Born-Oppenheimer Molecular Dynamics on the H2S + NO3 Reaction in the Presence andAbsence of Water: The Kinetic Isotope Effect

Maria Clara Leite Scaldaferri and Andre Silva Pimentel*Departamento de Quımica, Pontifıcia UniVersidade Catolica do Rio de Janeiro, Rua Marques de Sao Vicente,225 GaVea, 22453-900 Rio de Janeiro, RJ Brazil

ReceiVed: April 27, 2010; ReVised Manuscript ReceiVed: July 15, 2010

The chemical mechanism of the H2S + NO3 reaction in the absence and presence of water molecules wasinvestigated using the Born-Oppenheimer molecular dynamics. These calculations were performed to gaininsight into the underlying chemical mechanism and to evaluate the kinetic isotope effect in the H2S + NO3

and D2S + NO3 reactions. When H2O interacts with NO3, the rate coefficient of the H2S + NO3 reaction issmaller than that for H2O interacting with H2S. Deuterium generally decreases the rate when D2O interactswith D2S but has no effect when D2O interacting with NO3. When H2O or D2O interacts with NO3, the yieldsare larger compared to those for the reactions (H2O)H2S + NO3 and (D2O)H2S + NO3. Furthermore, theaverage reaction times of the reactions H2S + NO3(H2O) and H2S + NO3(D2O) are shorter than those whenH2O or D2O interacts with H2S. The (H2O)H2S + NO3 reaction may occur via two possible pathways: thenon-water-assisted and water-assisted hydrogen abstraction mechanisms. However, the H2S + NO3(H2O)reaction only happens via the non-water-assisted mechanism.

Introduction

The study of the abstraction reaction H2S/D2S + NO3 is ofcentral importance to the development of theories for under-standing the molecular dynamics and SH/SD kinetic isotopeeffect (KIE). Tyndall and Ravishankara1 suggested that the KIEsof the hydrogen abstraction reaction of H2S/D2S system wouldbe informative in deducing the real reaction mechanism.Specifically, they indicated that experimental measurements ofthese KIEs would clarify the involvement, if any, of an additioncomplex or any nonconventional water-assisted mechanism.Perhaps, the SH/SD may inform us about the formation of awater cluster which may be involved in the underlying reaction.Few experimental2-4 and theoretical5 studies have been devotedto the H2S + NO3 reaction. In contrast to the situation withrespect to this reaction, no kinetic study was devoted to theanalogous isotope reaction, D2S + NO3. The effect of gaseousH2O or D2O on this reaction system is also unknown.

There are many studies6-13 of the hydrogen abstractionreaction of H2S/D2S by different atoms and radicals. Thesummary of these investigations is presented in Table 1. In thissummary, the primary KIEs for abstractions of hydrogen anddeuterium atoms by O, Cl, F, OH, and CF3 radicals from H2Sand D2S, respectively, are clear. However, there is a lack ofinformation on the H2S + NO3 reaction. Therefore, this is themain motivation of this study. Particularly, the moleculardynamics and KIEs were not performed for this system. Abinitio calculations may offer an effective way to evaluate themolecular dynamics and KIEs of the H2S + NO3 reaction. Inthe present study we determined the KIE of the H2S + NO3

reaction in the presence and absence of H2O/D2O at 298 K.We intend to use this information to give a new insight on thechemical mechanism of the H2S + NO3 reaction.

The reaction H2S + NO3 in the presence of water in gas phasehas not been studied yet. Furthermore, this reaction has alsonot been studied experimentally or theoretically in the liquid

phase. Experimentally, the interaction of water or deuteratedwater molecules with H2S or NO3 could lead to differentproducts, which have never been investigated up to date. Themotivation of this work is that ab initio quantum chemicalcalculations may offer an alternative way for the understandingand predicting the KIE of the oxidation mechanism for thisimportant reduced sulfur compound.

Methodology

All quantum chemical calculations and Born-Oppenheimermolecular dynamics14-18 (BOMD) simulations in this work wereperformed using the Gaussian03 software.19 The quantumchemical calculations and molecular dynamics simulation wascalculated using the B3LYP/6-311++G(d,p) and B3LYP/6-31Gmethodologies, respectively.20 The geometries of the reactant,product, and transition state (TS) were fully optimized with theaid of analytical gradients using the Berny algorithm withredundant internal coordinates until a stationary point on thepotential surface is found. The TS was searched using thesynchronous transit-guided quasi-Newton method (STQN),* Corresponding author. E-mail: a_pimentel@puc-rio.br.

TABLE 1: SH/SD Kinetic Isotope Effect (KIE) of theHydrogen Abstraction Reactions of H2S by Atoms andRadicals

reaction kH/kD refs

H2S + O f SH + OH 3.42 6

H2S + Cl f SH + HCl 2.21 7

H2S + F f SH + HF 1.4 8, 9

H2S + CH3 f SH + CH4 0.25 10

H2S + CF3 f SH + CF3H 2.35 12

H2S + CH f SH + CH2 1.10 12

H2S + CD f SH + CDH 0.96 12

H2S + OH f SH + H2O 1.73 13

H2S + NO3 f SH + HNO3 2.56 this work

J. Phys. Chem. A 2010, 114, 8993–8998 8993

10.1021/jp103814s 2010 American Chemical SocietyPublished on Web 07/30/2010

which requires the reactant, product, and an initial guess forthe TS structure as input. The TS was verified by subsequentfrequency calculations, which allowed us to determine theimaginary vibrational frequencies related to the reaction path.The remaining M-3 points on the path were generated by twosuccessive linear interpolations, first between the reactant andTS and then between the TS and product. The intrinsic reactioncoordinate (IRC) was calculated to follow the reaction path andreassure us that the transition structure is really a saddle pointof the reaction path. The initial geometry for the TS structurewas used as a starting point to follow the path in both directions.Also, the computed force constants in Cartesian coordinates froma frequency calculation of the optimized TS geometry werecalculated. The Cartesian force matrix was diagonalized to getthe harmonic vibrational frequencies. The imaginary frequencywas specified to follow the reaction path. The geometry wasoptimized at each point along the reaction path so that thesegment of the reaction path between any two adjacent pointsis described by an arc of a circle and so that the gradients atthe end point of the arc are tangent to the path. The procedureis well-described in the literature.19

The thermodynamical properties calculated are calculated forthe reactants, products, and transition state. These quantities werecorrected for the zero-point energies (ZPE). The rate coefficientis calculated by the transition state theory (TST), which is givenby

where kB, h, and NA are the Boltzmann, Planck, and Avogadroconstants, respectively, κ is the transmission coefficient that isassumed to be 1, P0 is a reference pressure set to 1 atm, Qq isthe standard molar partition function per unit of volume for thetransition state, QH2S is the same function for the H2S molecule,QNO3 is the same function for the NO3 radical, and ∆E0 is thedifference in molar energies of the lowest level of the transitionstate and the lowest level of reactants. The standard Gibbs freeenergy ∆Gq,0 in gas phase between the transition state andreactant can be calculated by standard methods of statisticalmechanics to evaluate the equilibrium partition function.

Some rate enhancement is seen for compounds with lighterisotopes, possibly due to quantum mechanical tunneling. Thisis typically only observed for reactions involving bonds tohydrogen atoms. Tunneling occurs when a molecule penetratesthrough a potential energy barrier rather than over it. Althoughnot allowed by the laws of classical mechanics, particles canpass through classically forbidden regions of space in quantummechanics based on wave-particle duality. The tunneling canbe analyzed by calculating the tunneling factor, Γ, which isdescribed by

where R ) E/RT and � ) 2aπ2(2mE)1/2/h. In addition, the �term depends linearly with barrier width, 2a. The tunnelingdistances of protons between donor and acceptor atom dependon the kind of proton transfer, i.e., the strength of thedonor-acceptor interaction.

The Wigner correction for tunneling assumes a parabolicpotential for the nuclear motion near the transition state

where V0 is the energy at the top of the barrier and �q is theimaginary frequency of the transition state. The Wigner cor-rection κ(T) is then given by

In BOMD, the potential energy surface (PES) and the forcesare self-consistently calculated “on the fly”. The velocity-Verletalgorithm21,22 was used to integrate Newton’s equations ofmotion by using a very accurate Hessian-based algorithm thatincorporates a predictor step on the local quadratic surfacefollowed by a corrector step. The latter uses a fifth-orderpolynomial function fitted to the energy, gradient, and Hessianat the beginning and end points of each step. Since we are usingclassical dynamics to propagate the nuclei, we have replacedall hydrogen atoms for deuterium atoms, and particular hydrogenatoms with deuterium atoms to estimate the KIE. However, wecalculate the tunneling corrections for minimizing the errorassociated with neglecting quantum tunneling. Thus, the classicaldynamics is applied to the system with H atoms or D atoms ormixed H and D atoms. The stationary points on the PES wererecomputed for the systems with H atoms, D atoms, and mixedH and D atoms. Trajectories starting from the barrier in theforward and reverse directions were run for about 1 ps. Theintegration scheme employed was the Bulirsch-Stoer method.A total of 50 trajectories along the reaction coordinate wereperformed by thermal sampling and distribution at 298 K. Weacknowledge that many more trajectories would be required fora quantitative analysis of H2S + NO3 reaction dynamics;however, it is prohibitive in terms of computational cost; theintention of our study is, at least, to gain qualitatiVe insightinto this complex reaction. The Hessian was updated for fivesteps before being recalculated analytically. An integration stepsize of 0.25 amu1/2 bohr was used for all of the calculations,and the trajectories were stopped when the products were found.The time for a trajectory finds the products ranged from 10 to30 fs, and total energy was conserved to 10-5 hartree. Totalangular momentum was conserved to better than 10-9 hbar sinceprojection methods were used to remove the overall angularforces.

Results and Discussion

The equilibrium geometries and frequencies for reactants,products, and TS, in the presence and absence of water, werecalculated by using the B3LYP/6-311++G(3df,3pd) level oftheory. These geometries and frequencies were recalculated afterreplacing the hydrogen atoms by deuterium ones. The structuresof reactants, products, and TS were found to interact with onlyone water molecule. The water molecule may interact with theTS structure by both sides, the H2S end or the NO3 end. Eachtransition state complexed with water was found by using themethodology mentioned above, i.e., B3LYP. The reactionsinvolving the water clusters are presented in Figure 1.

Table 2 shows the rate coefficients for the H2S + NO3

reaction in the presence and absence of water molecules. Theenergy barrier for the TS formation in the H2S + NO3 reactionis 10.3 kcal mol-1, corresponding to a rate coefficient of 2.95× 10-16 cm3 molecule-1 s-1 at 298 K.5 The addition of a watermolecule in the H2S side of the TS-(H2O)1 complex has a

k(T) ) κkBT

hRT

P0NA

Qq

QNO3QH2Se-∆E0/kT ) κ

kBT

hRT

P0NAe

-∆Gq,0/RT

Γ ) eR

� - R(�e-R - Re-�)

V ) V0 - 12

m�qx2

κ(T) ) 1 + 124(p�qkT )2

8994 J. Phys. Chem. A, Vol. 114, No. 34, 2010 Scaldaferri and Pimentel

different effect compared to the addition of water in the NO3

side. The energy barriers for the formation of (H2O)H2S-NO3q

and H2S-NO3(H2O)q are 10.0 and 10.4 kcal mol-1, whichcorresponds to a rate coefficient of 4.67 × 10-16 and 2.30 ×10-16 cm3 molecule-1 s-1 at 298 K. Therefore, the H2S + NO3

reaction is faster when the water molecule interacts with theH2S side, which is reasonable because it is close to the regionof hydrogen transfer facilitating it. It is important to note thatthe rate coefficient of the H2S(D2O) + NO3 reaction barelyincreases to 5.17 × 10-16 cm3 molecule-1 s-1 at 298 K.Surprisingly, the presence of D2O molecules close to the NO3

side has a much larger effect in the rate coefficient than H2O ofthis reaction. The rate coefficient of the H2S + NO3(D2O)reaction increases almost 6 times, to 13.3 × 10-16 cm3

molecule-1 s-1 at 298 K, as compared to that for the H2S +NO3(H2O) reaction.

The D2S + NO3 reaction in the presence and absence of watermolecules is also presented in Table 2. The energy barrier forthe TS formation in the D2S + NO3 reaction is 10.8 kcal mol-1,which corresponds to a rate coefficient of 1.31 × 10-16 cm3

molecule-1 s-1 at 298 K. Therefore, substitution of H for Datoms decreases the rate coefficient as expected. The explanationfor that is the increase of the energy barrier. The KIE, kH/kD, isestimated to be 2.56 as presented in Table 2. This primary effectis one way which clues can be obtained as to whether the H2S

+ NO3 reaction proceeds directly or via a hydrogen-bondedadduct of significant lifetime.23

It is also surprising that, when a water molecule is added inthe transition state forming the (H2O)D2S-NO3

q complex, theeffect is the same in the energy barrier as compared to theaddition of water in the NO3 side of the transition state formingthe D2S-NO3(H2O)q complex. The energy barrier for theformation of both (H2O)D2S-NO3

q and D2S-NO3(H2O)q

complexes is 10.6 kcal mol-1. Thus, the rate coefficients of thereactions D2S(H2O) + NO3 and D2S + NO3(H2O) are practicallythe same, 1.7 × 10-16 cm3 molecule-1 s-1 at 298 K. On theother hand, the rate coefficients of the reactions D2S(D2O) +NO3 and D2S + NO3(D2O) are 2.02 × 10-16 and 5.83 × 10-16

cm3 molecule-1 s-1 at 298 K, respectively. Therefore, it seemsthat the addition of H2O is less important than the effectproduced by addition of D2O. It is interesting to recall the factthat this does not happen when the system is not deuterated asmentioned previously.

The rate coefficients of the reactions 1, 3, 9, and 10 decreasemore than twice as the H2S is deuterated, which confirms theprimary KIE. Surprisingly, the reaction 4 has a weak primaryKIE, k4/k6 ) 1.54. When the substitution is not involved in thebond that is breaking or forming, a secondary isotope effect istypically observed with a smaller rate change. This must be thecase when the water molecule is deuterated. However, the

Figure 1. Chemical mechanism of the H2S + NO3 f TS reaction in the presence of water. (a) H2O is bound to the H2S molecule, and (b) H2Ois attached to the NO3 radical. The yellow, red, blue, and white balls represent sulfur, oxygen, nitrogen, and hydrogen atoms, respectively.

TABLE 2: Energy Barriers, Rate Coefficients, k, Wigner Correction for Tunneling, and Kinetic Isotope Effects (KIEs ) kH/kD)for the H2S + NO3 Reaction System in the Presence and Absence of Water at 298 K

reactionenergy barrier(kcal mol-1)

k × 10-16

(cm3 molecule-1 s-1)Wigner

correction kH/kD

(1) H2S + NO3 f H2S - NO3q 10.29 2.95 1.50 k1/k2 ) 2.56

k1/k9 ) 0.25k1/k10 ) 0.63

(2) D2S + NO3 f D2S - NO3 10.77 1.31 1.32

(3) H2S(H2O) + NO3 f (H2O)H2S - NO3q 10.01 4.67 1.56 k3/k5 ) 3.03

k3/k7 ) 2.30k3/k10 ) 1.04

(4) H2S + NO3(H2O) f H2S - NO3(H2O)q 10.43 2.30 1.54 k4/k6 ) 1.54k4/k8 ) 0.39k4/k9 ) 0.20

(5) D2S(H2O) + NO3 f (H2O)D2S - NO3q 10.59 1.78 1.35 k5/k7 ) 0.76

(6) D2S + NO3(H2O) f D2S - NO3(H2O)q 10.60 1.72 1.34 k6/k8 ) 0.26

(7) D2S(D2O) + NO3 f (D2O)D2S - NO3q 10.51 2.02 1.57

(8) D2S + NO3(D2O) f D2S - NO3(D2O)q 9.88 5.83 1.55

(9) H2S + NO3(D2O) f H2S - NO3(D2O)q 9.39 13.3 1.34 k9/k8 ) 1.97

(10) H2S(D2O) + NO3 f (D2O)H2S - NO3q 9.95 5.17 1.35 k10/k7 ) 2.20

Kinetic Isotope Effect of the H2S + NO3 Reaction J. Phys. Chem. A, Vol. 114, No. 34, 2010 8995

k3/k10, k4/k9, k5/k7, and k6/k8 ratios are 1.04, 0.20, 0.76, and 0.26,respectively, showing that there is an increase in the ratecoefficient as the water molecule is deuterated. It is importantto note that the reactions 4 and 6 have a different behavior thanthat found for secondary isotope effect. The explanation for thatmay come from the interaction of H2O/D2O with the NO3 group.On the other hand, the rate coefficient of the H2S(H2O) + NO3

reaction increases in about 2.30 exchanging all the hydrogenatoms by deuterium, showing that the primary KIE is moreimportant than the secondary effect in this case. Surprisingly,the rate coefficient of the H2S + NO3(H2O) reaction is almost0.39 times slower than that for the D2S + NO3(D2O) reaction,showing that the secondary KIE is more important in this case.Again, the possible explanation for this secondary effect maycome from the interaction of H2O/D2O with the NO3 group.

The reason for this explanation may come from the electronicstructure differences in the water complexes. For example, howdoes NO3-H2O compare to the planar NO3 radical? The electrondensity and symmetry in NO3 and NO3-H2O are different. Thecomplexed NO3 is more C3V rather than D3h. These features maymake a difference in the reaction path.

Because there is a transfer of hydrogen/deuterium atoms, itis also important to estimate the tunneling effect on the H2S +NO3 and H2S + NO3 reactions. The Wigner correction fortunneling24,25 is presented in Table 2. It seems like a Wignerfactor of 1.33-1.55 is not huge though and makes a small effecton the reaction rates and KIE ratios. The probability of protontransfer (tunneling factor Γ) depends strongly on the overlapof its vibrational wave functions. An important quantitativeparameter of the oscillator’s wave function is the vibrationamplitude of a corresponding classical oscillator. For a typicalA-H covalent bond with a stretching vibration frequency about3000 cm-1, the zero-point vibration amplitude is 0.1 Å. In thisfirst approximation, it is the characteristic length determining astrong interacting proton-transfer mechanism. However, let usconsider the case when the proton donor and acceptor are heldat some large distance so that the distance between two minimais of order of 1 Å or more. It is easy to conclude that in thiscase the tunneling probability at the ground level is negligiblysmall. For such a large distance, the donor-acceptor interactionis weak, and hence the splitting of vibrational levels is negligible,so that it means the proton transfer on large distances of severalangstroms is improbable.

In the weakly interacting systems, the equilibrium distancebetween donor and acceptor equals the sum of their van derWaals radii. At the neutral H radius ∼1.2 Å, typical acceptoratom radius ∼1.5 Å, and the covalent bond length ∼1.1 Å, theequilibrium distance between two minima is ∼1.6 Å. This istoo large as compared to 0.1 Å, and hence the proton transferin this position is strongly unfavorable. However, the tunnelingprobability increases drastically with the closer approach ofreactants. The proton wave function decays exponentially withthe distance squared. Therefore, the tunneling probabilitydepends exponentially on the square of the tunneling distance.The decrease in the tunneling distance increases the tunnelingprobability. On the other hand, the approach of the reactantscannot be an unrestricted one because repulsion betweenreactants hinders their mutual approach. The repulsion energycan be described by a Born-Mayer potential. The two oppositetrends result in some optimal distance ensuring a maximumtunneling probability and, at the same time, not too large energyexpenditure necessary to overcome the repulsion. The estimatesfor proton transfer between two C atoms carried out withrealistic constants borrowed from independent experimental data

have shown that the optimum tunneling distance is much shorterthan the equilibrium one: about 0.4 Å instead of 1.5 Å.26 Theempirical parameters used in these calculations were, of course,only approximate ones. Furthermore, the formula for nonadia-batic tunneling of protons in a double well of two harmonicoscillators was employed, and hence the donor-acceptorinteraction even at small inter-reactant distance was neglected.Therefore, the result of these calculations cannot be consideredas a strict and quantitative one. Nevertheless, it shows unam-biguously that, in a transition configuration, a very substantialapproach of the reactants should take place and gives the realisticorder of its magnitude. It should be mentioned that thecalculations employing, instead of harmonic, a Morse potentialfor C-H and O-H covalent bonds and substituting anotherMorse potential for C · · ·O interaction have resulted in a quitesimilar value of the optimal tunneling distance, 0.46 Å.27

The other type of systems presents O-H and acids reactingwith O, N, and other bases. The donor-acceptor interaction israther strong already under equilibrium conditions, and thehydrogen bond is forming. For typical O-H · · ·O bond withO · · ·O distance of 2.8-3.0 Å and the O-H bond length of 1Å, the equilibrium interminima distance equals to 0.8-1.0 Å.This is also somewhat too large for an effective proton tunneling,and hence some approach of the reactants is necessary. Incontrast to the previous case, the process is facilitated by twocircumstances. First, the inter-reactant interaction makes theapproach substantially easier than described by the Born-Mayerpotential; the energy dependence on the distance is describedby a Morselike equation with a much more gentle energy riseupon decrease in the O · · ·O distance. Second, the energy curvealong the proton coordinate deviates substantially from twointersecting parabolas of harmonic oscillators. Correspondingly,the barrier along this coordinate is lower, and the tunnelingprobability is higher and is not obeying the exponential decayingon the squared distance. The form of the correspondingdependence can be determined, in principle, from quantumchemical calculations. In particular, at not too short distances,it follows an exponential form similar to this for the long-rangeelectron transfer, but with much larger coefficient a (about30-40 Å-1 against ∼1 Å-1 for electron transfer).28 As a result,proton transfer for the reactant of the first type is usuallymarkedly slower than for those of the second.

The system investigated in this study has an S-H reactingwith the NO2-O base via a water-assisted mechanism. Thedonor-acceptor interaction is also rather strong already underequilibrium conditions, and the hydrogen bond is forming. Fortypical S-H · · ·O bond with S · · ·O distance of 2.8-3.0 Å andthe O-H bond length of 1 Å, the equilibrium interminimadistance is around 1.0-1.2 Å. The tunneling factor, Γ, calculatedfor the H2S + NO3 and D2S + NO3 systems in the presence ofwater and deuterated water gave a ΓH/ΓD around 1.5-1.9 at298 K, considering a barrier width of 1.2-1.0 Å, respectively.These results are similar to the Wigner correction for tunnelingpresented previously.

For each reaction studied here, 50 trajectories were simulatedat 298 K. The results of yield and averaged reaction time forthe transition state decomposition into products at 298 K arepresented in Table 3. The two possible pathways for this reactionare shown in Figures 2 and 3. Figure 2 presents a simplehydrogen atom abstraction from the H2S molecule by the NO3

radical. The water-assisted mechanism29-39 for the hydrogenatom abstraction from the H2S molecule by the NO3 radical isshown in Figure 3.

8996 J. Phys. Chem. A, Vol. 114, No. 34, 2010 Scaldaferri and Pimentel

The H2S-NO3q decomposition into HNO3 and SH products

has a yield of about 98% with an average reaction time of 13.37fs. When the hydrogen atoms are replaced by the deuteriumatom, D2S-NO3

q, the yield barely decreases to 96% and theaverage reaction time slightly increase at 17.71 fs. Therefore,it shows that the D2S-NO3

q decomposition is slower than theH2S-NO3

q decomposition as expected due to its greater inertia.The yield and the average time reaction of the decomposition

of H2S-NO3(H2O)q, which has a water molecule interactingwith the NO3 group, are similar to those of the H2S-NO3

q

decomposition, about 98% and 12.84 fs, respectively. However,

when a water molecule interacts with the H2S side, the yield ofthe (H2O)H2S-NO3

q decomposition significantly decreases toabout 70% and the average reaction time increases to 23.63 fs.These results show that the (H2O)H2S-NO3

q decomposition isslower than those found for the H2S-NO3(H2O)q and H2S-NO3

q

decompositions.The (D2O)D2S-NO3

q and D2S-NO3(D2O)q decompositionswere calculated, and the results are also presented in Table 3.When all the hydrogen atoms are replaced by deuterium, theyield and the average reaction time of the D2S-NO3(D2O)q

decomposition are similar to those found for the decompositionH2S-NO3(H2O)q and H2S-NO3

q decompositions, about 98%and 12.80 fs, respectively. On the hand, as expected, the(D2O)D2S-NO3

q decomposition is slower than those found forthe (H2O)H2S-NO3

q and H2S-NO3q decompositions. The yield

and the average reaction time of the (D2O)D2S-NO3q decom-

position were calculated in about 60% and 27.59 fs, respectively.It is important to note that the (H2O)H2S-NO3

q and(D2O)D2S-NO3

q decompositions occur by a nonconventionalpathway, a water-assisted mechanism.29-39 In this mechanism,the hydrogen atom from the H2S molecule is transferred to thewater molecule, and then the other hydrogen atom from thewater molecule is transferred to the NO3 radical. There is asimilar water-assisted mechanism reported previously, which

TABLE 3: Yield (%) and Averaged Reaction Time (tavg infs) for the Transition State Decomposition into Products at298 K

reactionyield(%)

tavg

(fs)

(1) H2S - NO3q f HNO3 + SH 98 13.37

(2) D2S - NO3q f DNO3 + SD 96 17.71

(3) (H2O)H2S - NO3q f (H2O)SH + HNO3

70 23.63

(4) H2S - NO3(H2O)q f SH + HNO3(H2O) 98 12.84

(7) (D2O)D2S - NO3q f (D2O)DS + DNO3

60 27.59

(8) D2S - NO3(D2O)q f SD + DNO3(D2O) 98 12.80

Figure 2. Non-water-assisted hydrogen abstraction mechanism for the H2S + NO3 reaction starting from the transition state structure. The yellow,red, blue, and white balls represent sulfur, oxygen, nitrogen, and hydrogen atoms, respectively.

Figure 3. Water-assisted hydrogen abstraction mechanisms for the H2S + NO3 reaction starting from the transition state structure. The yellow, red,blue, and white balls represent sulfur, oxygen, nitrogen, and hydrogen atoms, respectively.

Kinetic Isotope Effect of the H2S + NO3 Reaction J. Phys. Chem. A, Vol. 114, No. 34, 2010 8997

is generally known by the water-assisted proton-transfermechanism.29-39 This mechanism usually occurs in aqueousphase. However, the mechanism presented here in this paper isunique for this system because it is a water-assisted H-atomtransfer mechanism in gas phase. It is important to mention thatit is a proton-transfer reaction, because the Mulliken chargedistribution in the H3O group is positive, around +0.8. To thebest of our knowledge, a similar mechanism is not reportedpreviously in the literature.

The yield of the (H2O)H2S-NO3q decomposition via the

assisted-water mechanism is about 5.7%. On the other hand,we found a yield of 3.3% for the (D2O)D2S-NO3

q decomposi-tion via the assisted-water mechanism. Remarkably, theH2S-NO3(H2O)q and D2S-NO3(D2O)q decompositions do nothappen via the assisted-water mechanism, certainly because theH2O/D2O molecules are bound to the NO3 group, too far awayfrom the reaction site. Experimentally, this could lead todifferent products from the conventional mechanism. Forexample, for (D2O)H2S + NO3 reaction, it would get DNO3

rather than HNO3, which may be verified experimentally.

Conclusion

In thisstudyitwaspossible toverify that theBorn-Oppenheimermolecular dynamics is a suitable method to investigate thechemical mechanism of the H2S + NO3 reaction in the presenceof water molecules. Molecular dynamics simulations wereperformed to evaluate the KIE in the H2S + NO3 and D2S +NO3 reactions. The rate coefficient of the H2S + NO3(H2O)reaction is smaller than that for H2O interacting with H2S.Exchange of H atoms for D atoms generally decreases the ratewhen D2O interacts with D2S but has no effect when D2Ointeracting with NO3. The yields of the H2S + NO3(H2O) andH2S + NO3(D2O) reactions are larger compared to those forthe reactions (H2O)H2S + NO3 and (D2O)H2S + NO3. Further-more, the average reaction times of the reactions H2S +NO3(H2O) and H2S + NO3(D2O) are shorter than those whenH2O or D2O interacts with H2S. It was demonstrated that the(H2O)H2S + NO3 and (D2O)D2S + NO3 reactions occur viatwo possible pathways: the non-water-assisted and water-assistedhydrogen abstraction mechanisms.

Acknowledgment. The authors are grateful to the CNPqfunding (no. 485364/2007-7). A.S.P is recipient of a CNPqproductivity fellowship (no. 304187/2009-7) and another oneawarded by the Pontificia Universidade Catolica at Rio deJaneiro. M.C.L.S. and A.S.P. also thank FAPERJ for a researchstudentship (no. 101.673/2009) and a young scientist fellowship(no. 101.452/2010), respectively.

References and Notes

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