Searching for biosignatures by their rotational spectrum: global fit and methyl group internal rotation features of dimethylsulphoxide up to 116 GHz

Abstract The identification and quantification of molecules in interstellar space and atmospheres of planets in the solar systems and in exoplanets rely on spectroscopic methods and laboratory work is essential to provide the community with the spectral features needed to analyse cosmological observations. Rotational spectroscopy in particular, with its intrinsic high resolution, allows the unambiguous identification of biomolecular building blocks and biosignature gases which can be correlated with the origin of life or the identification of habitable planets. We report the extension of the measured rotational transition frequencies of dimethylsulphoxide and its 34S and 13C isotopologues in the millimetre wave range (59.6–78.4 GHz) by use of an absorption spectrometer based on the supersonic expansion technique. Hyperfine patterns related to the methyl group internal rotation were analysed in the microwave range region (6–18 GHz) with a Pulsed Jet Fourier Transform spectrometer at extremely high resolution (2 kHz) and reliable predictions up to 116 GHz are provided. The focus on sulphur-bearing molecules is motivated by the fact that sulphur is largely involved in the intra- and inter-molecular hydrogen bonds in proteins and although it is the 10th most abundant element in the known Universe, understanding its chemistry is still a matter of debate. Moreover, sulphur-bearing molecules, in particular dimethylsulphoxide, have been indicated as possible biosignature gases to be monitored in the search of habitable exoplanets.


Introduction
The search for gaseous molecules in space is a guiding goal in the astrophysical community. The molecules searched for are of increasing complexity in the pursue of understanding the chemical steps that lead to the development of complex molecules, biomolecular building blocks and ultimately life. Another goal is the search for molecules produced by living organisms, called biosignatures, and accumulated in the atmospheres of planets and exoplanets to assess their habitability.
As regards the detection of biosignatures, the early paradigm for exoplanet life detection is the argument that only life can maintain gases severely out of thermodynamic equilibrium in the atmosphere. In particular, the detection of oxygen (O 2 ) and methane (CH 4 ) (Lederberg, 1965;Lovelock, 1965) was suggested as the most robust atmospheric evidence of life on Earth.
In general, biosignature gases can be those created directly by metabolic redox reactions or they can be 'secondary' metabolism byproducts: gases produced by life but not as byproducts of their central chemical functions. Such gases are usually related to stress or signalling in living beings and although expected to be produced in small quantities, their specificity makes them valuable as possible biosignatures as their detection is not likely to be a false positive (Seager et al., 2012). Some are also produced in sufficient amounts to affect atmospheric chemistry (such as isoprene or dimethyl sulphide) and they could possibly be detected remotely on planets and exoplanets. Examples include nitrous oxide (N 2 O) (Des Marais et al., 2002), dimethyldisulphide (CH 3 SSCH 3 ) (Pilcher, 2003), methyl chloride (CH 3 Cl) (Segura et al., 2005) and dimethyl sulphide (CH 3 SCH 3 , DMS) and other sulphur gases (Domagal-Goldman et al., 2011).
Recently, it has been pointed out that although atmospheric composition will be the primary observable that could imply the presence of life (Seager, 2013) the identification of a biosignature in a planet's atmosphere requires an understanding of the possible compositions of abiotic atmospheres (Shahar et al., 2019).
This last factor is important as the atmosphere is tied to the dynamics of the planet and some secondary metabolism gases are produced by geological processes as well as biological ones.
As an example, we can consider a sulphur-containing molecule, namely dimethylsulphoxide (CH 3 SOCH 3 , DMSO, Fig. 1). DMSO is the product of oxidation of DMS, it can be directly produced by some microorganisms from DMS or it can be produced in the atmosphere through a nonbiological chemical reaction which oxidizes DMS to DMSO, dimethyl sulphone (CH 3 SO 2 CH 3 ) and finally, methyl sulphate (CH 3 SO 3 H) (Seager et al., 2012). In any case the detection and quantification of a molecule like DMSO would be important either as a biosignature itself or in the construction of appropriate models of chemical reactivity in the atmosphere of planets and exoplanets.
The most informative method to investigate the chemical composition of the atmospheres of planets and exoplanets is high-resolution spectroscopy, which for exoplanets must rely on remotesensing techniques (Burrows, 2014). One of the possible approaches is via rotational spectroscopy in the microwave-to submillimetre range undertaken from the ground with radiotelescopes (see e.g. Greaves et al., 2021). As regards the interstellar space and star-forming regions, the unequivocal identification of the molecules in astronomical surveys is based on their rotational laboratory spectra and more than 200 molecules have been identified in space (CDMS, 2001;Müller et al., 2001Müller et al., , 2005. In addition to the characterization of the species, the features of molecular spectra also yield detailed physical information on the gas and its surroundings (Herbst and van Dishoeck, 2009).
Laboratory rotational spectroscopy data in the microwave, millimetre and submillimetre wavelengths are necessary to perform those searches and rotational spectroscopy performed in supersonic expansions has been proved to be particularly suitable to investigate complex spectra generated by molecules (Calabrese et al., 2016) and weakly bound molecular complexes (Velino et al., 2004;Favero et al., 2010). Those experiments allow us to identify multiple conformers of a flexible molecule (Vigorito et al., 2017a), different tautomers (Sanchez et al., 2007;Melandri et al., 2010) as well as and different isotopologues (Calabrese et al., 2014). The study of the different isotopologues of a molecule is of importance for different reasons. From a structural point of view, the analysis of the changes in the rotational constants upon isotopic substitution allows the determination of the position of the substituted atoms without any a priori assumptions (Evangelisti et al., 2015). If the collection of a complete set of data including all the isotopes is not possible to achieve, a partial structure can be obtained by refining a structure obtained as a result of quantum chemical calculations to reproduce all experimental data (Uriarte et al., 2018). From an astrochemical point of view the detected abundance of different isotopologues of a molecular species can give additional information on reaction mechanisms of formation (Neill et al., 2011) or on the environment in which the molecule is found or formed (Imai et al., 2018).
We concentrate here on DMSO, which as stated above, can be considered an important secondary metabolic product or the product of an abiogenic mechanism occurring in the atmosphere or in geological processes. Also, DMSO is an important substance commonly used as a polar aprotic solvent, antifreeze fluid and cryo-protectant owing to its beneficial properties including low toxicity and environmental compatibility (Akkök et al., 2009). In this paper, we report our investigation on DMSO: the extension of the analysis of the rotational spectra of the parent species and that of the mono-substituted 13 C and 34 S isotopologues to the 59.6-78.4 GHz frequency range observed with a Free Jet Absorption Millimetre Wave (FJ-AMMW) spectrometer and the measurements of some transitions in the lower frequency region (6-18 GHz) with a high-resolution cavity-based Fourier transform microwave (FTMW) spectrometer. The extension of the measurement of the rotational spectrum to relatively high frequencies (>40 GHz) is very important, in particular for remote sensing using telescopes, since many of them, including ALMA, work in higher frequency regions. Even if the theoretical model used to analyse the spectrum in the low frequency region is correct, the uncertainties on the parameters reflect on the predictions thus precise experimental frequencies are essential for the identification of molecular transition in astronomical surveys or complex spectra containing the signals of many other molecules.

Experimental methods
Two different spectrometers working in the microwave and millimetre frequency regions have been utilized in this experiment. DMSO was acquired from Sigma-Aldrich (purity >99%) and used without further purification and argon or helium, purchased from SIAD (Società Italiana Acetilene e Derivati), were used as carrier gas.
The rotational spectrum of DMSO was recorded in the millimetre wave region (59.6-78.4 GHz) using a stark-modulated FJ-AMMW spectrometer with a resolution of about 300 kHz and estimated uncertainties for the frequency measurements of about 50 kHz. The main features of the spectrometer have been previously described (Calabrese et al., 2013(Calabrese et al., , 2015Vigorito et al., 2018). In this experiment the sample was maintained at room temperature and a stream of argon (P 0 = 20 kPa) was flowed over it and the mixture was expanded to about P b = 0.5 Pa through a 0.3 mm diameter pinhole nozzle. The rotational temperature of the molecules in the jet has been estimated to be 5-10 K from relative intensity measurements of rotational transitions at different rotational quantum numbers.
The measurement of the rotational spectrum in the 6-18 GHz region was carried out in a COBRA-type, cavity-based, pulsed supersonic-jet FTMW spectrometer (Balle and Flygare, 1981;Grabow et al., 1996) previously described . The sample of DMSO was cooled to 273 K and helium was flowed over it at a stagnation pressure of about 3 bar resulting in a mixture of about 1%. The mixture was then expanded through a solenoid valve (General Valve, Series 9, nozzle diameter 0.5 mm) into a Fabry-Pérot cavity. During the expansion, the molecules can reach quite lowrotational temperatures (a few Kelvins) and the most stable forms can be trapped at their energy minimum when certain conditions are satisfied. To determine the position of the spectral lines, Fourier transformation of the time-domain signal perform 8k data points, recorded at a sampling interval of 100 ns.

Results and discussion
In terms of chemical structure, the rigid molecule of DMSO has idealized C s symmetry and a trigonal pyramidal molecular geometry (Fig. 1). DMSO is characterized by two equivalent methyl rotors and a Cs frame, therefore, its molecular symmetry group is G 18 WV in Altmann's notation (Smeyers and Niño, 1987) and C 3 − × C 3 v+ in Dreizler's approach (Dreizler, 1961). Due to the coupling of the methyl internal rotation to the overall rotation of the molecule, the rotational levels are split into a multiplet of four states labelled according to the irreducible representation in the above groups. Since, as Dreizler states, μ a and μ b transform as the AA 2 representation, in the vibronic ground state only four kinds of transitions are allowed: AA 1 -AA 2 , AE-AE, with spin statistical weights 16, 8, 8 and 32, respectively. In the following, we will use a simplified notation, referring to the AA 1 and AA 2 states as AA, to (E b A 1 + E a A 1 ) and (E b A 2 + E a A 2 ) as EA and to (E a E + E b E) and (E a E + E b E) as EE. A good general graphical representation of the energy levels for a two tops system has been recently published (Dindić and Nguyen, 2021). Due to this splitting of the rotational levels, DMSO exhibits a spectral splitting because of hindered internal rotation of its methyl rotors that leads to a triplets AA, AE (or EA) and EE splitting pattern, where A and E are the methyl torsional state symmetry labels (see e.g. Vigorito et al., 2017b).
The first rotational spectroscopy study on DMSO dates back to 1964 (Dreizler and Dendl, 1964) and several other studies followed focusing on the determination of the structure through the study of isotopologues (Feder et al., 1969;Typke, 1978;Kretschmer, 1995) and the dynamic effects such as the centrifugal distortion and the methyl internal rotation (Dreizler andDendl, 1965a, 1965b;Fliege et al., 1983). The analysis of the high resolution rotational spectrum of the parent species is reported in Fliege et al. (1983) who explored the microwave spectrum of DMSO using a Fourier transform spectrometer from 8 to 18 GHz. They report the fit of the new measured lines together with the lines previously measured in the 6-40 GHz frequency range at a lower resolution. The observed transitions involve the dipole moment component along the b principal axis of rotation (μ b -type) and the frequency values used are the weighted means of the internal rotation fine structure components. Also, seven other transitions involving the coupling of the radiation with the c principal axis (μ c -type) were measured by radiofrequency-double resonance with pump frequency adjustment and methyl internal rotation splittings are also given. Measurement of the high frequency (154-660 GHz) transitions of the parent species are reported by Margulès et al. (2010) for the ground state and by Cuisset et al. (2013) for the five lowest vibrational states.
As regards the parent species, we extended the spectral investigation to the 59.6-78.4 GHz frequency range and measured some transition lines in the 6-18 GHz frequency range using a higher resolution set-up. The AA transition lines reported by Fliege et al. (1983) were fitted using a semi-rigid Hamiltonian in the S-reduction and the III l representations (Watson 1977), suitable for oblate tops such as DMSO, by using the CALPGM suite of programs (Pickett, 1991) and the predictions were used to search for lines in the higher frequency range. Several μ b R-type lines with rotational quantum numbers J ranging from 4 to 9, and pseudo-quantum numbers K a from 0 to 5 and K c from 0 to 4 were measured. In the same way, starting from the lines measured by Feder et al. (1969), the transitions for the monosubstituted 34 S and 13 C isotopologues were observed in natural abundance and measured in the higher frequency range (accuracy 50 kHz). Some lines both for the parent species and its 34 S and 13 C monosubstituted isotopologues could be also detected with our cavity-based FTMW spectrometer where they could be measured with a higher accuracy (2 kHz). All newly measured AA lines and those reported in the previous works were analysed in a global semi-rigid fit where each set of lines was weighted accordingly to its measured accuracy. The measured frequencies of the parent species are listed in Table 1 and those of the isotopologues are reported in Table 2, whereas the spectroscopic parameters obtained from the fitting procedure are reported in Table 3.
While the set of AA lines can be fit by using a semi-rigid Hamiltonian, the full set of AA, AE, EA and EE of transition lines needs a global fitting approach which takes into account the coupling effect of the internal rotation of the methyl group on the rotational transitions. For this purpose, the XIAM program (Hartwig and Dreizler, 1996) was used. This program is based on the combined axis method (Woods 1966) and directly supplies the V 3 barrier to internal rotation, the angles between the internal rotation axis and the principal axes and the moment of inertia of the internal top. A total of 195 transitions (including many of those from Fliege et al., 1983) were included in the global fit yielding the values of the rotational constants, the quartic and some sextic centrifugal distortion constants and the internal rotation parameters such as the value of the barrier hindering the motion and the orientation of the internal rotors. The standard deviation of the global fit is 5 kHz which is very close to the best accuracy obtained in the different measurements. In the XIAM program the S-reduction can be used but only the I r representation is available and not the III l one which would be more suitable for an oblate rotor such as DMSO. In the two representations the centrifugal distortion constants have different values and this is the reason why, in order to compare the AA-fit and the global-fit, we performed different fittings using the two representations for the AA state of the parent species. The comparison of the corresponding spectroscopic parameters reported in Table 4 shows that they are in very good agreement. Predictions from this fit to the 59.6-78.4 GHz region have confirmed that the internal rotation splittings are not resolvable in this region with the absorption spectrometer (resolution 300 kHz).
The obtained results are in good agreement with those reported by Fliege et al. (1983) but the accuracy in the determination of the centrifugal distortion constants is better and so is the standard deviation of the fit which is five times better. The experimental results can also be compared to those obtained by in the optimization of the DMSO structure by quantum chemical methods with the Gaussian 16 program (Gaussian, Inc., Wallingford, CT, USA) with the MP2/aug-cc-pVTZ.
The calculated values of the rotational constants (A = 7000.6, B = 6989.0, C = 4243.1 all in MHz) and of the distortion constants in the S reduction and III l representation (D J = 6.1, D JK = −9.1, D K = 4.1, d 1 = −0.25, d 2 = −0.23 all in kHz) are also in good agreement with the experimentally determined ones.
The moment of inertia and orientation of the methyl group was deduced from the structure reported in Feder et al. (1969). While the angle δ = ∠(ai), between the i internal rotation axis of the methyl tops and the a principal axis of overall rotation could be fitted, the ϵ angle between the projection of i on the bc plane and the b axis was fixed to zero as it was undetermined in the fit. This results in experimentally derived values of ∠(ai) = 32.56(26)/147.44(26), ∠(bi) = 57.44(26) (°) for the two methyl tops and a fixed ∠(ci) angle of 90°.
As regards the methyl group internal rotation, the MP2/aug-cc-pVTZ potential energy surface of the methyl torsion around the SC bond in DMSO was calculated by changing the dihedral angle of τ = HC − SC on the regular grid with Δτ = 10°and is shown in Fig. 2. The calculated data marked in red bullets are well reproduced with the threefold function: V(τ) = ½V 3 [1 + cos(3τ)], which is shown as a green line where V 3 = 11.6 kJ mol −1 . This value is also in agreement with the experimentally determined value of 12.37(4) kJ mol −1 .
The V 3 barrier hindering the methyl torsion in DMSO is thus much higher than the ones found for other molecules which contain a methyl group attached to a sulphur atom such as methylmercaptan Table 1. Experimental transition frequencies ν and deviations δν = ν(obs) − ν(calc) of internal rotation components of DMSO. Calculated frequencies n(calc) are obtained using the spectroscopic parameters listed in Table 4 AA EE AE EA     (5.31(1) kJ mol −1 ) (Kojima, 1960), DMS (8.8030(5) kJ mol −1 ) (Pierce and Hayashi, 1961;Jabri et al., 2016) and dimethyl disulphide (6.44 kJ mol −1 ) (Hartwig et al., 1995). This could be due to electronic effects related to the presence of the oxygen atom or to an attractive interaction between the oxygen atoms and the methyl hydrogens which can increase the barrier to internal rotation of this group. Based on the obtained fittings, an overall prediction in the 0-1000 GHz range calculated at five different temperatures which could be found in different astronomical objects is reported in Fig. 3. While the measurements are performed up to 78.4 GHz, the predictions are quite reliable in the adjacent frequency range covered by band 3 of ALMA (84-116 GHz) for lines with rotational quantum number J less than 12. In the bottom panel of Fig. 3, an expanded view of this frequency range can be found where the frequencies and intensities of main lines calculated at different temperatures are reported. Here, we can see that the most intense transitions are somehow the same ones at different temperatures. Moreover, a thorough analysis of the predictions showed that in this frequency range the internal rotation splittings are units or tens of kilohertz thus, even if very small, they might be observable at the resolution of some astronomical surveys which can show linewidths as low as 10 kHz (see for example Loomis et al., 2021). For a quantitative analysis, the predicted frequencies with their uncertainties and intensities at different temperature are reported in Table 5 while the internal rotation components are given as supplementary material (Table S1). The AA predicted frequencies from our fit are accurate within ten kilohertz as assessed by performing some fits which included lines measured at higher frequencies by Margulès et al. (2010).

Conclusions
In this work, rotational spectroscopy coupled to supersonic expansions has been exploited to characterize the rotational spectrum of DMSO and its 34 S and 13 C monosubstituted isotopologues. The lines were measured in the 59.6-78.4 GHz frequency range with an absorption spectrometer while a cavity-   Fixed to the value obtained from the r z structure (Feder et al., 1969). based FTMW spectrometer has allowed to re-measure DMSO transitions split by the methyl rotor internal rotation in the 6-18 GHz region with unprecedented high resolution and accuracy. A global fit of 195 lines has allowed for an accurate modelling of the internal rotation lines and the accurate determination of the spectroscopic parameters obtained by applying appropriate models. The molecular parameters related to the geometry of the molecule or its internal dynamics (methyl torsional barrier) could also be used to model the ro-vibrational spectrum of DMSO.
The measured rotational lines can be confidently used for the analysis of astronomical surveys for the unequivocal identification of DMSO and its isotopologues in different astronomical environments such as the interstellar medium, star-forming regions and planetary atmospheres. A natural place where one would try is astronomical objects where organic molecules containing sulphur have been detected. For example, in giant molecular clouds like Sagittarius B2 (Müller et al., 2016) or protostars (Majumdar et al., 2016). Tentative detection of sulphur-containing molecules has also been attempted in prestellar cores (Maris et al., 2019) and molecular clouds (Song et al., 2022). Besides remote sensing, the value of rotational spectroscopy as a means of exact identification   The intensities were calculated using the partition function from the semirigid approximation. The following values were used: and quantification of molecules could also be exploited in the search of biosignatures using instruments for in situ analysis.