ACCURATE SPECTROSCOPIC CHARACTERIZATION OF ETHYL MERCAPTAN AND DIMETHYL SULFIDE ISOTOPOLOGUES: A ROUTE TOWARD THEIR ASTROPHYSICAL DETECTION

Given the improved capabilities of new astronomical observatories in terms of spectral coverage and spatial resolution, the corresponding surveys cover large frequency ranges and can contain many unidentified lines. The latter features usually correspond to "new" molecules and/or rare isotopologues of previously detected species. The "cleaning" of the corresponding spectral confusion implies the full assignment of astronomical spectra, which in turn requires a complete spectroscopic characterization of all of the involved species at different temperatures.

Organic molecules can be detected in low-energy, excited vibrational states in hot molecular cores through their rotational spectra. Furthermore, nonrigid species such as ethyl mercaptan and dimethyl sulfide present internal rotation motions restricted by energy barriers. These motions can produce splitting of the ground and low-excited vibrational levels through the tunneling effect. Their complete characterization at low temperatures requires analysis of the vibrational spectrum in the far-infrared region. Unfortunately, a large number of detectable molecules are not well characterized. For many species, although accurate spectroscopic data are available, they are limited to the vibrational ground state and to the most abundant isotopologues. The effect of temperature and the fact that isotopic composition can be very different from one extraterrestrial source to another are often not considered. However, species containing less abundant isotopes or molecules with populated low vibrational states can play important chemical roles in many sources. An example is provided by methyl formate (a nonrigid molecule), for which investigations have been reported for the rotational spectrum in the vibrational ground state for the main isotopic species (Brown et al. 1975; Churchwell & Winnewisser 1975) as well as for several isotopologues (Carvajal et al. 2009; Margulès et al. 2010; Tercero et al. 2012). Features due to the first excited torsional state have also been detected for the main isotopologue (Kobayashi et al. 2007; Demyk et al. 2008) and ¹³C-containing (Carvajal et al. 2010) isotopologues. The main isotopic species was also observed in the second excited torsional state (Takano et al. 2012).

State-of-the-art ab initio methods can be used to compute highly accurate spectroscopic constants, even for nonrigid molecules (Brites et al. 2008; Halvick et al. 2011; Puzzarini et al. 2014a; Senent et al. 2009, 2014). Today, these constants are known to provide the required accuracy to guide experimental investigations of rotational and far-infrared spectra. While experimental determinations for rare isotopic species can be hampered by their low natural abundance, computations provide the same accuracy for all isotopologues. Therefore, quantum-chemical calculations are well suited to support and complement experimental and astronomical studies that also involve rare isotopic species. Examples can be found in investigations of the main isotopologues and several other isotopologues containing D and ¹³C of dimethyl-ether (DME; Senent et al. 2012; Carvajal et al. 2012, 2014) or propane (Villa et al. 2013).

Recently, we conducted a study of the main isotopic species of dimethyl sulfide (DMS) and ethyl mercaptan (ETSH) at low temperatures (Senent et al. 2014) considering their potential astrophysical relevance. In particular, the latter molecule was considered to be a potential detectable sulfur organic compound based on different arguments: the importance of sulfur chemistry in the interstellar medium (Charnley 1997) and because the O-analog of ethyl mercaptan, ethanol, is a well-known astrophysical molecule. We should consider that usually, with few exceptions (Cernicharo et al. 1987), the detection of S-bearing species follows the detection of corresponding O-analogs. The expectations of astrophysicists were recently satisfied when an exhaustive search led to the detection of ethyl-mercaptan in Orion in 2014 (Kolesniková et al. 2014). For many years, methyl mercaptan was the only sulfur nonrigid molecule detected in astrophysical sources (Linke et al. 1979).

Differences in their formation processes have made determination of the isotopic abundances of different sources particularly interesting as a means of investigating interstellar and galactic evolution (Mauersberger et al. 2004). In addition, fluctuations of the relative isotopic abundances are tools for identifying chemical, geophysical, and biological processes (Canfield 2001; Farquhar & Wing 2003; Mauersberger et al. 2004). Hence, relative isotopic abundances have been estimated for meteorites, the moon, cosmic rays, and stars (Mauersberger et al. 2004). There is some evidence demonstrating that isotope yields follow different synthesis procedures. Whereas ³²S, ³⁴S, and ³³S are the primary products of oxygen burning in a star, ³⁶S is produced when the primary sulfur isotopes capture neutrons during helium and carbon burning (Mauersberger et al. 1996).

Considering their potential importance, in the present work, we investigated several rare monosubstituted isotopologues of ethyl mercaptan and dimethyl sulfide containing either a rare S-isotope or deuterium. Sulfur, the tenth most abundant cosmological element, presents four stable isotopes ³²S, ³⁴S, ³³S, and ³⁶S whose abundance ratios in the solar system were estimated to be 95.02%, 4.21%, 0.75%, and 0.021% (Anders & Grevesse 1989), respectively. Their relative abundances in Orion KL were determined to be ³²S/³⁴S = 20 ± 6, ³²S/³³S = 75 ± 29 (Tercero et al. 2010a, 2010b). The first molecule containing ³⁶S,C³⁶S, was detected in Galactic molecular hot cores by Mauersberger et al. (1996), who estimated a relative abundance of ³⁴S/³⁶S = 115 ± 17, which is smaller than that in the solar system. This ratio is consistent with what was later determined by Mauersberger et al. (2004), 107 ± 15, in the carbon star IRC+ 10216 based on the detection of the rotational transitions of C³⁶S and Si³⁶S. Moreover, several S-containing molecules were detected in the ISM raging from diatomics (e.g. NS, SO, and SH) to more complex small organic molecules (e.g. C₂S, H₂S, OCS, C₃S, H₂CS, HSCN, HNCS, CH₃CS, etc.; Ziurys 2006; Millar et al. 1986; Irvine et al. 1988; Goldsmith et al. 1981; Minh et al. 1991; Frerking et al. 1979; Linke et al. 1979). Si³⁶S is the first compound containing ³⁶S detected in a star (Mauersberger et al. 2004).

In the present work, by following the procedures of Senent et al. (2014), we have investigated the ³⁴S-, ³⁶S-, ³³S-, and deuterium-containing ETSH and DMS species, considering them not only in the vibrational ground state, but also in their excited torsional states because at the temperature of the hot molecular cores, these excited states and their splittings can be populated. Hence, we provide a detailed spectroscopic characterization of these S-containing molecules and isotopologues to help their detection in the ISM. Thus, the aim of this paper is to predict the isotopic substitution effect on the rotational and torsional parameters. To assess their accuracy, the computed properties were compared with the available experimental data, in particular, for the main isotopologues (Senent et al. 2014). While for the latter we refer to Senent et al. (2014) for an account on previous theoretical and experimental studies, here we mention that for other isotopic species, only a few studies are available (Hayashi et al. 1989; Schmidt & Quade 1975; Wolff & Szydlowski 1985; Manocha et al. 1973; Kretschmer et al. 1995; Kolesniková et al. 2014).

In this study, we followed the methodologies described in Puzzarini et al. (2010), Puzzarini (2013), and Senent (1998a, 1998b, 2001). In particular, we refer interested readers to Puzzarini et al. (2010) and Puzzarini (2013) for rotational spectroscopy and to Senent (1998a, 1998b, 2001) for torsional analysis. In particular, concerning the spectroscopic characterization of ETSH and DMS, all computational details can be found in Senent et al. (2014). In the following, only a brief summary is provided. Here, we also point out that DMS has two equivalent methyl groups leading to nine equivalent minima in the potential energy surface (PES), while ETSH has a unique methyl group which is responsible for three equivalent minima. In addition, for the latter, a second torsional coordinate, the thiol torsion (SH torsion), leads to two conformers, the gauche and trans forms. Then, the coupling of the two torsional motions in ETSH (methyl and thiol torsions) generates a PES with nine minima (for further details, see Senent et al. 2014).

2.1. Rotational Spectroscopy

To obtain accurate equilibrium rotational constants, the equilibrium structures of ETSH and DMS were determined by means of a composite scheme (see Senent et al. 2014) which is based on additivity at an energy-gradient level (Heckert et al. 2005, 2006) and employs the coupled-cluster singles and doubles approximation (CCSD) augmented by a perturbative treatment of triple excitations [CCSD(T)] (Raghavachari et al. 1989) in conjunction with correlation-consistent basis sets, cc-p(C)VnZ (n = T, Q, 5) (Dunning 1989; Woon & Dunning 1995). Second, to derive vibrational ground-state and torsional-excited-state rotational constants, the equilibrium rotational constants were corrected for vibrational effects with the corresponding corrections being obtained by means of second-order vibrational perturbation theory (VPT2; Mills 1972) at the MP2/cc-pVTZ, CCSD/cc-pVTZ, and CCSD(T)/cp-VTZ levels (for details, see Senent et al. 2014), where MP2 stands for the Møller–Plesset theory to the second order (Møller & Plesset 1934). These calculations implied the evaluation of cubic force fields, and therefore they also allowed us to determine quartic and sextic centrifugal-distortion constants. Different levels of theory were considered in order to verify the cheapest one while still providing reliable and accurate results. All of these calculations were carried out with the quantum-chemical CFOUR program package (2012).

To further improve the predictive capabilities of our computed parameters (i.e., rotational and centrifugal-distortion constants), an empirical scaling procedure was employed for the ground-state parameters. For a generic parameter X, the latter procedure is based on multiplying the computed value of X for a monosubstituted isotopologue (denoted by the superscript iso) for the corresponding experiment/theory ratio for the main (³²S-containing) isotopic species (denoted by the superscript main):

$$\begin{equation} X^{{\rm iso}} _{{\rm scal}} {\rm = }X^{{\rm iso}} _{{\rm calc}} \times \left(X^{{\rm main}} _{{\rm exp}} {\rm /}X^{{\rm main}} _{{\rm cal}} \right), \end{equation} \tag{ 1 }$$

where scal, exp, and calc denote the scaled, experimental, and quantum-chemically calculated values for X, respectively. This approach is extensively used in the field of rotational spectroscopy, and its validity has been discussed, for example, in Puzzarini et al. (2012). For gauche-ETSH, for which a complete set of experimental rotational and quartic centrifugal-distortion constants is available for the ³⁴S-containing species, the latter was used for the reference isotopologue in order to derive the scaled parameters for the main isotopic species.

2.2. Torsional Analysis

For the analysis of the vibrational spectrum in the far-infrared region, we have performed a torsional analysis following the theoretical methodology described in our previous paper (Senent et al. 2014). The energy levels are determined variationally by solving the following two-dimensional Hamiltonian:

$$\begin{eqnarray*} \hat{H}(q_i,q_j) &=& - \sum\limits_{i = 1}^2 {\sum\limits_{J = 1}^2 {\left({\frac{\partial }{{\partial q_i }}} \right)} } B_{q_i q_j} (q_i,q_j)\left({\frac{\partial }{{\partial q_j }}} \right)\nonumber\\ && + V(q_{i,}\, q_j) + V^{\prime}(q_i,\,q_j) + V^{{\rm ZPVE}} (q_i,q_j), \end{eqnarray*}$$

which depends on two independent coordinates q_i and q_j. For ETSH, q_i and q_j are identified as the CH₃ torsion (θ) and the SH torsion (α), respectively. In DMS, both coordinates correspond to methyl internal rotations (θ₁ and θ₂). V(q_i, q_j) represents the two-dimensional potential energy surface (2D-PES). V^ZPVE(q_i, q₂), B_qiqj, and V ' (q_i, q_j) denote the zero-point vibrational energy correction, the kinetic energy parameters, and the Podolsky pseudopotential, respectively. For their definition, the readers are referred to Senent (1998a, 1998b).

Since the 2D-PES is isotopically invariant, here we use the surfaces generated in our previous study to treat the main isotopologue. These surfaces were obtained from the total electronic energies calculated at the CCSD(T)/aug-cc-pVTZlevel of theory (Kendall et al. 1992) for a number NS of selected geometries defined for different values of the independent coordinates (NS = 26 for ETSH and NS = 7 for DMS). For each point of the PES, the remaining 3Na-6-n internal coordinates (Na = number of atoms, n = 2 dihedral angles) were optimized at the CCSD/aug-cc-pVTZ level.

V^ZPVE(q_i, q₂), B_qiqj, and V '(q_i, q_j) are, however, isotopically dependent. For each NS structure and for each isotopologue, B_qiqj and V '(q_i, q_j) were determined using the code ENEDIM, also employed in the variational calculation of the energy levels. V^ZPVE(q_i, q₂) was calculated within the harmonic approximation at the MP2/aug-cc-pVTZ level using the Gaussian 09 package. For all details, the reader is referred to Senent et al. (2014).

3.1. Rotational Parameters

3.2. Torsional Energy Levels and Splittings

The present contribution provides an accurate and reliable set of spectroscopic parameters for different isotopic species of DMS and ETSH. For this purpose, state-of-the-art computational methods and approaches have been employed. We thus determined highly accurate rotational and torsional parameters. Available experimental data were used to assess the reliability of our computations. For instance, relative accuracies of 0.1% and 5%–6% were observed for rotational and quartic centrifugal-distortion constants, respectively, and were further improved through empirical scaling. The rotational-spectroscopy characterization was complemented by the calculation of reliable sextic centrifugal-distortion terms. On the whole, our computed parameters allow us to predict rotational transitions with the proper accuracy for future laboratory and/or astronomical investigations.

The A/E splitting of the ground vibrational state of ETSH caused by the A/E torsion is almost negligible. However, a splitting of ∼0.060 cm⁻¹ due to the SH torsion is observed for the hydrogenated isotopologues of g-ETSH; this splitting is negligible in the deuterated species. In DMS, the low-energy torsional states split into nine components with separations of less than 0.001 cm⁻¹. Therefore, the vibrational ground-state rotational study based on the semi-rigid rotor approximation should be considered reliable; meanwhile, an appropriate treatment accounting for non-rigidity is required to describe the first and second excited states.

The overall conclusion is that based on the good agreement and well-established computational techniques employed, we are confident that the spectroscopic data provided herein are highly accurate and can therefore be useful for the identification of rare isotopologues of DMS and ETSH in the interstellar medium.

This research was supported by a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Program under grant No. PIRSES-GA-2012‐31754, the COST Action CM1002 CODECS, and the FIS2011‐28738-C02‐02 project (MINECO, Spain). In Bologna, this work was supported by MIUR (PRIN 2012 funds under the project "STAR: Spectroscopic and computational Techniques for Astrophysical and atmospheric Research") and by the University of Bologna (RFO funds). M.L.S., M.H., and M.A.M. acknowledge the Deanship of Scientific Research at King Saud University for its funding through the Research Group RGP-VPP-333.

The authors acknowledge CTI (CSIC) and CESGA for computing facilities.