1 Introduction

The astrochemistry of small, unsaturated molecules containing nitrogen, carbon, and sulfur is poorly understood. This observation applies, in particular, to the family of compounds containing the –NCS functional group which include species like isothiocyanic acid (HNCS) and thiocyanic acid (HSCN). Both have been detected in the interstellar medium (ISM) [1–4], and their astrochemical formation pathways recently proposed [2, 5]. These are the only such molecules detected in the interstellar medium which contain an atom each of carbon, sulfur, and nitrogen. Four-atomic [C, H, N, S] isomers have already been studied on theoretical and experimental grounds [6–8] and HNCS turns out to be the most stable among them with the HSCN molecule only 6.3 kcal/mol higher in energy. HCNS and HSNC arrangements may also be important, with energies only 34.4 and 36.0 kcal/mol higher than that of HNCS.

Many interstellar molecules like HCN, HNC, HC3N, HC5N, and SH2 have methyl-bearing analogues which have also been observed in the interstellar medium. It is therefore likely that methyl-bearing molecules featuring the –NCS functionality can also be found, potentially along with some of their structural isomers. As little spectroscopic data exists for the majority of species in the C2H3NS family, more must be known about them before any search can be contemplated. To date, no C2H3NS family member has been detected in space.

Among C2H3NS species, methyl isothiocyanate (CH3NCS) is perhaps the best known terrestrially. This is a volatile substance commonly used as a pesticide [9]. It easily reaches the atmosphere following application and photochemical processes contribute to its eventual decomposition and removal [10–12]. Although CH3SCN and CH3NCS are commercially available, their spectroscopy and photochemistry are poorly known. Electronic absorption spectra are similar to those reported for HNCS [13, 14]. Gas-phase photolysis products include CH3, NCS, and CN [15–20]. More decomposition products were reported for CH3SCN subjected to electric discharges [21]. Recently, Møllendal and collaborators measured the gas-phase rotational spectroscopy of mercaptoacetonitrile, another isomer of C2H3NS stoichiometry [22]. From this study, we know that mercaptoacetonitrile has two conformers with a calculated energetic separation between them of 4.68 kJ/mol [22]. To the best of our knowledge, no experimental data are available for the isomerisation reactions of C2H3NS family members. Such processes are potentially important, for studies of photochemical reactions in solid noble gases.

Fu et al. [23] analyzed the potential energy surface (PES) of the [CH3, N, C, S] system where the CH3 group remained an indivisible unit during the calculations. Here we consider the [2C, 3H, N, S] PES where all atoms can take any position and predict the spectroscopic properties of the relevant bound species. Very few high-level quantum chemical studies on simple thiocyanates or isothiocynates have been reported. The most advanced was carried out in 1996 by Koput [24], who used the coupled-cluster approach with a triple-zeta basis set to derive the potential energy surface for the CNC bending motion in CH3NCS and to predict its rotational energy levels. Rotational constants and geometric parameters of MeNCS were also reported by Palmer and Nelson [25].

The relatively large number of atoms in C2H3NS makes a search for all possible isomers based on chemical intuition impractical. To overcome this, Saunders [26] proposed a stochastic search method where an arbitrarily selected structure is first optimized and used as a starting point in the search for further isomers. The next arrangement can then be generated by a “kick” that slightly (and randomly) changes the positions of all atoms. Each kick is followed by geometry optimization. This iteratively repeated procedure, while simple and efficient, may fail when the energy minima are too far apart (as is likely in our case). Therefore, an alternative approach was applied here, based on randomly chosen atomic configurations [27, 28].

2 Theoretical methods

2.1 General procedure

A procedure similar to that implemented here in the search for all possible energy minima on the potential energy surface (PES) has been described previously [28]. Starting structures were repeatedly generated as random arrangements of atoms placed at the nodes of a grid (spaced by 0.6 Å) inside a 6.5 × 6.5 × 6.5 Å rectangular box. Such initial atomic configurations were subjected to geometry optimization using density functional theory (DFT) at the B3LYP/4-31G** [29–33] level. Resultant structures were added to a database of bound species if they were different from any of those previously generated. Intermolecular complexes were not included in this database. The search procedure was terminated after completion of approximately 3000 optimization runs. At this number of runs, each structure had appeared at least twice. B3LYP/aug-cc-pVDZ [29, 34, 35] geometries were subsequently calculated for each molecule from this database. This second round of calculations allowed us to distinguish the most stable isomers with more certainty. The geometries predicted at this level are used as a starting point for a final round of very precise calculations providing final energies and spectroscopic constants.

A more detailed study of the most stable atomic arrangements (at the B3LYP/aug-cc-pVTZ level [29, 34, 35]) included geometry optimizations which were then followed by anharmonic calculations (VPT2 [36]) with numerical differentiation along normal modes. This supplied harmonic (\(\omega_{B3LYP}\)) and anharmonic (\(\nu_{B3LYP}\)) frequencies, as well as vibration–rotation coupling constants and quartic centrifugal distortion constants. Raman intensities and natural bond orbitals [37–39] (NBO) were also calculated at the same level of theory.

Next, coupled-cluster computations (CCSD [40–42] with the cc-pVTZ [34, 35] basis set) were performed to improve the precision of molecular geometry predictions. Equilibrium electric dipole moment values were obtained at the same level of theory. Consequently, geometry optimizations were carried out for the 12 most stable isomers with the CCSD(T) method (singles, doubles, and the perturbative treatment of triple excitations) in the frozen-core approximation. Harmonic vibrational frequencies \(\omega_{CCSD\left( T \right)}\) were obtained using numerical second derivatives of the total energy with respect to nuclear positions.

Calculations at the B3LYP/aug-cc-pVDZ and CCSD/cc-pVTZ levels of theory were used to search for low-lying triplet electronic states for each of the C2H3NS isomers using singlet structures as starting points. Additional calculations searching for singlet excited states were performed in two steps. First, vertical excitation energies were calculated by EOM-CCSD/cc-pVTZ. Next, selected structures were optimized using CIS/aug-cc-pVDZ. These calculations are used to confirm that each molecule has a singlet ground state as well as to determine potential photochemical decomposition pathways.

The recommended vibrational frequencies were based on harmonic values obtained at the CCSD(T) level and on B3LYP-derived anharmonic corrections, as detailed elsewere [28, 43–46]. Similarly, our recommended ground-state geometric structures (and the rotational constants that depend on them) were based on both coupled-cluster and DFT calculations [5, 27, 28, 45–48]. Vibration–rotation coupling constants were obtained at the VPT2-B3LYP/aug-cc-pVTZ level. The software package Gaussian 09 [49] was used in these computations for the whole set of isomers. The frozen-core approximation was used for all ab initio calculations.

2.2 The most stable isomers

The three lowest energy C2H3NS isomers were subjected to a more accurate theoretical treatment. Their molecular structures were derived at the CCSD(T)/cc-pVQZ level. The following formula, similar to that employed in our previous report [28], was used to obtain final energy values:

$$\begin{aligned} E & = \mathop E\nolimits_{cc - pVQZ}^{corr,CCSD(T)} + \left( {E_{CBS}^{corr,MP2} - E_{cc - pVQZ}^{corr,MP2} } \right) \\&\quad + \left( {E_{cc - pCVQZ}^{MVD2, MP2} + E_{aug - cc - pCVQZ}^{corr,MP2} - E_{cc - pVQZ}^{corr,MP2} } \right) \\ & \quad + \left( {E_{cc - pVTZ}^{corr,CCSDT} - E_{cc - pVTZ}^{corr,CCSD\left( T \right)} } \right) + E_{cc - pV5Z}^{total,HF} \\&\quad + E_{cc - pVQZ}^{DBOC,CCSD} + E_{cc - pVTZ}^{ZPE,CCSD\left( T \right)} \\ \end{aligned}$$
(1)

The meanings of the sub- and superscripts in the energy terms \(\mathop E\nolimits_{C}^{A,B}\) are the following: A (energy type)—this can be any of the correlation (corr), total (total), diagonal Born–Oppenheimer correction (DBOC) [50], mass-velocity and Darwin term (MVD2) [51, 52], or zero-point energy (ZPE); B—method; C—basis set (CBS denotes the complete basis set). All contributions to the energy were calculated assuming the CCSD(T)/cc-pVQZ geometry, except for diagonal Born–Oppenheimer corrections \(\mathop E\nolimits_{cc - pVQZ}^{DBOC,CCSD}\) (CCSD/cc-pVQZ geometry) and zero-point energy values \(\mathop E\nolimits_{cc - pVTZ}^{ZPE,CCSD\left( T \right)}\) (CCSD(T)/cc-pVTZ geometry).

The 1/X 3 error law [53, 54] (X denoting the basis set cardinal number) served to estimate the complete basis set (CBS) limits of correlation energy [53, 54] which is given by:

$$E_{CBS}^{corr,MP2} = E_{cc - pVQZ}^{corr,MP2} + \frac{{125 \left( { E_{cc - pV5Z}^{corr,MP2} - E_{cc - pVQZ}^{corr,MP2} } \right)}}{61}$$
(2)

Anharmonic (VPT2) calculations, performed at the CCSD(T)/cc-pVTZ level, supplied the zero-point vibrational energy \(\left( {\mathop E\nolimits_{cc - pVTZ}^{ZPE,CCSD\left( T \right)} } \right)\) values, electric dipole moment for the ground vibrational states (μ 0), infrared absorption intensities of overtone and combination transitions, vibration–rotation coupling constants (α A i , α B i , α C i ), and the rotational distortion constants. The software package CFOUR v.1 [55] was used in these computations for the three lowest energy isomers. The frozen-core approximation was not used in these computations. The estimation of room-temperature thermodynamic stabilities relied on partition functions obtained using B3LYP/aug-cc-pVTZ-derived anharmonic vibrational frequencies [56] and were carried out using the Gaussian 09 package [49].

3 Results and discussion

3.1 Stability of isomers

More than 100 species were found in course of preliminary studies using B3LYP/4-31G** and B3LYP/aug-cc-pVDZ calculations. From the list generated by these runs, we selected 45 of the most stable isomers for further CCSD/cc-pVTZ studies. From this set of 45, the 20 most stable isomers are presented in Fig. 1. Species, including thionitroso ethane [57], 1,3-didehydro-1-methyl-1H-1λ4-thiazirine [23], 2-thia-4-azabicyclo[1.1.0]butane [58], and 2-methyl-3-thiaziridinylidene [23] are in the longer list but not included on Fig. 1, because they have high relative energies with respect to 1: 183, 204, 238, 282 kJ/mol, respectively.

Fig. 1
figure 1

Molecular structures corresponding to the lowest energy minima within a potential energy surface describing C2H3NS singlet species. Isomer labels are followed by ZPE-corrected CCSD/cc-pVTZ relative energies, calculated with respect to species 1. More precise CCSD(T)/cc-pVTZ relative energies are given in parentheses, when available. Atomic charges (for the first 14 isomers) and Lewis-type dash formulae are based on NBO analysis at the B3LYP/aug-cc-pVTZ level. Circles drawn with gray full lines, black full lines, and dashed gray lines represents the atoms situated, respectively, in the plane of the figure, in front of the plane or behind the plane

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Figure 1 presents the most stable C2H3NS isomers together with their corresponding (relative) energy values. Mean absolute errors of 65.1 and 10.5 kJ/mol have been reported [59] for the predictions of atomisation energies and reaction enthalpies, respectively, using all-electron correlation and CCSD/cc-pCVTZ. Considering these values and the results of our earlier CCSD/cc-pVTZ study on C2HNS-stoichiometry molecules [28], we estimate the precision of our relative energy calculations to be better than 30 kJ/mol. This is sufficient to identify isomers 1, 2, and 3 as the most stable, but do not permit reliable prediction of the order of stability for the three lowest energy isomers.

Our most precise calculations (Table 1) reduced the energetic difference between 1 and 3 from 12.4 to 6.0 kJ/mol. Inclusion of thermal corrections at the VPT2-B3LYP/aug-cc-pVTZ level significantly changed the results. For standard (298.15 K, 1 bar) conditions and including thermal corrections, 2 becomes the most stable isomer, but energetic differences remain small (Table 1). It seems likely that the thermodynamic stability under normal conditions decreases in the flowing order with the first being the most stable: 2, 1, 3. However, the energetic differences between these isomers are low and of the same order of magnitude as the uncertainty of the calculation. The fact that 1 is among the three lowest energy chemicals seems to contradict what is known about the stability of molecules 1, 2, and 3 from reports where handling of the chemicals was described. The last two chemicals are commercially available and can be stored with no difficulty, unlike species 1 [60, 61]. The lower stability of 1 may be determined by other factors, such as the existence of a low energetic barrier to a thermally activated reaction or susceptibility to a photochemical transformation.

Table 1 Relative energies (\(\Delta E\)) and relative standard Gibbs free energies (\(\Delta G_{298.15 K}\)) for the three most stable C2H3NS stoichiometry molecules, together with energy terms of the Eqs. 1 and 2
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3.2 Spectroscopic properties of selected isomers

3.2.1 Rotational spectroscopy

Calculated rotational constants are collected in Table 2. Available experimental values, concerning the vibrationless states of species 1, 2 and 3 [22, 62, 63], allow estimation of the precision of these predictions. Absolute differences between experimental and theoretical values are 0.4 and 0.2 %, for C 0 and B 0 of 3, respectively. In the case of 1, corresponding values are even smaller, while for 2, these values are 0.2 and 1.0 %. A significant error observed for the predicted B 0 value of 2 may stem from the large amplitude of the low frequency vibration. In previous studies, employing the same theoretical approach, the absolute deviation from experimental B 0 and C 0 values varied between 0.05 and 0.6 % [5, 45]. Differences between equilibrium and ground-state rotational constants are on the order of 0.5 %. Electric dipole moments calculated for the most stable isomers fall in the range between 0.8 and 6 D. This should allow for microwave detection of at least some of these molecules.

Table 2 Recommended equilibrium rotational constants and ground-state rotational constants of C2H3NS isomers computed using the hybrid CCSD(T) + B3LYP approach [5, 27, 28, 45–48] (see the text)
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3.2.2 Infrared spectroscopy

Tables 3, 4, 5 and 6 (see Online Resource for their full versions) collect information concerning the vibrational spectroscopy of molecules 1, 2, 3, and 9 for which experimental values are also available. Additional data for less stable C2H3NS species are provided in the Online Resource. Focusing our attention on theoretical results alone, for the three lowest energy isomers, the vibrational frequencies predicted by hybrid CCSD(T) + VPT − B3LYP [28, 43–46] calculations and by the standard VPT2-CCSD(T) procedure can be compared. As reported previously [28, 43–46], the hybrid approach satisfactorily reproduces fundamental frequencies. For overtone and combination modes, the discrepancy between VPT2-CCSD(T) and hybrid methods is higher, especially in the case of low-energy vibrations. In spite of its slightly lower accuracy, CCSD(T) + VPT − B3LYP predictions are still sufficient for the identification of isomers by IR absorption spectroscopy. Isomers 1 and 3 feature rather low IR intensities, while for each of the following species: 2, 4, 6, 7, 9, 10, 11, 12, and 14, at least one intense (in excess of 100 km/mol) IR transition is to be expected. While our theoretical predictions already allow for a critical evaluation of some published spectral assignments concerning 1, 2, 3, and 9, the reliable identification of combination and overtone modes will require further, dedicated experimental studies.

Table 3 Vibrational spectroscopy of 1
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Table 4 Vibrational spectroscopy of 2
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Table 5 Vibrational spectroscopy of 3
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Table 6 Vibrational spectroscopy of 9
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Calculations can be compared to limited experimental data as well. No IR spectra have been measured for the isomers 4–14, with the exception of the cryogenic argon matrix-isolated species 9 [64]. We limit our discussion here to 1, 2, and 3. Mathias and Shimanski [61], after having synthesized compound 1, reported on its most prominent IR bands measured in the condensed phase. These bands are in acceptable agreement with our ab initio results. However, the complete IR spectrum of 1 was not given. Because of this, no experimental values are listed in Table 3. Our predictions suggest low intensities for each of the IR transitions of 1. The only exception is the anharmonic prediction for the \(\nu_{8}\) vibration, for which the intensity is surprisingly high in comparison with harmonic result. We identified a strong resonance between \(\nu_{8}\) and \(\nu_{10} + \nu_{14}\) as the main contributor to this intensity increase. A reliable prediction of resonances is challenging, even at a high level of theory, so this anharmonic intensity may be significantly overestimated.

For 2, IR [65–68] and Raman [65] spectra have been measured. Gas-phase frequencies [68] of the fundamental modes match our present theoretical predictions fairly well (Table 4). More complicated is the case of overtone and combination modes, some of which were identified for gaseous- and condensed-phase samples [65, 66]. Our theoretical predictions deserve several comments:

  1. 1.

    As pointed out elsewhere [24], the internal rotation of a methyl group is a large-amplitude vibration that cannot be treated using VPT2. With this in mind, we give no predictions regarding the \(\nu_{15}\) anharmonicity or any parameters of related overtone or combination bands.

  2. 2.

    Interpretation of IR spectra in the 2000–2300 cm−1 region, where our ab initio calculations locate the fundamental band \(\nu_{4}\) (“antisymmetric” NCS stretching), is very challenging. The band \(\nu_{6} + \nu_{11}\) (CH3 antisymmetric deformation coupled to the NCS “symmetric” stretching) should be a factor of two less intense than \(\nu_{4}\). In the same region one can also expect to find an overtone of a CH3 twisting mode (\(2 \nu_{10}\)), as well as the \(\nu_{4} + \nu_{14}\) combination (\(\nu_{14}\) is the CNC bending), with their predicted intensities about two times lower than that of \(\nu_{6} + \nu_{11}\). An additional band in this region might come from \(\nu_{8} + \nu_{10}\) and \(\nu_{7} + \nu_{11}\) vibrational transitions. These are predicted to be 6 and 12 times less intense in IR than \(\nu_{6} + \nu_{11}\). Reliable spectral assignments of all combination bands will require further experimental studies and possibly the use of isotopologues.

  3. 3.

    The combination band \(\nu_{4} + \nu_{11}\), arising from NCS “antisymmetric” and “symmetric” stretches, is predicted to have a sizable IR intensity. Its calculated position agrees well with the experimental [66] frequencies: 2789 (gas-phase) and 2791 cm−1 (argon matrix). This fits with the fundamental frequencies proposed by Zheng et al. [68].

  4. 4.

    The assignment of weak bands observed in the gas phase [65, 66] at 2823 and 2900 cm−1 or in solid argon [66] at 2818 and 2887 cm−1, is not easy. These were interpreted in the gas phase as the overtones of CH3 antisymmetric deformation modes (\(2 \nu_{5}\) or \(2 \nu_{6}\)), possibly overlapping with the overtone of CH3 antisymmetric deformation (\(2 \nu_{7}\)) or the combination of CH3 antisymmetric deformations (\(\nu_{6} + \nu_{5}\)). Yet another explanation of the bands detected in that region may involve a combination of symmetric and antisymmetric CH3 deformation modes, \(\nu_{6} + \nu_{7}\) and/or \(\nu_{5} + \nu_{7}\). Compared to prior assignments, the predicted frequencies of either \(\nu_{6} + \nu_{7}\) or \(\nu_{5} + \nu_{7}\) would be higher than the sum of the fundamentals.

Comparisons between the IR spectra of 3 and our results are not straightforward. Firstly, no obvious assignment of the band observed by Sullivan et al. [69] at 2112 (strong) and 2106 cm−1 (medium intensity) in gas and solid phases, respectively, can be given. Fundamental transitions are not expected there, while overtone and combination bands are predicted to be weak. The band most likely comes from impurities as it was not reported in another study [70].

3.2.3 Excited electronic states

Searches for both singlet (EOM-CCSD/cc-pVTZ and CIS/aug-cc-pVDZ) and triplet (B3LYP/aug-cc-pVDZ and CCSD/cc-pVTZ) excited states were performed. The results of the triplet search indicated that all ground electronic states are of singlet multiplicity. No minima corresponding to 1 or 4 could be found on the triplet potential energy surface. Instead, 1 and 4 converged to H2C–CN + SH or H2C–NC + SH, respectively. Table 7 lists singlet–triplet energy splittings predicted for the whole family of isomers.

Table 7 ZPE-corrected singlet–triplet energetic separation (eV), as derived for the C2H3NS isomers using B3LYP/aug-cc-pVDZ and CCSD/cc-pVTZ calculations
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Table 8 presents vertical electronic excitation energies for the most stable isomers. Strong UV absorption bands are predicted for species 2, 7, 8, 9, 10, 11, and 12. Differences between isomers 2 and 3, both featuring methyl groups and NCS structural units, are notable. The main UV absorption band of 2 is predicted to be far more intense (f = 0.5) than any of the bands predicted for 3 (f < 0.01, at least up to energies of 8.6 eV). This difference in intensities is rooted in the electronic structures of these molecules, differences between which can be seen in the results of charge distribution calculations given in Fig. 1. Only six of the discussed species, namely 6, 8, 9, 10, 11, and 12, have their first singlet excited states at less than 5 eV (248 nm).

Table 8 Energy (eV) and oscillator strength values for vertical transitions (∆E vert < 7.75 eV) from the ground electronic states of C2H3NS isomers, as derived using EOM-CCSD/cc-pVTZ
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Geometry optimizations using CIS/aug-cc-pVTZ, for selected excited singlet electronic states of the 14 most stable C2H3NS isomers, did not point to many significant changes in atomic arrangements that might occur as a result of excitation. We found that 9 dissociates in its first singlet excited state, reached through a vertical excitation energy of approximately 4.8 eV, into CH3–CN and S. In the case of 7, electronic excitation breaks apart the bonds between sulfur and carbon atoms. For 14 an SNC ring can be created. The excitation of 1 to the second excited state is likely to yield the SH radical. This ease of photodecomposition may contribute to the reported low stability of 1. A similar process is to be expected for 4, but the breaking of C–S is accompanied by the creation of an H–C bond. As a result, S and HCNCH2 may be created.

4 Summary and conclusions

Methyl isothiocyanate (CH3–NCS, 2), methyl thiocyanate (CH3–SCN, 3), and, surprisingly, mercaptoacetonitrile (HS–CH2–CN, 1) are identified as the most thermodynamically stable molecules of C2H3NS stoichiometry. These three species are separated in energy by no more than 10 kJ/mol. Molecular constants for rotational, vibrational, and electronic spectroscopy were predicted for the 14 most stable isomers. Quantum chemical calculations suggest the susceptibility of mercaptoacetonitrile (1), mercaptoacetoisonitrile (HS–CH2–NC, 4), and N-sulfide acetonitrile (CH3–CNS, 9) to UV-induced decomposition.