First detection of the rare hydrogen sulfide isotopologue: The pure rotational and ν2 bands of HD33S

Journal of Quantitative Spectroscopy & Radiative Transfer 232 (2019) 108–115

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First detection of the rare hydrogen sulfide isotopologue: The pure rotational and ν 2 bands of HD33 S O.N. Ulenikov a,∗, E.S. Bekhtereva a, O.V. Gromova 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 6 February 2019 Revised 4 April 2019 Accepted 5 May 2019 Available online 6 May 2019 Keywords: HDS high resolution spectra v2 band: line positions and strengths Spectroscopic parameters

a b s t r a c t The high–resolution infrared spectrum of the HDS isotopologue was recorded and analyzed in the region of the ν 2 fundamental band region (70 0–140 0 cm−1 ) with a Bruker IFS 125HR Fourier transform infrared spectrometer (Zurich prototype ZP2001). Among the lines of the ν 2 band of the HD32 S and HD34 S molecules, 801 transitions of HD33 S were found in the spectrum and assigned for the first time (Jmax = 19 and Kamax = 12). Also for the first time, rotational energies of the ground vibrational state were determined from the 87 ground state combination differences obtained from the experimental data. Fits of parameters of the Watson hamiltonian with both ground state combination differences and ro–vibrational energy values (line positions) of the (010) vibrational state were made. Parameters of the effective dipole moments of the pure rotational transitions and of the ν 2 band are obtained. Line lists (line positions and line strengths) of the pure rotational transitions and transitions belonging to the ν 2 band are generated which can be useful for astrophysical and planetological applications. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction Hydrogen sulfide is an important species in many fields of science as planetology, astrophysics, atmospheric optics, chemistry, etc. Generated by volcanic eruptions and by fuel combustion in human activities [1–4], it plays an important role as a pollutant and trace species in the terrestrial atmosphere. Different isotopologues of hydrogen sulfide, which are involved in the sulfur cycle, are the basis both for the study of processes which had taken place in the Earth’s early history [5], and for determining the sulfur isotope compositions of atmospheric species in our days [6]. Hydrogen sulfide shows a relatively high abundance in the atmospheres of gas solar system giants, brown dwarfs, extra–solar planets, interstellar clouds, etc., [7–12]. Different isotopologues of hydrogen sulfide (first of all HDS) also have been detected in space, see [7,13– 17]. Therefore, extensive laboratory investigations of spectra of the hydrogen sulfide molecule and of its isotopologues have been performed in the previous years (we mention here only a few of them, Kissel et al. [18], Azzam et al. [19], Cazzoli et al. [20] and references cited therein).

∗

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

https://doi.org/10.1016/j.jqsrt.2019.05.004 0022-4073/© 2019 Elsevier Ltd. All rights reserved.

In the present work we focus on the study of spectroscopic properties of the HDS molecule which can occur in nature in the form of the four stable isotopologues, HD32 S, HD34 S, HD33 S, and HD36 S with the abundance of 95.041 %, 4.196 %, 0.748 %, and 0.015 %, respectively. The first two of them have been presented earlier in the literature (see, e.g., [21–29]), while the spectroscopic properties of the two other isotopologues never have been discussed earlier. In this paper we present results of the first recording and analysis of the high resolution spectrum of the more abundant of them, namely, the HD33 S isotopologue. 2. Experimental details Two spectra have been measured for the present analysis with a IFS 125HR Bruker Fourier–transform infrared spectrometer (FTIR, Zurich prototype ZP2001) at an optical resolution of 0.002 cm−1 (spectrum I) and 0.003 cm−1 (spectrum II). Two optical multiple– path cells made from stainless steel were used at a pathlength of 4 m (spectrum I) and 163 (spectrum II) m in the spectral range between 600 and 3000 cm−1 from which 70 0–140 0 cm−1 is important in the present work. For more details see Table 1 and our recent study of D2 S, [30]. Rapid deuterium–hydrogen exchange of a certain amount of the D2 S molecules was exploited to generate the HDS species with the help of residual H2 O vapor from the surface of the cell, of the KBr and CsI windows and from small amounts of water vapor penetrat-

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Fig. 1. Experimental survey spectrum I of HDS in the region of 70 0–140 0 cm−1 (trace 1a; for the experimental conditions see Table 1). Centers of the ν 2 band of HD32 S, HD33 S, and HD34 S are marked by dark triangles. (c)–(e) show the simulated spectra of the HD32 S, HD33 S, and HD34 S species. (b) is the sum of the simulated spectra (c)–(e).

Table 1 Experimental setup for the analysed region of 70 0–140 0 cm−1 of the infrared spectrum of HDS. Spectr.

Resolution /cm−1

No. of scans

Spectral range /cm−1

Detector

Beamsplitter

Opt. pathlength/m

Aperture /mm

Temp. /o C

Pressure /Pa

Calibr. gas

I II

0.002 0.003

960 1200

600 - 3000 600 - 2200

MCT–D316 MCT–D316

KBr KBr

4 163

1.15 1.7

23 ± 0.8 23 ± 0.8

450 450

CO2 , N2 O CO2 , N2 O

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Fig. 2. Illustration of the high–resolution experimental spectrum II (upper trace 2a). Assigned lines of HD33 S are marked by dark circles. (b) shows the simulated spectrum in this region.

Fig. 3. Fragment of the high–resolution experimental spectrum II (a). Assigned lines of HD33 S are marked by dark circles. (b) shows the simulated spectrum in this region.

ing into the cells. The latter cannot be completely avoided due to the long measuring duration over about 28 and 33 hours for the two spectra. In this way considerably high amounts of HDS and even H2 S are formed. To determine the average partial pressure of the HDS species during the recording time, we used a method which utilizes the main effective dipole–moment parameters of the H2 S isotopologue via the isotopic substitution theory, [31]. At 298 K, the Doppler broadening for HD33 S differs only slightly compared to HD34 S and was calculated to be in the range of

0.0 014–0.0 029 cm−1 at the borders of the ν 2 band region (700 and 1400 cm−1 ). For the used pressure the pressure broadening is roughly 0.0013 cm−1 . It only delivers a small contribution to the total line widths between 0.0 023–0.0 038 cm−1 for minimum and maximum conditions of the used spectral region, optical resolutions and pressure. These total line widths can be approximated by the root sum square of the convolution of Doppler, pressure and instrumental line widths. They are in accordance with the experimental results.

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Table 2 Statistical information for the ν 2 band of HD33 S. Band

Center/cm−1

Jmax

Kamax

Ntr a

Nl b

m1 c

m2

1 Ground

2

3 16 19

4 8 12

5 87 787

6

7 78.2 88.7

8 15.0 7.8

ν2

1032.09327

203

c

m3 c

m4 c

9 5.7 2.0

10 1.1 1.5

a

Ntr is the number of assigned experimental transitions; for the ground state it is the number of ”experimental” GSCD. b Nl is the number of obtained ro–vibrational energies of the (v2 = 1 ) vibrational state. c Here mi = ni /Nl × 100% (i = 1, 2, 3, 4); n1 , n2 , n3 , and n4 are the numbers of upper-state energies for which the differences δ = | (E exp − E calc ) | satisfy the conditions δ ≤ 10 × 10−5 cm−1 , 10 × 10−5 cm−1 < δ ≤ 20 × 10−5 cm−1 , 20 × 10−5 cm−1 < δ ≤ 30 × 10−5 cm−1 , and δ > 30 × 10−5 cm−1 . Table 3 “Experimental” ground state combination differences for HD33 S (in cm−1 ). J 1

Ka

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

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

a

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

J 2

Ka

6 5 2 7 7 3 6 2 3 3 7 4 4 2 4 4 4 6 7 4 4 3 5 5 5 3 3 4 6 4 5 4 6 4 3 8 8 8 4 8 6 2 4 3

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

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

Value 3 3.93004 6.45518 12.88523 13.13705 16.39360 16.56279 17.73769 19.91572 24.03135 24.05412 26.04494 29.73798 30.47382 32.80095 33.05405 33.46839 37.00605 37.60827 38.19514 38.70586 39.07337 40.61691 41.34297 41.40333 49.39159 52.59886 52.92131 54.52789 56.87186 60.21175 60.45591 61.62126 63.17488 63.68864 65.41658 65.89257 66.41191 66.62408 68.44395 69.32163 69.35430 71.09068 72.17425 72.51458

δa 4 −4 8 4 7 3 7 −7 −4 −12 3 −13 1 1 0 1 −2 −3 −6 7 −6 1 10 0 −19 2 11 8 −1 5 −3 6 −6 4 5 15 2 24 14 5 9 5 6 −9 6

J 1

Ka

Kc

J 2

Ka

Kc

Value 3

8 6 6 6 8 6 3 3 4 4 5 7 7 6 6 3 3 4 7 8 7 4 6 7 9 9 7 5 4 4 10 4 6 8 5 11 11 7 5 5 16 16 8

5 0 2 1 2 2 1 3 3 3 1 1 0 2 1 2 2 3 3 0 2 2 2 2 1 0 2 2 4 4 0 3 2 8 4 1 0 3 5 5 1 0 5

4 6 5 5 7 4 3 0 2 1 4 7 7 5 5 1 2 1 4 8 6 3 4 5 9 9 5 4 0 1 10 2 5 0 1 11 11 4 0 1 16 16 4

9 4 7 7 8 7 4 1 2 2 6 5 5 7 7 4 4 2 8 6 5 5 7 5 7 7 8 6 2 2 8 5 7 9 3 9 9 5 3 3 14 14 8

5 0 2 2 4 3 3 1 2 2 3 1 0 3 3 4 4 1 4 0 1 4 4 2 1 0 4 4 2 2 0 5 4 5 2 1 0 2 3 3 1 0 8

4 4 5 5 5 4 1 0 0 1 4 5 5 5 5 1 0 1 4 6 4 1 4 3 7 7 5 2 0 1 8 0 3 4 1 9 9 4 0 1 14 14 0

75.63718 77.98180 78.00562 81.93555 82.54231 82.91680 84.26587 85.39981 85.65270 86.38970 87.09199 90.18267 90.60267 91.14278 95.07261 98.91782 100.69466 100.82866 101.35389 103.31939 107.82514 109.84734 114.94927 115.61400 116.01740 116.09266 119.76672 120.04683 124.72607 125.09556 128.88724 130.54691 131.88039 140.10332 140.32101 141.67151 141.68313 146.09177 163.60096 163.65341 205.44367 205.44367 215.74050

δa 4 2 10 −9 −23 23 −8 −1 10 −9 6 −2 −5 4 9 −15 11 −1 6 −13 5 13 −8 −9 −4 0 0 −35 19 −7 −1 0 −7 16 0 −22 −16 23 5 −6 −6 0 −6 2

The δ is the difference (GSCDexp - GSCDcalc ) in 10−5 cm−1 .

3. Line positions and rotational energy levels of the ground and (010) vibrational states An experimental overview spectrum (Fourier transform infrared spectrum) is shown in Fig. 1a, compare spectrum I in Table 1. Most of the lines in Fig. 1a belong to the considerably stronger ν 2 bands of the HD32 S and HD34 S species (see Fig. 1c and e). However, weak lines belonging to the HD33 S molecule also can be recognized in the spectrum. As an illustration, Figs. 2a and 3a present

two small fragments of the high resolution spectrum with lines of HD33 S marked. Because the lines belonging to the HD33 S species are very weak, the experimental spectrum II was used for the analysis which is 40 times stronger than spectrum I. It should be noted that information about microwave transitions or ground state rotational energies of HD33 S is absent in the literature. For that reason, it was not possible (at least, in the first step of the analysis) to use the traditional ground state combination differences (GSCD) method, and

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Table 4 Ro-vibrational term values for the (010) vibrational state of HD33 (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

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

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

E 2



δ

3

4

1032.09324 1040.29718 1045.29493 1047.12163 1056.28792 1059.87006 1065.34876 1080.33395 1080.74852 1079.35564 1081.49644 1092.38851 1104.91117 1106.86001 1134.66591 1134.72615 1108.87287 1109.96360 1127.79698 1137.35245 1142.56870 1168.05416 1168.46367 1208.76670 1208.77378 1144.58950 1145.08450 1170.88997 1177.39130 1187.80634 1209.84723 1211.38457 1250.46580 1250.52926 1302.68352 1302.68427 1186.51489 1186.72270 1220.84447 1224.72911 1242.11539 1259.91126 1264.02782 1300.73528 1301.04208 1352.52080 1352.52904 1416.34056 1416.34056 1234.71128 1234.79382

2 10 13 7 6 5 5 11 4 7 16 8 21 4 4 8 13 5 9 9 5 2 5 11 7 9 6 9 10 10 12 10 6 1 9 5 7 9 10 6 7 12 7 13 9 11 19 19 7 9

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

J 1

Ka

7 7 7 7 7 7 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 10 10 10

1 2 2 3 3 4 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 9 9 0 1 1

Kc 6 6 5 5 4 4 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 1 1 0 10 10 9

E 2 1277.01988 1279.07226 1304.80052 1318.01209 1326.67912 1359.60568 1360.66742 1410.91521 1410.96383 1474.21420 1474.21508 1549.62813 1549.62813 1289.21951 1289.25095 1339.18625 1340.16869 1374.98493 1383.84114 1399.11950 1427.02052 1429.91202 1477.95900 1478.16335 1540.58939 1540.59606 1615.43459 1615.43477 1702.41916 1702.41916 1350.05728 1350.06890 1407.39457 1407.83155 1451.75534 1457.05559 1480.71233 1502.81446 1509.28537 1553.71771 1554.39675 1615.55833 1615.59106 1689.68277 1689.68347 1776.04252 1874.57128 1874.57128 1417.22864 1417.23279 1481.75473



δ

3

4

11 8 6 8 9 12 8 15 6

9 9 4 14 11 13 8 12 9 5 9 4 9 11 7 5 8

6 9 7 13 11 9 9 10 13 15 5 15 9 6 12 12 9 11

1 3 3 5 −7 −3 3 6 0 4 −4 −2 −2 1 1 −5 −6 −4 1 6 −1 −8 −1 4 0 0 −13 −6 0 0 3 4 4 −2 −6 −7 −3 0 5 4 5 −4 −4 9 −3 30 −10 −10 7 −13 −8

J 1

Ka

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 12 12 12 12 12 12 12 12 12 12 12 12 12 12

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

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

E 2 1481.93864 1534.47480 1537.32244 1570.57654 1586.71879 1598.96032 1638.19518 1640.07457 1699.21632 1699.34348 1772.45031 1772.45495 1858.04670 1858.04670 1955.88156 1955.88156 2065.92887 2065.92887 1562.34472 1562.41875 1622.95725 1624.35680 1667.68630 1698.56405 1731.30160 1735.73521 1791.64674 1792.05982 1863.82497 1863.84523 1948.49772 2045.51247 2045.51247 2154.78534 2154.78534 2276.32331 2276.32331 1649.20330 1649.23190 1717.30297 1717.94465 1771.06283 1777.45341 1807.29342 1832.83553 1841.84829 1892.89505 1894.05368 1963.89985 1963.97550 2047.46957



δ

3

4

18 3 17 7 8 4 12 18 4 1 2 8 34 34

22 4 20 9 5 15 1 10 13 22 1 13

11 11 5 5 11 9 9 5 6 18 9 12 13 10 4 4 4 20

−8 −5 1 11 −6 0 −1 0 −5 −1 0 3 13 3 1 1 −5 −5 2 3 −10 5 39 −8 3 7 5 2 1 −13 −11 8 7 −17 −17 5 5 2 −7 6 0 −5 −3 10 −11 1 −4 2 −1 3 −1

J 1

Ka

12 12 12 12 12 12 12 12 12 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 15 15 15 16 16 16 17 17 18 18 19 19

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

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

E 2 2047.47264 2143.51979 2143.51979 2251.90058 2251.90058 2372.57569 2372.57569 2505.57413 2505.57413 1742.34527 1742.35615 1817.66519 1817.94375 1880.09319 1883.54790 1924.10250 1942.49277 1958.46639 2002.93698 2005.78460 2072.76522 2073.00837 2155.04358 2155.05573 2249.96609 2357.32271 2357.32271 1841.77242 1841.77624 1924.15294 1994.64817 1996.36741 2059.89598 2121.64664 2127.81220 2191.18100 2364.91866 2364.92040 1847.90250 1847.90250 1947.48073 1952.93921 1952.93921 2059.45827 2064.25165 2064.25165 2181.82778 2181.82778 2305.65428 2305.65428



δ

3

4

9 27 27 8 8

7 5 14 10 11 24 8 10 5

12

4 4

10 9 23

1 11 4 4 8 2 2 21

15 10 3 −7 −7 −1 −1 −1 −1 5 18 12 3 9 4 6 −8 5 3 −8 −38 20 −2 3 23 3 2 23 14 16 −9 4 −27 −36 4 −3 3 3 −5 −7 1 −6 −7 −15 −6 −7 10 10 1 1

a In Table 4,  is the experimental uncertainty of the energy value, equal to one standard error in units of 10−5 cm−1 ; δ is the difference Eexp. -Ecalc. , also in units of 10−5 cm−1 . When the -value is absent, the corresponding energy level was determined from the single transition.

Fig. 4. Experimental minus calculated ground state combination differences (in cm−1 ), (a), line positions (in cm−1 ), (b), and ro–vibrational energies (in cm−1 ), (c), including fit statistics for the ν 2 band of HD33 S.

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Table 5 Spectroscopic parameters of the ground vibrational states of HD32 S, HD33 S, and HD34 S (in cm−1 )a . Parameter

HD32 Sb

HD33 Sc

HD33 Sd

HD33 Se

HD34 Sb

1

2

3

4

5

6

A B C

9.751784129 4.932138444 3.225702843 −0.3771252 0.9564675 0.0872091 0.6483833 0.02844470 0.41916 −0.67733 0.433135 0.0023077 0.99320 0.209789 0.0011999 −2.26558 3.7600 −1.1895 −0.12010 −1.17229 −0.4793 −0.06566 0.29224 −6.435

9.740616615 4.925241922 3.221492772 −0.3808946 0.9568688 0.0867788 0.6480798 0.0282735 0.41916 −0.67733 0.433135 0.0023077 0.99320 0.209789 0.0011999 −2.26558 3.7600 −1.1895 −0.12010 −1.17229 −0.4793 −0.06566 0.29224 −6.435

9.7402286(33) 4.9250483(38) 3.2213711(14) −0.382108(85) 0.95701(13) 0.086812(30) 0.6480798 0.028289(16) 0.41916 −0.67733 0.433135 0.0023077 0.99320 0.209789 0.0011999 −2.26558 3.7600 −1.1895 −0.12010 −1.17229 −0.4793 −0.06566 0.29224 −6.435 10.00

9.754835087 4.928416308 3.227987808 −0.606436 1.167621 0.040211 −0.020598 −0.025351 −0.33423 0.29120 0.19440 −0.01594 0.00233 0.00854 −0.00182

9.7294491 4.9183454 3.2172827 −0.384664 0.957270 0.0863485 0.6477763 0.0281023 0.41916 −0.67733 0.433135 0.0023077 0.99320 0.209789 0.0011999 −2.26558 3.7600 −1.1895 −0.12010 −1.17229 −0.4793 −0.06566 0.29224 −6.435

K × 103 JK × 103 J × 103 δ K × 103 δ J × 103

HK × 106 HKJ × 106 HJK × 106 HJ × 106 hK × 106 hJK × 106 hJ × 106 LK × 109 LKKJ × 109 LJK × 109 LJJK × 109 lK × 109 lKJ × 109 lJK × 109 PK × 1012 pK × 1012 drms × 105

Values in parentheses are 1σ statistical confidence intervals. Reproduced from [24]. c Predicted on the basis of data from columns 2 and 6 (see text for details). d Obtained from the fit in this paper. Parameters presented without confidence intervals were constrained to predicted values from column 3. e Reproduced from [20]. a

b

assignment of transitions was made step by step simultaneously with the determination of the upper ro–vibrational energies and the ground state combination differences. On the concrete “n”-step of the analysis, the upper ro–vibrational energies and the ground state combination differences with the values of quantum number J from 0 up to Jn were used in the fit. Spectroscopic parameters obtained from the fit on this step were used for prediction of the rotational energy values of the ground and (010) vibrational states and the assignment of transitions with the quantum number J up = Jn + 1 was fulfilled. Assigned transitions were used then for determination of the “experimental” upper ro-vibrational energies and additional ground state combination differences. After that the “(n+1)”-step of the analysis was realized, etc. Finally, 801 transitions have been assigned in the experimental spectrum to the ν 2 band of HD33 S (J max = 19, Kamax = 12). The list of assigned transitions is given in column 4 of the Supplementary material I (see also Figs. 2 and 3 and statistical information in Table 2). In this case, 87 ground state combination differences also have been determined (the values of quantum numbers are J max = 16, Kamax = 8, Kcmin = 0, J = 0, 1, 2, Ka = 0, ±1, ±2, Kc = 0, ±2, ±4). They are shown in column 3 of Table 3. For the (010) vibrational state the 203 ro–vibrational energies were obtained. They are shown in column 2 of Table 4 together with their experimental uncertainties  which are shown in column 3.

4. Spectroscopic parameters of the ground and (010) vibrational states of HD33 S To be able to determine spectroscopic characteristics of both the possible pure rotational transitions and a larger number of infrared transitions (in comparison with the number of assigned transitions) we used the experimental information on the GSCD and upper ro–vibrational energies for the fit of spectroscopic pa-

rameters of the Watson hamiltonian (see, e.g. [32]): 1 1 (v ) Heff = E (v ) + [A(v ) − (B(v ) + C (v ) )]Jz2 + (B(v ) + C (v ) )J 2 2 2 1 (v ) (v ) 2 + (B − C )Jxy 2 (v ) 2 2 2 2 −K(v ) Jz4 − JK Jz J − J(v ) J 4 − δK(v ) [Jz2 , Jxy ] − 2δJ(v ) J 2 Jxy + HK(v ) Jz6 (v ) 4 2 (v ) 2 4 (v ) 2 2 2 +HKJ Jz J + HJK Jz J + HJ(v ) J 6 + [Jxy , hK(v ) Jz4 + hJK J Jz + hJ(v ) J 4 ] (v ) 4 4 (v ) 2 6 +LK(v ) Jz8 + LK(vK)J Jz6 J 2 + LJK Jz J + LKJJ Jz J + LJ(v ) J 8 (v ) 2 4 (v ) 4 2 2 +[Jxy , lK(v ) Jz6 + lKJ J Jz + lJK J Jz + lJ(v ) J 6 ]+ + PK(v ) Jz10 + PK(vK)K J Jz8 J 2 2 +PK(vK)J Jz6 J 4 + PJ(JvK) Jz4 J 6 + PJ(JvJK) Jz2 J 8 + [Jxy , p(Kv ) Jz8 + p(KvK)J J 2 Jz6 ]+

+ p(JKv ) J 2 Jz6 + QK(v ) Jz12 + QK(vK)K J Jz10 J 2 ,

(1)

where Jα (α = x, y, z) are the components of the angular momentum operator which is defined in the molecule-fixed coordinate system; A(v) , B(v) , C(v) , etc., are the effective spectroscopic parameters of the ground vibrational state (for (v ) = (0 0 0 )) or the (010) vibrational state (for (v ) = (010 )); [., ..]+ is an anticommutator; 2 = J 2 − J 2 ; and the other parameters are the different order cenJxy x y trifugal distortion coefficients. The correct choice of the initial values of spectroscopic parameters is important for the analysis considered. Following Ref. [33] one can assume that the value of any spectroscopic parameter of the ground or (010) vibrational state of HD33 S in Eq. (1) can be estimated as the mean value of corresponding parameters of the HD32 S and HD34 S species. The latter can be taken from [24,34] and are reproduced in columns 2 and 6 of Table 5 and in columns 2 and 5 of Table 6. Estimated values of parameters of the HD33 S isotopologue are shown in column 3 of these Tables. Results of the fit of parameters of the hamiltonian, Eq. (1), are given in column 4 of Tables 5 and 6 together with their 1σ uncertainties which are shown in parenthesis (parameters presented without confidence

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O.N. Ulenikov, E.S. Bekhtereva and O.V. Gromova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 232 (2019) 108–115 Table 6 Spectroscopic parameters of the (010) vibrational state of HD32 S, HD33 S, and HD34 S (in cm−1 )a . Parameter

HD32 Sb

1

2

3

4

5

E A B C

1032.715193 10.0271335 5.0245746 3.19122513 −0.30303 1.042391 0.099853 0.824949 0.0350241 0.8504 −1.1627 0.63952 0.005964 1.5855 0.30286 0.003135 −4.162 5.757 −1.7650 −0.22202 −0.001058 −2.798 −0.6184 −0.13201 −0.0 0 0548 4.494 −6.628 2.608 −2.191 −2.124 0.2155 −0.831 0.654

1032.111404 10.0154103 5.0187868 3.18708489 −0.30796 1.042939 0.099372 0.824046 0.0348235 0.8428 −1.1557 0.63723 0.005962 1.5843 0.30185 0.003135 −4.141 5.733 −1.759 −0.22071 −0.001058 −2.798 −0.6184 −0.13201 −0.0 0 0548 4.494 −6.628 2.608 −2.191 −2.124 0.2155 −0.831 0.654

1032.093267(15) 10.0150167(15) 5.01730163(80) 3.18696504(42) −0.308638(28) 1.043225(25) 0.0993664(30) 0.823916(11) 0.0348205(13) 0.84346(16) −1.15181(25) 0.636444(96) 0.005962 1.5843 0.30185 0.003135 −4.141 5.723 −1.759 −0.22071 −0.001058 −2.798 −0.6184 −0.13201 −0.0 0 0548 4.494 −6.628 2.608 −2.191 −2.124 0.2155 −0.831 0.654 8.35

1031.507615 10.0036871 5.01044009 3.18294464 −0.312897 1.043486 0.0988919 0.823140 0.0346228 0.83524 −1.14868 0.63493 0.0059599 1.5831 0.30084 0.003135 −4.1204 5.7085 −1.7530 −0.21940 −0.001058 −2.798 −0.6184 −0.13201 −0.0 0 0548 4.494 −6.628 2.608 −2.191 −2.124 0.2155 −0.831 0.654

K × 103 JK × 103 J × 103 δ K × 103 δ J × 103

HK × 106 HKJ × 106 HJK × 106 HJ × 106 hK × 106 hJK × 106 hJ × 106 LK × 109 LKKJ × 109 LJK × 109 LJJK × 109 LJ × 109 lK × 109 lKJ × 109 lJK × 109 lJ × 109 PK × 1012 PKKKJ × 1012 PKKJ × 1012 pK × 1012 pKKJ × 1012 pJK × 1012 QK × 1015 QKKKJ × 1015 drms × 105

HD33 Sc

HD33 Sd

HD34 Sb

Values in parentheses are 1σ statistical confidence intervals. Reproduced from [34]. Predicted on the basis of data from columns 2 and 5 (see text for details). d Obtained from the fit in this paper. Parameters presented without confidence intervals were constrained to predicted values from column 3. a

b c

Table 7 The ν 2 effective dipole moment parameters of HDS (in Debye)a . Operator 1

Parameter 2

HD32 S 3

HD33 S 4

HD34 S 5

kzx {ikzy , Jz } {kzz , iJy } kzz 1 k , iJy } − {ikzy , Jx }] 2 [{ zx 1 k , iJy } + {ikzy , Jx }] 2 [{ zx

010

μ˜ x1 × 10 μ˜ x4 × 103 010 μ˜ x5 × 104 010 μ˜ z1 × 102 010 μ˜ z4 × 103 010 μ˜ z6 × 103

0.19615 0.6673 0.407 −0.8987 0.453 −0.598

0.196155 0.6673 0.407 −0.8759 0.453 −0.598

0.19616 0.6673 0.407 −0.853 0.453 −0.598

a

010

2 = Jx2 − Jy2 . In Table 7, {A, B} = AB + BA, and Jxy

intervals were constrained to their predicted values from column 3). For comparison, columns 2 and 6 of Table 5 and columns 2 and 5 of Table 6 present the values of corresponding parameters of the ground and (010) vibrational states of HD32 S and HD34 S. From comparison of the values in columns 3 and 4 of Tables 5 and 6 one can see more than satisfactory agreement between predicted values of spectroscpic parameters and corresponding values obtained from the fit. The correctness of the obtained results is confirmed by the small drms −values both for the ground vibrational state (the 87 experimental GSCD are reproduced by the parameters from column 4 of Table 5 with the drms = 10.00 ×10−5 cm−1 ) and for the (010) vibrational state (the 203 experimental energy values are reproduced by the parameters from column 4 of Table 6 with the drms = 8.35 ×10−5 cm−1 ). Column 4 of Tables 3 and 4 gives the

values of differences δ between experimental and calculated values of the GSCD and of the upper ro-vibrational energies (one can see good agreement between the two sets of values), and Fig. 4a– c show fit residuals for the GSCD, line positions and ro-vibrational energies for the (010) state as a function of the quantum number J. Also as an illustration, Figs. 2b and b show small parts of the simulated spectra for all three discussed isotopologues, HD32 S, HD33 S, and HD34 S. Note that the values of rotational parameters, /δ , and H/h parameters of the ground vibrational state of HD33 S have been estimated earlier in [20] based on experimentally scaled quantum– chemical calculations. Column 5 of Table 5 presents values of these parameters reproduced from Table A.1 of [20]. One can see that the values of three rotational parameters are predicted in [20] with a high accuracy. At the same time, the prediction of centrifugal distortion coefficients is far from the experimental values of corresponding parameters presented in column 4. 5. Individual line strengths in the pure rotational and ν2 band regions Because of the small natural abundance of the HD33 S molecule in the sample (see above), the lines of HD33 S are very weak. For that reason we did not make an analysis of the experimental strengths of the HD33 S molecule lines. As the above analysis of line positions and energies showed, the assumption that the value of any spectroscopic parameter of HD33 S is very close to the mean

O.N. Ulenikov, E.S. Bekhtereva and O.V. Gromova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 232 (2019) 108–115

value of the corresponding parameters of the HD32 S and HD34 S species is valid with a high accuracy. So, one can assume that for the effective dipole moment parameters this assumption is valid also. The effective dipole moment parameters of the ν 2 band obtained by this way are shown in column 4 of Table 7 (columns 3 and 5 of this Table present the values of corresponding parameters of the HD32 S and HD34 S isotopologues which are reproduced from [34]. Taking into account the values of the obtained effective dipole moment parameters and the values of spectroscopic parameters of HD33 S from column 4 of Tables 5 and 6, we generated line lists of transitions belonging to the ν 2 band. Corresponding results are presented in columns 3 and 7 of the Supplementary material I. For comparison, column 6 of the Supplementary material I shows transmittances of corresponding lines. Spectroscopic parameters of the ground vibrational state obtained by the analysis of the GSCD from Table 3 (see column 4 of Table 5) were used for calculation of the pure rotational line positions of HD33 S (see Supplementary material II). The permanent dipole moment parameter 000 μx1 = 0.978325 D of the H2 32 S species, which is necessary for calculation of line strengths, was taken from [21]. If one takes into account that the transition from H2 32 S to the HDS species leads to a rotation of the molecular fixed coordinate system by the angle of 38.20◦ (Kxxe = 0.785882, Kzxe = −0.785882; see Ref. [34]), then it is possible to obtain the components of the permanent dipole moment of HDS as 010 μ ˜ x1 = 0.768846 D and 010 μ ˜ z1 = 0.604977 D. These values were used for the line strengths calculations. 6. Conclusion The high resolution spectrum of HD33 S was recorded for the first time in the region of the ν 2 band and analyzed. Rotational parameters, centrifugal distortion coefficients and effective dipole moment parameters were determined for the first time which offers the possibility to predict line positions and strengths in the microwave, submillimeter wave and infrared spectral regions, especially around the ν 2 band. Line lists are generated in corresponding spectral regions. The data from Supplementary materials I and II (especially the first information on the microwave and submillimeter wave transitions) should be useful for problems of astrophysics and planetology. Acknowledgments The research was funded by the Tomsk Polytechnic University Competitiveness Enhancement Program (project VIU-63/2019), by the Deutsche Forschungsgemeinschaft (grants BA 2176/4-1, BA 2176/4-2, and BA 2176/5-1) and by the Volkswagen Foundation (grant 90239), Germany. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jqsrt.2019.05.004 References [1] Brimblecombe P, Hammer C, Rodhe H, Ryaboshapko A, Boutron CF. Evolution of the global biogeochemical sulphur cycle, 77. Chichester, NY: John Wiley & Sons, Ltd; 1989. [2] Paytan A, Kastner M, Campbell D, Thiemens MH. Sulfur isotopic composition of cenozoic seawater sulfate. Science 1998;282. 1459–62

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