Marvel analysis of the measured high-resolution rovibrational spectra of H2S

TL;DR

This paper compiles and critically reviews high-resolution rovibrational spectra of H2S, determining energy levels with the MARVEL technique and comparing results with theoretical models, enhancing spectroscopic data accuracy.

Contribution

It presents a comprehensive, critically reviewed database of H2S spectra and applies the MARVEL method to derive precise energy levels, distinguishing ortho and para states.

Findings

Determined 3969 ortho and 3467 para energy levels.

Compiled 44,325 measured transitions from 33 publications.

Validated MARVEL results against theoretical linelists.

Abstract

44325 measured and assigned transitions of H$_2^{32}$S, the parent isotopologue of the hydrogen sulfide molecule, are collated from 33 publications into a single database and reviewed critically. Based on this information, rotation-vibration energy levels are determined for the ground electronic state using the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The ortho and para principal components of the measured spectroscopic network of H$_2^{32}$S are considered separately. The verified set of 25293 ortho- and 18778 para- H$_2^{32}$S transitions determine 3969 ortho and 3467 para energy levels. The Marvel results are compared with alternative data compilations, including a theoretical variational linelist.

Tables

Table 1. Table 1: Quantum numbers used to label the upper and lower energy states of H 2 32 S.

Label	Description
$v_1$	S-H symmetric stretch ($\sim$ 2614.4cm-1)
$v_2$	Symmetric bending mode ($\sim$ 1182.6cm-1)
$v_3$	S-H antisymmetric stretch ($\sim$ 2628.5cm-1)
$J$	Rotational angular momentum
$K_a,K_c$	Projections of rotational angular momentum
ortho/para	Nuclear spin state (see text)

Table 2. Table 2: Symmetry of the rovibrational states of H 2 32 S

Symmetry	A1	A2	B1	B2
Parity	$+$	$-$	$-$	$+$
Nuclear spin state	para	para	ortho	ortho

Table 3. Table 3: Extract from the Marvel  input file for the ortho transitions for H 2 32 S. The full file is supplied as part of the supplementary information to this paper. All energy term values and uncertainties are in units of cm -1 . The meaning of the upper and lower state assignments can be found in Table 1 .

Transition	Uncertainty	Upper state assignment	Lower state assignment	Reference
33.12631	0.00015	0 0 0 5 2 3 ortho	0 0 0 5 1 4 ortho	94YaKl_1
33.12631	0.00018	0 0 0 3 0 3 ortho	0 0 0 2 1 2 ortho	94YaKl_2
34.00529	0.00010	0 0 0 8 7 2 ortho	0 0 0 8 6 3 ortho	94YaKl_5
34.15779	0.00010	0 0 0 11 9 2 ortho	0 0 0 11 8 3 ortho	94YaKl_7
34.21980	0.00010	0 0 0 6 4 3 ortho	0 0 0 6 3 4 ortho	94YaKl_8
34.24062	0.00012	0 0 0 4 2 3 ortho	0 0 0 4 1 4 ortho	94YaKl_9
35.73512	0.00010	0 0 0 8 6 3 ortho	0 0 0 8 5 4 ortho	94YaKl_13

Table 4. Table 4: Data sources used in this study with frequency range, numbers of transitions (A/V for assigned/verified), and comments, which are detailed in Section  3.1 . As far as we are aware all experiments were conducted at room temperature.

Tag	Ref.	Range (cm-1)	A/V	Comments
72HeCoLu	[34]	1.17–25.55	37/35	(4a)
95BeYaWiPo	[35]	4.39–85.41	112/84	(4b)
68CuKeGa	[36]	5.63–14.15	6/6
71Huiszoon	[37]	5.63–7.23	2/2
14CaPu	[38]	7.23–53.17	70/70
85BuFeMeSh	[39]	10.02–20.9	6/6
94YaKl	[40]	33.13–259.76	366/366
13CaPu	[41]	33.97–37.45	4/4
13AzYuTeMa	[42]	45.25–359.79	1158/1139	(4c)
83FlCaJo	[43]	50.77–307.51	426/387	(4d)
18UlBeGr	[44]	729.78–1735.41	2267/2267
82LaEdGiBo	[45]	1003.46–1495.28	397/396	(4e)
83Strow	[46]	1082.03–1257.07	123/123
96UlMaKoAl	[47]	1178.05–1359.78	41/41
98BrCrCrNa	[48]	2141.30–4249.85	7473/7473
18Horneman	[49]	2180.35–4220.46	4460/4460
84LeFlCaJo	[50]	2180.36–2945.81	2113/2111	(4f)
81GiEd	[51]	2192.48–2823.11	715/704	(4g)
96UlOnKoAl	[52]	3614.70–3887.66	106/106
05UlLiBeGr	[53]	4000.59–6653.79	2347/2347
97BrCrCrNa	[54]	4500.88–5595.01	5221/5219	(4h)
18Liu	[55]	4514.79–5555.58	3337/3335	(4i)
04BrNaPoSi_c	[56]	5688.27–6676.71	3178/3178
04BrNaPoSi_a	[57]	7169.19–7898.97	2878/2876	(4j)
04UlLiBeGr_b	[58]	7226.81–7994.09	1855/1855
04UlLiBeGr_a	[59]	8405.91–8905.28	589/589
04BrNaPoSi_b	[60]	8412.73–8906.11	1179/1175	(4k)
03DiNaHuZh	[61]	9541.01–10000.71	1736/1728	(4l)
01NaCa_a	[62]	10787.33–11297.99	1105/1097	(4m)
94GrRaStDe	[63]	11948.91–12246.28	227/145	(4n)
97VaBiCaFl	[64]	12324.55–12670.68	399/387	(4o)
99CaFl	[65]	13060.51–13357.14	219/206	(4p)
01NaCa_b	[66]	16186.25–16436.57	173/154	(4q)
Total		1.17–16436.57	44 325/44 071

Table 5. Table 5: Data sources considered but not used in this work.

Tag	Ref.	Comments
02CoRoTy	[67]	Data taken from other sources
94WaKuSu	[68]	Data taken from other sources
96SuMeKr	[69]	Data taken from other sources
97SuMeKr	[70]	Data taken from other sources
97Sumpf	[71]	Data taken from other sources
98PiPoCoDe	[72]	Data from http://spec.jpl.nasa.gov. Data does not appear to be experimental.
73HeDeKi	[73]	Data taken from other sources, [36, 34, 37]
02KiSuKrTi	[74]	Data appears to be taken from the 1996 edition of HITRAN [75]
06Polovtseva	N/A	Thesis, no citation. Referenced in [14]
87LeFlCaAr	[76]	Energy levels
13Azzam	[77]	All results are given in 13AzYuTeMa [42]
94KoJe	[78]	Energy levels
95FlGrRa	[79]	Energy levels
85LaEdGiBo	[80]	Calculated values, compared to experimental values from 83FlCaJo [43]
94ByNaSmSi	[81]	Energy Levels
01TyTaSc	[82]	Vibrational energy Levels
69MiLeHa	[83]	Could not be validated with the other sources to a reasonable accuracy (see Section 3.2)
56AlPl	[31]	Could not be validated with the other sources to a reasonable accuracy (see Section 3.2)
69SnEd	[84]	Could not be validated with the other sources to a reasonable accuracy (see Section 3.2)

Table 6. Table 6: Extract from the Marvel  output file for the ortho energy levels of H 2 32 S. The full file is supplied as part of the supplementary information to this paper. All energies and uncertainties are in units of cm -1 . NumTrans gives the number of transitions which are linked to that particular energy level. Assignments are as given by Table 1 .

Assignment							Energy	Uncertainty	NumTrans	Sym
0	0	0	1	0	1	ortho	13.746310	0.000001	177	B1
0	0	0	1	1	0	ortho	19.375630	0.000001	153	B2
0	0	0	2	1	2	ortho	38.297765	0.000002	271	B2
0	0	0	2	2	1	ortho	55.161605	0.000002	265	B1
0	0	0	3	0	3	ortho	71.424233	0.000002	282	B1
0	0	0	3	1	2	ortho	95.056325	0.000001	344	B2
0	0	0	3	2	1	ortho	107.368228	0.000001	331	B1
0	0	0	4	1	4	ortho	114.177613	0.000001	282	B2
0	0	0	3	3	0	ortho	117.392015	0.000001	265	B2
0	0	0	4	2	3	ortho	148.418340	0.000001	379	B1

Table 7. Table 7: Original sources of energy level data from 94KoJe [ 78 ] .

Tag	Ref.	Vibrational bands	Comments
83FlCaJo	[43]	(0,0,0)	Experimental source used in this work
85LaEdGiBo	[80]	(0,1,0)	Calculated values, compared to experimental values from 83FlCaJo [43]
84LeFlCaJo	[50]	(0,2,0) (1,0,0) (0,0,1)	Experimental source used in this work
69SnEd	[84]	(1,1,0) (0,1,1)	Experimental source used in this work
56AlPl	[31]	(0,2,1) (2,0,0) (1,0,1) (3,0,0) (2,0,1) (1,0,2) (0,0,3) (2,1,1) (3,0,1) (2,0,2) (1,0,3) (3,1,1)	Data source not considered reliable. All $J=0$ levels only.
87LeFlCaAr	[76]	(2,1,0) (1,1,1)	94KoJe [78] only contains levels from this source up to $J=5$. See text and Figure 2 for a full comparison.

Table 8. Table 8: Comparison of pure rotational levels from this work with those of 94KoJe [ 78 ] (see Table  LABEL:t:96KoJe ) and AYT2 [ 91 ] up to J 𝐽 J =5. NumTrans gives the number of transitions linking a particular state. All energies and uncertainties are in cm -1 . The uncertainty refers to this work.

$J$ $K_a$ $K_c$	State	Sym	NumTrans	Uncertainty	This work	94KoJe	Difference	AYT2	Difference
0 0 0	para	A1	58	0.000098	0	0	0	0	0
1 0 1	ortho	B1	170	0.000001	13.746310	13.74631	0.00000	13.746340	0.000030
1 1 1	para	A2	157	0.000002	15.090119	15.09011	$-$0.00001	15.090151	0.000032
1 1 0	ortho	B2	147	0.000001	19.375630	19.37563	0.00000	19.375563	$-$0.000067
2 0 2	para	A1	223	0.000001	38.016095	38.01607	$-$0.00003	38.016264	0.000169
2 1 2	ortho	B2	258	0.000002	38.297765	38.29775	$-$0.00001	38.297961	0.000196
2 1 1	para	A2	211	0.000001	51.140188	51.14016	$-$0.00003	51.140060	$-$0.000128
2 2 1	ortho	B1	253	0.000002	55.161605	55.16158	$-$0.00003	55.161460	$-$0.000145
2 2 0	para	A1	181	0.000001	58.368870	58.36884	$-$0.00003	58.368621	$-$0.000249
3 0 3	ortho	B1	265	0.000002	71.424221	71.42426	0.00004	71.424760	0.000539
3 1 3	para	A2	213	0.000001	71.465192	71.46515	$-$0.00004	71.465653	0.000461
3 1 2	ortho	B2	329	0.000001	95.056313	95.05630	$-$0.00001	95.056267	$-$0.000046
3 2 2	para	A1	272	0.000001	96.392529	96.39246	$-$0.00007	96.392428	$-$0.000101
3 2 1	ortho	B1	313	0.000001	107.368216	107.36820	$-$0.00002	107.367927	$-$0.000289
4 0 4	para	A1	205	0.000001	114.172246	114.17217	$-$0.00008	114.173085	0.000839
4 1 4	ortho	B2	270	0.000001	114.177601	114.17758	$-$0.00002	114.178495	0.000894
3 3 1	para	A2	250	0.000002	115.340656	115.34059	$-$0.00007	115.340038	$-$0.000618
3 3 0	ortho	B2	247	0.000001	117.392003	117.39199	$-$0.00001	117.391407	$-$0.000596
4 1 3	para	A2	306	0.000001	148.140653	148.14058	$-$0.00007	148.140740	0.000087
4 2 3	ortho	B1	362	0.000001	148.418328	148.41831	$-$0.00002	148.418470	0.000142
5 0 5	ortho	B1	264	0.000045	166.343488	166.34345	$-$0.00004	166.344887	0.001399
5 1 5	para	A2	196	0.000077	166.344005	166.34417	0.00016	166.345606	0.001601
4 2 2	para	A1	308	0.000001	170.335799	170.33574	$-$0.00006	170.335471	$-$0.000328
4 3 2	ortho	B2	383	0.000002	173.967266	173.96726	$-$0.00001	173.966794	$-$0.000472
4 3 1	para	A2	261	0.000001	182.648548	182.64849	$-$0.00006	182.647978	$-$0.000570
4 4 1	ortho	B1	290	0.000002	195.661414	195.66142	0.00001	195.659965	$-$0.001449
4 4 0	para	A1	219	0.000003	196.802189	196.80212	$-$0.00007	196.800713	$-$0.001476
5 1 4	ortho	B2	356	0.000037	210.217262	210.21727	0.00001	210.217731	0.000469
5 2 4	para	A1	270	0.000001	210.264821	210.26477	$-$0.00005	210.265229	0.000408
5 2 3	ortho	B1	387	0.000001	243.343434	243.34344	0.00001	243.343211	$-$0.000223
5 3 3	para	A2	333	0.000001	244.392517	244.39250	$-$0.00002	244.392149	$-$0.000368
5 3 2	ortho	B2	363	0.000001	263.738931	263.73895	0.00002	263.738560	$-$0.000371
5 4 2	para	A1	298	0.000001	271.106067	271.10604	$-$0.00003	271.104809	$-$0.001258
5 4 1	ortho	B1	316	0.000002	277.337562	277.33758	0.00002	277.336633	$-$0.000929
5 5 1	para	A2	229	0.000002	296.104442	296.10442	$-$0.00002	296.101282	$-$0.003160
5 5 0	ortho	B2	278	0.000001	296.677577	296.67760	0.00002	296.674560	$-$0.003017

Table 9. Table 9: Comparison of pure vibrational levels ( J = 0 𝐽 0 J=0 ) from this work with those of 94KoJe [ 78 ] (see Table  LABEL:t:96KoJe ) and AYT2 [ 91 ] . NT stands for NumTrans, the number of transitions linking a particular state. All energies and uncertainties are in cm -1 . The uncertainty refers to this work. State is from this work and Sym is the corresponding symmetry label as used in AYT2 [ 91 ] (see Section  2.2 ).

${\nu }_1$ ${\nu }_2$ ${\nu }_3$	State	Sym	NT	Uncertainty	This work	94KoJe	Difference	AYT2	Difference
0 0 0	para	A1	58	0.000098	0			0	0
0 1 0	para	A1	5	0.000477	1182.576991	1182.5742	$-$0.0028	1182.569618	$-$0.007373
0 2 0	para	A1	4	0.000629	2353.964679	2353.9655	0.0008	2353.907317	$-$0.057362
1 0 0	para	A1	3	0.000663	2614.407743	2614.4074	$-$0.0003	2614.394829	$-$0.012914
0 0 1	ortho	B2	2	0.000669	2628.454821	2628.4552	0.0004	2628.463320	0.008499
0 3 0	para	A1	3	0.000621	3513.789974			3513.705072	$-$0.084902
1 1 0	para	A1	3	0.000390	3779.166566	3779.1710	0.0044	3779.189348	0.022782
0 1 1	ortho	B2	2	0.000625	3789.269211	3789.2720	0.0028	3789.269878	0.000667
0 4 0	para	A1	1	0.001000	4661.672219			4661.605794	$-$0.066425
1 2 0	para	A1	2	0.000707	4932.699369			4932.688937	$-$0.010432
0 2 1	ortho	B2	2	0.000707	4939.104010	4939.2300	0.1260	4939.129851	0.025841
2 0 0	para	A1	2	0.000707	5144.986319	5145.1200	0.1337	5145.031868	0.045549
1 0 1	ortho	B2	2	0.000707	5147.220560	5147.3600	0.1394	5147.166622	$-$0.053938
0 0 2	para	A1	2	0.000707	5243.101919			5243.158956	0.057037
1 3 0	para	A1	2	0.000928	6074.581067			6074.566059	$-$0.015008
0 3 1	ortho	B2	2	0.000707	6077.594560			6077.626636	0.032076
2 1 0	para	A1	2	0.000707	6288.146119	6288.1428	$-$0.0033	6288.134723	$-$0.011396
1 1 1	ortho	B2	3	0.000637	6289.172875	6289.1739	0.0010	6289.128284	$-$0.044591
1 2 1	ortho	B2	4	0.000632	7420.092707			7420.077786	$-$0.014921
1 0 2	para	A1	1	0.002000	7576.381719	7576.3000	$-$0.0817	7576.413281	0.031562
2 0 1	ortho	B2	2	0.001414	7576.544710	7576.3000	$-$0.2447	7576.596211	0.051501
3 0 0	para	A1	2	0.001414	7752.263219	7751.9000	$-$0.3632	7752.343205	0.079986
0 0 3	ortho	B2	2	0.001414	7779.321260	7779.2000	$-$0.1213	7779.352004	0.030744
1 3 1	ortho	B2	1	0.002000	8539.561310			8539.565999	0.004689
1 1 2	para	A1	2	0.001414	8697.141469			8697.133905	$-$0.007564
2 1 1	ortho	B2	2	0.001481	8697.154984	8697.3000	0.1450	8697.179341	0.024357
1 4 1	ortho	B2	1	0.005000	9647.167310			9647.098855	$-$0.068455
2 2 1	ortho	B2	1	0.005000	9806.667310			9806.712978	0.045668
1 2 2	para	A1	1	0.005000	9806.733119			9806.748170	0.015051
2 0 2	para	B2	1	0.005000	9911.023119	9911.0500	0.0269	9911.102285	0.079166
3 0 1	ortho	A1	1	0.005000	9911.023310	9911.0500	0.0267	9911.112478	0.089168
3 1 1	ortho	A1	1	0.005000	11008.695310	11008.7800	0.0847	11008.774494	0.079184
3 0 2	para	A1	1	0.001000	12149.460119			12149.552318	0.092199
1 0 4	para	A1	1	0.015000	12524.637119			12524.834491	0.197372
4 0 1	ortho	B2	1	0.015000	12525.214310			12525.346292	0.131982
3 1 2	para	B2	1	0.015000	13222.762119			13222.790827	0.028708
2 1 3	ortho	A1	1	0.015000	13222.772310			13222.798559	0.026249

Table 10. Table 10: Supplied supplementary data files.

File	Name
1	H2S_ortho_input_transitions.txt
2	H2S_para_input_transitions.txt
3	H2S_ortho_energylevels_output.txt
4	H2S_para_energylevels_output.txt

Table 11. Table 11: Definition of columns in files 1 and 2.

Column	Label	Description
1	Energy (cm-1)	Transition wavenumber
2	Uncertainty (cm-1)	Associated uncertainity
	Upper assignments:
3	$v_1$	S-H symmetric stretch
4	$v_2$	Symmetric bending mode
5	$v_3$	S-H antisymmetric stretch
6	$J$	Rotational angular momentum
7	$K_a$	Projection of rotational angular momentum
8	$K_c$	Projection of rotational angular momentum
9	ortho/para	Nuclear spin state
	Lower assignments:
10	$v_1$	S-H symmetric stretch
11	$v_2$	Symmetric bending mode
12	$v_3$	S-H antisymmetric stretch
13	$J$	Rotational angular momentum
14	$K_a$	Projection of rotational angular momentum
15	$K_c$	Projection of rotational angular momentum
16	ortho/para	Nuclear spin state
17	Ref	Unique reference label

Table 12. Table 12: Definition of columns in files 3 and 4.

Column	Label	Description
1	$v_1$	S-H symmetric stretch
2	$v_2$	Symmetric bending mode
3	$v_3$	S-H antisymmetric stretch
4	$J$	Rotational angular momentum
5	$K_a$	Projection of rotational angular momentum
6	$K_c$	Projection of rotational angular momentum
7	ortho/para	Nuclear spin state
8	Energy (cm-1)	Marvel energy assignment
9	Uncertainty (cm-1)	Marvel uncertainty
10	Num Trans	The number of transitions in the dataset which link to this state

Equations

$$\Delta J=0,\pm 1,$$

$$J^{\prime }+J^{\prime \prime }\ne 0,$$

$$-\leftrightarrow +$$

Full text

1 Introduction

Hydrogen sulfide, H2S, is a volcanic gas present on earth and other geologically active planets and moons, such as Io [1], Venus [2], and, theoretically, hot super-earth "lava" exoplanets [3]. It has recently been detected above the clouds in the atmosphere of Uranus [4]. On earth, microbial respiration of seawater sulfate creates a hydrogen sulfide-rich ecosystem [5], suggesting that H2S is a component for a potential microbial life sustaining atmosphere on Venus [2], and a potential biomarker for life on exoplanets [6]. H2S influences many physiological processes [7], it is of importance in the treatment of respiratory diseases [8], and it is used as a measure of the quality of air near oil refineries [9]. The parent isotopologue, H232S, was first detected in interstellar space in 1972 [10]. Many of the scientific and engineering applications mentioned require the detailed knowledge of the rovibrational energy levels of H232S.

As part of this work, we present the largest compilation of published experimental rovibrational transition data for H232S. The experimental database of H232S transitions has been formatted and analysed using the Marvel (Measured Active Rotational-Vibrational Energy Levels) spectroscopic network (SN) software [11, 12, 13]. This study builds on the 2012 W@DIS information system for the hydrogen sulfide molecule [14].

As to the structure of this paper, the next section provides the theory underlying the present study. Section 3 presents and discusses the experimental sources used, with results given in Section 4. Section 5 discusses these results and compares the empirical rovibrational energies presented in this work with corresponding levels previously determined both by experiment and theory. Finally, Section 6 provides our conclusions. All transition data and energy levels resulting from this work are included as supplementary data files.

2 Theory

2.1 Marvel

The Marvel procedure [11, 12, 13] is based on the theory of spectroscopic networks [15, 16], with the energy levels represented as nodes and the transitions between them as edges. The related Marvel  code can be used to critically evaluate and validate experimentally-determined transition wavenumbers and uncertainties collected from the literature, inverting the wavenumber information to obtain accurate empirical energy levels with an associated uncertainty. Marvel has been successfully used to evaluate the energy levels for molecules such as 12C2 [17], 48Ti16O [18], water vapour [19, 20, 21, 22, 23], H${}_{3}^{+}$ [24], H2D+ and D2H+ [25], 12C2H2 [26], 14NH3 [27, 28], and 12C2H216O [29]. Marvel requires each measured transition to have an associated uncertainty and for each energy level considered to possess a unique set of quantum numbers.

2.2 Quantum number labelling

The seven quantum numbers that were used for labelling the upper and lower rovibrational states of H232S are the same as those used in a previous Marvel investigation to classify water [19]. These quantum numbers are summarised in Table 1. Normal-mode labelling is used for the vibrations, where $\nu_{1},\nu_{2}$ and $\nu_{3}$ stand for the symmetric stretch, bend, and antisymmetric stretch vibrations, respectively. Standard asymmetric-top quantum numbers are used for the rotations, where $J,K_{a}$, and $K_{c}$ are the three quantum numbers associated with rotational angular momentum, ${\bf J}$, and the two projections along the $A$ and $C$ axes. We also provide, as part of the label, the nuclear spin state (ortho or para), which is deduced by whether ($v_{3}+K_{a}+K_{c}$) is odd (ortho) or even (para) [26, 30]. Hyperfine coupling associated with nuclear spins has been neglected.

When local-mode notation was used by an experimental source considered in this work, the quantum numbers were transformed to the normal-mode notation $(v_{1}v_{2}v_{3})$ to describe a vibrational state. Note that some of the data sources considered in this study use $J$ and $\tau=K_{a}-K_{c}$ instead of $J,K_{a}$, and $K_{c}$ [31], where $\tau$ runs from $-J,-J+1,...,J-1,+J$, with energy increasing from $\tau=-J$. The $+/-$ parity of an asymmetric top molecule such as H232S is defined by $(-1)^{K_{c}}$ [19]. H232S belongs to the $C_{2\rm{v}}$(M) MS group [32], which contains irreducible representations A1, A2, B1, and B2, as given in Table 2.

2.3 Selection rules

The rigorous selection rules governing rotation-vibration transitions for a molecule of the $C_{2\rm{v}}$(M) MS group are given by:

[TABLE]

The ortho states of H232S have the nuclear spin statistical weight $g_{\rm ns}=3$, while for the para states $g_{\rm ns}=1$, thus, ortho transitions have three times the intensity of para transitions. This is sometimes referred to as intensity alternation. It is assumed that ortho and para states do not interconvert. Such transitions are very weakly allowed [33] but have yet to be observed for H232S.

3 Experimental sources

A large number of experimentally determined transition wavenumbers can be found in the literature for the main isotopologue of hydrogen sulfide, H232S. We have attempted to conduct a rigorous and comprehensive search for all useable spectroscopic data. Fortunately, much of the data up to 2012 was previously collated as part of the 2012 W@DIS information system for hydrogen sulfide [14], in which some of the authors of this paper were involved. These data were converted to Marvel format for this work and analysed alongside data from newly collected sources. This requires the transition wavenumber (in cm*-1*) and the associated uncertainty, along with quantum number assignments for both the upper and lower energy states, and a unique reference label for each transition. This reference indicates the data source the transition originates from. The data source tag is based on the notation employed by an IUPAC Task Group on water spectroscopy [19]. An extract of the input file in the required format is given in Table 3; the full file can be found in the supplementary data for this work.

33 sources of experimental data were used in the final data set. The data from more recent papers are generally provided in digital format, but some of the older papers had to be processed through digitalisation software, or even manually entered in the worst cases. After digitalisation the data were converted to Marvel format, as described above.

Table LABEL:t:sources gives a summary of all the data sources used in this work, along with the energy range, number of transitions (assigned (A) and verified (V)), and comments, which are detailed in Section 3.1. Table LABEL:t:notused lists those data sources which were considered but not used, with comments on the reasons for their exclusion from the analysis. The IUPAC reference tag given in these tables matches those used in the unique labels in the Marvel input files, given in the supplementary data and illustrated in Table 3.

As transitions have never been observed between ortho and para states of H232S, they form two separate principal components (PCs) of the experimental spectroscopic network. All input and output files supplied in the supplementary data to this work are split into either ortho or para.

3.1 Comments on the experimental sources of Table LABEL:t:sources

(4a) 72HeCoLu [34] contains 2 lines which have been cited as taken from other experimental sources, for which the original data are already in our dataset. These duplicates were removed.

(4b) 95BeYaWiPo [35] contains 28 lines which have been cited as from other experimental sources, for which the original data are already in our dataset. These duplicates were removed.

(4c) 13AzYuTeMa [42] gives data for rotational lines recorded at room temperature. The equipment used provides spectra with very high sensitivity and this enabled transitions between highly rotationally excited states to be recorded, even at room temperature. These high rotational excitations may not be so accurately assigned as those of lower energy, as there are no data from other sources in the same region to confirm these measurements. The supplementary data from the original paper does not contain the original experimental transitions; this was provided by the corresponding author. There were 19 lines which could not be validated against other data and so were removed from our dataset (see Section 3.2).

(4d) 83FlCaJo [43] contains 39 lines which have been cited as from other sources which are already present in our dataset. The duplicates were removed.

(4e) 82LaEdGiBo [45] contains one line which could not be validated and so has been removed from our dataset.

(4f) 84LeFlCaJo [50] contains 2 lines which could not be validated against other more recent data and were removed from our dataset. All data from this source were recalibrated; the calibration factor employed was 0.999 999 746 below 2450 cm*-1* and 1.000 000 0714 above 2450 cm*-1*.

(4g) 81GiEd [51] contains 11 lines which could not be validated against more recent data and thus were removed from our dataset.

(4h) 97BrCrCrNa [54] contains 2 lines with no corresponding energy in the AYT2 linelist (see Section 5) and so were removed from our dataset.

(4i) 18Liu [55] contains 2 lines with no corresponding energy in the AYT2 linelist and so were removed from our dataset.

(4j) 04BrNaPoSi_a [57] contains 2 lines with no corresponding energy in the AYT2 linelist and so were removed from our dataset.

(4k) 04BrNaPoSi_b [60] contains 4 lines which could not be validated and were removed from our dataset.

(4l) 03DiNaHuZh [61] contains one blended line which has been removed from our dataset. A further 7 lines were found to include a level with no corresponding energy in the AYT2 linelist and so were removed from our dataset.

(4m) 01NaCa_a [62] contains 8 transitions which were found to have no corresponding levels in the AYT2 linelist and so were removed from our dataset.

(4n) 94GrRaStDe [63] tentatively assigned the vibrational band in their data as ($v_{1},v_{2},v_{3}$)=(2,2,2); however, in 95FlGrRaSt [79], a paper published later with the same authors, the revised assignment is ($v_{1},v_{2},v_{3}$)=(3,0,2). We adopt the latter vibrational label in our dataset. No other data sources probe this vibrational band. The frequency is only given to 3 decimal places, so the uncertainty was altered to match. The original dataset has 82 transitions either labelled with an asterisk to indicate lines from the H234S isotopologue, or labelled with a dagger to indicate lines which have been perturbed due to those from H234S [63]. We have commented these out by adding a minus sign to the wavenumber and added the label $\_pt$ to the end.

(4o) 97VaBiCaFl [64] contains 4 lines which could not be validated and so were removed from our dataset. A further 8 lines were found to contain a level with no corresponding energy in the AYT2 linelist and so were removed from our dataset.

(4p) The assignment for 99CaFl_185_na_ct from 99CaFl [65] leads to different spin states (ortho/para) for the upper and lower state, which is forbidden. We have removed this transition from our dataset. 5 other lines could not be validated and so were removed from our dataset. 7 lines were found to have no variational counterparts in the AYT2 linelist and so were removed.

(4q) 01NaCa_b [66] contains one line which could not be validated and so was removed from our dataset. A further 18 lines were found to contain levels with no corresponding energies in the AYT2 linelist and so were removed from our dataset.

3.2 General comments

All transitions which were considered but not processed in the final dataset have a minus sign in front of the transition wavenumber (indicating that Marvel will ignore it) in the input files provided as supplementary material and are labelled with a comment at the end of the reference (see the comments of Section 3.1). We used a cut-off of 0.035 cm*-1* as the largest acceptable uncertainty and removed any transitions with an uncertainty greater than this this, with a note in Section 3.1 to indicate how many transitions from a particular data source could not be validated to within this accuracy.

The publications 97BrCrCrNa [54], 04BrNaPoSi_c [56], 04BrNaPoSi_a [57], and 04BrNaPoSi_b [60] include just a short description of the assignment and modelling of the Fourier Rransform (FT) spectra between 4500 and 8900cm*-1*. Detailed information on the theoretical treatment of these spectra will be published separately in due course. Some of these transitions, between 4400–8000 cm*-1*, were previously reported in the HITRAN-2012 [85] and HITRAN-2016 [86] databases, while the second decade region, 8400–8900cm*-1*, is presented for the first time. It is also worth mentioning that the Marvel dataset includes a considerable number of transitions which include new, unpublished energy levels. As only the upper energy levels of the transitions were reported in 05UlLiBeGr [53], 04UlLiBeGr_b [58], and 04UlLiBeGr_a [59], the corresponding transition wavenumbers were recovered from A.-W. Liu (18Liu [55]) using the energy levels obtained from 97BrCrCrNa [54], 04BrNaPoSi_c [56], 04BrNaPoSi_a [57], and 04BrNaPoSi_b [60]. For this reason, the transitions in the Marvel dataset which are referred to as from 05UlLiBeGr [53], 04UlLiBeGr_b [58], and 04UlLiBeGr_a [59] contain a larger number of assignments than reported in the original publications. The data of the first hexad region between 4500–5600cm*-1* were totally assigned based on the energy levels reported in 97BrCrCrNa [54]. The highly accurate (an accuracy of 0.0005cm*-1*) set of H232S transitions recorded using a FT spectrometer between 2200–4250cm*-1* was provided by V.-M. Horneman (18Horneman [49]) and assigned using the energy levels reported in 98BrCrCrNa [48].

3.3 Sources from the HITRAN database

H232S has been included in the HITRAN database [87, 88, 89, 90, 85, 86] since 1991 [87]. The following are sources for the line positions and energy levels of the H232S data in the HITRAN database, up to the 2016 release: 96UlMaKoAl [47], 83FlCaJo [43], 98BrCrCrNa [48], 13AzYuTeMa [42], 94YaKl [40], 95BeYaWiPo [35], 05UlLiBeGr [53], 04UlLiBeGr [58], 03DiNaHuZh [61], 01NaCa_b [66], 84LeFlCaJo [50], 82LaEdGiBo [45], 85LaEdGiBo [80], 94ByNaSmSi [81]. The variational ExoMol AYT2 linelist [91] was used to assign transitions in the $\nu_{2}$ excited vibrational state in the 2012 release [85].

4 Results

The Marvel website (http://kkrk.chem.elte.hu/marvelonline) has a version of Marvel which can be run online. The variable NQN (number of quantum numbers) is 7 in the case of hydrogen sulfide, as illustrated in Table 3 which shows an extract of the ortho input file to Marvel.

Marvel automatically assigns the lowest energy state in a particular component of the spectroscopic network to 0. The ground rovibrational state is included in the para set of energy levels, however there needs to be a “magic number”, corresponding to the energy of the lowest ortho state, which is added to all the Marvel  ortho-symmetry energies. Here, this was taken as the ground vibrational state $(v_{1}v_{2}v_{3})=(000)$ with the lowest rotational energy (see Section 2.2), $J=1,K_{a}=0,K_{c}=1$, of 94KoJe [78], who determined the value of 13.74631 cm*-1*. The output for the ortho energies in the supplementary data, and the extract in Table 6, all have this magic number added for the principal spectroscopic network. There are a small number (4 para) of energy levels which are not joined to either of the principal components. If more experimental transitions became available in the future it would be possible to link these to the principal network.

We collated and considered a total of 44 325 transitions from 33 experimental sources (25 474 ortho and 18 851 para). Of those 254 were found to be inconsistent (could not be validated to within 0.035 cm*-1*) with others and so removed from the final data set, leaving a total of 44 071 transitions used as input into Marvel (25 293 ortho and 18 778 para).

Figure 1 gives a visual representation of NumTrans which link the states of the Marvel ortho-H232S network, against corresponding upper state energies. Those upper states which are dark blue in colour, linked by only 1 transition, should be considered less reliable than those in red, which are supported by hundreds of different transitions, up to 404. The values of NumTrans for each level are given in the energy level files in the supplementary data.

5 Comparison to other derived energy levels

We used a number of sources to compare energy level values against those determined in this work. 94KoJe [78] contains a list of energy levels, which are taken or calculated from other sources [43, 80, 50, 84, 31, 76]; see Table LABEL:t:96KoJe for a breakdown by vibrational band. AYT2 [91] is a theoretical variational linelist for H232S calculated as part of the ExoMol project [92, 93], a database of theoretical linelists for molecules of astrophysical importance. AYT2 is appropriate up to temperatures of around 2000 K and designed for use in characterising the atmospheres of cool stars and exoplanets. The states file, available from www.exomol.com, gives the calculated energy levels, which can be compared against our empirical energy levels. For more information on the format of the ExoMol data files, please refer to [93]. 95FlGrRaSt [79] contains rovibrational energy levels from the ($v_{1},v_{2},v_{3}$)=(2,0,3) and (3,0,2) vibrational bands. The authors outline an experimental procedure used to deduce these levels but they do not provide the experimental transition data so we could not include the data from this source in our dataset. 87LeFlCaAr [76] has a table of rovibrational energy levels for the ($v_{1},v_{2},v_{3}$)=(2,1,0), (1,1,1) and (0,1,2) vibrational bands. 96UlMaKoAl [47] contains rovibrational energy levels from the ($v_{1},v_{2},v_{3}$)=(0,1,0) vibrational band.

We compared the pure rotational levels determined in this work both against those given in 94KoJe [78] and the calculated values from the AYT2 linelist [91], up to $J$=5. These data are given in Table LABEL:t:compare. The pure rotational levels are closer to those from the experimentally determined sources of 94KoJe than to those of variationally calculated AYT2, as would be expected.

The pure vibrational levels from this work are also compared with those from 94KoJe [78] and AYT2 [91], see Table LABEL:t:compare_vib. It should be noted here that there are some differences in labelling between these data sources and those used in this work. For example, the pure vibrational levels of 94KoJe [78] which are labelled ($v_{1},v_{2},v_{3}$)=(2,0,2), (1,0,2) and (3,0,0), match the normal mode labelling of (4,0,0), (3,0,0) and (1,0,2), respectively, according to the labelling of 01TyTaSc [82] and the experimental sources used in this work.

We compared all the rovibrational energy levels given in 94KoJe [78], 95FlGrRaSt [79], 96UlMaKoAl [47], and 87LeFlCaAr [76] against our set of Marvel energy levels, taking the aforementioned labelling differences into account for 94KoJe [78] (see Table LABEL:t:96KoJe). These comparisons are illustrated in Figure 2. Most levels are in good agreement, with only a few levels with differences between 0.1–0.4 cm*-1*. These levels with the largest differences are from 87LeFlCaAr [76] and 56AlPl [31]. All the levels which are compared to those of 87LeFlCaAr [76] have several transitions which link them to other energy levels in our Marvel dataset, and originate from different sources, which increases their reliability. This indicates that the lack of accuracy for these particular energies originates from 87LeFlCaAr [76] and not the Marvel dataset. The transition data from 56AlPl [31] was considered for use in the current study, but the data could not be validated with that from newer sources (see Table LABEL:t:notused), and so the energy levels are also assumed to be unreliable.

As mentioned above, AYT2 [91] is a theoretical variational linelist for H232S calculated as part of the ExoMol project [92, 93]. Highly accurate experimental energy levels provide essential input for testing and improving theoretically calculated line positions such as those within AYT2. The ExoMol data format convention is to have a ‘states’ and a ‘trans’ file. The states file gives the calculated rovibrational energy levels, which can be compared against our empirical energy levels, and the trans file contains the Einstein–$A$ coefficients for transitions between these states [93]. This format allows calculated linelists to be retrospectively updated using more reliable experimental energy levels in order to improve their accuracy, see [94] for an example.

To compare our energy levels with those from the AYT2 [91] linelist, a comparable states file was made; we labelled our states with the same A1, A2, B1, B2 symmetry labels which are given in the AYT2 states file, see Table 2. We then matched all states with this same symmetry, $v_{2}$, $v_{1}+v_{3}$, and $J$, and searched for the closest value within these given parameters. Figure 3 gives the result of this comparison.

Work is underway to update the existing ExoMol AYT2 states file and linelist based on the energy levels obtained in this work, using only those levels based on the transitions we are most sure about. Care should be taken in general when using Marvel energy levels with a low value of NumTrans (see Figure 1). This, along with the uncertainty, gives an indication of the reliability of a particular energy level.

6 Conclusions

A total of 44 325 measured experimental rovibrational transitions of H232S from 31 publications have been considered in this work. From this set, 3969 ortho- and 3467 para-H232S energy levels have been determined using the Measured Active Rotational-Vibrational Energy Levels (Marvel) technique. These results have been carefully compared with alternative compilations of energy levels.

A variational high-temperature linelist for H232S has been computed as part of the ExoMol project, AYT2 [91]. Our new Marvel energy levels will be used to improve the accuracy of this theoretical linelist.

A significant part of this work was performed by pupils from Highams Park School in London, as part of a project known as ORBYTS (Original Research By Young Twinkle Students) [95]. The Marvel studies of 12C2H2 [26] and 48Ti16O [18] were also performed as part of the ORBYTS project and further studies on other key molecules will be published in due course, involving high-school students from the UK, Australia, and Hungary. A paper discussing our experiences of performing original research in collaboration with school children can be found elsewhere [96].

7 Supplementary Data

Please refer to the web version of this work for access to the supplementary data. There are four files provided, as listed in Table 10. The column definitions are given in Table 11 for files 1 and 2 (Marvel input files) and Table 11 for files 3 and 4 (Marvel output files).

8 Acknowledgements

We would like to thank Jon Barker, Fawad Sheikh, and Sheila Smith from Highams Park School for continued support and enthusiasm, along with Highams Park students Jack Franklin and Samuel Sheppard for their assistance in this project. We are grateful to Laura McKemmish for helpful discussions and advice, Clara Sousa-Silva for setting up the ORBYTS education project, and to Anita Heward, Will Dunn, Marcell Tessenyi, and the rest of the Twinkle team for their ongoing support. We give thanks to Shuiming Hu for contributions to the data used in this work. This work was supported by STFC Project ST/J002925, the RSF (grant 17-12-01204), the ERC under Advanced Investigator Project 267219, NKFIH (grant K119658), and the COST action MOLIM: Molecules in Motion (CM1405).