New Insight into the Formation of Nitrogen Sulfide: A Quantum

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J. Phys. Chem. A 2010, 114, 509–515

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New Insight into the Formation of Nitrogen Sulfide: A Quantum Chemical Study Priscila S. S. Pereira,† Luiz G. M. Macedo,‡ and Andre´ S. Pimentel*,† Departamento de Quı´mica, Pontifı´cia UniVersidade Cato´lica do Rio de Janeiro, Rua Marqueˆs de Sa˜o Vicente 225, Ga´Vea, 22453-900 Rio de Janeiro, RJ Brazil, and Departamento de Biotecnologia, Pre´dio do ICB, UniVersidade Federal do Para´, Rua Augusto Correa 1, 66075-110 Bele´m, PA, Brazil ReceiVed: July 31, 2009; ReVised Manuscript ReceiVed: NoVember 23, 2009

We studied the chemical mechanism for the formation of 2NS in the interstellar medium was by using the CCSD/6-311++G(d,p) and CCSD(T)/6-311++G(3df,3pd) levels of theory. To the best of our knowledge, this is the first detailed study of the chemical mechanism for the formation of 2NS. Several reactions proposed in this article are spin-forbidden. They were treated with the Landau-Zener theory and by the MRCI methodology. The following reactions paths proposed in this article are energetically favorable: (1) 1NH + 2 SH f cis-2HNSH f TS1 f trans-2HNSH f TS2 f 2H2NS f TS3 f 2NS + H2 and (2) 4N + 1SH f 1 NSH f TS13 f 1HNS f 2NS + 2H. However, the latter reaction, 4N + 1SH f 1NSH, is spin-forbidden, and its probability of occuring (psh) is zero. The chemical mechanism for the formation of 2NS in the interstellar medium is now presented in more detail, which is of great importance. I. Introduction Nitrogen sulfide (NS) is a diatomic radical isovalent with nitrogen oxide (NO). Sulfur-bearing molecules such as NS are presented under a wide variety of interstellar conditions such as in dense interstellar clouds in regions of massive star formation.1 NS was first identified in the giant molecular cloud by Gottlieb et al. in 1975.2 They detected the presence of NS toward the giant molecular cloud SGR B2 and estimated its column density to be 1014 cm-2. Other Sulfur-bearing gases were detected in SGR B2, such as, SO, CS, H2S, OCS, and CH2S, but just the NS and SO would be comparable in abundance. NS was also detected in the dark clouds TMC-1 and L134N.3 The column densities for the TMC-1 and L134N were estimated to be (∼8 and ∼3) × 1012 cm-2, respectively. In 2000, Irvine et al. reported the first NS detection in the coma of Comet HaleBopp and found its production rate to be at least a few hundredths of a percent compared with that of water and a total column density of 6.8 × 1012 cm-2.4 The gas-phase reaction in dense clouds, SH + N f NS + H, was proposed by Duley et al. in 1980.5 Canaves et al.6 modeled the NS abundance using the chemical mechanism proposed by Duley et al. in 1980,5 which is at least 103 smaller than that found by Irvine et al.4 Canaves et al.6 used a model of cometary comae to predict molecular abundances in the inner coma region for two of the brightest comets in the past 20 years. In this article, it found that the main process to form the NS radical is electron dissociative recombination of the HNS+ ion: HNS+ + e- f NS + H, whereas another reaction to form NS is the neutral rearrangement, HS + N f NS + H, as proposed by Duley et al.5 Because these chemical reactions do not explain the NS abundance in cometary comae, it is very important to propose new sources of NS to reconcile the NS abundance in astronomical regions. The aim of this work is to demonstrate the formation of NS in the NHx and SHy systems (x ) 0-3 and y ) 0-2). This article reports ab initio quantum chemical calculations to * Corresponding author. E-mail: [email protected]. † Pontifı´cia Universidade Cato´lica do Rio de Janeiro. ‡ Universidade Federal do Para´.

compute the geometries, frequencies, and energies for H2S, SH, NH3, NH2, NH, H3NS, H2NS, HNS, and NS species. The reaction paths and TS structures for the elementary reactions involved in the conversion of such species are also discussed here. The chemical mechanisms described in this manuscript would require that the corresponding NHx and SHy fragments are present in nonzero concentration and that the process should have no barrier above the energy of the starting fragments for cold regions (T < 200 K). Otherwise, the abstraction reactions may also take place in hot regions. II. Methodology Stationary points on the potential energy surface of the reaction system were fully optimized, followed by evaluation of harmonic vibration frequencies to characterize their nature as minima or first-order saddle points. The coupled cluster with single and double excitations (CCSD)7 was used to calculate the optimized structures, frequencies and intrinsic reaction coordinates (IRCs) using the 6-311++G(d,p) basis sets. The stabilities of these Hartree-Fock (HF) wave functions were tested with respect to relaxing various constraints, allowing a restrict HF determinant to become unrestricted, allowing orbitals to become complex, and reducing the symmetry of the orbitals. If some instability is found, then the wave function is reoptimized with the appropriated reduction in constraints, repeating stability tests, and reoptimization until a stable wave function is found. Then, the stable wave function is used in the subsequent calculations. The criteria used for wave function stability is to check if the resulting determinant is a local minimum with the specified degrees of freedom taken into consideration. Single-point energies for reactants, products, and TSs were calculated using the coupled cluster with single and double and perturbative triple excitations, CCSD(T), with the 6-311++G(3df,3pd) basis sets. The TS was verified by subsequent frequency calculations, which allowed us to determine the imaginary vibrational frequencies related to the reaction path. The IRC was calculated to follow the reaction path of the reaction and reassure that the transition structure is really a saddle point of the reaction path. The electronic structure

10.1021/jp907384d  2010 American Chemical Society Published on Web 12/11/2009

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calculations were carried out with the Gaussian03 quantum chemistry codes, unless otherwise stated.8 Several reactions proposed in this article involve a change in spin state and are called spin-forbidden. To occur, this system is required to leap from the potential energy surface corresponding to the initial spin state onto that to the product state of the reaction. This kind of system has been dealt with the Landau-Zener theory,9,10 which calculates the probability (PLZ) for hopping from one adiabatic surface to another during a single pass through the crossing region. The PLZ is defined as

(

PLZ(E) ) exp

-π2H212 h∆F



µ 2(E - EMECP)

)

where H12 is the spin-orbit coupling-derived off-diagonal Hamiltonian matrix element between the two electronic states, ∆F is the relative slope of the two surface at the crossing seam between the two electronic states, µ is the reduced mass of the system, E is the kinetic energy of the system, and EMECP is the relative energy of the minimum energy crossing point (MECP) between potential energy surfaces corresponding to the different spin states. The probability of hopping from one diabatic state to the other on the first pass through the crossing region is (1 - PLZ). The probability of hopping during a potential double pass is (1 - PLZ) plus the probability of not hopping on the first pass, then hopping on the second pass, PLZ(1 - PLZ). The probability of hopping (ph) is then

ph(E) ) (1 - PLZ(E))(1 + PLZ(E)) The spin-orbit coupling-derived off-diagonal Hamiltonian matrix element between the two electronic states, H12,11 for each spin-forbidden reaction was calculated using the multireference configuration interaction (MRCI)12,13 methodology using ccpVTZ14,15 basis sets. The MRCI calculations were carried out with the internally contracted MRCI method of Werner and Knowles12,13 implemented in the MOLPRO2008 suite of programs.16 III. Results and Discussion The geometry and frequency calculations were performed using the CCSD/6-311++G(d,p) method and the single-point energies were calculated using the CCSD(T)/6-311++G(3df,3pd) method. The single-point energies at the CCSD(T)/6-311++ G(3df,3pd) and CCSD/6-311++G(d,p) levels of theory reported at the CCSD/6-311++G(d,p) optimized geometries for each reactant, product, and transition state studied in this article are presented in the Supporting Information. Figure 1 shows the optimized structures for reactants and products. Table 1 presents the calculated N-S bond lengths and the literature values16,17 for the species trans-1H2NSH, cis1 H2NSH, 1HNSH2, 1NSH3, 1H3NS, 2H2NS, cis-2HNSH, trans2 HNSH, 2NSH2, 1HNS, 3HNS, and 2NS. The theoretical bond lengths found in this study are in good agreement with the literature values. The complete discussion about the comparison of our calculated bond lengths and literature data is also shown in the Supporting Information. Table 2 presents the vibrational frequencies for the chemical species shown in Figure 1. Energetic and Reaction Paths. In the following discussion, the formation of NS is presented through several reaction paths, which is illustrated by different possible mechanisms, as found in Figures 2-5. Some reaction pathways are energetically favorable. It is important to note that H atom abstraction reactions were not proposed here. Because of their energy barriers, this kind of reaction is unlikely to be important under

Figure 1. Optimized structures for the species cis-1H2NSH, trans1 H2NSH, 1HNSH2, 1NSH3, 2H2NS, 1H3NS, cis-2HNSH, trans-2HNSH, 2 NSH2, 1NH3, 2NH2, 1H2S, 1HNS, 3HNS, 1NSH, 3NSH, 2SH, 1NH, 3NH, and 2NS. The sulfur, hydrogen, and nitrogen atoms are represented by black, white, and gray balls, respectively.

TABLE 1: N-S Bond Length, in Angstroms, of the Species trans-1H2NSH, cis-1H2NSH, 1HNSH2, 1NSH3, 1H3NS, 2H2NS, cis-2HNSH, trans-2HNSH, 2NSH2, 1HNS, 3HNS, and 2NS Calculated Using the CCSD Level of Theory and the Basis Sets 6-311++G(d,p) species

d N-S (Å)

1

trans- H2NSH cis-1H2NSH 1 HNSH2 1 NSH3 1 H3NS 2 H2NS cis-2HNSH trans-2HNSH 2 NSH2 1 HNS 3 HNS 1 NSH 3 NSH 2 NS

literature 17

1.719 1.73218 1.7119 1.5919 1.4719 1.88920 1.639,21 1.64122 1.62922 1.63922 1.56722 1.58023 1.55323 1.51323 1.66023 1.494,25 1.5021,25 1.50126

1.729 1.714 1.591 1.469 1.86 1.644 1.653 1.661 1.574 1.578 1.562 1.509 1.671 1.506

TABLE 2: Vibrational Frequencies, in cm-1, of the cis-1H2NSH, trans-1H2NSH, 1HNSH2, 1NSH3, 1H3NS, 2H2NS, cis-2HNSH, trans-2HNSH, 2NSH2, 1NH3, 2NH2, 1H2S, 1HNS, 3 HNS, 1NSH, 3NSH, 2SH, 1NH, 3NH, and 2NS Species Calculated Using the CCSD/6-311++G(d,p) Method species

ν1

ν2

ν3

ν4

ν5

ν6

ν7

ν8

ν9

cis-1H2NSH trans-1H2NSH 1 HNSH2 1 NSH3 1 H3NS 2 H2NS cis-2HNSH trans-2HNSH 2 NSH2 1 NH3 2 NH2 1 H2S 2 HNS 3 HNS 1 NSH 3 NSH 2 SH 1 NH 3 NH 2 NS

531 439 644 810 589 189 467 633 801 1087 1527 1237 1067 786 1053 767 2736 3283 3283 1256

660 685 888 810 866 951 791 813 822 1675 3390 2765 1226 1087 1172 895

885 898 891 1215 866 1059 972 983 928 1675 3484 2782 3378 3589 2206 2684

1059 1075 969 1215 1430 1652 1178 1249 1342 3514

1137 1146 1208 1240 1624 3610 2651 2737 2386 3648

1645 1659 1335 1449 1624 3730 3496 3462 2441 3648

2665 2739 2410 2177 3489

3573 3571 2449 2177 3584

3673 3662 3509 2349 3584

cold conditions found in interstellar medium. The transition state structures found in this study are presented in Figure 6, and their imaginary frequencies are shown in Table 3. The imaginary

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Figure 2. Energetic diagram (in kilojoules per mole) of the reactions 1NH + 2SH, 3S + NH2, and 4N + 1H2S for the formation of 2NS. The total energy of cis-2HNSH is set to zero. The relative energies shown are single-point energies at the CCSD(T)/6-311++G(3df,3pd) level of theory after optimization using the CCSD/6-311++G(d,p) method. The dashed line represents a spin-forbidden reaction.

Figure 3. Energetic diagram (in kilojoules per mole) of the reactions 2NH2 + 2SH and 3S + 1NH3 for the formation of 1NSH and 1HNS. The energy of the cis-1H2NSH molecule is set to zero. The relative energies shown are single-point energies at the CCSD(T)/6-311++G(3df,3pd) level of theory after optimization using the CCSD/6-311++G(d,p) method. The dashed line represents a spin-forbidden reaction.

frequencies of transition states in this system confirm them as a saddle point in the potential energy surfaces for the reactions investigated in this study. The intrinsic coordinated calculation for each reaction also confirmed them as transition states. Table 4 presents the energy barriers for the reactions studied in this work. Several reactions presented in this study involve a change of spin. These reactions are spin-forbidden. They may occur on more than one potential energy surfaces. The system is required to leap from the potential energy surface corresponding to the initial spin state onto that corresponding to the product state for reaction to happen.9 The relative energies, in kilojoules per mole, of the spin states of each species are presented in Table 1S in the Supporting Information. By calculating the relative energies of the spin states of each species, it is possible to verify that the most stable species are 2NH2, 1H2S, 1NH, 1NH3, 2SH,

3

S, 4N, 1HNS, and 1NSH. As will be seen later, the reactions N + 1H2S f 2NSH2, 3S + 1NH3 f 1H3NS, and 4N + 2SH f 1 NSH are spin-forbidden. Figure 7 show scans performed by single-point calculations on the potential energy surfaces to obtain the MECP of the spin-forbidden reactions. Table 5 presents the N-S bond length of the transient species on the MECP, the MECP energies of them, and the relative slope (∆F) of the two surfaces at the crossing seam, which are required for the calculation of the Landau-Zener probability (PLZ) for the hopping between the two surfaces. The H12 spin-orbit coupling for these spin-forbidden reactions was calculated using the MRCI/cc-pVTZ method. Table 6 presents the H12 spin-orbit coupling for each reaction. Using the H12 matrix element, the probability of hopping for each spin-forbidden reaction is calculated. Because the tunneling effects may be negligible for the species in this study, the probability, ph, was calculated as 4

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Figure 4. Energetic diagram (in kilojoules per mole) of the reaction 1NH + 1H2S for the formation of 1NSH and 1HNS. The energy of cis-1HNSH2 is set to zero. The relative energies shown are single-point energies at the CCSD(T)/6-311++G(3df,3pd) level of theory after optimization using the CCSD/6-311++G(d,p) method.

Figure 5. Energetic diagram (in kilojoules per mole) of the reaction 4N + 2SH for the formation of 2NS via H atom elimination from 1HNS molecule. The energy of 1NSH is set to zero. The relative energies shown are single-point energies at the CCSD(T)/6-311++G(3df,3pd) level of theory after optimization using the CCSD/6-311++G(d,p) method. The dashed line represents a spin-forbidden reaction.

a function of an energy, E, greater than the MECP energy. Then, the ph was averaged because it is much more dependent on H12 than E. The averaged probability, ph, is also presented in Table 6. The values for probabilities indicate that the hopping between the two surfaces for these species is unlikely. Therefore, it is unlikely that these spin-forbidden reactions happen under normal conditions. Figure 2 shows three reaction paths for the formation of the 2 NS radical starting from the reactions 1NH + 2SH, 3S + 2NH2, and 4N + 1H2S, respectively. The reaction 1NH + 2SH may form the cis-2HNSH radical through a barrierless association reaction, with an energy of -481 kJ mol-1 that is distributed in the normal modes of the cis-2HNSH radical. Similarly, the reaction 1NH + 2SH may also form the trans-2HNSH radical by an energy well of -490 kJ mol-1. The trans isomer is more stable than the cis isomer. The same result is also found for the cis-HNOH and trans-HNOH isomers by Jalbout and Sawaya.27

The cis-2HNSH radical may isomerize to form the trans-2HNSH species through the transition state TS1 with a barrier of 80 kJ mol-1. In the study performed by Jalbout and Sawaya,27 the barrier for the cis-trans HNOH isomerization was estimated to be 23 kJ mol-1 using the CQS-Q and B1LYP/6-311++G (3df, 3pd) levels of theory and ∼33 kJ mol-1 for the MP2/631G(d′) method.27 Kurosaki and Takayanagi28 estimated that this reaction barrier is 32 kJ mol-1 at the PMP4(full, SDTQ)/ cc-pVTZ//MP2(full)/cc-pVTZ+ZPE level. Therefore, the barrier for the cis-trans HNSH isomerization is higher than that for the HNOH system. The trans-2HNSH radical has about the same stored energy as that for the cis isomer. It may use this energy to form the 2H2NS radical by an H-shift isomerization. This reaction has a transition state TS2 with an energy barrier of 176 kJ mol-1. The energy barrier for the H-shift isomerization in the trans-HNOH was calculated to be 182 kJ mol-1 by Kurosaki and Takayanagi.28 Therefore, the energy barriers for

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Figure 6. Optimized structures for the transition states. The sulfur, hydrogen, and nitrogen atoms are represented by black, white, and gray balls, respectively.

TABLE 3: Imaginary Frequencies, ν in cm-1, of the Transition States (TS) Calculated by Using the CCSD/ 6-311++G(d,p) Method TS

ν (cm-1)

TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9 TS10 TS11 TS12 TS13

1548i 1981i 1958i 1461i 1473i 433i 1470i 1317i 1441i 1636i 1773i 676i 1960i

TABLE 4: Energy Barriers, in kilojoules per mole, for the Reactions Studied in This Study Calculated by Using the CCSD(T)/6-311++G(3df,3pd) Method reactions

energy (kJ mol-1)

cis-2HNSH f TS1 f trans-2HNSH trans-2HNSH f TS2 f 2H2NS 2 H2NS f TS3 f 2NS + H2 2 NSH2 f TS4 f 2NS + H2 cis-1H2NSH f TS5 f 1HNSH2 cis-1H2NSH f TS6 f trans-1H2NSH 1 HNSH2 f TS7 f 1NSH3 1 NSH3 f TS8 f 1NSH + H2 1 HNSH2 f TS9 f 1HNS + H2 trans-1H2NSH f TS10 f 1NSH + H2 1 H3NS f TS11 f trans-1H2NSH trans-1HNSH2 f TS12 f cis-1HNSH2 1 NSH f TS13 f 1HNS

80 176 356 123 327 29 438 162 150 397 126 42 187

Figure 7. Minimum energy crossing point (MECP) for reactions (a) 4 N + H2S f 2NSH2, (b) 3S + 1NH3 f 1H3NS, and (c) 4N + 2SH f 1 NSH.

TABLE 5: N-S Bond Length (dMECP) of the Species on the Minimum Energy Crossing Point (MECP), the MECP Energy (EMECP), and the Relative Slope of the Two Surfaces at the Crossing Seam (∆F) for the Spin-Forbidden Reactions chemical reactions

dMECP (Å)

EMECP (a.u.)

∆F (J m-1)

N + H2S f 2NSH2 S + 1NH3 f 1H3NS 4 N + 2SH f 1NSH

2.07 2.39 1.58

-453.37287544 -454.10047669 -452.86142337

1.12 × 10-8 5.52 × 10-9 9.40 × 10-9

4

3

the H-shift isomerization in both trans-HNOH and trans-HNSH species are similar. Finally, the 2H2NS radical may eliminate an H2 molecule to form the 2NS radical through the transition state TS3 with an energy barrier of 356 kJ mol-1. Kurosaki and Takayanagi28 estimated the H2 elimination in the H2NO species and found a similar energy barrier of 376 kJ mol-1. Another reaction related to the formation of 2H2NS is the reaction 3S + 2NH2, which has an energy well of -323 kJ mol-1, as shown in Figure 2. Walch29 calculated an energy well of -334 kJ mol-1 for the similar reaction O + NH2 f H2NO using the CASSCF/cc-VTZ methodology. The reaction 4N + 1H2S may yield the 2NSH2 radical, which is located in an energy well of -33 kJ mol-1. Then, 2NS may be formed through an H2-

elimination from the 2NSH2 radical, which has only -33 kJ mol-1 of stored energy in its normal modes. This H2-elimination reaction has a transition state TS4 with an energy barrier of 123 kJ mol-1. Therefore, the H2-elimination from the 2NSH2 radical is energetically unfavorable. As presented previously, the reaction 4N + 1H2S is a spin-forbidden reaction to form the 2 NSH2 radical. This reaction would be allowed if it leads to the 4 NSH2 species. Otherwise, the singlet H2S molecule needs to react with 2N atoms for the formation of 2NSH2. A simple examination of the proposed reactions above shows that the 2NS radical is unlikely to be formed through the

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TABLE 6: Spin-Orbit Coupling (H12) and the Probability of Hopping (ph) Using the MRCI/cc-pVTZ Level of Methodologiesa MRCI/cc-pVTZ species

active space (N,M)

H12 (cm-1)

ph

(13,10) (14,11) (12,9)

4.3 207 1.9

2.53 × 10-6 1.64 × 10-2 1.65 × 10-6

2

NSH2 H3NS 1 NSH 1

a Active space is represented by the number of electrons (N) and the number of orbitals (M).

reactions 4N + 1H2S and 3S + 2NH2. This is because the stored energies in the normal modes of the 2NSH2 and 2H2NS radicals are not high enough for overcoming the energy barriers of the transition states TS4 and TS3, respectively. The reaction 1NH + 2SH leads to the formation of 2NS. In accordance with Figure 2, the energetically favorable reaction path is as follows 1

NH + 2SH f cis-2HNSH f TSI f trans-2HNSH f TS2 f 2H2NS f TS3 f 2NS + H2 ∆E ) -389 kJ mol-1

Figure 3 presents several routes to the formation of 1NSH and 1HNS molecules from the reactions 2NH2 + 2SH and 3S + 1 NH3. The 2NH2 radical may react with 2SH radical through an association reaction to form cis-1H2NSH and trans-1H2NSH, with an energy well of about -283 kJ mol-1. The similar reaction NH2 + OH to form the H2NOH molecule was suggested by Wang et al.30 The energy well for this reaction is about -280 kJ mol-1, which is in agreement with our results. From the cis1 H2NSH molecule, there are two possible routes: (1) through the transition state TS5, with an energy barrier of 327 kJ mol-1, and (2) through the transition state TS6, with an energy barrier of 29 kJ mol-1. When the cis-1H2NSH molecule has the energy to overcome the barrier of the transition state TS5, the H-shift isomerization occurs to form 1HNSH2. Then, this molecule may produce 1NSH3 through an H-shift isomerization. This reaction has an energy barrier of 438 kJ mol-1, passing by the transition state, TS7. Finally, 1NSH3 may eliminate H2 to form 1NSH through the transition state TS8, which has an energy barrier of 162 kJ mol-1. 1HNSH2 may also eliminate H2 to yield the 1 HNS species if 1HNSH2 has enough energy to overcome the barrier of 150 kJ mol-1 through the transition state TS9. If the cis-1H2NSH molecule isomerizes to its trans isomer through the transition state TS6, then the trans isomer may eliminate H2 to form the 1NSH species by the transition state TS10. The energy barrier for this reaction is 397 kJ mol-1. The energy barrier for the H2NOH decomposition leading to NOH + H2 species is 401 kJ mol-1, as calculated by Wang.30 Figure 3 also presents the formation of 1NSH by the reaction 3 S + 1NH3. 1H3NS may be produced from the reaction 3S + 1 NH3, which has an energy well of -103 kJ mol-1. However,

this is a spin-forbidden reaction, as previously shown. The reaction 3S + 1NH3 would be allowed if it leads to 3H3NS. Otherwise, 1NH3 needs to react with the singlet 1S species for the formation of 1H3NS. 1H3NS may isomerize through an H-shift to trans-1H2NSH by passing the transition state TS11 with an energy barrier of 126 kJ mol-1. Then, through the transition state TS12, trans-1H2NSH may form 1NSH by an H2elimination reaction. According to Figure 3, the formation of 1 NSH and 1HNS does not occur by the presented reaction paths under normal conditions. The necessary energies to form the transition states are superior to the released energies in the first stage of the reactions; therefore, these particular reactions are energetically unfavorable. In fact, it is important to note that any reaction path presented in Figure 3 is energetically favorable. Figure 4 also shows the formation of 1NSH and 1HNS. These species may be formed from the association reaction 1NH + 1 H2S. First, 1HNSH2 may be formed by this reaction, which has an energy well of -297 kJ mol-1. Then, trans-1HNSH2 may isomerize through the transition state TS12 with the energy barrier of 42 kJ mol-1 to produce cis-1HNSH2 by an H-shift reaction. This species may isomerize to three different species 1 NSH3, cis-1H2NSH, and 1HNS, passing through the transition states TS7, TS5, and TS9, respectively. The energy barriers for these reactions are 438, 327, and 150 kJ mol-1, respectively. On the formation of 1NSH3, 1NSH may be formed from the H2-elimination through the transition state TS8, which has an energy barrier of 162 kJ mol-1. If the reaction occurs through the transition state TS5, then the cis-1H2NSH molecule would be formed and then isomerized to the trans-1H2NSH isomer by an H-shift reaction through the transition state TS6. Then, trans1 H2NSH may form 1NSH through the transition state TS10 by eliminating H2. Also, 1HNS may be formed through the transition state TS9. Figure 4 shows that the transition states TS5 and TS7 have high energy barriers. The reactions related to these transition states are unlikely to occur under normal conditions. Nevertheless, the sequence reaction below is likely to occur under the same conditions. 1

NH + 1H2S f trans-1HNSH2 f TS12 f cis-1HNSH2 f TS9 f 1HNS + H2 ∆E ) -272 kJ mol-1

Figure 5 shows the formation of 2NS from the reaction 4N + SH. 1NSH may be produced by the association reaction 4N + 2 SH, which has an energy well of -275 kJ mol-1. As previously presented, this is a spin-forbidden reaction. The reaction 4N + 2 SH would be allowed if it leads to 3NSH. Otherwise, 2SH needs to react with the doublet 2N species for the formation of 1NSH. 1 NSH may isomerize to 1HNS by an H-shift reaction, which is more stable. This reaction has an energy barrier of 187 kJ mol-1 to overcome the transition state TS13. 1HNS may undergo H-atom elimination to form 2NS, which has an energy barrier of 281 kJ mol-1. It is important to note that the 1NH + 1H2S reaction presented in the previous paragraph becomes unfavor2

TABLE 7: Variations of Energy, ∆E, and Enthalpy, ∆H, in kilojoules per mole for the Chemical Reactions ∆E (kJ mol-1)

∆H (kJ mol-1)

2

-386 -152

-154 -119

N + 1H2S f 2NS + H2 NH2 + 2SH f 2NS + 2H + H2 3 S + 1NH3 f 2NS + 2H + H2 1 NH + 1H2S f 2NS + 2H + H2 4 N + 2SHf 2NS + 2H

-145 205 319 9 -85

-383 202 302 202 -319

reactions 1 3

4 2

NH + SH f NS + H2 S + 2NH2 f 2NS + H2 2

comment energetically energetically TS3 is high energetically energetically energetically energetically energetically

favorable favorable, but the energy barrier for transition state favorable but spin-forbidden unfavorable unfavorable and spin-forbidden unfavorable favorable but spin-forbidden

New Insight into the Formation of Nitrogen Sulfide able energetically because of the high energy barrier found in the H-atom elimination of the 1HNS species.

N + 2SH f 1NSH f TS12 f 1HNS f 2NS + 2H ∆E ) -85 kJ mol-1

4

Table 7 summarizes the chemical reactions that are investigated in this study for the formation of 2NS. The variations of energy, ∆E, and enthalpy, ∆H, in kilojoules per mole, are also presented in Table 7. Unfortunately, there are no thermodynamic and kinetic data for these chemical reactions in the literature. It is important to note that the reaction 1NH + 2SH is the only energetically favorable and spin-allowed reaction. By comparison with the PHx-SHy and PHx-NHx systems,31-32 reactions 1 PH + 1SH and 3PH + 3NH are also energetically favorable, which is in agreement with this study. IV. Conclusions The CCSD(T)/6-311++G(3df,3pd) methodology applied in this study was successful to investigate the formation of 2NS from different reaction paths. In terms of energy, the most favorable reactions for the formation of 2NS are: reactions 1NH + 2SH (Figure 2) and 4N + 2SH (Figure 5). However, the reaction 4N + 2SH f 1NSH is spin-forbidden, and its probability of occuring is estimated to be zero. The reactions 4N + 1H2S, 2 NH2 + 2SH, 3S + 1NH3, and 1NH + 1H2S are not energetically favorable. This is the first detailed study of the chemical mechanism for the formation of 2NS, which is of great importance for understanding the chemistry of 2NS in the interstellar medium. Acknowledgment. We are grateful to the CNPq funding (no. 485364/2007-7) and the Dean’s office of the Scientific and Technology Center, Pontificia Universidade Cato´lica at Rio de Janeiro, which provided the computational capability for this research. P.S.S.P. also thanks CAPES for a research studentship. L.G.M.M. thanks FAPESP for financial support (no. 54976-5). We thank Dr. Jeremy N. Harvey, who provided the computational code for finding the minimum energy crossing point (MECP) between potential energy surfaces corresponding to the different spin states. Supporting Information Available: Single-point energies at the CCSD(T)/6-311++G(3df,3pd) and CCSD/6-311++G(d,p) levels of theory reported at the existing optimized geometries Z-matrix for each reactant, product, and transition state studied in the article. The geometries were optimized at the CCSD/6311++G(d,p) level of theory and presented here. Also, the complete discussion about the comparison of our calculated bond lengths and literature data is shown. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) McGonagle, D., Irvine, W. M., Minh, Y. C. In Astrochemistry of Cosmic Phenomena, Proceedings of the 150th Symposium of the International Astronomical Union, Campos do Jorda˜o, Sa˜o Paulo, Brazil, Aug 59, 1991; Kluwer Academic Publishers: Boston, 1992; p 227.

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