A THEORETICAL STUDY ON THE INTERSTELLAR SYNTHESIS OF H₂NCS⁺ AND HNCSH⁺ CATIONS

More than 20 cationic isomers containing differently linked atoms C, H, H, N, and S were initially proposed and investigated at the B3LYP/aug-cc-pVTZ level of theory. Structures corresponding to the deepest minima on the singlet PES, numbered in order of increasing electronic energy, are shown in Figure 1. Geometry optimizations always departed from several qualitatively dissimilar starting geometries. Vibrational frequency calculations allowed for a distinction between true minima and saddle points. The energetic separation of the most stable isomers H₂NCS⁺ and HNCSH⁺ (38 kJ mol⁻¹ at the B3LYP level; see Figure 1) is by far smaller than in an otherwise analogous oxygen-bearing pair H₂NCO⁺/HNCOH⁺, for which Green (1981) calculated the difference of 75 kJ mol⁻¹. Coupled cluster calculations confirmed the rather high electronic energies of the more exotic isomers HSNCH⁺ and H₂CNS⁺ preliminarily predicted with DFT. Such high-energy values do not necessarily rule out interstellar detection, as exemplified by the isomeric species HC₂NC and C₃NH—less stable than HC₃N (cyanoacetylene) by 111 kJ mol⁻¹ and 213 kJ mol⁻¹, respectively (Kołos & Dobrowolski 2003)—and yet observed in space (Kawaguchi et al. 1992a, 1992b) with abundances that are two orders of magnitude smaller than that of cyanoacetylene. Here, however, we have decided to focus on the chemistry and reactivity of H₂NCS⁺ and HNCSH⁺. Energies of the most stable triplet isomers, corresponding to the a³A' PES, were systematically higher than those of their respective (i.e., similarly linked) singlet counterparts. The smallest singlet–triplet splitting (0.8 eV at the B3LYP/aug-cc-pVTZ level of theory) was found for H₂CNS⁺. We have not investigated the triplet species any further.

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Equilibrium rotational constants A_e, B_e, and C_e of the cationic isomers H₂NCS⁺ and HNCSH⁺ were obtained following the geometry correction recipe, which has been shown to produce reliable results in our former studies (Kołos et al. 2009; Gronowski & Kołos 2007; Gronowski et al. 2013). Namely, the interatomic distances derived with CCSD(T)/cc-pVTZ, downscaled by a factor of 0.9949, were used for the C–N and C–S bonds, while the unscaled B3LYP/aug-cc-pVTZ results served for C–H, N–H, and S–H. Rotational constants in the ground vibrational state (A₀, B₀, and C₀; Table 2) were given by

$$\begin{equation} B_{0}=B_{e}-0.5\sum _{i=1}^{9} \alpha _{i}^{B}. \end{equation} \tag{ 6 }$$

To check the adequacy of this procedure, we have applied it to quasi-linear NCSH and HNCS molecules of known rotational spectroscopy (Brünken et al. 2009b; Beard & Dailey 1950; Kewley et al. 1963). The resultant molecular constants were acceptably close to experimental values with B₀ and C₀ deviations of −0.6% for NCSH and −0.3% for HNCS. These errors, slightly larger than in our previous studies, stem primarily from C–S bond lengths. The isomers H₂NCS⁺ and HNCSH⁺ are prolate symmetric tops. Of importance to microwave spectroscopy, all of these molecules bear substantial equilibrium electric dipole moments (Table 2), similar to NCSH or HNCS.

Electronic energy values for diverse chemical species possibly involved in the creation of H₂NCS⁺ or of its isomers are listed in Table 3 (calculations on several [N, C, S] triatomics, including NCS, NCS⁻, and NCS⁺, were already carried out by Fitzgerald & Bowie 2004 at a theory level lower than that applied here).

Table 3. Theoretical (UCCSD(T)/cc-pVTZ) Energies (Hartree) for Molecules Relevant to the Synthesis of CH₂NS⁺ Isomers

Molecules	State	E
NCS+	a1Σ	−489.944732
NCS+	X3Π	−489.982554
NCS	X2Σ	−490.368970
HNCS+	X2Π	−490.648683
NCSH+	X2A''	−490.600933
HNCS	X1A'	−491.006385
NCSH	X1A'	−490.996757
CS	X1Σ	−435.668390
CS+	X2Σ	−435.274742
CSH+	X1A'	−435.878239
HCS+	X1Σ	−435.991341
SH	X2Π	−398.280950
SH+	a1Π	−397.850392
SH+	X3Σ	−397.906742
$\mathrm{SH_2^{+}}$	X2B1	−435.991342
SH2	X1A'	−398.895543
HNC	X1Σ	−93.235892
HNC+	X2Σ	−92.797605
H2NC	X2B2	−93.748824
H	X2S1/2	−0.499810
H2	X1Σg	−1.162290
$\mathrm{H_3^{+}}$	X1A'	−1.321137
H2NCS+	X1A1	−491.302137
HNCSH+	X1A'	−491.288083
HNSCH+	X1A	−491.116465
H2NCSH+	X2A1	−491.842936
H2NC(H)S+	X2A	−491.881119
H2NSCH+	X2A	−491.787160
H3NCSH+	X1A'	−492.418957
H3NC(H)S+	X1A'	−492.490735
NH	X3Σ	−55.133245
NH2	X2B1	−55.774534
$\mathrm{NH_2^{+}}$	X3B1	−55.371741
$\mathrm{NH_3^{+}}$	X2A'	−56.072518
NH3	X1A'	−56.438679
NH4	X2A1	−56.917631
$\mathrm{NH_4^{+}}$	X1A1	−56.765475

Note. Values corrected for the zero-point vibrational energy.

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Chemical pathways toward H₂NCS⁺ and HNCSH⁺, involving NCS⁺ cations, have been proposed (Adande et al. 2010; see the Introduction). Our present study indicates the reaction between NCS⁺ and H₂, barrierless and exothermic, as a highly probable source of interstellar HNCS⁺, but not of the more (by 125 kJ mol⁻¹) energetic isomer NCSH⁺. The next step postulated by Adande et al. (2010) was expected to yield H₂NCS⁺ or HNCSH⁺ via HNCS⁺ colliding with H₂. Our calculations, however, indicate endothermicity of as much as 23.7 kJ mol⁻¹ (2900 K) and 60.6 kJ mol⁻¹ (7300 K) for the respective H₂NCS⁺ and HNCSH⁺ branches. These processes do not therefore seem to be of importance within the cold interstellar clouds.

As pointed out by Milligan et al. (2002), proton transfer from highly energetic species, e.g., $\mathrm{H_3^{+}}$ or H₃O⁺, may efficiently produce bonding between hydrogen and a heavy atom. This process, involving the ubiquitous $\mathrm{H_3^{+}}$ cation, has in fact been postulated for the creation of S–H bonds (Prasad & Huntress 1982). Indeed, according to our prediction, not only HNCS⁺ (a species of no direct interest to H₂NCS⁺ or HNCSH⁺ synthesis, as discussed above) can be produced that way from neutral NCS molecules:

$\mathrm{NCS + H_3^{+} \rightarrow HNCS^{+} + H_2}$ + 362 kJ mol⁻¹,

but also the HSCN⁺ cation:

$\mathrm{NCS + H_3^{+} \rightarrow HSCN^{+} + H_2}$ + 244 kJ mol⁻¹,

since both reactions are exothermic and (at the CCSD/aug-cc-pVDZ level of theory) barrierless. The route to HNCSH⁺, making use of HSCN⁺,

NCSH⁺ + H₂ → HNCSH⁺ + H + 65 kJ mol⁻¹,

is also exothermic, but requires activation energy (36 kJ mol⁻¹ or 4300 K), which makes it improbable for the cold interstellar medium.

On the other hand, another set of exothermic and barrierless reactions,

$\mathrm{HNCS \,{+}\, H_3^{+} \!\rightarrow\! HNCSH^{+} }$/H₂NCS⁺  +  H₂ + 323/359 kJ mol⁻¹

$\mathrm{NCSH + H_3^{+} \rightarrow HNCSH^{+} + H_2}$ + 348 kJ mol⁻¹,

seems to be an important factor shaping the balance between HNCS isomers and H₂NCS⁺ isomers (keeping in mind that the latter are the source of the former via dissociative recombination).

As an alternative to the reactions involving NCS or NCS⁺, it is of interest to consider whether the N–C–S backbone of the H₂NCS⁺ or HNCSH⁺ cations could be assembled either via the collision of an N-containing reactant with a CS-containing one, or from colliding S- and NC-containing reactants. In this context, investigating the reactivity of the HCS⁺ and CSH⁺ cations seems to be promising. These can be regarded as analogous to HCO⁺ and COH⁺ (the interstellar abundance of HCO⁺ is higher by two orders of magnitude than that of COH⁺ (Fuente et al. 2003; Apponi & Ziurys 1997).

HCS⁺ was detected in Sgr B2 and in Ori A (Thaddeus et al. 1981) in several translucent molecular clouds (Turner 1996), and also beyond the Galaxy (Muller et al. 2013). CSH⁺ has not as yet been discovered in space. For the HCS⁺ and CSH⁺ cations, generally much less studied than the HCO⁺/COH⁺ pair, the theoretical analysis of PESs has been reported (Bruna 1978; Puzzarini 2005). HCS⁺ is linear, unlike CSH⁺, with the latter being significantly bent and less stable than the former by 302 kJ mol⁻¹. The CSH⁺ → HCS⁺ isomerization barrier amounts to 5.4 kJ mol⁻¹ (Puzzarini 2005).

CSH⁺ and HCS⁺ may arise in collisions between relatively abundant $\mathrm{H_3^{+}}$ and CS species,

$\mathrm{CS + H_3^{+} \rightarrow HCS^{+}}$ / CSH⁺ + H₂ + 78/375 kJ mol⁻¹,

in a process analogous to that proposed by Le et al. (2010) for HCO⁺/COH⁺ synthesis. Our calculations indicate that both HCS⁺ and CSH⁺ can thus be formed without a barrier. The CCSD/cc-pVTZ-derived polarizability (3.5 ų) and the experimental value of the electric dipole moment, 1.958 D, as measured by Winnewisser & Cook (1968), were used to predict the reaction rate constants. According to Harrison (2006) and our present CCSD/cc-pVTZ calculations, the carbon atom of CS bears a fractional negative charge, pointing to HCS⁺ as the main reaction product (which is also predicted by the modeling described in Section 3.2.3).

Next, we analyze the possible elongation of HCS⁺ or CSH⁺ chains with a nitrogen atom. To the best of our knowledge, reactions involving any of these cations and nitrogen hydrides, NH_n, have not been studied. We have carried out CCs calculations for n equal from one to three, as all three hydrids have quite similar abundances in the interstellar medium (Persson et al. 2010).

According to our predictions, CSH⁺ + NH_n reactions lead without barriers to intermediate products of the general formula H_nNCSH⁺. Once formed, the latter bear excess energy (726, 540, 268 kJ mol⁻¹, for n equal 1, 2, and 3, respectively), which they cannot easily get rid of—the radiative relaxation is slow, and collision-induced energy exchange processes can be neglected. The fate of this cation is determined by energetically available unimolecular rearrangements that eventually result in its disintegration, accompanied by the transformation of chemical energy into kinetic energy. The resultant products are diverse; we focus here on the formation of doubly hydrogenated NCS cationic chains.

The synthesis of HNCSH⁺ through the association of CSH⁺ and NH is formally possible, requiring no activation energy and being exothermic. This is not, however, an efficient pathway toward HNCSH⁺, since the newly formed, energy-rich cation is a short-lived intermediate species, prone to spontaneous dissociation in processes that occur at the singlet PES:

CSH⁺ + NH → [HNCSH⁺] → HNCS⁺ + H + 360 kJ mol⁻¹

                                             → NCSH⁺ + H + 234 kJ mol⁻¹

                                             → HNC + SH⁺ + 344 kJ mol⁻¹.

More promising are the reactions involving NH₂ and CSH⁺ (Figure 2). The intermediate product H₂NCSH⁺ may serve as an efficient precursor for CH₂NS⁺ isomers (Figure 2). The following processes are possible even within cold interstellar regions, requiring no external energy:

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$\mathrm{CSH^{+} \,{+}\, NH_2 \!\rightarrow\! [H_2NCSH^{+}] \rightarrow H_2NCS^{+} \,{+}\, H}$ + 392 kJ mol⁻¹

                                                  → HNCSH⁺ + H + 355 kJ mol⁻¹.

One can expect H₂NCS⁺ and HNCSH⁺ to be the most important products. Competing paths would include

CSH⁺ + NH₂ → [H₂NCSH⁺] → H₂NC + SH⁺ + 7 kJ mol⁻¹.

Finally, CSH⁺ may react with NH₃, creating a variety of products (see Figure 3); only the processes directly relevant to the synthesis of HNCSH⁺ or H₂NCS⁺ are discussed here. The involved activation barriers can be crossed for

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CSH⁺ + NH₃ → [H₃NCSH⁺] → HNCSH⁺ + H₂ + 350 kJ mol⁻¹

                                                → H₂NCS⁺ + H₂ + 387 kJ mol⁻¹.

We note that H₂NCSH⁺ can also be formed:

CSH⁺ + NH₃ → [H₃NCSH⁺] → H₂NCSH⁺ + H + 68 kJ mol⁻¹.

The dissociative recombination of the latter triply hydrogenated species can presumably be regarded as an additional source of HNCS and NCSH. In what follows, we have not, however, included that possibility.

Important reactions competing with the formation of H₂NCS⁺ or HNCSH⁺ involve proton transfer processes leading from CSH⁺ to HCS⁺:

CSH⁺ + NH₂ → [H₂NCSH⁺] → HCS⁺ + NH₂ + 297 kJ mol⁻¹

CSH⁺ + NH₃ → [H₃NCSH⁺] → [H₃NC(H)S⁺] → HCS⁺ + NH₃ + 297 kJ mol⁻¹.

As mentioned above, the HCS⁺ cation is more stable by far than CSH⁺, which makes it much less reactive. Collisions involving HCS⁺ and NH_n may produce, for n = 1, the HNSCH⁺ cation, which quickly breaks apart. The other expected short-lived products are

• 1.  
  for n = 2: H₂NSCH⁺(with excess energy of 56 kJ mol⁻¹) and H₂NC(H)S⁺ (excess energy 303 kJ mol⁻¹);
• 2.  
  for n = 3: H₃NC(H)S⁺ (excess energy 159 kJ mol⁻¹),

of which, as illustrated by Figures 2 and 3, only the H₂NC(H)S⁺ cation possesses enough excess energy to follow the paths toward the hydrogen abstraction products HNCSH⁺ and H₂NCS⁺:

HCS⁺ + NH₂  →  [H₂NC(H)S⁺]  →  [H₂NCSH⁺]  →  HNCSH⁺ + H + 58 kJ mol⁻¹,

or to direct dissociation:

HCS⁺  +  NH₂ → [H₂NC(H)S⁺] → H₂NCS⁺  +  H + 95 kJ mol⁻¹.

Note that our analysis did not reveal any minimum corresponding to the H₃NSCH⁺ cation (which could be viewed as a direct product of the HCS⁺ + NH₃ reaction). Exothermic processes,

HCS⁺ + NH₃ → HNCSH⁺ + H₂ + 53 kJ mol⁻¹

                      → H₂NCS⁺ + H₂ + 90 kJ mol⁻¹,

(shown in Figure 3) are not interesting in the discussed astrochemical context, as both require an external input of energy for the creation of intermediate products.

Important processes competing with the formation of H₂NCS⁺ or HNCSH⁺, and occurring neither via bound, intermediate products nor with any other energetic barriers, involve proton transfers from CSH⁺ or HCS⁺ to NH_n:

$\mathrm{CSH^{+} + NH \rightarrow NH_2^{+} + CS}$ + 99 kJ mol⁻¹,

$\mathrm{CSH^{+} + NH_2 \rightarrow NH_3^{+} + CS}$ + 231 kJ mol⁻¹,

$\mathrm{CSH^{+} + NH_3 \rightarrow NH_4^{+} + CS}$ + 307 kJ mol⁻¹,

$\mathrm{HCS^{+} + NH_3 \rightarrow NH_4^{+} + CS}$ + 10 kJ mol⁻¹.

Next, it is of interest to discuss an a priori possible synthetic route toward H₂NCS⁺ or HNCSH⁺, occurring via a molecule possessing an –NC (isocyano) group, which would collide with a sulfur-containing reaction partner. The present study indicates that HNC and $\mathrm{SH_2^{+}}$ do not react with each other, forming only a weak intermolecular complex, with a C–S distance of about 2.5 Å. The creation, out of that complex, of a cationic [C, H, H, N, S] isomer would require some external energy (the same is true for the reaction of HCN with $\mathrm{SH_2^{+}}$). An analogous reaction of HNC⁺ and SH₂ is less predisposed to theoretical treatment. The intermolecular complex formed by these reactants represents in fact an electronically excited state of the above-mentioned $\mathrm{HNC\ldots SH_2^{+}}$ system, and therefore its investigation necessitates an analysis of the corresponding excited state PES. Preliminary TD-B3LYP/aug-cc-pVDZ calculations indicate that the reaction involves a barrierless channel leading to HNCSH⁺, but no path toward H₂NCS⁺ is predicted to exist. This result has to be verified with high-level ab initio calculations.

The search for interstellar H₂NCS⁺ and/or HNCSH⁺ seems to be an important observational task; we have therefore calculated the basic molecular parameters relevant to the radio astronomical detection of these cations and have also tried to estimate their abundance. The chemical model employed here makes use of the KIDA database and the Nahoon code (Wakelam et al. 2012; see Section 2.3). The kida.uva.2011 network comprises 783 reactions of 44 sulfur-bearing species, but it is obviously not complete, just as any astrochemical database, and, importantly, it does not include any molecules simultaneously containing carbon, sulfur, and nitrogen. In tandem with Nahoon, KIDA proved to make satisfactory abundance predictions for some 79% of the molecules detected in TMC-1 (Wakelam et al. 2010). The best agreement between available observations and modeling has been found for the times 4.7 × 10⁵ to 6.3 × 10⁵ yr. KIDA is not successful, however, in modeling the abundance of HCS⁺ (a crucial precursor in the proposed synthetic pathway toward H₂NCS⁺ and HNCSH⁺). The abundance sets LM and HM (see Section 2.3) lead to the respective HCS⁺ abundances of 2 × 10⁻¹² and 9 × 10⁻¹², relative to H₂, while the value observed for TMC-1 is as high as 6 × 10⁻¹⁰ (Irvine et al. 1987).

We have assumed the dissociative recombination of HNCSH⁺ and H₂NCS⁺ with electrons to be the most important decay mechanism for these cations. Such reactions have been computationally studied by Gronowski & Kołos (2012). The modeling presented here makes use of these previous findings and of our new theoretical results concerning the rearrangement of neutral H₂NCS species. We have appended the database with 48 reactions (Table 4) and 7 additional molecules. The ionization of HNCS and NCSH by atomic cations has been included (note that HNCS cannot be ionized by S⁺, in contrast to NCSH).

Table 4. Gas-phase Reactions Related to the Synthesis and Destruction of HNCSH⁺ and H₂NCS⁺

Substrates		Products		α	β	γ
NH	CSH+	H	HNCS+	0.579E00	0.779E-09	0.480E+01
NH	CSH+	H	NCSH+	0.185E-01	0.779E-09	0.480E+01
NH	CSH+	HNC	HS+	0.402E+00	0.779E-09	0.480E+01
NH	CSH+	$\mathrm{NH_2^{+}}$	CS	0.189E-04	0.779E-09	0.480E+01
NH2	CSH+	H	H2NCS+	0.839E+00	0.899E-09	0.469E+01
NH2	CSH+	H	HNCSH+	0.154E-00	0.899E-09	0.469E+01
NH2	CSH+	$\mathrm{NH_3^{+}}$	CS	0.136E-02	0.899E-09	0.469E+01
NH2	CSH+	HCS+	NH2	0.625E-02	0.899E-09	0.469E+01
NH3	CSH+	H2	H2NCS+	0.342E+00	0.951E-09	0.377E+01
NH3	CSH+	H2	HNCSH+	0.960E-06	0.951E-09	0.377E+01
NH3	CSH+	$\mathrm{NH_4^{+}}$	CS	0.570E+00	0.951E-09	0.377E+01
NH3	CSH+	HCS+	NH3	0.879E-01	0.951E-09	0.377E+01
NH2	HCS+	H	H2NCS+	0.504E-00	0.899E-09	0.469E+01
NH2	HCS+	H	HNCSH+	0.183E-02	0.899E-09	0.469E+01
NH2	HCS+	H	H2NCS+	0.484E-00	0.899E-09	0.469E+01
NH3	HCS+	$\mathrm{NH_4^{+}}$	CS	1.000E+00	0.951E-09	0.377E+01
HNCSH+	e −	HNC	HS	0.526E-07	0.500E-01	0.000E+00
HNCSH+	e −	HNCS	H	0.195E-07	0.500E-01	0.000E+00
HNCSH+	e −	NCSH	H	0.194E-07	0.500E-01	0.000E+00
HNCSH+	e −	H2NC	S	0.709E-10	0.500E-01	0.000E+00
HNCSH+	e −	CS	NH2	0.161E-09	0.500E-01	0.000E+00
H2NCS+	e −	HNCS	H	0.718E-07	0.500E-01	0.000E+00
H2NCS+	e −	H2NC	S	0.844E-09	0.500E-01	0.000E+00
H2NCS+	e −	CS	NH2	0.192E-08	0.500E-01	0.000E+00
H2NCS+	e −	HNC	HS	0.155E-07	0.500E-01	0.000E+00
H2NCS+	e −	NCSH	H	0.100E-07	0.500E-01	0.000E+00
H3O+	CS	H2O	CSH+	0.315E-07	0.134E-08	0.334E+01
CS	HCO+	CO	CSH+	0.300E-07	1.160e-09	3.280e+00
$\mathrm{H_3^{+}}$	CS	H2	CSH+	0.350E-01	0.285E-08	0.334E+01
H2S	C+	H	CSH+	0.262E+00	0.151E-08	0.184E+01
HNCS	C+	HNCS+	C	0.100E+01	0.185E-08	0.292E+01
HNCS	F+	HNCS+	F	0.100E+01	0.154E-08	0.292E+01
HNCS	H3O+	HNCSH+	H2O	0.100E+01	0.154E-08	0.292E+01
HNCS	H3O+	H2NCS+	H2O	0.100E+01	0.154E-08	0.292E+01
HNCS	$\mathrm{H_3^{+}}$	HNCSH+	H2	0.100E+01	0.347E-08	0.292E+01
HNCS	$\mathrm{H_3^{+}}$	H2NCS+	H2	0.100E+01	0.347E-08	0.292E+01
HNCS	He+	HNCS+	He	0.100E+01	0.303E-08	0.292E+01
HNCS	H+	HNCS+	H	0.100E+01	0.591E-08	0.292E+01
HNCS	N2H+	HNCSH+	N2	0.100E+01	0.133E-08	0.292E+01
HNCS	N2H+	H2NCS+	N2	0.100E+01	0.133E-08	0.292E+01
HNCS	P+	HNCS+	P	0.100E+01	0.130E-08	0.292E+01
HNCS	S+	HNCS+	S	0.100E+01	0.129E-08	0.292E+01
NCSH	C+	NCSH+	C	0.100E+01	0.171E-08	0.517E+01
NCSH	F+	NCSH+	F	0.100E+01	0.143E-08	0.517E+01
NCSH	H3O+	HNCSH+	H2O	0.100E+01	0.143E-08	0.517E+01
NCSH	$\mathrm{H_3^{+}}$	HNCSH+	H2	0.100E+01	0.320E-08	0.517E+01
NCSH	He+	NCSH+	He	0.100E+01	0.280E-08	0.517E+01
NCSH	H+	NCSH+	H	0.100E+01	0.546E-08	0.517E+01
NCSH	N2H+	HNCSH+	N2	0.100E+01	0.123E-08	0.517E+01

Note. Dissociative recombination reaction rate constants in units of cm³ s⁻¹ can be calculated from tabulated coefficients according to α × (T/300)^β × exp (− γ/T) while ion–neutral reaction rate constants can be calculated using α × β × (0.62 + 0.4767 × γ × (300/T)^0.5).

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To investigate the importance of inaccuracies in the applied reaction rate constants, we randomly varied the k_i values for newly added reactions. Consequently, 220 chemical models, differing by their k_i sets, have been created. The rate constants used in the models came from log (k_i) values given by log-normal distributions, with the maxima defined by the logarithms of theoretically predicted k_i's (see Section 2) and with the half-widths arbitrarily set to log (5). This implies a standard deviation of approximately log(2) in any log (k_i) distribution; formally, then, with a probability of ca. 70%, the k_i's are expected to be known within a factor of two. A similar level of accuracy has, for example, been found by Pu & Truhlar (2002) using the transition state theory approach to the CH₄ + H reaction. As expected, the predicted abundances of H₂NCS⁺, HNCSH⁺, HNCS, and NCSH (Figure 4) were significantly dependent on the employed set of rate constants.

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The relative abundance of NCSH (see Figure 4) is for the HM set of elemental composition higher than for LM (Figures 4(a) and (b)). In any case, the observed value of 6 × 10⁻¹² (Adande et al. 2010) was, for t = 5 × 10⁵ yr, within the specified inaccuracy range; the same applies to the comparison of the predicted (Figures 4(c) and (d)) HNCS/NCSH ratio to that measured in TMC-1: 1.4 ± 0.7 (Adande et al. 2010). The latter value was best reproduced with the HM abundance set.

The most important result of the chemical modeling presented here concerns the cationic species HNCSH⁺ and H₂NCS⁺. The rapid increase of their abundance is predicted to occur for times from 1000 to 2000 yr; the abundance then continues to grow until approximately 2 × 10⁵ yr, reaches a plateau, and slightly decreases for times longer than 5 × 10⁵ yr. The modeled H₂NCS⁺ abundance is one order of magnitude higher than that of HNCSH⁺ (see Figure 4). The H₂NCS⁺/NCSH ratio (unlike HNCSH⁺/NCSH) significantly varies with time, which is consistent with the scheme that predicts H₂NCS⁺ to be the earliest synthesized NCS-containing molecule. For t = 5 × 10⁵ yr, H₂NCS⁺/NCSH falls between 1 (for the LM elemental abundance set) and 0.02 (HM). The low relative abundance of H₂NCS⁺ for a HM (i.e., high-sulfur) content set originates mainly from the corresponding high abundance of NCSH.

Based on the LM model and on the calculated electric dipole moment values (Section 3.1.2), the total intensity of rotational lines coming from H₂NCS⁺ is expected to be of the same order of magnitude as that due to NCSH.

The influence of the newly introduced 48 sulfur-related reactions on the time evolution of molecular abundances—apart from NCS-bearing species—deserves comment. The effect was not, generally, notable with the LM set. In particular, the molecules NS, HCS⁺, S₂, $\mathrm{S_2^{+}}$, and H₂S have not been affected. An important exception concerns the SH radical, the simplest sulfur-containing molecule. Neither SH nor SH⁺ have as of yet been detected in any cold interstellar region. Recently, however, SH was observed in absorption toward a submillimeter continuum source W49N (Neufeld et al. 2012), and SH⁺ toward Sgr B2 (Menten et al. 2011). Neutral SH is one of the main products of the HNCSH⁺ dissociative recombination, which increases the abundance of this diatomic compared to what was indicated with the original kida.uva.2011 reaction set. Our estimated SH/H₂S and SH⁺/H₂S values are about 0.1 (see Figure 5), which is close to the SH/H₂S ratio of 0.13 measured for W49N and rather far from a lower limit of approximately 2 established for SH⁺/H₂S in Sgr B2 observations. Each of these two regions, however, is characterized by qualitatively different physical conditions than TMC-1.

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On the other hand, the effect of added reactions was widely seen with the HM elemental abundance set. An example is offered by HC_{2n + 1}N molecules, for which the abundance was altered at t = 5 × 10⁵ yr by −4%, −10%, and −16% for n = 0, 1, and 2, respectively—or by the elements of the NH_n series, where the analogous abundance changes are predicted as +2%, −5%, and −16%, for n = 1, 2, and 3.