The rotational spectrum of hydrogen sulfide: The H233 S and H232 S isotopologues revisited

Journal of Molecular Spectroscopy 298 (2014) 31–37

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The rotational spectrum of hydrogen sulfide: The H233 S and H232 S isotopologues revisited Gabriele Cazzoli, Cristina Puzzarini ⇑ Dipartimento di Chimica ‘‘Giacomo Ciamician’’, Università degli Studi di Bologna, Via Selmi 2, I-40126 Bologna, Italy

a r t i c l e

i n f o

Article history: Received 5 October 2013 In revised form 5 February 2014 Available online 20 February 2014 Keywords: Hydrogen sulfide 33 S-containing isotopologue Lamb-dip technique Hyperfine parameters High-order centrifugal-distortion constants

a b s t r a c t The rotational spectra of two isotopic species of hydrogen sulfide have been revisited. For H233 S, which was detected in natural abundance, accurate measurements were performed in the submillimeter-wave region, from 500 GHz up to 1.56 THz, thus allowing improvement of the spectroscopic parameters as well as determination of new high-order centrifugal-distortion constants. The rotational spectrum of the main isotopologue was investigated in the millimeter- and submillimeter-wave region up to 1.6 THz, employing the Lamb-dip technique to obtain sub-Doppler resolution. As a consequence, transition frequencies at 1 THz were retrieved with an accuracy of 1 kHz and the hyperfine structure due to hydrogens was resolved, thus allowing the first determination of the spin–rotation tensor of H in H2S. Improved and new spectroscopic parameters were then provided that allow accurate predictions of rotational transitions up to 20 THz; in particular, the newly determined constants permit prediction of rotational transitions with J < 15, K a < 12 (up to about 10 THz) with expected uncertainties of a few hundreds of kHz. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction Over the last few decades, the study of the Earth’s and planetary atmospheres and of the interstellar medium by means of spectroscopic techniques has developed rapidly. The Herschel Space Observatory, Stratospheric Observatory for Infrared Astronomy (SOFIA), and Atacama Large Millimeter Array (ALMA) have made available the submillimeter-wave region of the electromagnetic spectrum for astronomical investigations at unprecedented highsensitivity and angular resolution. These new facilities have granted access to higher-lying rotational levels, thus allowing the observation of H2S at THz frequencies for the first time [1]. The accurate knowledge of transition frequencies is thus a key issue; in particular, an accuracy better than 100 kHz in the THz region is preferable, thus requiring the extension of accurate laboratory investigation in this frequency range. The transition frequencies and the derived spectroscopic parameters are collected in databases, which are continuously updated and improved. For example, the HITRAN [2,3], JPL [4] and CDMS [5,6] databases provide comprehensive molecular line lists. In particular, the ExoMol project [7] aims to systematically provide line lists for astronomically important molecules. Within this project, new measurements of the rotational spectrum for four isotopologues

⇑ Corresponding author. E-mail address: [email protected] (C. Puzzarini). http://dx.doi.org/10.1016/j.jms.2014.02.002 0022-2852/Ó 2014 Elsevier Inc. All rights reserved.

of hydrogen sulfide (H232 S, H233 S, H234 S, and H236 S) were carried out in the region 1.4–10.5 THz (45–360 cm1) at the SOLEIL synchrotron [8]. Furthermore, Ref. [8] reports the spectroscopic parameters obtained from global fits, including all available frequency values, for these isotopic species. Although the spectroscopic constants listed in Ref. [8] provide a rather good description of the rotational spectra of the investigated species, relevant improvements may still be obtained. For the 33 S-containing isotopologue, except the hyperfine components of two rotational transitions lying at 168.3 GHz and 215.5 GHz, the transition frequencies reported in the literature are affected by uncertainties greater than or, in the best case, equal to 100 kHz up to 1.07 THz and by uncertainties greater than 4.5 MHz at higher frequencies. For the main isotopologue, a better situation is observed; some transitions up to 2.5 THz are characterized by uncertainties of 500 kHz. A complete account of the previous investigations can be found in Ref. [8]. In the context of this study, Saleck et al. [9] reported the observation of the rotational spectra of rare isotopologues of hydrogen sulfide in the 165–1072 GHz frequency range, while Belov et al. [10] investigated the main isotopic species up to 2.56 THz. The first measurements of the far-infrared spectrum of H232 S, H233 S, and H234 S were performed by Flaud et al. [11] in the 1.5–9.2 THz region. The improvements provided by the present work can be summarized as follows. For H233 S, Doppler-limited measurements up to 1.56 THz are reported with accuracies ranging from 20 to

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90 kHz (according to the intensity of the recorded transitions); the recent sub-Doppler measurements we carried out (200–450 GHz) to determine the hyperfine parameters of 33 S accurately [12] were also considered. For H2S, we exploited the Lamb-dip technique in the millimeter- and submillimeter-wave region up to 1.2 THz [13] to provide frequency values with an accuracy of 1 kHz and to resolve the hyperfine structure due to hydrogens of the ortho transitions. We also recorded transitions at Doppler-limited resolution, primarily in the 1.3–1.6 THz frequency range (with frequency accuracy generally of 50 kHz). These new measurements were included in global fits similar to those performed by Azzam et al. [8] and allowed us to improve the known spectroscopic parameters by more than one order of magnitude in some cases, such as the rotational constants, and to provide new high-order centrifugal-distortion terms. Inconsistencies in the previous centrifugal-distortion constants were also noted. Therefore, the present investigation is an important step toward a complete and accurate line list for hydrogen sulfide isotopic species.

2. Experimental details The measurements were performed with a frequency-modulated, computer-controlled spectrometer working from 65 GHz to 1.6 THz [14,15], exploiting the Lamb-dip technique [16,17] to obtain sub-Doppler resolution [13,18]. The Doppler-limited measurements were carried out using a free-space cell with a single-path arrangement, while either the double-path configuration or a terahertz Fabry–Perot interferometer constructed using suitable metallic meshes, were employed in the Lamb-dip measurements (for details, the reader is referred to Ref. [13]). Regarding the experimental details, the millimeter- and submillimeter-wave sources employed were frequency multipliers driven by Gunn diode oscillators and were phase-locked to a rubidium frequency standard. The frequency modulation was obtained by sine-wave modulating the 60 MHz local oscillator of the synchronization loop. For H233 S, the Doppler-limited measurements were performed in the 500–800 GHz and 1.0–1.56 THz frequency ranges. For the main isotopic species, we explored almost the entire frequency region covered by our spectrometer, and the Lamb-dip measurements carried out in the 168 GHz to 1.2 THz range. For the Doppler-limited measurements, the modulation depth was varied from 300 kHz to 2.4 MHz, according to the transition frequency under consideration. For the Lamb-dip recordings, modulation-depth values ranging from 2 kHz to 90 kHz were used. Liquid-He cooled Ge bolometer and InSb detector were used; their output was processed by means of a Lock-in amplifier tuned to twice the modulation frequency, thus performing second harmonic detection. In passing, we note that for H233 S the Lamb-dip measurements were carried out in the 200–450 GHz frequency range to establish a new improved NMR shielding scale for 33 S [12]. Regarding the experimental conditions, a commercial sample was used and the 33 S-containing isotopologue was detected in natural abundance (0.76%). The Doppler-limited measurements were carried out at pressure values ranging from 10 to 50 mTorr. Instead, for the Lamb-dip measurements, low pressure values (0.1–0.6 mTorr) were chosen to minimize the dip widths as much as possible and to avoid frequency shifts. Fig. 1 shows the J ¼ 44;1 43;2 rotational transition of H233 S (at 646.9 GHz) recorded at Doppler-limited resolution: the hyperfine structure due to the 33 S quadrupole coupling is evident. Despite performing the measurements in natural abundance, a very good signal-to-noise ratio (S/N) is noted. This good S/N is also maintained when moving to the THz region, as demonstrated by Fig. 2, which reports the J ¼ 42;3 41;4 rotational transition of H233 S at 1025.6 GHz. Our spectrometer permits the resolution of

Fig. 1. The hyperfine structure of the J ¼ 44;1 43;2 rotational transition (646.9 GHz) of H233 S recorded in natural abundance at Doppler-limited resolution (P = 20 mTorr, mod. depth = 800 kHz). The corresponding calculated stick spectrum is also depicted.

Fig. 2. The hyperfine structure of the J ¼ 42;3 41;4 rotational transition (1025.7 GHz) of H233 S recorded in natural abundance at Doppler-limited resolution (P = 40 mTorr, mod. depth = 1.26 MHz). The corresponding calculated stick spectrum is also depicted.

the hyperfine structure also in the THz domain. In both figures, we make use of the F quantum number coming from the F ¼ J þ I coupling scheme to label the hyperfine components, where I is the nuclear spin quantum number (I = 3/2 for 33 S). Furthermore, in both figures the stick spectra calculated from the spectroscopic parameters obtained in this work (see next section) are shown. Fig. 3 depicts a representative H2S line in the THz region (the J ¼ 64;3 63;4 rotational transition at 1025.9 GHz) recorded using the Lamb-dip technique. The latter allows for a full line width below 100 kHz for a transition characterized by a Doppler full width of 2.175 MHz (leading with the collisional broadening and the modulation depth to a full width of approximately 4 MHz), enabling the retrieval of the transition frequency with a 1 kHz accuracy. According to the Fermi–Dirac statistics, the presence of two equivalent hydrogen nuclei (I = 1/2) leads to the existence of ortho

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Fig. 3. The J ¼ 64;3 63;4 rotational transition of H2S at 1025.9 GHz recorded at Doppler-limited resolution (black curve; P = 4.5 mTorr, mod. depth 1.35 MHz) as well as with the Lamb-dip technique (red curve; P = 0.3 mTorr in static condition, mod. depth = 45 kHz). In the inset, the Lamb-dip recording is better shown. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

and para species. Ortho-H2S corresponds to the case of total nuclear spin, IH;tot = 1, while para-H2S is characterized by IH;tot ¼ 0. Consequently, only the transitions of the ortho species exhibit a hyperfine structure. An example is provided by Fig. 4, which shows the J = 33,0 32,1 transition of ortho-H2S. This figure demonstrates that both the real transitions and the crossover resonances (also known as ghost transitions) are responsible for the actual spectrum. The crossover resonances are experimental artifacts due to the saturation of overlapping Gaussian profiles of two or more transitions with a common rotational energy level [19,20]. The stick spectra also indicate how many transitions are responsible for the actual spectrum recorded. The last comment concerns the intensity of the ghost transitions: a comparison of the simulated and experimental spectra suggests that the crossover resonances are slightly more intense than those calculated according to Refs. [21].

3. Results For the 33 S-containing isotopologue, a total of 127 distinct frequency lines in the 500–1563 GHz frequency range have been measured (plus 69 distinct frequency lines – with 38 at sub-Doppler resolution – in the 200–450 GHz range from Ref. [12] and 1

hyperfine component at sub-Doppler resolution at 1.197 THz from Ref. [13]). For the main isotopic species, we recorded 33 transitions at Doppler-limited resolution, mainly in the 1.3–1.6 THz frequency region, and 33 transitions were observed using the Lamb-dip technique (plus 4 other Lamb-dip measurements from Ref. [13] and 1 sub-Doppler recording obtained using electric resonance spectroscopy, from Ref. [26]). To accurately retrieve the transition frequencies from the recorded spectra, for the distorted and/or partially blended features, we resorted to a line-profile analysis [22,23]; in all the other cases, the experimental data points were fit with a parabolic function. In all cases, the frequency values have been obtained as averages of sets of measurements. Based on the standard deviations of these averages, the transition intensities and the S/N [24,25], we estimated the experimental uncertainties to conservatively be 1 kHz for the Lamb-dip measurements (with only a few exceptions due to the low S/N) and to range from 20 kHz to 100 kHz for the others. The frequency values for H2S and H233 S are provided in the supplementary material, together with the fit outputs. For both isotopic species, the new measurements were included in global fits involving all previously available frequency (or wavenumber) values for the vibrational ground state up to approximately 11 THz [8–13,26,27] (Table 1 summarizes the numbers of lines in the final data sets coming from different sources). The fittings were carried out using Pickett’s SPFIT program [28,29] and Watson’s S-reduced Hamiltonian in the Ir representation [30], with each transition weighted proportionally to the inverse square of its experimental uncertainty. Both Watson’s S and A reduced Hamiltonians were used for fitting, but the S reduction provided the best description (i.e., the smallest standard deviation in conjunction with the lowest number of parameters). In total, 52 (plus 4 hyperfine parameters) and 44 distinct constants were determined for H2S and H233 S, respectively, up to the 16th-order centrifugal-distortion terms for the former and up to the dodectic level for the latter. These high order terms of the Hamiltonian were necessary due to the strong centrifugal-distortion effects that characterize hydrogen sulfide (similarly to water) and the very extensive coverage of the energy and quantum number values (J max ; K max ¼ 25, 16 and a J max ; K max ¼ 20, 13 for H2S and H233 S, respectively). The sensitivity a of our spectrometer enabled the observation of weak transition lines characterized by peak absorption coefficients (amax ) as low as 1  106 cm1; some of these transitions involve J values (J = 15, 16) higher than those of previous high-resolution measurements (i.e., measurements with uncertainties < 1 MHz). Consequently, higher-order centrifugal-distortion constants were required. Due to the limited use of such high-order terms, the SPFIT/SPCAT identifiers are also provided when reporting the results. For both H2S and H2S33 S, the obtained spectroscopic parameters are collected in Table 2 where they are compared to the most Table 1 Summary of the transitions included in the global fits for H233 S and H2S.

Fig. 4. The J ¼ 33;0 32;1 rotational transition of H232 S at 300.5 GHz recorded with the Lamb-dip technique (black curve; P = 0.1 mTorr, mod. depth = 6 kHz). The stick spectra for the real and crossover transitions are reported in blue and green, respectively; the overall calculated spectrum is depicted in red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Num. transitions

Jmax ; K max a

Frequency range

Reference

H2S 1 13 334 50 1208 70

1, 0 9, 6 19, 9 13, 8 25, 16 16, 10

168 GHz 35–690 GHz 1.6–6.0 THz 131 GHz–2.56 THz 1.0–10.9 THz 217 GHz–1.6 THz

[26] [27] [11] [10] [8] This work, [13]

H233 S 43 71 431 267

8, 6 13, 9 16, 13 10, 8

168 GHz–1.1 THz 1.8–6.0 THz 1.5–10.5 THz 203 GHz–1.6 THz

[9] [11] [8] This work, [12]

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Table 2 Ground-state spectroscopic parameters (MHz) for H233 S and H2S. Parameter

Identifiera

A0 B0 C0 DJ DJK DK d1 d2 HJ HJK HKJ HK h1  103 h2  103 h3  103 LJ  106 LJJK  103 LJK  103 LKKJ  103 LK  103 l1  106 l2  106 l3  106 l4  106 P J  109 P JJK  106 P JK  106 P KJ  106 P KKJ  106 P K  106 p1  109 p2  109 p3  109 p4  109 p5  109 SJ  109 SJK  109 SJJK  109 SKKKJJJ 109 SKKJ  109 SKJ  109 s2  109 s3  1012 s4  1012 s5  1012 s6  1012 T J 1015 T JK 1012 T KKKJ 1012 T KKJ 1010 T KJ 1010 T K 1012 t7  1015 V JK 1015 V JJK 1015 V JJJKKK 1012 V KKKJ 1012 V KKJ 1012 V KJ 1012 V K  1012 C aa (H)b  103 C bb (H)b  103 C cc (H)b  103 Daa (H-H)b  103 vaa (33 S)

10 000 20 000 30 000 200 1100 2000 40 100 50 000 300 1200 2100 3000 40 200 50 100 60 000 400 1300 2200 3100 4000 40 300 50 200 60 100 70 000 500 1400 2300 3200 4100 5000 40 400 50 300 60 200 70 100 80 000 600 1500 2400 3300 4200 5100 50 400 60 300 70 200 80 100 90 000 700 1600 4300 5200 6100 7000 100 000 1700 2600 4400 5300 6200 7100 8000

H233 S

H2S This work 310583.57681(33) 270367.68173(51) 141820.025852(31) 20.861454(35) 76.231602(67) 117.726650(67) 8.8662557(94) 0.6417890(32) 0.01021992(80) 0.0902210(32) 0.1556075(83) 0.0336226(69) 2.888706(268) 0.955353(154) 1.245524(48) 5.5184(59) 0.069827(82) 0.217178(26) 0.270147(18) 0.162376(13) 1.09370(23) 0.39555(16) 1.68252(14) 0.40426(55) 3.3764(15) 0.04535(68) 0.17700(16) 0.29910(31) 0.2335(42) [0.0] 1.0143(58) 0.5886(48) 0.4386(92) 0.6962(51) 0.41109(16) [0.0] 0.03277(21) [0.0] 0.9580(25) 2.001(33) 1.2431(25) [0.0] 0.3299(19) 0.2289(12) 0.7307(64) 0.10162(26) 0.9313(29) 0.0384(32) 5.573(19) 0.1454(46) 0.1234(42) 2.945(14) 0.13115(25) 0.08470(21) 0.7362(14) 0.02361(47) 0.10952(22) 0.2004(42) 0.1631(38) 0.04880(13) 17.93(25) 14.53(25) 17.23(25) 33.447(35)

Azzam et al. [8] 310583.580(11) 270367.682(12) 141820.0415(69) 20.86177(26) 76.23237(64) 117.72636(68) 8.865995(99) 0.641960(33) 0.0102269(31) 0.090353(13) 0.155866(35) 0.033836(30) 2.8814(15) 0.96339(71) 1.24685(33) 5.670(19) 0.07287(18) 0.22325(78) 0.27447(96) 0.16145(53) 1.0205(81) 0.2743(37) 1.7256(50) 0.3978(14) 4.801(60) 0.0683(13) 0.2466(58) 0.4541(77) 0.4151(40) 0.0983(26) 0.827(14) [0.] 0.795(28) 0.673(10) 0.3376(26) 0.003664(90) 0.0734(25) 0.246(11) 0.260(13) [0.] 0.1150(63) 0.930(19) 0.509(48) 0.214(20) 0.4382(77) 0.0211(15) [0.] [0.] [0.] [0.] [0.] [0.] [0.] [0.] [0.] [0.] [0.] [0.] [0.] [0.]

This work 310025.8404(11) 270367.3005(16) 141702.4195(10) 20.88408(10) 76.35264(35) 117.59920(33) 8.866638(68) 0.654498(24) 0.0102205(50) 0.090420(15) 0.156141(39) 0.034203(34) 2.8845(25) 0.9624(14) 1.25768(52) 5.510(41) 0.06956(30) 0.21347(95) 0.2669(12) 0.16186(77) 1.154(20) 0.380(11) 1.7161(68) 0.4164(25) 3.62(11) 0.0400(15) 0.1454(70) 0.335(17) 0.359(18) 0.0724(85) 1.197(55) 0.487(33) 0.652(27) 0.656(14) 0.3678(86) [0.] [0.] [0.] [0.] 0.129(28) 0.200(34) [0.] [0.] [0.] 0.626(21)

Azzam et al. [8] 310025.774(20) 270367.169(22) 141702.407(17) 20.87749(84) 76.3367(23) 117.5822(20) 8.86383(28) 0.65448(11) 0.0100421(84) 0.089668(58) 0.15495(13) 0.03383(12) 2.8209(39) 0.9726(23) 1.2510(13) 4.066(29) 0.05882(30) 0.1857(15) 0.2382(31) 0.1481(23) 0.649(14) 0.2523(93) 1.5518(71) 0.4483(58) [0.] [0.] [0.] 0.094(11) 0.181(24) 0.054(15) [0.] [0.] [0.] 0.788(20) 0.317(12) [0.] [0.] [0.] [0.] [0.] [0.] 0.511(22) [0.] [0.] 0.549(34)

32.7875(65)

32.841(78)

vbb (33 S) vcc (33 S)

8.6623(33)

8.635(98)

C aa (33 S)  103 C bb (33 S)  103 C cc (33 S)  103

21.61(28) 58.90(25) 23.92(68)

41.4498(64) 28.1(77)

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G. Cazzoli, C. Puzzarini / Journal of Molecular Spectroscopy 298 (2014) 31–37 Table 2 (continued) Parameter

Identifiera

H233 S

H2S This work

v

2 c

Jmax d d K max a a b c d

Azzam et al. [8]

This work

Azzam et al. [8]

1.02

0.93

0.92

0.93

25 16

25 16

20 13

20 13

Pickett’s program SPFIT/SPCAT identification code [28]. Hyperfine parameters of H for H2S determined from a separated fit, see text. Dimensionless (weighted) standard deviation. Maximum value referred to the starting energy levels of the rotational transition.

recent results reported in the literature (i.e., those by Azzam et al. [8]). According to the SPFIT/SPCAT identifiers [28] reported in Table 3 of Ref. [8], Azzam et al. employed Watson’s S reduction in their fittings despite labeling the corresponding parameters according the A reduction. Concerning the main isotopic species, we note that the sub-Doppler measurements in the THz regime have a strong impact on the derived spectroscopic constants. In fact, a preliminary fit including only 12 frequency transitions accurate to 1 kHz (all but one having a 2 kHz error) in a set of 1423 distinct frequency (or wavenumber) lines, revealed that all of determined parameters were improved relative to Ref. [8]; the uncertainties on the rotational constants were reduced by one order of magnitude. The inclusion of all the new measurements improved the spectroscopic constants further and enabled the determination of several new centrifugal-distortion terms up to 16th order. The improvements obtained and the revision of some parameters are not an artifact due to fitting a limited number of highly accurate frequencies, but they are reliable because the number of improved frequency values was more than sufficient. In fact, the improved data set consists of 70 newly recorded transitions: 37 at sub-Doppler resolution and 33 at Doppler-limited resolution with an accuracy on average of 50 kHz, replacing frequency values characterized by uncertainties at least 2 order of magnitude larger. In particular, the 38 sub-Doppler measurements available are more than sufficient to guarantee the reliability of the parameters up to at least the 10th order. However, the terms of the 14th and 16th orders require further improved measurements at frequencies

above 1.6 THz to be definitely confirmed. These high-order centrifugal-distortion constants were required to reproduce our transition frequencies properly. This is exemplified by Fig. 5, which shows the (observed–calculated)/error ratio (OC/E) for the transitions recorded in the 500 GHz to 1.6 THz frequency range as obtained from our fit as well as from the parameters of Ref. [8]. For the latter, in several cases, the OC/E absolute value exceeds 50 and in almost all cases, this ratio is larger than the corresponding value determined in our fit. Because our improved measurements cover a rather large range of J; K a where the maximum value for
J (J max ) is 16 and the maximum value of K a K max is 11, the spectroa scopic parameters determined in this work should be reliable and accurate in predicting rotational transitions with J < 15, K a < 12. These predicted transitions should have an uncertainty of a few hundreds of kHz at most up to 10 THz (the corresponding file reporting such predictions can be found in the supplementary material). For H2S, the hyperfine parameters were determined by fitting only the hyperfine components of 8 ortho transitions (one from Ref. [26]), with crossover transitions included in the fit as the arithmetic mean of the frequencies of the two generating hyperfine components. This approach allows us to gain additional information, regarding the hyperfine components that are too weak to be observed, as made evident in Fig. 6, which depicts the J ¼ 43;2 42;4 rotational transition at 765.9 GHz. For blended lines, the hyperfine components and/or ghost transitions are weighted according to their intensity. The derived unperturbed transition

Fig. 5. The (observed–calculated)/error ratio for the H232 S rotational transitions recorded in the 500 GHz to 1.6 THz frequency range: black squares refer to the global fit reported in this work (the corresponding parameters given in Table 2), while the red circles refer to the parameters of Table 3 from Ref. [8]. In the inset, the portion ranging from 1.0 to 1.2 THz in frequency and from 50 to +50 for the (observed–calculated)/error ratio is highlighted. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 6. The J ¼ 43;2 42;3 rotational transition of H232 S at 765.9 GHz recorded with the Lamb-dip technique (black curve; P = 0.25 mTorr, mod. depth = 12 kHz). The stick spectra for the real and crossover transitions are reported in blue and green, respectively; the overall calculated spectrum is depicted in red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

frequencies were subsequently used in the global fit mentioned above. The hyperfine constants are the diagonal elements of the spin–rotation interaction tensor of hydrogens, specifically C aa ; C bb and C cc , and the aa component of the dipolar spin–spin coupling tensor, Daa (with Daa ¼ 2  Dbb ¼ 2  Dcc , and all offdiagonal terms being null). The only previous determination of the hyperfine parameters of H2S available in the literature dates back to 1968 [26]. In Ref. [26], Cupp et al. accurately determined the dipolar spin–spin coupling constant; however, they could only derive the isotropic spin–rotation constants for the two rotational states involved in the J ¼ 11;0 10;1 rotational transition at 168.8 GHz. Therefore, the present study provides the first complete set of the hyperfine parameters determined for H2S. While the hyperfine components from Ref. [26] only improve the spin–rotation constants (i.e., the error approximately halves: from 0.53 kHz to 0.24 kHz), their inclusion is mandatory for obtaining an accurate value of Daa : from 41.6(30) kHz to 33.447(35) kHz. The reason is related to the fact that the investigation of Ref. [26] is characterized by higher resolution, which is

mandatory for resolving the effects due to the dipolar spin–spin coupling. For the 33 S-containing isotopologue, the hyperfine structure due to hydrogens has not been resolved, while that due to 33 S is already well resolved at a Doppler-limited resolution, as shown above and in Figs. 1 and 2. Therefore, the set of spectroscopic parameters also includes the full sulfur quadrupole-coupling and spin–rotation tensors. For the 33 S-containing isotopologue, the improvements in the determination of the spectroscopic constants are evident. With respect to Ref. [8], our accurate Doppler-limited measurements in the THz frequency range improved all parameters and enabled the determination of additional dectic and dodectic centrifugal-distortion constants. These additional parameters were needed to reproduce our frequency values correctly. This is well demonstrated by Fig. 7, which shows the OC/E for the transitions recorded in the 1.0–1.2 THz frequency range: we note that in the case of the present fit this ratio usually does not exceed 2.0, while if a global fit is performed without introducing any additional parameters relative to those in Ref. [8], most transitions present a ratio exceeding 2.0. The OC/E’s are even larger if the spectroscopic constants from Ref. [8] are used. However, the availability of Lamb-dip measurements with an accuracy of 2 kHz [12] allows the improvement of the rotational and nuclear quadrupole-coupling constants by more than one order of magnitude and the accurate and reliable derivation of the spin–rotation constants. As noted in Ref. [12], the lack of sub-Doppler measurements led to the incorrect determination of the spin–rotation tensor components in Ref. [9], the problem still persisting in the investigation of Ref. [8]. The hyperfine parameters determined using the global fit procedure employed here agree with those obtained in Ref. [12] using only the sub-Doppler measurements there reported, with the present uncertainties being only a little bit larger. We also note that the differences in the rotational constants are due to the different Watson-reduced Hamiltonian used in this work (S reduction) and in Ref. [12] (A reduction). The centrifugal-distortion terms of both isotopologues deserve further comment. First, we only considered those parameters determinable with a relative standard deviation 610%. Table 2 shows that in most cases, the present results do not agree with those of Ref. [8] within the given uncertainties and with deviations

Fig. 7. The (observed–calculated)/error ratio for the H233 S rotational transitions recorded in the 1.0–1.2 THz frequency range: the black squares refer to the global fit reported in this work (the corresponding parameters given in Table 2), the red circles refer to a global fit performed without introducing any additional parameters relative to Ref. [8], and the blue triangles refer to the parameters of Table 3 from Ref. [8]. In the inset, the range 7 to +7 for the (observed–calculated)/error ratio is highlighted. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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ranging from a few per cents up to 50–100 %. In some cases sign inversion was observed. Due to the improvements described and based on the discussion reported above, our values are not only more accurate, but also more reliable for predicting higher frequency values. For H233 S, deviations are even observed for the rotational constants: A and B given in Ref. [8] deviate from ours by approximately 5–6 times the given uncertainties. Due to the accuracy of our sub-Doppler and Doppler-limited transitions and their large number (196 in all), our values for the rotational constants cannot be questioned. We finally note that the fits for both isotopic species are able to well reproduce the experimental transitions, as demonstrated by the dimensionless (weighted) standard deviations reported in Table 2. In the case of the main isotopic species, only 5 transitions show OC/E’s greater than 5.0 and greater than 4.0; the corresponding numbers of lines decrease to 0 and 3 for H233 S. While for H233 S no transitions were excluded from the fit, for the main isotopologue 7 frequencies (5 from Ref. [8] and 2 from our measurements) were discarded from the fit because showing OC/E values larger than 6 (up to 12.2). A 5.5-times-the-uncertainty filtering criterion was used for H2S. The distinct frequency (or wavenumber) lines used in the fits are 1456 and 652 for H2S and H233 S, respectively. For those transitions with different measurements available, only the most accurate ones were included in our fits. 4. Conclusions Accurate transition frequencies for the main and 33 S-containing isotopologues of hydrogen sulfide are reported. These frequency values have been obtained from measurements up to 1.6 THz. The Lamb-dip technique has also been employed to exploit subDoppler resolution. Our measurements were included in global fits involving all previous available data up to 11 THz, providing improved and extended sets of spectroscopic parameters for both isotopic species. In particular, the availability of sub-Doppler measurements for H233 S, recently obtained by the present authors [13], allowed us to provide the correct determination of the sulfur spin–rotation tensor for the first time in the context of a global fit sampling transitions up to J = 20 and K a ¼ 13, in terms of quantum numbers, and up to 10.51 THz, in terms of frequency. For H2S, the new spectroscopic parameters include centrifugal-distortion terms up to the 16th order; their determination is possible because transitions involving at the same time rather large J and K a values
J max ; K max ¼ 25; 16 have been recorded. The hyperfine structure a due to the hydrogens has been resolved for the first time in the submillimeter-wave region, enabling a complete and accurate determination of the corresponding hyperfine parameters. In conclusion, the new transition frequency values are useful for improving all of the available spectroscopic databases, as well as the line lists of the ExoMol project. In addition to the measurements reported here, our global fits should predict transition frequencies within approximately 0.001 cm1 (30 MHz), or even better for low J; K a transitions up to about 670 cm1 (20 THz). According to the discussion in the results section, the expected uncertainties for the rotational transitions with J < 15, K a < 12 are as small as a few hundreds of kHz up to 10 THz. Consequently, we made the corresponding prediction file available in the supplementary material.

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