitative Spectroscopy & Radiative Transfer 233 (2019) 99–109

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First high-resolution analysis of the ν2 + ν6 band of the cis-C2 H2 D2 isotopologue of ethylene O.N. Ulenikov a,∗, O.V. Gromova a, E.S. Bekhtereva a, Yu.V. Konova a, C. Sydow 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 23 April 2019 Revised 19 May 2019 Accepted 19 May 2019 Available online 20 May 2019 Keywords: High-resolution spectra of C2 H2 D2 -cis ν2 + ν6 band of C2 H2 D2 -cis ethylene Ro-vibrational resonance interactions Spectroscopic parameters

a b s t r a c t The high–resolution infrared spectrum of C2 H2 D2 -cis was recorded for the first time and analyzed in the region of 240 0–270 0 cm−1 , where the ν2 + ν6 band is located. 1987 transitions were assigned to the ν2 + ν6 band and 623 ro–vibrational energies of the (v2 = v6 = 1 ) vibrational state were determined from the assigned transitions. Parameters of the effective Hamiltonian were determined from the weighted fit, which takes into account the studied (v2 = v6 = 1 ) vibrational state and six other closely located (but experimentally here not visible) vibrational states of C2 H2 D2 -cis. The obtained “experimental” energy values were used as initial information in the fit. Determined from the fit, a set of 95 parameters reproduces 623 initial energy values of the (v2 = v6 = 1 ) vibrational state, representing 1987 line positions of the ν2 + ν6 band with the drms = 3.98 × 10−3 cm−1 .

1. Introduction 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 [1,2]. Ethylene acts as a hormone in plants and its role in plant biochemistry, physiology, mammal’s metabolism, and ecology is the subject of extensive research (see, e.g., [3,4]). Its contribution to atmospheric chemistry makes ethylene a climate-relevant trace gas and its air concentration, sources and sinks are of interest to atmospheric science. Ethylene is one of the most important substances of study in astrophysics [5–8], and was found in the atmospheres of giant planets of the Solar system and their satellites [9–23]. Apart from the applied interest, 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. Study of many problems needs in as correct as possible intramolecular potential energy surface of the ethylene molecule. The latter is impossible without knowledge of the precise spectroscopic information about ro–vibrational structures of different vibrational bands of different isotopologues of

∗

Corresponding author. E-mail addresses: [email protected] (O.N. Ulenikov), [email protected] (S. Bauerecker). https://doi.org/10.1016/j.jqsrt.2019.05.019 0022-4073/© 2019 Elsevier Ltd. All rights reserved.

© 2019 Elsevier Ltd. All rights reserved.

the ethylene molecule (first of all, its deuterated species). In this case, the larger the number of experimentally recorded and analyzed ro–vibrational bands, the more precise results one can expect to obtain. For these reasons, for many years the ethylene molecule and its different isotopologues have been subject of extensive experimental and theoretical studies. Without having the opportunity to mention all of them we quote here as examples (from a very large literature on the topic) only spectroscopic studies of the “parent” molecule during twenty last years (see Refs. [24–52] and references cited therein). As to C2 H2 D2 -cis, this isotopologue (as was mentioned, e.g., in Ref. [47]), as well as other deuterated ethylene species, should always be incorporated in the analysis of Titan’s atmosphere, and importance of deuterated species of different small molecules (deuterated ethylene, as well) was discussed in [48]. The physiological effect of deuterated ethylene in plant biochemistry was considered in [49]. In the present study we focus on the C2 H2 D2 -cis isotopologue of ethylene. This molecule was discussed earlier in [53–61]. The low resolution spectrum of C2 H2 D2 -cis in a mixture with the C2 H2 D2 −trans isotopomer was recorded in [53]. In [54] already high resolution microwave (MW) spectra of C2 H2 D2 -cis and a few other ethylene isotopic species were recorded with the goal to analyze the dipole moment and rz structure. Regular high resolution studies of C2 H2 D2 -cis were made by Hegelund and Nicolaisen [55–57] and Tan et al. [58–61]. Hegelund and Nicolaisen analyzed nine ro-vibrational bands, ν 5 , ν 6 , ν 7 , ν 9 , ν 12 , ν2 + ν12 , ν3 + ν6 ,

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ν4 + ν7 , and ν7 + ν8 . Tan with co-authors re-analyzed the bands ν 6 , ν 7 , ν 12 , and ν7 + ν8 on the basis of IR spectra, which have been recorded with a higher resolution than in the studies of Hegelund and Nicolaisen. The present paper is focused on the ν2 + ν6 band of the C2 H2 D2 -cis isotopologue. This band, which is located around 2600 cm−1 , was not discussed earlier and can be important for further applications because it it is strong enough and practically is not crossed with the bands of the other ethylene isotopologues (see Fig. 2). As a consequence, it can be used for indication of C2 H2 D2 -cis among the other ethylene isotopologues.

2. Experimental details The experiment is similar to those described in [62]. Only one spectrum has been measured in the region of 180 0–280 0 cm−1 with an indium–antimonide (InSb) semiconductor detector in a Bruker IFS120HR Fourier transform infrared spectrometer. A Globar IR radiation source, a CaF2 beamsplitter, and an optical multiple– path White cell from stainless steel with one meter basis-length including KBr windows were used. The C2 H2 D2 -cis sample, manufactured by Cambridge Isotope Laboratories with a purity of 99.99%, was recorded at 440 Pa with an absorption path length of 24.0524 ± 0.02 m (24 pathes) and an aperture of 1.15 mm; 530 scans have been co–added. The temperature was monitored with an Ahlborn Almemo 2590 resistance thermometer to be (25 ± 0.8) ◦ C. The used nominal optical resolution was 0.0025 cm−1 resulting in an almost Doppler limited spectrum in combination with the weak Norton–Beer apodization. As the Doppler broadening for C2 H4 at 298 K between 1800 and 2800 cm−1 is between 0.0 041 and 0.0 063 cm−1 , the full pressure line width at 440 Pa is 0.0 0 088 cm−1 , which is almost negligible, and the instrumental line width is 0.0020 cm−1 (product of nominal instrumental resolution of 0.0025 cm−1 and Norton–Beer weak apodization factor of 0.81), the total line width results to be in the range of 0.0046 and 0.0067 cm−1 . The total line widths can be approximated by the root sum square of the convolution of Doppler, pressure and instrumental line widths and are in accordance with the experimental results. The calibration of the spectral line positions was performed with N2 O lines [63–65].

3. Description of the spectrum and assignment of transitions The survey spectrum of the C2 H2 D2 -cis ethylene molecule in the region of 2550–2660 cm−1 is shown in Fig. 2. All the three branches of the ν2 + ν6 band are clearly pronounced. A small part of the high resolution spectrum in the region of the Q−branch is shown in the top part of Fig. 3. The bottom part of Fig. 3 presents in more detail structures of the Q Q7 (J), Q Q8 (J), and Q Q9 (J) clusters which are marked by dark triangles, open and dark circles, respectively. The P 168 (Q) transitions of the 2ν4 + ν10 band which strongly perturbs the Q 168 (Q) transitions of the ν2 + ν6 band (see also Fig. 4) is marked by a dark star. The C2 H2 D2 -cis molecule is an asymmetric top with the value of the asymmetry parameter κ = (2B − A − C )/(A − C )  −0.868 and with the symmetry isomorphic to the C2v point symmetry group. The symmetry properties of C2 H2 D2 -cis are presented in Table 1. The list of irreducible representations and the table of characters of the C2v symmetry group are shown in columns 1– 5. Symmetries of vibrational coordinates, qλ , rotational operators Jα , and direction cosines kZα are shown in column 6 and 7. Column 8 presents symmetries of rotational operators Jα and direction cosines kZα , which correspond to the Ir representation in asymmetric top molecules [66,67].

Table 1 Symmetry types and characters of irreducible representations of the C2v group (application to C2 H2 D2 -cis). Repr. 1

E 2

C2 3

σ v (xz)

σ v (yz)

4

5

Vibr. 6

Rot. 7

Rot.(Ir ) 8

A1 A2 B1 B2

1 1 1 1

1 1 −1 −1

1 −1 1 −1

1 −1 −1 1

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

Jz , kZz Jy , kZy Jx , kZx

Jx , kZx Jy , kZy Jz , kZz

In accordance with the selection rules for the asymmetric top molecules of the C2v symmetry (see, e.g., Refs. [68–75]), there are three types of vibrational bands which are allowed in absorption: (1) the a−type bands with the selection rules for them J = 0, ±1 and Ka = even, Kc = odd; (2) the b−type bands with the selection rules J = 0, ±1 and Ka = odd, Kc = odd; (3) 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., Refs. [70,74]) is valid: type of vibrational band (a−, b−, or c−) for an asymmetric top molecule is determined by the symmetry (kZ α ) = A2  γ v1  γ v2 , where  (kZα ) is the symmetry of kZα (see column 8 of Table 1), 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 H2 D2 -cis molecule, γ v1 is A1 (ground vibrational state). As a consequence, (A1 ← A1 ) are the bands of the b−type, (B1 ← A1 ) are the bands of the a−type, and (B2 ← A1 ) are the bands of the c−type. The assignment of 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 [76] (they are reproduced in column 2 of Table 2). As the result of assignment, 1987 transitions with the maximum values of quantum numbers J max = 35 and Kamax = 17 were assigned to the ν2 + ν6 band. Note that, in addition to the ν2 + ν6 (B1 ) band, there are six other very weak vibrational bands of different symmetry type whose centers are very close to the center of the ν2 + ν6 (B1 ) band and which are totally covered by the ν2 + ν6 band. They are the ν3 + 2ν10 (A1 ), 2ν4 + ν10 (A1 ), ν6 + ν7 + ν10 (A2 ), ν3 + ν8 + ν10 (A2 ), ν4 + ν7 + ν8 (B2 ), and ν6 + 2ν8 (B1 ) bands (see also Fig. 5 where a scheme of the mentioned band centers is shown). Note that all of these bands are so weak that their lines are comparable with noise and they practically do not appear in our experiment (more than 95% of the experimental transition with transmittances less than 0.9 have been assigned to the ν2 + ν6 band), and we were able to assign only six transitions without doubt (two upper energy levels) to the 2ν4 + ν10 band. One of these transitions is marked by dark star in Fig. 3. 4. Theoretical background and the Hamiltonian model The effective Hamiltonian model which was used for the theoretical analysis of the experimental data was discussed in the literature many times (see, e.g., Refs. [77–79]). For that reason we will mention it here very briefly. In its general form, the effective Hamiltonian can be written as (see, e.g., Refs. [80–82])

H vib.−rot. =



|vv˜ |v,v˜ H,

(1)

v,v˜

where the summation is taken on all interacting vibrational states. It is important to note that, in spite of the fact of weakness

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Fig. 1. Comparison of the experimental spectra of different ethylene isotopologues in the region of 2550–2670 cm−1 which have been recorded under close experimental conditions. One can see considerably stronger absorbtion by the C2 H2 D2 -cis species in comparison with the absorbtion by the other ethylene species.

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Fig. 2. Survey spectrum of C2 H2 D2 -cis in the region of the ν2 + ν6 band (upper trace). Experimental conditions: sample pressure is 440 Pa, absorption path length is 24 m; room temperature; number of scans is 530. Lower trace is the simulation spectrum.

Fig. 3. Detail of the high resolution experimental spectrum of C2 H2 D2 -cis in the Q−branch region of the ν2 + ν6 band. Some sets of transitions belonging to the Q−branch of the ν2 + ν6 band are marked in the spectrum. The transition P 168 (Q) belonging to the 2ν4 + ν10 band is marked by a star.

of the bands ν3 + 2ν10 (A1 ), 2ν4 + ν10 (A1 ), ν6 + ν7 + ν10 (A2 ), ν3 + ν8 + ν10 (A2 ), ν4 + ν7 + ν8 (B2 ), and ν6 + 2ν8 (B1 ), the band centers of all seven bands (six mentioned bands and the band ν2 + ν6 (B1 ) discussed in this paper) are located so close to each other, that it is not possible to eliminate even one of them from the consideration (see Section 6). For that reason, the summation in Eq. (1) is taken

from 1 to 7 for both v and v˜ , which represent the seven above discussed vibrational states: |1 = (v3 = 1, v10 = 2, A1 ), |2 = (v4 = 2, v10 = 1, A1 ), |3 = (v6 = v7 = v10 = 1, A2 ), |4 = (v3 = v8 = v10 = 1, A2 ), |5 = (v4 = v7 = v8 = 1, B2 ), |6 = (v6 = 1, v8 = 2, B1 ), and |7 = (v2 = v6 = 1, B1 ). Any diagonal block Hvv in Eq. (1) describes the unper-

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103

Fig. 4. Deviations E exp − E calc in cm−1 plotted as a function against the upper state J value for Ka = 8 levels of the ν2 + ν6 band of the C2 H2 D2 -cis molecule.

turbed rotational structure of the vibrational state |v and has the form of a reduced effective Hamiltonian in A−reduction and Ir representation (see, e.g., Ref. [66]):





v ,v H = E v + Av − 1 ( B v + C v ) J 2 + 1 ( B v + C v ) J 2 + 1 ( B v − C v ) J 2 z xy

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 ]+ + . . . , 2 Jxy

J2

− J2

(2) Av ,

where = x Bv , y ; [. . . , . . .]+ denotes anticommutators; and 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 v, v H (v = v˜ ) describe different kinds of resonance interactions between the discussed vibrational states (see Fig. 5): (a). The Fermi–type interaction operator connects vibrational states of the same symmetry and has the following form: v,v˜ H = v,v˜ F + v,v˜ F J 2 + v,v˜ F J 2 + v,v˜ F J 4 + v,v˜ F J 2 J 2 + v,v˜ F J 4 0 K z J KK z KJ z JJ

+ . . . + v,v˜ Fxy (Jx2 − Jy2 ) + v,v˜ FKxy [Jz2 , (Jx2 − Jy2 )]+ + v,v˜ FJxy J 2 (Jx2 − Jy2 ) + . . .

(3)

Fig. 5. Part of the vibrational energy level diagram of C2 H2 D2 -cis ethylene. The figure shows the situation of the levels in the polyad (v3 = 1, v10 = 2, A1 ), (v4 = 2, v10 = 1, A1 ), (v6 = v7 = v10 = 1, A2 ), (v3 = v8 = v10 = 1, A2 ), (v4 = v7 = v8 = 1, B2 ), (v6 = 1, v8 = 2, B1 ), and (v2 = v6 = 1, B1 ). Possible types of resonance interactions between the states are shown: F denotes the Fermi interaction; ζ α (α = x, y, z) denotes three different types of the Coriolis interactions.

The first parameter, v,v˜ F0 , in Eq. (3) is a pure vibrational interaction term; all the other parameters describe rotation-vibration corrections to the main Fermi-interaction parameter.

Fig. 6. Experimental minus calculated line positions (in cm−1 ), Fig. 6a, ro-vibrational energy values (in cm−1 ), Fig. 6b, including fit statistics for the ν2 + ν6 band of C2 H2 D2 -cis ethylene.

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Table 2 Spectroscopic parameters of some vibrational states of C2 H2 D2 -cis, in cm−1 .a Parameter 1 E A B C

2 3.32454251 0.84782640 0.67376942 4.87566 0.36926 0.117707 0.64297 0.0287597 3.302 −0.380 0.0527 0.0015

K × 105 JK × 105 J × 105 δ K × 105 δ J × 105 HK × 109 HKJ × 109 HJK × 109 HJ × 109

a b

(ground)b

(v3 = 1, v10 = 2 )

(v4 = 2, v10 = 1 )

(v6 = v7 = v10 = 1 )

(v3 = v8 = v10 = 1 )

( v4 = v7 = v8 = 1 )

( v6 = 1, v 8 = 2 )

( v2 = v6 = 1 )

3 2546.71(75) 3.3642(36) 0.8034(34) 0.6718(55) 4.87566 0.36926 0.117707 0.64297 0.0287597 3.302 −0.380 0.0527 0.0015

4 2639.98(70) 3.504(14) 0.8315(21) 0.6726(31) 4.87566 0.36926 0.117707 0.64297 0.0287597 3.302 −0.380 0.0527 0.0015

5 2550.12(27) 3.476(13) 0.8106(33) 0.6477(61) 4.87566 0.36926 0.117707 0.64297 0.0287597 3.302 −0.380 0.0527 0.0015

6 2633.99(95) 3.352(21) 0.8581(33) 0.6712(16) 4.87566 0.36926 0.117707 0.64297 0.0287597 3.302 −0.380 0.0527 0.0015

7 2575.42(95) 3.298(15) 0.8468(30) 0.6734(33) 4.87566 0.36926 0.117707 0.64297 0.0287597 3.302 −0.380 0.0527 0.0015

8 2562.11(50) 3.3863(92) 0.8155(43) 0.7855(58) 4.87566 0.36926 0.117707 0.64297 0.0287597 3.302 −0.380 0.0527 0.0015

9 2608.4617(35) 3.401330(88) 0.846751(14) 0.667129(19) 4.87566 0.36926 0.117707 0.64297 0.0287597 3.302 −0.380 0.0527 0.0015

Values in parentheses are 1σ statistical confidence intervals. Reproduced from [76].

(b). The B−type Coriolis interaction operator v,v˜ H, (v = v˜ ) connects such pairs of vibrational states (state v of the symmetry γ v and state v˜ of the symmetry γ v˜ ) for which the condition γ v  γ v˜ = B2 is valid: v,v˜ H = iJ v,v˜ H (1 ) + v,v˜ H (1 ) iJ + [J , J ] v,v˜ H (2 ) + v,v˜ H (2 ) [J , J ] x x y z + y z +

+[iJx , (Jx2 − Jy2 )]+ v,v˜ H (3) + v,v˜ H (3) [iJx , (Jx2 − Jy2 )]+ + . . .

(4)

(c). The C−type Coriolis interaction operator v,v˜ H, (v = v˜ ) connects such pairs of vibrational states (state v of the symmetry γ v and state v˜ of the symmetry γ v˜ ) for which the condition γ v  γ v˜ = B1 is valid: v,v˜ H = iJ v,v˜ H (1 ) + v,v˜ H (1 ) iJ + [J , J ] v,v˜ H (2 ) + v,v˜ H (2 ) [J , J ] y y x z + x z +

+[iJy , (Jx2 − Jy2 )]+ v,v˜ H (3) + v,v˜ H (3) [iJy , (Jx2 − Jy2 )]+ + . . .

(5)

(d). The A−type Coriolis interaction operator v,v˜ H, (v = v˜ ) connects such pairs of vibrational states (state v of the symmetry γ v and state v˜ of the symmetry γ v˜ ) for which the condition γ v  γ v˜ = A2 is valid: v,v˜ H = 2iJ v,v˜ H (1 ) + [J , J ] v,v˜ H (2 ) + v,v˜ H (2 ) [J , J ] z x y + x y +

+[iJz , (Jx2 − Jy2 )]+ v,v˜ H (3) + v,v˜ H (3) [iJz , (Jx2 − Jy2 )]+ + . . .

(6) 6. Discussion

In Eqs. (4)–(6) it is denoted v,v˜ H (i ) = 1 vv˜ C i + vv˜ C i J 2 + 1 vv˜ C i J 2 + vv˜ C i J 4 + vv˜ C i J 2 J 2 + 1 vv˜ C i J 4 K z J KK z KJ z JJ

2

2

i +vv˜ CKi K K Jz6 + vv˜ CKi K J Jz4 J 2 + vv˜ CKJJ Jz2 J 4 +

(2) in the presence of a set of interacting vibrational states (5–6 states and, first of all, Fermi and/or Darling-Dennison interactions), reducing of number of fitted centrifugal distortion parameters can be compensated by increase of number of interaction parameters, we varied only band centers and rotational parameters. Results of the fit with the Hamiltonian, Eqs. (1)–(7), are presented in columns 3–9 of Table 2 and in Table 4 (values in parentheses are 1σ statistical confidence intervals). The parameters presented without confidence intervals have been constrained to their initially estimated values, as was discussed above. Obtained from the fit a set of parameters (28 parameters of the diagonal blocks and 67 resonance interaction parameters) reproduces the initial experimental data with a drms = 3.98 ×10−3 cm−1 . To illustrate the quality of the analysis, differences between experimental and calculated values of the ro–vibrational energies are shown in column 4 of Table 3. To give the reader the possibility to judge the quality of the results, Fig. 6 shows the fit residuals for the ro–vibrational transitions of the ν2 + ν6 band (Fig. 6a) and (ro–vibrational energies of the (v2 = v6 = 1 ) vibrational state (Fig. 6b) as functions of the quantum number J which demonstrates an acceptably good agreement between the experimental and calculated results.

2

1 vv˜ i 6 CJJJ J + . . . 2

(7)

5. Rotational structure of the ν2 + ν6 vibrational state From the assigned 1987 transitions (see Section 3) we obtained 623 upper ro-vibrational energies of the ν2 + ν6 vibrational state which are presented in column 2 of Table 3 together with their experimental uncertainties , which are given in column 3. The obtained upper energies were used then as input data in a weighted least square fit with the goal to determine rotational and centrifugal distortion parameters of the (v2 = v6 = 1 ) state. The fit was made with the Hamiltonian model discussed in Section 4. The initial values of the rotational and centrifugal distortion coefficients of all seven vibrational states used in the analysis have been set equal to the values of the corresponding parameters of the ground vibrational state. Following the statements of the general vibration–rotation theory that (1) the diagonal block parameters can differ from corresponding parameters of the ground vibrational state no more than for some percent, see, e.g., Ref. [69]), and

We would like to note two points: (a). as can be seen from Table 4, the number of interaction parameters is rather large and (b). the accuracy of reproduction of the ro–vibration energy values is about ten times worse than the experimental accuracy in line positions (energy levels). Both of these circumstances are the consequence of two facts. On the one hand, the ν3 + 2ν10 , 2ν4 + ν10 , ν6 + ν7 + ν10 , ν3 + ν8 + ν10 , ν4 + ν7 + ν8 , and ν6 + 2ν8 bands are so weak in comparison with the ν2 + ν6 band that their lines are practically absent in our experiment (more than 95% of the detectable experimental lines have been assigned to the ν2 + ν6 band). As a consequence, we were able to assign only six lines without doubt (two upper energy levels) to the 2ν4 + ν10 band. For this reason it is not possible to obtain values of the band centers and rotational parameters for the states |1 = (v3 = 1, v10 = 2, A1 ), |2 = (v4 = 2, v10 = 1, A1 ), |3 = (v6 = v7 = v10 = 1, A2 ), |4 = (v3 = v8 = v10 = 1, A2 ), |5 = (v4 = v7 = v8 = 1, B2 ), and |6 = (v6 = 1, v8 = 2, B1 ) in an unambiguous way. At the same time, all seven vibrational states are located so close to each other (see Fig. 5) and the interaction ”picture“ is so complicated (see Fig. 7) that it is not possible to eliminate interaction between the studied ν2 + ν6 band and even one of the other six ν3 + 2ν10 , 2ν4 + ν10 , ν6 + ν7 + ν10 , ν3 + ν8 + ν10 , ν4 + ν7 + ν8 , and ν6 + 2ν8 bands (see Fig. 8). Fig. 8 illustrates the results of the testing fits

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Table 3 Ro–vibrational term values for the (v2 = v6 = 1 ) vibrational state of the C2 H2 D2 -cis molecule (in cm−1 )a . J 1

Ka

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 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8

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

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

Eexp 2 2608.4715 2609.9852 2612.5398 2612.7191 2613.0039 2615.3882 2615.9268 2623.5899 2623.5990 2617.5090 2619.6548 2620.7313 2628.1311 2628.1767 2641.3540 2641.3540 2623.4745 2625.3338 2627.1265 2634.1790 2634.3144 2647.4269 2647.4269 2665.9074 2665.9074 2630.8675 2632.4170 2635.1011 2641.7274 2642.0386 2655.0229 2655.0309 2673.4956 2673.4956 2697.2466 2697.2466 2639.6536 2640.8955 2644.6402 2650.7688 2651.3756 2664.1469 2664.1708 2682.6076 2682.6076 2706.3495 2706.3495 2735.3563 2735.3563 2649.8012 2650.7611 2655.7253 2661.2936 2662.3474 2674.8003 2674.8603 2693.2469 2693.2469 2716.9753 2716.9753 2745.9699 2745.9699 2780.2466 2780.2466 2661.2861 2662.0034 2668.3322 2673.2923 2674.9668 2686.9845 2687.1146 2705.4184 2705.4201 2729.1258



δ 4

J 1

Ka

3

0.4 0.2 0.4 −0.1 0.3 0.8 0.1 0.9 0.8 0.2 1.0 −0.7 0.6 0.6 1.0 0.7 0.5 1.5 −1.0 0.4 0.2 1.7 −0.3 1.0 0.9 0.5 1.8 −1.4 0.2 −0.1 0.9 0.9 1.6 1.5 0.4 0.4 0.7 1.8 −2.2 0.1 −0.7 0.6 0.4 1.9 1.6 1.7 1.7 −5.9 −5.9 1.0 2.4 −2.9 −0.5 −1.6 0.1 0.3 2.3 1.0 3.5 3.5 −6.7 −6.7 11.8 11.8 1.3 2.4 −3.4 −0.6 −2.3 −0.2 0.0 3.7 1.6 4.8

9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 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

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

0.1 0.2 0.1 0.2 0.1 0.1 0.1 0.2 0.4 0.2 0.8 0.8 0.1 0.3 0.2 0.1 1.7 1.7 0.1 0.1 0.1

0.1 0.1 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.3 0.2 0.2 0.1 0.3 0.4 0.4 0.2 0.2 0.4 0.4 0.1 0.3 0.2 0.2 0.2 0.3 0.3 0.8 0.8 0.3 0.3 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.4 0.2 0.1 0.4 0.3 0.3

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

Eexp 2 2719.1221 2719.1338 2742.8047 2742.8047 2771.7669 2771.7669 2806.0352 2806.0352 2845.5290 2845.5290 2890.2563 2890.2563 2688.2173 2688.5865 2697.9884 2701.6609 2705.1416 2715.9380 2716.4013 2734.3630 2734.3845 2758.0154 2758.0154 2786.9548 2786.9548 2821.2126 2821.2126 2860.6961 2860.6961 2905.4159 2905.4159 2955.3532 2955.3532 2703.6564 2703.9130 2714.9655 2718.0064 2722.6693 2732.6994 2733.4822 2751.1504 2751.1976 2774.7603 2774.7603 2803.6692 2803.6692 2837.9139 2837.9139 2877.3847 2877.3847 2922.0947 2922.0947 2972.0251 2972.0251 3027.1562 3027.1562 2720.4125 2720.5882 2733.3243 2735.7748 2741.7935 2750.9743 2752.2222 2769.4821 2769.5749 2793.0433 2793.0433 2821.9153 2821.9153 2856.1413 2856.1413 2895.5956 2895.5956 2940.2940



δ 4

J 1

Ka

3

2.3 4.3 6.4 6.2 −5.2 −5.2 1.0 1.0 −3.1 −3.1 0.2 0.2 1.7 2.2 −3.5 −2.5 −3.6 −1.9 −0.9 −0.8 −1.6 8.4 7.8 −2.9 −2.9 −1.3 −1.3 −2.1 −2.1 0.2 0.2 2.1 2.1 1.8 2.0 3.9 −3.2 −3.8 −4.1 −1.9 0.3 0.2 9.4 8.0 −2.8 −2.8 −2.0 −2.0 −0.7 −0.7 0.5 0.5 0.7 0.7 2.3 2.3 1.4 1.7 −8.7 −3.6 −3.5 1.1 −2.1 0.5 0.0 9.6 6.2 −2.2 −2.3 −1.0 −1.0 0.3 0.3 1.3

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 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

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 13 13 14 14 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

0.2 0.3 0.3 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.1 0.1 0.5 0.5 0.1 0.5 0.5 0.8 0.8 0.1 0.1 0.1 0.1 0.3 0.3 0.1 0.1 0.1 0.1 0.1 0.3 0.1 0.1 0.1 0.2 0.1 1.4 1.4 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.3 0.3 0.4 0.4 0.4 0.2 0.1 0.2 0.2 0.4 0.4 0.1 2.7 2.7 0.4 0.4 0.9 0.9 0.1 0.1 0.2

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

Eexp 2 2789.3605 2789.5327 2812.8693 2812.8769 2841.6951 2841.6951 2875.8963 2875.8963 2915.3308 2915.3308 2960.0146 2960.0146 3009.9260 3009.9260 3065.0395 3065.0395 3125.3386 3125.3386 3190.8014 3190.8014 2757.8895 2757.9687 2774.0587 2775.5274 2784.7085 2792.0335 2794.7450 2810.7856 2811.0889 2834.2425 2834.2574 2863.0101 2863.0101 2897.1818 2897.1818 2936.5920 2936.5920 2981.2579 2981.2579 3031.1551 3031.1551 3086.2586 3086.2586 3146.5481 3146.5481 3212.0015 3212.0015 3282.6059 3282.6059 2778.6148 2778.6678 2796.3907 2797.4876 2808.4273 2814.7873 2818.5355 2833.7566 2834.2651 2857.1638 2857.1959 2885.8656 2885.8656 2920.0 0 03 2920.0 0 03 2959.3809 2959.3809 3004.0252 3004.0252 3053.9066 3053.9066 3108.9971 3108.9971 3169.2754 3169.2754



δ 4

J 1

Ka

3 0.2 0.1 0.4 0.4 0.7 0.7 0.1 0.1 0.1 0.1 0.2 0.2 0.6 0.6 0.1 0.1 0.3 0.3

3.2 −0.3 9.9 9.9 −1.9 −2.1 0.3 0.3 1.2 1.2 1.8 1.8 0.4 0.4 −0.4 −0.4 0.2 0.2 −3.3 −3.3 0.9 1.3 −6.1 −4.1 −2.2 −0.1 −0.9 1.1 −0.7 1.3 9.7 −3.2 −3.6 1.6 1.6 2.1 2.1 2.4 2.4 −0.6 −0.6 −1.1 −1.1 0.5 0.5 −0.9 −0.9 −3.7 −3.7 0.1 −1.1 −5.3 −3.9 −1.3 −1.2 −0.4 1.1 −1.1 9.5 9.9 −4.7 −3.6 1.9 1.8 3.0 3.0 3.0 3.0 −0.5 −0.5 −1.7 −1.7 0.2 0.2

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 17 17 17 17 17 17 17 17 17 17 17 17 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

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

0.1 0.1 0.2 0.1 0.4 0.2 0.1 0.2 0.5 0.4 0.6 0.6 0.2 0.2 0.1 0.1 0.7 0.7 0.2 0.2 0.4 0.4 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.3 0.2 0.4 0.1 0.3 0.1 0.1 0.3 1.5 1.0 1.0 0.1 0.1 0.7 0.7 0.1 0.1 0.1 0.1

0.2 0.2

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

Eexp 2 2859.0852 2881.6420 2881.70 0 0 2910.2649 2910.2649 2944.3546 2944.3546 2983.7194 2983.7194 3028.3175 3028.3175 3078.1800 3078.1800 3133.2556 3133.2556 3193.5210 3193.5210 3258.9534 3258.9534 3329.5417 3329.5417 3405.2479 3405.2479 3486.0569 3486.0569 2824.0521 2824.0743 2844.9455 2845.5204 2860.1873 2864.6834 2871.1083 2884.3180 2885.5754 2907.6776 2907.7822 2936.2062 2936.2102 2970.2478 2970.2478 3009.5369 3009.5369 3054.1356 3054.1356 3103.9765 3103.9765 3159.0348 3159.0348 3219.2854 3219.2854 3284.7052 3284.7052 3355.2863 3355.2863 3430.9786 3430.9786 3511.7802 3511.7802 3597.6584 3597.6584 2848.7670 2848.7783 2871.1722 2871.5767 2888.1394 2891.7963 2899.8357 2911.8956 2913.7588 2935.2693 2935.4529 2963.7003 2963.7083 2997.6838



δ

3

4

0.1 0.2 0.9 1.3 1.3 0.2 0.2 0.3 0.3 0.6 0.6 0.1 0.1 0.2 0.2 0.1 0.1 0.3 0.3 0.3 0.3 0.2 0.2

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

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

−2.2 13.4 12.0 −5.1 −2.7 0.4 0.2 24.3 24.3 3.5 3.5 −0.6 −0.6 −2.4 −2.4 −0.6 −0.6 −1.0 −1.0 3.6 3.6 0.0 0.0 −2.4 −2.4 0.5 1.9 −1.3 −1.1 1.4 7.2 0.3 1.0 −3.3 −5.9 −4.0 −5.1 −6.1 −2.2 −2.6 −6.2 −6.2 3.4 3.4 −0.7 −0.7 −3.0 −3.0 −1.7 −1.7 −1.6 −1.6 7.0 7.0 −0.1 −0.1 3.9 3.9 3.0 3.0 −3.8 1.5 3.1 0.9 1.5 −3.5 0.5 1.7 −5.0 2.8 2.3 −3.2 −4.9 −3.9

(continued on next page)

106

O.N. Ulenikov, O.V. Gromova and E.S. Bekhtereva et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 233 (2019) 99–109

Table 3 (continued) J 1

Ka

8 8 8 8 8 8 8 9 9 9 9 9 9 9 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 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

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

Kc

3 3 2 2 1 1 0 9 9 8 8 7 7 6 4 3 4 3 2 2 1 19 19 17 17 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 4 3 3 2 20 19 18 17 17 16 16 15 15 14 13 12 12 11 11 10 10 9 9 8 8 7

Eexp 2 2729.1258 2758.1062 2758.1062 2792.3803 2792.3803 2831.8821 2831.8821 2674.0936 2674.6145 2682.4315 2686.7516 2689.2349 2700.6979 2700.9538 3382.5450 3458.2240 3458.2240 3539.0034 3539.0034 3624.8799 3624.8799 2874.8069 2874.8124 2917.4233 2920.3353 2930.1427 2940.9900 2943.6518 2964.4234 2964.7291 2992.7458 2992.7635 3026.6678 3026.6678 3065.8369 3065.8369 3110.3584 3110.3584 3160.1442 3160.1442 3215.1599 3215.1599 3275.3728 3275.3728 3340.7638 3340.7638 3411.3206 3411.3206 3486.9845 3486.9845 3567.7583 3567.7583 3653.6152 3653.6152 2902.1801 2927.5316 2948.0099 2962.0192 2971.5913 2975.2637 2995.1367 2995.6307 3023.3474 3023.3794 3096.2904 3096.2904 3140.7652 3140.7652 3190.5173 3190.5173 3245.5059 3245.5059 3305.6978 3305.6978 3371.0716 3371.0716



δ 4

J 1

Ka

3 0.3 0.2 0.2 0.3 0.3 0.2 0.2 0.1 0.1 0.2 0.1 0.3 0.2 0.2 0.2 0.4 0.4 0.3 0.3

4.8 −6.3 −6.3 5.4 5.4 −3.4 −3.4 1.6 2.4 −3.8 −1.9 −2.9 −0.9 −0.6 8.1 0.6 0.6 −8.7 −8.7 9.8 9.8 1.5 −2.4 1.2 6.9 13.4 1.1 −8.4 4.0 2.2 −1.6 −2.0 1.3 0.3 −3.4 −3.4 4.9 4.9 0.4 0.4 −2.0 −2.0 −3.1 −3.1 −1.8 −1.8 8.5 8.5 −4.4 −4.4 −3.1 −3.1 6.6 6.6 3.6 −0.4 0.2 13.0 1.5 −11.6 3.9 2.0 0.9 0.5 −3.7 −3.7 4.8 4.8 0.9 0.9 −2.2 −2.2 −3.0 −3.0 −1.6 −1.6

12 12 12 12 12 12 12 13 13 13 13 13 13 13 20 20 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 23 23 23 23 23

9 10 10 11 11 12 12 0 1 1 2 2 3 3 17 17 0 1 2 2 3 3 4 5 5 8 8 9 9 10 10 11 11 12 12 13 13 14 14 16 16 17 17 0 1 2 2 3 3 4 4 5 5 6 6 8 8 9 9 10 10 11 11 12 12 13 13 14 14 16 16 0 1 1 2 2

0.3 0.3 0.2 0.1 0.7 0.5 0.4 0.1 0.2 0.3 0.7 0.6 0.6 0.3 0.3 0.3 0.3 0.1 0.1 0.8 0.8 0.2 0.2 0.2 0.2 0.9 0.9 0.3 0.3

4.5 0.4 0.1 0.2 0.2 0.2 0.2 0.3 0.2 0.1 0.5 0.5 0.1 0.1 0.3 0.3 0.1 0.1 0.5 0.5 0.3 0.3

Kc

3 3 2 2 1 1 0 13 13 12 12 11 11 10 4 3 21 20 20 19 19 18 18 17 16 14 13 13 12 12 11 11 10 10 9 9 8 8 7 6 5 5 4 22 22 21 20 20 19 19 18 18 17 17 16 15 14 14 13 13 12 12 11 11 10 10 9 9 8 7 6 23 23 22 22 21

Eexp 2 2940.2940 2990.2155 2990.2155 3045.3382 3045.3382 3105.6458 3105.6458 2738.4893 2738.6080 2753.0309 2754.9530 2762.4846 2770.7637 2772.6398 3683.8634 3683.8634 2930.8800 2957.6701 2957.8182 2979.8810 2981.5887 2995.3507 3003.6842 3027.4063 3028.1795 3128.2832 3128.2832 3172.7057 3172.7057 3222.4181 3222.4181 3277.3772 3277.3772 3337.5450 3337.5450 3402.8991 3402.8991 3473.4312 3473.4312 3629.7995 3629.7995 3715.6252 3715.6252 2960.9165 2960.9191 2989.2488 3013.0284 3014.3058 3030.1455 3037.2542 3043.6046 3061.2308 3062.3993 3089.2263 3089.3232 3161.8202 3161.8202 3206.1806 3206.1806 3255.8500 3255.8500 3310.7739 3310.7739 3370.9108 3370.9108 3436.2460 3436.2460 3506.7680 3506.7680 3663.0891 3663.0891 2992.2728 2992.2728 3021.9406 3022.0145 3047.4516



δ 4

J 1

Ka

3 0.2 0.2 0.2 0.4 0.4 0.2 0.2 0.1 0.2 0.1 0.3 0.2 0.4 0.1 0.4 0.4 0.8 0.2 0.1 0.2 0.2 0.2 0.4 0.9 0.8 0.8 0.8 0.2 0.2 0.9 0.9 0.1 0.1 2.3 2.3 0.3 0.3 0.3 0.3 0.2 0.2

1.3 0.0 0.0 −0.1 −0.1 0.8 0.8 1.1 1.5 −7.1 −3.7 −2.9 2.5 −1.8 −2.0 −2.0 8.1 2.4 2.4 −1.0 −9.8 −0.4 1.1 2.4 1.3 −5.1 −5.1 4.8 4.8 0.5 0.5 −1.5 −1.5 −1.9 −1.9 −0.5 −0.5 5.2 5.2 4.0 4.0 −1.5 −1.5 6.8 7.1 −3.8 −5.1 −5.9 −2.1 0.5 −0.4 2.7 −1.1 0.8 4.1 −5.4 −5.6 3.3 3.3 1.1 1.1 −1.2 −1.2 −4.0 −4.0 1.0 1.0 −0.6 −0.6 2.6 2.6 −2.4 −5.1 −4.7 −0.4 6.2

15 15 15 15 15 15 16 16 16 16 16 16 16 16 23 23 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 24 24 24 24 24 24 24 24 24 24 24 24 24 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25

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

0.4 0.8 0.2 0.1 0.3 0.8 0.4 0.2 0.3 0.3 0.2 0.1 0.5 0.5 0.2 0.2 0.3 0.3 0.2 0.2 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 1.3 1.3 0.1 0.2 0.6

Kc

3 2 2 1 1 0 16 16 15 15 14 14 13 13 17 16 15 15 14 14 13 13 12 12 11 11 10 10 9 8 7 24 24 23 22 21 21 20 19 19 18 17 16 16 15 15 14 13 14 13 12 11 12 11 10 9 8 25 25 24 23 23 22 22 21 20 18 17 17 16 16 15 15 14 13 14

Eexp 2 3234.7188 3234.7188 3305.3152 3305.3152 3381.0304 3381.0304 2800.6691 2800.7037 2820.0198 2820.8214 2833.6112 2839.0101 2843.9977 2858.2692 3124.6587 3196.9017 3196.9017 3241.1928 3241.1928 3290.8121 3290.8121 3345.6971 3345.6971 3405.8016 3405.8016 3471.1142 3471.1142 3541.6322 3541.6322 3697.8961 3697.8961 3024.9754 3024.9754 3056.0592 3083.8376 3103.8951 3108.7626 3133.5074 3135.9552 3161.3304 3161.5616 3233.5345 3233.5345 3277.7440 3277.7440 3327.3071 3327.3071 3382.1483 3382.1483 3442.2141 3442.2141 3507.5031 3507.5031 3578.0469 3578.0469 3734.2185 3734.2185 3059.0010 3059.0010 3091.5028 3120.1176 3120.6371 3142.7653 3146.6738 3171.9412 3175.3298 3271.7188 3271.7188 3315.8363 3315.8363 3365.3350 3365.3350 3420.1275 3420.1275 3480.1535 3480.1535



δ 4

J 1

Ka

3 0.2 0.2 0.6 0.6

−0.6 −0.6 0.9 0.9 −5.5 −5.5 0.5 1.8 −3.8 −2.2 2.8 0.9 0.0 1.0 −3.2 −7.0 −7.3 1.5 1.5 0.3 0.3 −1.1 −1.1 −3.1 −3.1 3.1 3.1 −8.6 −8.6 −1.1 −1.1 −2.1 8.8 −1.5 0.8 −2.1 −0.3 4.5 −7.5 −8.2 5.9 −5.1 −5.8 −0.4 −0.4 −0.1 −0.1 −0.3 −0.3 −3.4 −3.4 0.1 0.1 5.6 5.6 2.4 2.4 4.4 4.1 8.4 −0.4 −2.8 3.9 5.5 4.1 −4.8 −2.0 −3.3 −1.2 −1.2 −0.4 −0.4 −0.1 −0.1 −1.9 −1.9

18 18 18 18 18 18 18 18 18 18 18 18 18 18 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 28 28 28 28 28 28 28 28 28 28 28 28 28 28 29 29 29 29 29 29 29 29 29 30 30 31 31 32 32 33

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

0.2 0.1 0.1 0.1 0.4 0.2 0.1 0.1 0.2 0.4 0.4 0.2 0.2 0.3 0.3 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.9 0.9 0.3 0.5 0.1 0.4 0.2 0.2 0.8 0.8 0.2 0.2 0.5 0.5 0.2 0.2 0.3 0.3

0.4 0.4 0.3 0.3 0.8 0.8 0.1 0.2 0.2 0.1 0.1 0.2 0.2

0.2 0.2 0.2 0.2

0.1 0.1

Kc

11 11 10 10 9 9 8 8 7 7 6 6 5 5 23 22 22 19 18 18 17 17 16 16 15 14 15 13 14 27 27 25 25 24 23 23 20 19 19 18 18 17 16 17 15 16 28 28 27 25 24 24 21 20 20 19 19 18 16 15 29 29 26 22 21 20 19 17 16 30 30 31 31 32 32 33

Eexp 2 2997.6838 3036.9201 3036.9201 3081.4825 3081.4825 3131.2978 3131.2978 3186.3360 3186.3360 3246.5689 3246.5689 3311.9753 3311.9753 3382.5450 3185.9765 3200.0828 3211.8887 3311.4544 3311.4544 3355.4717 3355.4717 3404.8994 3404.8994 3459.6381 3459.6381 3519.6174 3519.6174 3584.8510 3584.8510 3131.0423 3131.0423 3198.0015 3198.2639 3226.6967 3243.0170 3253.3340 3352.7522 3352.7558 3396.6543 3396.6543 3446.0013 3446.0013 3500.6787 3500.6787 3560.6065 3560.6065 3169.0568 3169.0568 3205.7951 3268.7991 3287.4119 3296.2673 3395.6155 3395.6215 3439.3840 3439.3840 3488.6429 3488.6429 3668.2922 3668.2922 3208.4007 3208.4007 3312.2752 3440.0543 3440.0610 3532.8359 3532.8359 3712.3006 3712.3006 3249.0726 3249.0726 3291.0743 3291.0743 3334.4035 3334.4035 3379.0603



δ

3

4

0.6 0.2 0.2 0.3 0.3 0.1 0.1 0.4 0.4 0.1 0.1 0.3 0.3 0.2 0.3 0.5 0.2 1.2 1.2 0.2 0.2 0.3 0.3 0.3 0.3 0.1 0.1 0.3 0.3 0.5 0.5 0.3 0.4 0.2 0.6

−3.2 −4.0 −4.0 4.4 4.4 0.0 0.0 −2.9 −2.9 −2.7 −2.7 −1.8 −1.8 8.1 −8.9 9.8 4.3 −1.0 −3.3 −0.4 −0.5 1.7 1.7 2.2 2.2 −1.9 −1.9 −2.4 −2.4 3.0 2.9 1.7 7.8 −3.7 −2.9 1.2 4.7 3.5 2.3 2.1 3.8 3.8 −4.0 −4.0 2.5 2.5 1.5 1.5 −9.6 8.4 −7.3 −3.3 3.5 1.8 −9.0 −9.4 −0.7 −0.8 2.0 2.0 0.4 0.3 −4.4 4.5 −6.1 −6.0 −6.0 0.9 0.9 −1.2 −1.1 −0.5 −0.6 0.2 0.1 0.5

0.1 0.2 0.5 0.5 0.1 0.1 0.4 0.4 0.3 0.3 0.4 0.4 0.4 0.8 0.3 0.1 0.2 0.6 0.6 0.4 0.4 0.2 0.2 0.3 0.3 0.4

0.2 0.2 0.4 0.4 0.2 0.2 0.2 0.2 0.2 0.2 0.5

(continued on next page)

O.N. Ulenikov, O.V. Gromova and E.S. Bekhtereva et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 233 (2019) 99–109

107

Table 3 (continued) J 1

Ka

20 20 20 20 20 20

14 14 15 15 16 16

Kc

7 6 6 5 5 4

Eexp 2 3441.6167 3441.6167 3517.2611 3517.2611 3598.0205 3598.0205



δ 4

J 1

Ka

3 0.1 0.1 0.2 0.2

0.1 0.1 −8.9 −8.9 −1.3 −1.3

23 23 23 23 23 23

3 3 4 5 5 6

Kc

21 20 20 19 18 18

Eexp 2 3048.3909 3066.3418 3072.2864 3096.6005 3098.3179 3124.5020



δ 4

J 1

Ka

3 0.4 0.3 0.2 0.3

−3.8 −3.5 0.5 0.6 −3.3 −8.9

26 26 26 26 26 26

0 1 1 2 2 3

0.1

Kc

26 26 25 25 24 24

Eexp 2



δ

3

4

3094.3570 3094.3570 3128.2612 3128.3014 3158.4146 3158.7781

0.6 0.6 0.4 0.1 0.1 0.5

4.1 3.9 −4.7 2.4 −1.4 10.5

J 1

Ka

33 34 34 35 35

1 0 1 0 1

Kc

33 34 34 35 35

Eexp 2



δ

3

4

3379.0603 3425.0461 3425.0461 3472.3591 3472.3591

0.5 0.3 0.3 0.3 0.3

0.4 1.2 1.1 1.0 1.0

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

Table 4 Resonance interaction parameters for the ν2 + ν6 and some other closely located vibrational states of C2 H2 D2 -cis (in cm−1 )a . Parameter

Value

1,7 C 1 × 102 K 1,7 C 1 × 107 KKJ 1,7 C 2 × 103 J 1,7 C 2 × 108 KKK 1,7 C 2 × 109 JJJ 2,7 C 1 × 103 J 2,7 C 1 × 107 KKK 2,7 C 2 × 104 J 2,7 C 2 × 107 JJ 3,7 C 1 × 10 K 3,7 C 1 × 105 KJ 3,7 C 1 × 108 JJJ 3,7 C 2 × 106 KK 4,7 C 1 × 102 K 4,7 C 2 × 105 J 5,7 C 1 × 104 KK 5,7 C 1 × 107 KJJ 5,7 C 2 × 108 KKK 1,6 C 1 × 102 J 2,5 C 1 × 102 J 6,7 F 0 6,7 F 5 KKK × 10 6,7 F 3 Kxy × 10 6,7 F 6 KJxy × 10 6,7 F 9 KJJxy × 10

1 × 104 −0.493(61) 1,7CKJ

a

Parameter

1 × 107 0.365(21) 1,7CKJJ 2 × 105 −0.1191(12) 1,7CKJ

0.185(52)

1,7 C 2 KKJ

× 108

Value 0.123(17) −0.108(14) 0.1047(11) −0.1497(19)

Parameter

Value

1,7C 1 × 106 JJ 1,7C 2 × 103 K 1,7C 2 × 106 JJ 1,7C 2 × 109 KJJ

−0.291(22) −0.2007(33) 0.246(34) −0.623(75)

−0.188(28) 1 × 104 −0.208(31) 2,7CKK

−0.74(22) 0.2644(89) −0.4823(84) 0.118(33) 0.933(93) −0.319(43)

2,7C 1 × 107 KKJ 2,7C 2 × 106 KK 2,7C 2 × 109 KJJ 3,7C 1 × 102 J 3,7C 1 × 105 JJ 3,7 C2 × 10

−0.586(83) 3,7CK2K J × 108 0.739(35) 4,7 C2 × 102 2 × 105 −0.295(75) 4,7CKK −0.351(28) 0.1287(11) −0.133(29) −0.1849(74) −0.307(70) −0.66(10) 0.105(19)) 0.188(24)) −0.612(65)) 0.411(54))

5,7C 1 × 105 KJ 5,7C 2 × 103 K 5,7C 2 × 109 KJJ 1,6 C 1 × 107 KKK 2,5C 1 × 105 JJ 6,7 F 3 KK × 10 6,7 F × 107 JJJ 6,7 F 4 Jxy × 10 6,7 F 8 × KKKxy 10

0.634(87) 2,7CJJ1 × 106

0.326(47)

−0.384(95) 2,7CK2 × 103

−0.110(25)

2 × 106 −0.661(98) 2,7CKJ

−0.204(51)

0.449(71) 1 × 104 −0.1587(15) 3,7CKK

−0.152(31)

1 × 108 0.391(49) 3,7CKJJ

−0.788(86)

0.1009(61) 3,7CJ2 × 104

−0.1161(96)

0.2656(91) 4,7C 2 × 103 K 2 × 106 0.1587(45) 4,7CKJ

0.217(49)

−0.574(81) 0.1387(91) −0.576(34)

2,7C 1 × 107 KKJ 5,7C 2 × 107 JJ 5,7C 2 × 1010 JJJ

−0.311(35) 0.192(57) 0.502(42) −0.326(64) 0.567(14)

0.393(64) 0.452(68) 0.711(65) −0.2357(86) 0.1412(89) 0.357(59)

6,7 F

× 104

0.1492(93) −0.387(35) −0.266(56) KKxy 6,7 F 8 0.283(69) KKJxy × 10 6,7 F 6,7 F

JJ

xy × 10

2

× 105

Values in parentheses are 1σ standard errors.

Fig. 7. Fragment of ro-vibrational energy levels of the (v3 = 1, v10 = 2, A1 ), (v4 = 2, v10 = 1, A1 ), (v6 = v7 = v10 = 1, A2 ), (v3 = v8 = v10 = 1, A2 ), (v4 = v7 = v8 = 1, B2 ), (v6 = 1, v8 = 2, B1 ), and (v2 = v6 = 1, B1 ) vibrational states. The energies have been calculated from the constants given in Tables 2 and 4. In order to suppress most of the J−slope, the calculated energies have been reduced by B+2 C J (J + 1 ) (here B and C are rotational parameters of the ground vibrational state). Levels belonging to the (v2 = v6 = 1 ), (v4 = v7 = v8 = 1 ), (v6 = v7 = v10 = 1, (v4 = 2, v10 = 1, (v6 = 1, v8 = 2 ), (v3 = 1, v10 = 2 ), and (v3 = v8 = v10 = 1 ) vibrational states are marked by open stars, open and dark circles, open and dark triangles, open and dark squares, respectively.

of the Hamiltonian parameters, Eqs. (1)–(7), with the same set of the initial experimental energy values as in the main fit. The drms value is shown vs the “n/7” value, where “n/7” means that the resonance interaction between the vibrational state 7 and the vibrational state n was eliminated from the consideration. One can see that elimination of any of the six sets of interaction parameters leads to considerable deterioration of the result (strong increase of the drms value). For all the above mentioned reasons, the drms value of the fit in the present study is about ten times worse than the experimental uncertainties in line positions. The situation can

Fig. 8. The value of drms vs “n/7”. The “n/7” on the abscissa corresponds to the situation for which the resonance interaction between the vibrational state 7 and the vibrational state n is eliminated from the consideration. One can see that any of the resonance types has large enough influence on the drms .

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O.N. Ulenikov, O.V. Gromova and E.S. Bekhtereva et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 233 (2019) 99–109

be improved by one of the two following ways: (a). the correct prediction (and further fixing) of the band centers and rotational parameters of all six above discussed vibrational states, or (b). assignments of, at least, 10–15 transitions for all of these six bands (the latter again can give the possibility to correctly estimate the values of their band centers and rotational parameters). Thus the obtained drms -value has to be evaluated in this context and seems to be not too bad. 7. Conclusion We made an analysis of the high resolution IR spectrum of the C2 H2 D2 -cis ethylene isotopologue in the region of 2400– 2700 cm−1 , where the strong ν2 + ν6 band is located. 1987 transitions were assigned with the maximum values of the upper quantum numbers J max = 35 and Kamax = 17. Experimental information obtained from the experimental data was used in the weighted fit procedure with the Hamiltonian which takes into account strong resonance interactions of the (v2 = v6 = 1 ) vibrational state with six other closely located states. A set of 95 spectroscopic parameters obtained from a weighted least square fit reproduces the initial experimental data with the drms = 3.98 ×10−3 cm−1 . For a future study it could be worthwhile to use a bigger multipath cell and increase the optical path by a factor 5 to 10 to get sufficient information about the discussed six weaker combination bands which would be possible in our laboratory [83]; however one would need a considerable amount of the expensive C2 H2 D2 -cis isotopologue. Acknowledgments The work was funded by the Tomsk Polytechnic University Competitiveness Enhancement Program (project VIU-63/2019), by the grant RFBR 18-32-00116-mol-a, and by the Deutsche Forschungsgemeinschaft (grants BA 2176/4–1, BA 2176/4–2, and BA 2176/5–1). Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jqsrt.2019.05.019. References [1] Abeles FB, Heggetad HE. Ethylene: an urban air pollutant. J Air Pollut Control Assoc 1973;23. 517–21 [2] Niki H, Maker PD, Savage CM, Breitenbach LP. Mechanism for hydroxyl radical initiated oxidation of olefin–nitric oxide mixtures in parts per million concentrations. J Phys Chem 1978;82. 135–7 [3] Coheur PF, Herbin H, Clerbaux C, Hurtmans D, Wespes C, Carleer M, Turquety S, Rinsland CP, Remedios J, Hauglustaine D, Boone CD, Bernath PF. ACE–FTS Observation of a young biomass burning plume: first reported measurements of C2 H4 , C3 H6 O, H2 CO and PAN by infrared occultation from space. Atm Chem Phys 2007;7. 5437–46 [4] 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 [5] Betz L. Ethylene in IRC.10216. Astrophys J 1981;244. L103–5 [6] Griffith CA, Bézard B, Greathouse TK, Kelly DM, Lacy JH, Noll KS. 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 [7] Schulz B, Encrenaz T, Bézard B, Romani P, Lellouch E, Atreya SK. Detection of C2 H4 in neptube fom ISO/PHTS observations. Astron Astrophys 1999;350. L13–7 [8] Cernicharo J, Heras AM, Pardo JR, Tielens AGGM, Guelin M, Dartois E, et al. Walters LBFM. methylpolyynes and small hydrocarbons in CRL 618. Astrophys J 2001;546. L127–30 [9] Saslaw WC, Wildey RL. On the chemistry of jupiter’s upper atmosphere. Icarus 1967;7:85–93. [10] Encrenaz T, Combes M, Zeau Y, Vapillon L, Berenze J. A tentative identification of C2 H4 in the spectrum of saturn. Astron Astrophys J 1975;42. 355–6 [11] Bar-Nun A, Podolak M. The photochemistry of hydrocarbons in Titan’s atmosphere. Icarus 1979;38. 115–22

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