New Insight into the Formation of Nitrogen Sulfide: A Quantum Chemical Study

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 Quımica, Pontifıcia UniVersidade Catolica do Rio de Janeiro, Rua Marques de Sao Vicente225, GaVea, 22453-900 Rio de Janeiro, RJ Brazil, and Departamento de Biotecnologia, Predio do ICB,UniVersidade Federal do Para, Rua Augusto Correa 1, 66075-110 Belem, 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 theCCSD/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 proposedin this article are spin-forbidden. They were treated with the Landau-Zener theory and by the MRCImethodology. The following reactions paths proposed in this article are energetically favorable: (1) 1NH +2SH f cis-2HNSH f TS1 f trans-2HNSH f TS2 f 2H2NS f TS3 f 2NS + H2 and (2) 4N + 1SH f1NSH 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 interstellarmedium is now presented in more detail, which is of great importance.

I. IntroductionNitrogen sulfide (NS) is a diatomic radical isovalent with

nitrogen oxide (NO). Sulfur-bearing molecules such as NS arepresented under a wide variety of interstellar conditions suchas in dense interstellar clouds in regions of massive starformation.1 NS was first identified in the giant molecular cloudby Gottlieb et al. in 1975.2 They detected the presence of NStoward the giant molecular cloud SGR B2 and estimated itscolumn density to be 1014 cm-2. Other Sulfur-bearing gases weredetected 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 estimatedto be (∼8 and ∼3) × 1012 cm-2, respectively. In 2000, Irvineet al. reported the first NS detection in the coma of Comet Hale-Bopp and found its production rate to be at least a fewhundredths of a percent compared with that of water and a totalcolumn 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 mechanismproposed by Duley et al. in 1980,5 which is at least 103 smallerthan that found by Irvine et al.4 Canaves et al.6 used a model ofcometary comae to predict molecular abundances in the innercoma region for two of the brightest comets in the past 20 years.In this article, it found that the main process to form the NSradical is electron dissociative recombination of the HNS+ ion:HNS+ + e- f NS + H, whereas another reaction to form NSis the neutral rearrangement, HS + N f NS + H, as proposedby Duley et al.5 Because these chemical reactions do not explainthe NS abundance in cometary comae, it is very important topropose new sources of NS to reconcile the NS abundance inastronomical regions.

The aim of this work is to demonstrate the formation of NSin the NHx and SHy systems (x ) 0-3 and y ) 0-2). Thisarticle reports ab initio quantum chemical calculations to

compute the geometries, frequencies, and energies for H2S, SH,NH3, NH2, NH, H3NS, H2NS, HNS, and NS species. Thereaction paths and TS structures for the elementary reactionsinvolved in the conversion of such species are also discussedhere. The chemical mechanisms described in this manuscriptwould require that the corresponding NHx and SHy fragmentsare present in nonzero concentration and that the process shouldhave no barrier above the energy of the starting fragments forcold regions (T < 200 K). Otherwise, the abstraction reactionsmay also take place in hot regions.

II. Methodology

Stationary points on the potential energy surface of thereaction system were fully optimized, followed by evaluationof harmonic vibration frequencies to characterize their natureas minima or first-order saddle points. The coupled cluster withsingle and double excitations (CCSD)7 was used to calculatethe optimized structures, frequencies and intrinsic reactioncoordinates (IRCs) using the 6-311++G(d,p) basis sets. Thestabilities of these Hartree-Fock (HF) wave functions weretested with respect to relaxing various constraints, allowing arestrict HF determinant to become unrestricted, allowing orbitalsto become complex, and reducing the symmetry of the orbitals.If some instability is found, then the wave function is reopti-mized with the appropriated reduction in constraints, repeatingstability tests, and reoptimization until a stable wave functionis found. Then, the stable wave function is used in thesubsequent calculations. The criteria used for wave functionstability is to check if the resulting determinant is a localminimum with the specified degrees of freedom taken intoconsideration. Single-point energies for reactants, products, andTSs were calculated using the coupled cluster with single anddouble and perturbative triple excitations, CCSD(T), with the6-311++G(3df,3pd) basis sets. The TS was verified by subse-quent frequency calculations, which allowed us to determinethe imaginary vibrational frequencies related to the reaction path.The IRC was calculated to follow the reaction path of thereaction and reassure that the transition structure is really asaddle point of the reaction path. The electronic structure

* Corresponding author. E-mail: [email protected].† Pontifıcia Universidade Catolica do Rio de Janeiro.‡ Universidade Federal do Para.

J. Phys. Chem. A 2010, 114, 509–515 509

10.1021/jp907384d 2010 American Chemical SocietyPublished on Web 12/11/2009

calculations were carried out with the Gaussian03 quantumchemistry codes, unless otherwise stated.8

Several reactions proposed in this article involve a changein spin state and are called spin-forbidden. To occur, this systemis required to leap from the potential energy surface corre-sponding to the initial spin state onto that to the product stateof the reaction. This kind of system has been dealt with theLandau-Zener theory,9,10 which calculates the probability (PLZ)for hopping from one adiabatic surface to another during a singlepass through the crossing region. The PLZ is defined as

PLZ(E) ) exp(-π2H122

h∆F � µ2(E - EMECP))

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

ph(E) ) (1 - PLZ(E))(1 + PLZ(E))

The spin-orbit coupling-derived off-diagonal Hamiltonianmatrix element between the two electronic states, H12,11 for eachspin-forbidden reaction was calculated using the multireferenceconfiguration interaction (MRCI)12,13 methodology using cc-pVTZ14,15 basis sets. The MRCI calculations were carried outwith the internally contracted MRCI method of Werner andKnowles12,13 implemented in the MOLPRO2008 suite of pro-grams.16

III. Results and Discussion

The geometry and frequency calculations were performedusing the CCSD/6-311++G(d,p) method and the single-pointenergies 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 reportedat the CCSD/6-311++G(d,p) optimized geometries for eachreactant, product, and transition state studied in this article arepresented in the Supporting Information.

Figure 1 shows the optimized structures for reactants andproducts. Table 1 presents the calculated N-S bond lengthsand the literature values16,17 for the species trans-1H2NSH, cis-1H2NSH, 1HNSH2, 1NSH3, 1H3NS, 2H2NS, cis-2HNSH, trans-2HNSH, 2NSH2, 1HNS, 3HNS, and 2NS. The theoretical bondlengths found in this study are in good agreement with theliterature values. The complete discussion about the comparisonof our calculated bond lengths and literature data is also shownin the Supporting Information. Table 2 presents the vibrationalfrequencies 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 foundin Figures 2-5. Some reaction pathways are energeticallyfavorable. It is important to note that H atom abstractionreactions were not proposed here. Because of their energybarriers, this kind of reaction is unlikely to be important under

cold conditions found in interstellar medium. The transition statestructures found in this study are presented in Figure 6, andtheir imaginary frequencies are shown in Table 3. The imaginary

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

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

species d N-S (Å) literature

trans-1H2NSH 1.729 1.71917 1.73218

cis-1H2NSH 1.714 1.7119

1HNSH2 1.591 1.5919

1NSH3 1.469 1.4719

1H3NS 1.86 1.88920

2H2NS 1.644 1.639,21 1.64122

cis-2HNSH 1.653 1.62922

trans-2HNSH 1.661 1.63922

2NSH2 1.574 1.56722

1HNS 1.578 1.58023

3HNS 1.562 1.55323

1NSH 1.509 1.51323

3NSH 1.671 1.66023

2NS 1.506 1.494,25 1.5021,25 1.50126

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

species ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9

cis-1H2NSH 531 660 885 1059 1137 1645 2665 3573 3673trans-1H2NSH 439 685 898 1075 1146 1659 2739 3571 36621HNSH2 644 888 891 969 1208 1335 2410 2449 35091NSH3 810 810 1215 1215 1240 1449 2177 2177 23491H3NS 589 866 866 1430 1624 1624 3489 3584 35842H2NS 189 951 1059 1652 3610 3730cis-2HNSH 467 791 972 1178 2651 3496trans-2HNSH 633 813 983 1249 2737 34622NSH2 801 822 928 1342 2386 24411NH3 1087 1675 1675 3514 3648 36482NH2 1527 3390 34841H2S 1237 2765 27822HNS 1067 1226 33783HNS 786 1087 35891NSH 1053 1172 22063NSH 767 895 26842SH 27361NH 32833NH 32832NS 1256

510 J. Phys. Chem. A, Vol. 114, No. 1, 2010 Pereira et al.

frequencies of transition states in this system confirm them asa saddle point in the potential energy surfaces for the reactionsinvestigated in this study. The intrinsic coordinated calculationfor each reaction also confirmed them as transition states. Table4 presents the energy barriers for the reactions studied in thiswork.

Several reactions presented in this study involve a change ofspin. These reactions are spin-forbidden. They may occur onmore than one potential energy surfaces. The system is requiredto leap from the potential energy surface corresponding to theinitial spin state onto that corresponding to the product statefor reaction to happen.9 The relative energies, in kilojoules permole, of the spin states of each species are presented in Table1S in the Supporting Information. By calculating the relativeenergies of the spin states of each species, it is possible to verifythat the most stable species are 2NH2, 1H2S, 1NH, 1NH3, 2SH,

3S, 4N, 1HNS, and 1NSH. As will be seen later, the reactions4N + 1H2S f 2NSH2, 3S + 1NH3 f

1H3NS, and 4N + 2SH f1NSH are spin-forbidden. Figure 7 show scans performed bysingle-point calculations on the potential energy surfaces toobtain the MECP of the spin-forbidden reactions. Table 5presents the N-S bond length of the transient species on theMECP, the MECP energies of them, and the relative slope (∆F)of the two surfaces at the crossing seam, which are requiredfor the calculation of the Landau-Zener probability (PLZ) forthe hopping between the two surfaces. The H12 spin-orbitcoupling for these spin-forbidden reactions was calculated usingthe MRCI/cc-pVTZ method. Table 6 presents the H12 spin-orbitcoupling for each reaction. Using the H12 matrix element, theprobability of hopping for each spin-forbidden reaction iscalculated. Because the tunneling effects may be negligible forthe species in this study, the probability, ph, was calculated as

Figure 2. Energetic diagram (in kilojoules per mole) of the reactions 1NH + 2SH, 3S + NH2, and 4N + 1H2S for the formation of 2NS. The totalenergy 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 afteroptimization 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. Theenergy 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) levelof theory after optimization using the CCSD/6-311++G(d,p) method. The dashed line represents a spin-forbidden reaction.

New Insight into the Formation of Nitrogen Sulfide J. Phys. Chem. A, Vol. 114, No. 1, 2010 511

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 Table6. The values for probabilities indicate that the hopping betweenthe two surfaces for these species is unlikely. Therefore, it isunlikely that these spin-forbidden reactions happen under normalconditions.

Figure 2 shows three reaction paths for the formation of the2NS radical starting from the reactions 1NH + 2SH, 3S + 2NH2,and 4N + 1H2S, respectively. The reaction 1NH + 2SH mayform the cis-2HNSH radical through a barrierless associationreaction, with an energy of -481 kJ mol-1 that is distributedin the normal modes of the cis-2HNSH radical. Similarly, thereaction 1NH + 2SH may also form the trans-2HNSH radicalby an energy well of -490 kJ mol-1. The trans isomer is morestable than the cis isomer. The same result is also found for thecis-HNOH and trans-HNOH isomers by Jalbout and Sawaya.27

The cis-2HNSH radical may isomerize to form the trans-2HNSHspecies through the transition state TS1 with a barrier of 80 kJmol-1. In the study performed by Jalbout and Sawaya,27 thebarrier for the cis-trans HNOH isomerization was estimatedto 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 MP2/6-31G(d′) method.27 Kurosaki and Takayanagi28 estimated thatthis reaction barrier is 32 kJ mol-1 at the PMP4(full, SDTQ)/cc-pVTZ//MP2(full)/cc-pVTZ+ZPE level. Therefore, the barrierfor the cis-trans HNSH isomerization is higher than that forthe HNOH system. The trans-2HNSH radical has about the samestored energy as that for the cis isomer. It may use this energyto form the 2H2NS radical by an H-shift isomerization. Thisreaction has a transition state TS2 with an energy barrier of176 kJ mol-1. The energy barrier for the H-shift isomerizationin the trans-HNOH was calculated to be 182 kJ mol-1 byKurosaki and Takayanagi.28 Therefore, the energy barriers for

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 usingthe 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 1HNSmolecule. 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 oftheory after optimization using the CCSD/6-311++G(d,p) method. The dashed line represents a spin-forbidden reaction.


the H-shift isomerization in both trans-HNOH and trans-HNSHspecies are similar. Finally, the 2H2NS radical may eliminatean H2 molecule to form the 2NS radical through the transitionstate TS3 with an energy barrier of 356 kJ mol-1. Kurosakiand Takayanagi28 estimated the H2 elimination in the H2NOspecies and found a similar energy barrier of 376 kJ mol-1.

Another reaction related to the formation of 2H2NS is thereaction 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 + NH2f H2NO usingthe CASSCF/cc-VTZ methodology. The reaction 4N + 1H2Smay yield the 2NSH2 radical, which is located in an energy wellof -33 kJ mol-1. Then, 2NS may be formed through an H2-

elimination from the 2NSH2 radical, which has only -33 kJmol-1 of stored energy in its normal modes. This H2-eliminationreaction has a transition state TS4 with an energy barrier of123 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 the2NSH2 radical. This reaction would be allowed if it leads to the4NSH2 species. Otherwise, the singlet H2S molecule needs toreact with 2N atoms for the formation of 2NSH2.

A simple examination of the proposed reactions above showsthat the 2NS radical is unlikely to be formed through the

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

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

TS ν (cm-1)

TS1 1548iTS2 1981iTS3 1958iTS4 1461iTS5 1473iTS6 433iTS7 1470iTS8 1317iTS9 1441iTS10 1636iTS11 1773iTS12 676iTS13 1960i

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

reactions energy (kJ mol-1)

cis-2HNSH f TS1 f trans-2HNSH 80trans-2HNSH f TS2 f 2H2NS 1762H2NS f TS3 f 2NS + H2 3562NSH2 f TS4 f 2NS + H2 123cis-1H2NSH f TS5 f 1HNSH2 327cis-1H2NSH f TS6 f trans-1H2NSH 291HNSH2 f TS7 f 1NSH3 4381NSH3 f TS8 f 1NSH + H2 1621HNSH2 f TS9 f 1HNS + H2 150trans-1H2NSH f TS10 f 1NSH + H2 3971H3NS f TS11 f trans-1H2NSH 126trans-1HNSH2 f TS12 f cis-1HNSH2 421NSH f TS13 f 1HNS 187

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

1H3NS, and (c) 4N + 2SH f1NSH.

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

chemical reactions dMECP (Å) EMECP (a.u.) ∆F (J m-1)4N + H2S f 2NSH2 2.07 -453.37287544 1.12 × 10-8

3S + 1NH3 f1H3NS 2.39 -454.10047669 5.52 × 10-9

4N + 2SH f 1NSH 1.58 -452.86142337 9.40 × 10-9


reactions 4N + 1H2S and 3S + 2NH2. This is because the storedenergies in the normal modes of the 2NSH2 and 2H2NS radicalsare not high enough for overcoming the energy barriers of thetransition states TS4 and TS3, respectively. The reaction 1NH+ 2SH leads to the formation of 2NS. In accordance with Figure2, the energetically favorable reaction path is as follows

1NH + 2SH f cis-2HNSH f TSI f trans-2HNSH fTS2 f 2H2NS f TS3 f 2NS + H2

∆E ) -389 kJ mol-1

Figure 3 presents several routes to the formation of 1NSHand 1HNS molecules from the reactions 2NH2 + 2SH and 3S +1NH3. The 2NH2 radical may react with 2SH radical through anassociation reaction to form cis-1H2NSH and trans-1H2NSH,with an energy well of about -283 kJ mol-1. The similarreaction NH2 + OH to form the H2NOH molecule was suggestedby Wang et al.30 The energy well for this reaction is about -280kJ mol-1, which is in agreement with our results. From the cis-1H2NSH molecule, there are two possible routes: (1) throughthe transition state TS5, with an energy barrier of 327 kJ mol-1,and (2) through the transition state TS6, with an energy barrierof 29 kJ mol-1. When the cis-1H2NSH molecule has the energyto overcome the barrier of the transition state TS5, the H-shiftisomerization occurs to form 1HNSH2. Then, this molecule mayproduce 1NSH3 through an H-shift isomerization. This reactionhas an energy barrier of 438 kJ mol-1, passing by the transitionstate, TS7. Finally, 1NSH3 may eliminate H2 to form 1NSHthrough the transition state TS8, which has an energy barrierof 162 kJ mol-1. 1HNSH2 may also eliminate H2 to yield the1HNS species if 1HNSH2 has enough energy to overcome thebarrier of 150 kJ mol-1 through the transition state TS9. Ifthe cis-1H2NSH molecule isomerizes to its trans isomer throughthe transition state TS6, then the trans isomer may eliminateH2 to form the 1NSH species by the transition state TS10. Theenergy barrier for this reaction is 397 kJ mol-1. The energybarrier 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 reaction3S + 1NH3. 1H3NS may be produced from the reaction 3S +1NH3, which has an energy well of -103 kJ mol-1. However,

this is a spin-forbidden reaction, as previously shown. Thereaction 3S + 1NH3 would be allowed if it leads to 3H3NS.Otherwise, 1NH3 needs to react with the singlet 1S species forthe formation of 1H3NS. 1H3NS may isomerize through anH-shift to trans-1H2NSH by passing the transition state TS11with an energy barrier of 126 kJ mol-1. Then, through thetransition state TS12, trans-1H2NSH may form 1NSH by an H2-elimination reaction. According to Figure 3, the formation of1NSH and 1HNS does not occur by the presented reaction pathsunder normal conditions. The necessary energies to form thetransition states are superior to the released energies in the firststage of the reactions; therefore, these particular reactions areenergetically unfavorable. In fact, it is important to note thatany reaction path presented in Figure 3 is energetically favorable.

Figure 4 also shows the formation of 1NSH and 1HNS. Thesespecies may be formed from the association reaction 1NH +1H2S. First, 1HNSH2 may be formed by this reaction, whichhas an energy well of -297 kJ mol-1. Then, trans-1HNSH2 mayisomerize through the transition state TS12 with the energybarrier of 42 kJ mol-1 to produce cis-1HNSH2 by an H-shiftreaction. This species may isomerize to three different species1NSH3, cis-1H2NSH, and 1HNS, passing through the transitionstates TS7, TS5, and TS9, respectively. The energy barriers forthese reactions are 438, 327, and 150 kJ mol-1, respectively.On the formation of 1NSH3, 1NSH may be formed from theH2-elimination through the transition state TS8, which has anenergy barrier of 162 kJ mol-1. If the reaction occurs throughthe transition state TS5, then the cis-1H2NSH molecule wouldbe formed and then isomerized to the trans-1H2NSH isomer byan H-shift reaction through the transition state TS6. Then, trans-1H2NSH may form 1NSH through the transition state TS10 byeliminating H2. Also, 1HNS may be formed through thetransition state TS9. Figure 4 shows that the transition statesTS5 and TS7 have high energy barriers. The reactions relatedto these transition states are unlikely to occur under normalconditions. Nevertheless, the sequence reaction below is likelyto occur under the same conditions.

1NH + 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 +2SH. 1NSH may be produced by the association reaction 4N +2SH, which has an energy well of -275 kJ mol-1. As previouslypresented, this is a spin-forbidden reaction. The reaction 4N +2SH would be allowed if it leads to 3NSH. Otherwise, 2SH needsto react with the doublet 2N species for the formation of 1NSH.1NSH may isomerize to 1HNS by an H-shift reaction, which ismore stable. This reaction has an energy barrier of 187 kJ mol-1

to overcome the transition state TS13. 1HNS may undergoH-atom elimination to form 2NS, which has an energy barrierof 281 kJ mol-1. It is important to note that the 1NH + 1H2Sreaction presented in the previous paragraph becomes unfavor-

TABLE 6: Spin-Orbit Coupling (H12) and the Probability ofHopping (ph) Using the MRCI/cc-pVTZ Level ofMethodologiesa

species

MRCI/cc-pVTZ

active space(N,M) H12 (cm-1) ph

2NSH2 (13,10) 4.3 2.53 × 10-6

1H3NS (14,11) 207 1.64 × 10-2

1NSH (12,9) 1.9 1.65 × 10-6

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

TABLE 7: Variations of Energy, ∆E, and Enthalpy, ∆H, in kilojoules per mole for the Chemical Reactions

reactions ∆E (kJ mol-1) ∆H (kJ mol-1) comment1NH + 2SH f 2NS + H2 -386 -154 energetically favorable3S + 2NH2 f

2NS + H2 -152 -119 energetically favorable, but the energy barrier for transition stateTS3 is high

4N + 1H2S f 2NS + H2 -145 -383 energetically favorable but spin-forbidden2NH2 + 2SH f 2NS + 2H + H2 205 202 energetically unfavorable3S + 1NH3 f

2NS + 2H + H2 319 302 energetically unfavorable and spin-forbidden1NH + 1H2S f 2NS + 2H + H2 9 202 energetically unfavorable4N + 2SHf 2NS + 2H -85 -319 energetically favorable but spin-forbidden


able energetically because of the high energy barrier found inthe H-atom elimination of the 1HNS species.

4N + 2SH f 1NSH f TS12 f 1HNS f 2NS + 2H∆E ) -85 kJ mol-1

Table 7 summarizes the chemical reactions that are investi-gated in this study for the formation of 2NS. The variations ofenergy, ∆E, and enthalpy, ∆H, in kilojoules per mole, are alsopresented in Table 7. Unfortunately, there are no thermodynamicand kinetic data for these chemical reactions in the literature. Itis important to note that the reaction 1NH + 2SH is the onlyenergetically favorable and spin-allowed reaction. By compari-son with the PHx-SHy and PHx-NHx systems,31-32 reactions1PH + 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 inthis study was successful to investigate the formation of 2NSfrom different reaction paths. In terms of energy, the mostfavorable reactions for the formation of 2NS are: reactions 1NH+ 2SH (Figure 2) and 4N + 2SH (Figure 5). However, thereaction 4N + 2SHf 1NSH is spin-forbidden, and its probabilityof occuring is estimated to be zero. The reactions 4N + 1H2S,2NH2 + 2SH, 3S + 1NH3, and 1NH + 1H2S are not energeticallyfavorable. This is the first detailed study of the chemicalmechanism for the formation of 2NS, which is of greatimportance for understanding the chemistry of 2NS in theinterstellar medium.

Acknowledgment. We are grateful to the CNPq funding (no.485364/2007-7) and the Dean’s office of the Scientific andTechnology Center, Pontificia Universidade Catolica at Rio deJaneiro, which provided the computational capability for thisresearch. 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 computa-tional code for finding the minimum energy crossing point(MECP) between potential energy surfaces corresponding to thedifferent spin states.

Supporting Information Available: Single-point energiesat the CCSD(T)/6-311++G(3df,3pd) and CCSD/6-311++G(d,p)levels of theory reported at the existing optimized geometriesZ-matrix for each reactant, product, and transition state studiedin the article. The geometries were optimized at the CCSD/6-311++G(d,p) level of theory and presented here. Also, thecomplete discussion about the comparison of our calculated bondlengths and literature data is shown. This material is availablefree of charge via the Internet at http://pubs.acs.org.

References and Notes

(1) McGonagle, D., Irvine, W. M., Minh, Y. C. In Astrochemistry ofCosmic Phenomena, Proceedings of the 150th Symposium of the Interna-tional Astronomical Union, Campos do Jordao, Sao Paulo, Brazil, Aug 5-9, 1991; Kluwer Academic Publishers: Boston, 1992; p 227.

(2) Gottlieb, C. A.; Ball, J. A.; Gottlieb, E. W.; Lada, C. J.; Penfield,H. Astrophys. J. 1975, 200, 147.

(3) McGonagle, D.; Irvine, W. M.; Ohishi, M. Astrophys. J. 1994, 422,621.

(4) Irving, W. M.; Senay, M.; Lovell, A. J.; Matthews, H. E.;McGonagle, D.; Meier, R. Icarus 2000, 143, 412.

(5) Duley, W. W.; Millar, T. J.; Williams, D. A. R. Astron. Soc. 1980,192, 945.

(6) Canaves, M. V.; Almeida, A. A.; Boice, D. C.; Sanzovo, G. C.Earth, Moon, Planets. 2002, 90, 335.

(7) Scuseria, G. E.; Schaefer, H. F. J. Chem. Phys. 1989, 90, 3700.(8) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,

M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.;Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li,X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.;Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.;Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.;Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich,S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.;Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.;Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.;Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson,B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03,revision E.01; Gaussian, Inc.: Wallingford, CT, 2004.

(9) Harvey, J. N. Phys. Chem. Chem. Phys. 2007, 9, 331.(10) Nikitin, E. E. Annu. ReV. Phys. Chem. 1999, 50, 1.(11) Berning, A.; Schweizer, M.; Werner, H.-J.; Knowles, P. J.; Palmieri,

P. Mol. Phys. 2000, 98, 1823.(12) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1988, 89, 5803.(13) Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1988, 145, 514.(14) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007.(15) Woon, D. E., Jr. J. Chem. Phys. 1993, 98, 1358.(16) Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schutz,

M.; Celani, P.; Korona, T.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B.;Amos, R. D.; Bernhardsson, A.; Berning, A.; Cooper, D. L.; Deegan,M. J. O.; Dobbyn, A. J.; Eckert, F.; Goll, E.; Hampel, C.; Hetzer, G.; Hrenar,T.; Knizia, G.; Koppl, C.; Liu, Y.; Lloyd, A. W.; Mata, R. A.; May, A. J.;McNicholas, S. J.; Meyer, W.; Mura, M. E.; Nicklass, A.; Palmieri, P.;Pfluger, K.; Pitzer, R.; Reiher, M.; Schumann, U.; Stoll, H.; Stone, A. J.;Tarroni, R.; Thorsteinsson, T.; Wang, M.; Wolf, A. MOLPRO, version2008.1, a package of ab initio programs. http://www.molpro.net.

(17) Lovas, F. J.; Suenram, R. D.; Stevens, W. J. J. Mol. Spectrosc.1983, 100, 316.

(18) Dobado, J. A.; Martınez-Garcıa, H.; Molina, J. M.; Sundberg, M. R.J. Am. Chem. Soc. 1998, 120, 8461.

(19) Burtzoff, M. D.; Peter, L.; Lepse, P. A.; Zhang, D. Y. THEOCHEM2002, 619, 229.

(20) Altmann, J. A.; Handy, N. C.; Ingamells, V. E. Int. J. Quant. Chem.1996, 57, 533–542.

(21) Habara, H.; Yamamoto, S.; Saito, S. J. Chem. Phys. 1998, 109,2700.

(22) Nguyen, M. T.; Vanquickenborne, L. G.; Flammang, R. J. Chem.Phys. 1994, 101, 6.

(23) Denis, P. A.; Ventura, O. N.; Mai, H. T.; Nguyen, M. T. J. Phys.Chem. A 2004, 108, 23.

(24) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules; VanNostrand Reinhold: New York, 1979; Vol. IV.

(25) Czernek, J.; Zivny, O. Chem. Phys. 2004, 303, 137.(26) Boere, R. T.; Tuononen, H. M.; Chivers, T.; Roemmele, T. L. J.

Organomet. Chem. 2007, 692, 2683.(27) Jalbout, A. F.; Sawaya, B. E. THEOCHEM 2002, 618, 225.(28) Kurosaki, Y.; Takayanagi, T. J. Phys. Chem. A 1999, 103, 436.(29) Walch, S. P. J. Chem. Phys. 1993, 99, 3804.(30) Wang, L.; Mebel, A. M.; Yang, X.; Wang, X. J. Phys. Chem. A

2004, 108, 11644.(31) Vianna, R. B.; Pimentel, A. S. J. Chem. Phys. 2007, 127, 204306.(32) Vianna, R. B.; Pereira, P. S. S.; Macedo, L. G. M.; Pimental, A. S.

Chem. Phys. 2009, 363, 49.

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