J. Phys. Chem. A 2010, 114, 8993–8998
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Born-Oppenheimer Molecular Dynamics on the H2S + NO3 Reaction in the Presence and Absence of Water: The Kinetic Isotope Effect Maria Clara Leite Scaldaferri and Andre Silva 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 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 was investigated using the Born-Oppenheimer molecular dynamics. These calculations were performed to gain insight 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 is smaller than that for H2O interacting with H2S. Deuterium generally decreases the rate when D2O interacts with D2S but has no effect when D2O interacting with NO3. When H2O or D2O interacts with NO3, the yields are larger compared to those for the reactions (H2O)H2S + NO3 and (D2O)H2S + NO3. Furthermore, the average reaction times of the reactions H2S + NO3(H2O) and H2S + NO3(D2O) are shorter than those when H2O or D2O interacts with H2S. The (H2O)H2S + NO3 reaction may occur via two possible pathways: the non-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 of central importance to the development of theories for understanding the molecular dynamics and SH/SD kinetic isotope effect (KIE). Tyndall and Ravishankara1 suggested that the KIEs of the hydrogen abstraction reaction of H2S/D2S system would be informative in deducing the real reaction mechanism. Specifically, they indicated that experimental measurements of these KIEs would clarify the involvement, if any, of an addition complex or any nonconventional water-assisted mechanism. Perhaps, the SH/SD may inform us about the formation of a water cluster which may be involved in the underlying reaction. Few experimental2-4 and theoretical5 studies have been devoted to the H2S + NO3 reaction. In contrast to the situation with respect to this reaction, no kinetic study was devoted to the analogous isotope reaction, D2S + NO3. The effect of gaseous H2O or D2O on this reaction system is also unknown. There are many studies6-13 of the hydrogen abstraction reaction of H2S/D2S by different atoms and radicals. The summary of these investigations is presented in Table 1. In this summary, the primary KIEs for abstractions of hydrogen and deuterium atoms by O, Cl, F, OH, and CF3 radicals from H2S and D2S, respectively, are clear. However, there is a lack of information on the H2S + NO3 reaction. Therefore, this is the main motivation of this study. Particularly, the molecular dynamics and KIEs were not performed for this system. Ab initio calculations may offer an effective way to evaluate the molecular dynamics and KIEs of the H2S + NO3 reaction. In the 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 the chemical mechanism of the H2S + NO3 reaction. The reaction H2S + NO3 in the presence of water in gas phase has not been studied yet. Furthermore, this reaction has also not been studied experimentally or theoretically in the liquid * Corresponding author. E-mail:
[email protected].
TABLE 1: SH/SD Kinetic Isotope Effect (KIE) of the Hydrogen Abstraction Reactions of H2S by Atoms and Radicals reaction
kH/kD
H2S + O f SH + OH H2S + Cl f SH + HCl H2S + F f SH + HF H2S + CH3 f SH + CH4 H2S + CF3 f SH + CF3H H2S + CH f SH + CH2 H2S + CD f SH + CDH H2S + OH f SH + H2O H2S + NO3 f SH + HNO3
3.42
6
refs
2.21
7
1.4
8, 9
0.25
10
2.35
12
1.10
12
0.96
12
1.73
13
2.56
this work
phase. Experimentally, the interaction of water or deuterated water molecules with H2S or NO3 could lead to different products, which have never been investigated up to date. The motivation of this work is that ab initio quantum chemical calculations may offer an alternative way for the understanding and predicting the KIE of the oxidation mechanism for this important reduced sulfur compound. Methodology All quantum chemical calculations and Born-Oppenheimer molecular dynamics14-18 (BOMD) simulations in this work were performed using the Gaussian03 software.19 The quantum chemical calculations and molecular dynamics simulation was calculated using the B3LYP/6-311++G(d,p) and B3LYP/6-31G methodologies, respectively.20 The geometries of the reactant, product, and transition state (TS) were fully optimized with the aid of analytical gradients using the Berny algorithm with redundant internal coordinates until a stationary point on the potential surface is found. The TS was searched using the synchronous transit-guided quasi-Newton method (STQN),
10.1021/jp103814s 2010 American Chemical Society Published on Web 07/30/2010
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which requires the reactant, product, and an initial guess for the TS structure as input. The TS was verified by subsequent frequency calculations, which allowed us to determine the imaginary vibrational frequencies related to the reaction path. The remaining M-3 points on the path were generated by two successive linear interpolations, first between the reactant and TS and then between the TS and product. The intrinsic reaction coordinate (IRC) was calculated to follow the reaction path and reassure us that the transition structure is really a saddle point of the reaction path. The initial geometry for the TS structure was used as a starting point to follow the path in both directions. Also, the computed force constants in Cartesian coordinates from a frequency calculation of the optimized TS geometry were calculated. The Cartesian force matrix was diagonalized to get the harmonic vibrational frequencies. The imaginary frequency was specified to follow the reaction path. The geometry was optimized at each point along the reaction path so that the segment of the reaction path between any two adjacent points is described by an arc of a circle and so that the gradients at the end point of the arc are tangent to the path. The procedure is well-described in the literature.19 The thermodynamical properties calculated are calculated for the reactants, products, and transition state. These quantities were corrected for the zero-point energies (ZPE). The rate coefficient is calculated by the transition state theory (TST), which is given by
k(T) ) κ
kBT RT kBT RT -∆E0 -∆Gq,0/ Qq RT N e /kT ) κ N e A h P0 QNO3QH2S h P0 A
where kB, h, and NA are the Boltzmann, Planck, and Avogadro constants, respectively, κ is the transmission coefficient that is assumed to be 1, P0 is a reference pressure set to 1 atm, Qq is the standard molar partition function per unit of volume for the transition state, QH2S is the same function for the H2S molecule, QNO3 is the same function for the NO3 radical, and ∆E0 is the difference in molar energies of the lowest level of the transition state and the lowest level of reactants. The standard Gibbs free energy ∆Gq,0 in gas phase between the transition state and reactant can be calculated by standard methods of statistical mechanics to evaluate the equilibrium partition function. Some rate enhancement is seen for compounds with lighter isotopes, possibly due to quantum mechanical tunneling. This is typically only observed for reactions involving bonds to hydrogen atoms. Tunneling occurs when a molecule penetrates through a potential energy barrier rather than over it. Although not allowed by the laws of classical mechanics, particles can pass through classically forbidden regions of space in quantum mechanics based on wave-particle duality. The tunneling can be analyzed by calculating the tunneling factor, Γ, which is described by
Γ)
eR (βe-R - Re-β) β-R
where R ) E/RT and β ) 2aπ2(2mE)1/2/h. In addition, the β term depends linearly with barrier width, 2a. The tunneling distances of protons between donor and acceptor atom depend on the kind of proton transfer, i.e., the strength of the donor-acceptor interaction. The Wigner correction for tunneling assumes a parabolic potential for the nuclear motion near the transition state
Scaldaferri and Pimentel
1 V ) V0 - mqx2 2 where V0 is the energy at the top of the barrier and q is the imaginary frequency of the transition state. The Wigner correction κ(T) is then given by
κ(T) ) 1 +
( )
1 pq 24 kT
2
In BOMD, the potential energy surface (PES) and the forces are self-consistently calculated “on the fly”. The velocity-Verlet algorithm21,22 was used to integrate Newton’s equations of motion by using a very accurate Hessian-based algorithm that incorporates a predictor step on the local quadratic surface followed by a corrector step. The latter uses a fifth-order polynomial function fitted to the energy, gradient, and Hessian at the beginning and end points of each step. Since we are using classical dynamics to propagate the nuclei, we have replaced all hydrogen atoms for deuterium atoms, and particular hydrogen atoms with deuterium atoms to estimate the KIE. However, we calculate the tunneling corrections for minimizing the error associated with neglecting quantum tunneling. Thus, the classical dynamics is applied to the system with H atoms or D atoms or mixed H and D atoms. The stationary points on the PES were recomputed for the systems with H atoms, D atoms, and mixed H and D atoms. Trajectories starting from the barrier in the forward and reverse directions were run for about 1 ps. The integration scheme employed was the Bulirsch-Stoer method. A total of 50 trajectories along the reaction coordinate were performed by thermal sampling and distribution at 298 K. We acknowledge that many more trajectories would be required for a quantitative analysis of H2S + NO3 reaction dynamics; however, it is prohibitive in terms of computational cost; the intention of our study is, at least, to gain qualitatiVe insight into this complex reaction. The Hessian was updated for five steps before being recalculated analytically. An integration step size 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 to 30 fs, and total energy was conserved to 10-5 hartree. Total angular momentum was conserved to better than 10-9 hbar since projection methods were used to remove the overall angular forces. Results and Discussion The equilibrium geometries and frequencies for reactants, products, and TS, in the presence and absence of water, were calculated by using the B3LYP/6-311++G(3df,3pd) level of theory. These geometries and frequencies were recalculated after replacing the hydrogen atoms by deuterium ones. The structures of reactants, products, and TS were found to interact with only one water molecule. The water molecule may interact with the TS structure by both sides, the H2S end or the NO3 end. Each transition state complexed with water was found by using the methodology mentioned above, i.e., B3LYP. The reactions involving 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. The energy barrier for the TS formation in the H2S + NO3 reaction is 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 water molecule in the H2S side of the TS-(H2O)1 complex has a
Kinetic Isotope Effect of the H2S + NO3 Reaction
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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) H2O is 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 reaction
energy barrier (kcal mol-1)
k × 10-16 (cm3 molecule-1 s-1)
Wigner correction
kH/kD
(1)
H2S + NO3 f H2S - NO3
10.29
2.95
1.50
(2)
10.77
1.31
1.32
(3)
D2S + NO3 f D2S - NO3 H2S(H2O) + NO3 f (H2O)H2S - NO3q
10.01
4.67
1.56
(4)
H2S + NO3(H2O) f H2S - NO3(H2O)q
10.43
2.30
1.54
(5)
D2S(H2O) + NO3 D2S + NO3(H2O) D2S(D2O) + NO3 D2S + NO3(D2O) H2S + NO3(D2O) H2S(D2O) + NO3
10.59
1.78
1.35
k3/k5 ) 3.03 k3/k7 ) 2.30 k3/k10 ) 1.04 k4/k6 ) 1.54 k4/k8 ) 0.39 k4/k9 ) 0.20 k5/k7 ) 0.76
10.60
1.72
1.34
k6/k8 ) 0.26
10.51
2.02
1.57
5.83
1.55
(6) (7) (8) (9) (10)
q
f f f f f f
(H2O)D2S - NO3q D2S - NO3(H2O)q (D2O)D2S - NO3q D2S - NO3(D2O)q H2S - NO3(D2O)q (D2O)H2S - NO3q
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, which corresponds 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 the H2S side, which is reasonable because it is close to the region of hydrogen transfer facilitating it. It is important to note that the rate coefficient of the H2S(D2O) + NO3 reaction barely increases 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 of this 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 water molecules is also presented in Table 2. The energy barrier for the 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 D atoms decreases the rate coefficient as expected. The explanation for that is the increase of the energy barrier. The KIE, kH/kD, is estimated to be 2.56 as presented in Table 2. This primary effect is one way which clues can be obtained as to whether the H2S
9.88 9.39 9.95
13.3 5.17
k1/k2 ) 2.56 k1/k9 ) 0.25 k1/k10 ) 0.63
1.34
k9/k8 ) 1.97
1.35
k10/k7 ) 2.20
+ NO3 reaction proceeds directly or via a hydrogen-bonded adduct of significant lifetime.23 It is also surprising that, when a water molecule is added in the transition state forming the (H2O)D2S-NO3q complex, the effect is the same in the energy barrier as compared to the addition of water in the NO3 side of the transition state forming the D2S-NO3(H2O)q complex. The energy barrier for the formation of both (H2O)D2S-NO3q and D2S-NO3(H2O)q complexes is 10.6 kcal mol-1. Thus, the rate coefficients of the reactions D2S(H2O) + NO3 and D2S + NO3(H2O) are practically the same, 1.7 × 10-16 cm3 molecule-1 s-1 at 298 K. On the other 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 seems that the addition of H2O is less important than the effect produced by addition of D2O. It is interesting to recall the fact that this does not happen when the system is not deuterated as mentioned previously. The rate coefficients of the reactions 1, 3, 9, and 10 decrease more than twice as the H2S is deuterated, which confirms the primary KIE. Surprisingly, the reaction 4 has a weak primary KIE, k4/k6 ) 1.54. When the substitution is not involved in the bond that is breaking or forming, a secondary isotope effect is typically observed with a smaller rate change. This must be the case when the water molecule is deuterated. However, the
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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 rate coefficient as the water molecule is deuterated. It is important to note that the reactions 4 and 6 have a different behavior than that found for secondary isotope effect. The explanation for that may 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 hydrogen atoms by deuterium, showing that the primary KIE is more important than the secondary effect in this case. Surprisingly, the rate coefficient of the H2S + NO3(H2O) reaction is almost 0.39 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 may come from the interaction of H2O/D2O with the NO3 group. The reason for this explanation may come from the electronic structure differences in the water complexes. For example, how does NO3-H2O compare to the planar NO3 radical? The electron density and symmetry in NO3 and NO3-H2O are different. The complexed NO3 is more C3V rather than D3h. These features may make a difference in the reaction path. Because there is a transfer of hydrogen/deuterium atoms, it is also important to estimate the tunneling effect on the H2S + NO3 and H2S + NO3 reactions. The Wigner correction for tunneling24,25 is presented in Table 2. It seems like a Wigner factor of 1.33-1.55 is not huge though and makes a small effect on the reaction rates and KIE ratios. The probability of proton transfer (tunneling factor Γ) depends strongly on the overlap of its vibrational wave functions. An important quantitative parameter of the oscillator’s wave function is the vibration amplitude of a corresponding classical oscillator. For a typical A-H covalent bond with a stretching vibration frequency about 3000 cm-1, the zero-point vibration amplitude is 0.1 Å. In this first approximation, it is the characteristic length determining a strong interacting proton-transfer mechanism. However, let us consider the case when the proton donor and acceptor are held at some large distance so that the distance between two minima is of order of 1 Å or more. It is easy to conclude that in this case the tunneling probability at the ground level is negligibly small. For such a large distance, the donor-acceptor interaction is weak, and hence the splitting of vibrational levels is negligible, so that it means the proton transfer on large distances of several angstroms is improbable. In the weakly interacting systems, the equilibrium distance between donor and acceptor equals the sum of their van der Waals radii. At the neutral H radius ∼1.2 Å, typical acceptor atom radius ∼1.5 Å, and the covalent bond length ∼1.1 Å, the equilibrium distance between two minima is ∼1.6 Å. This is too large as compared to 0.1 Å, and hence the proton transfer in this position is strongly unfavorable. However, the tunneling probability increases drastically with the closer approach of reactants. The proton wave function decays exponentially with the distance squared. Therefore, the tunneling probability depends exponentially on the square of the tunneling distance. The decrease in the tunneling distance increases the tunneling probability. On the other hand, the approach of the reactants cannot be an unrestricted one because repulsion between reactants hinders their mutual approach. The repulsion energy can be described by a Born-Mayer potential. The two opposite trends result in some optimal distance ensuring a maximum tunneling probability and, at the same time, not too large energy expenditure necessary to overcome the repulsion. The estimates for proton transfer between two C atoms carried out with realistic constants borrowed from independent experimental data
Scaldaferri and Pimentel have shown that the optimum tunneling distance is much shorter than the equilibrium one: about 0.4 Å instead of 1.5 Å.26 The empirical parameters used in these calculations were, of course, only approximate ones. Furthermore, the formula for nonadiabatic tunneling of protons in a double well of two harmonic oscillators was employed, and hence the donor-acceptor interaction even at small inter-reactant distance was neglected. Therefore, the result of these calculations cannot be considered as a strict and quantitative one. Nevertheless, it shows unambiguously that, in a transition configuration, a very substantial approach of the reactants should take place and gives the realistic order of its magnitude. It should be mentioned that the calculations employing, instead of harmonic, a Morse potential for C-H and O-H covalent bonds and substituting another Morse potential for C · · · O interaction have resulted in a quite similar value of the optimal tunneling distance, 0.46 Å.27 The other type of systems presents O-H and acids reacting with O, N, and other bases. The donor-acceptor interaction is rather strong already under equilibrium conditions, and the hydrogen bond is forming. For typical O-H · · · O bond with O · · · O distance of 2.8-3.0 Å and the O-H bond length of 1 Å, 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. In contrast to the previous case, the process is facilitated by two circumstances. First, the inter-reactant interaction makes the approach substantially easier than described by the Born-Mayer potential; the energy dependence on the distance is described by a Morselike equation with a much more gentle energy rise upon decrease in the O · · · O distance. Second, the energy curve along the proton coordinate deviates substantially from two intersecting parabolas of harmonic oscillators. Correspondingly, the barrier along this coordinate is lower, and the tunneling probability is higher and is not obeying the exponential decaying on the squared distance. The form of the corresponding dependence can be determined, in principle, from quantum chemical calculations. In particular, at not too short distances, it follows an exponential form similar to this for the long-range electron transfer, but with much larger coefficient a (about 30-40 Å-1 against ∼1 Å-1 for electron transfer).28 As a result, proton transfer for the reactant of the first type is usually markedly slower than for those of the second. The system investigated in this study has an S-H reacting with the NO2-O base via a water-assisted mechanism. The donor-acceptor interaction is also rather strong already under equilibrium conditions, and the hydrogen bond is forming. For typical S-H · · · O bond with S · · · O distance of 2.8-3.0 Å and the O-H bond length of 1 Å, the equilibrium interminima distance is around 1.0-1.2 Å. The tunneling factor, Γ, calculated for the H2S + NO3 and D2S + NO3 systems in the presence of water and deuterated water gave a ΓH/ΓD around 1.5-1.9 at 298 K, considering a barrier width of 1.2-1.0 Å, respectively. These results are similar to the Wigner correction for tunneling presented previously. For each reaction studied here, 50 trajectories were simulated at 298 K. The results of yield and averaged reaction time for the transition state decomposition into products at 298 K are presented in Table 3. The two possible pathways for this reaction are shown in Figures 2 and 3. Figure 2 presents a simple hydrogen atom abstraction from the H2S molecule by the NO3 radical. The water-assisted mechanism29-39 for the hydrogen atom abstraction from the H2S molecule by the NO3 radical is shown in Figure 3.
Kinetic Isotope Effect of the H2S + NO3 Reaction
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TABLE 3: Yield (%) and Averaged Reaction Time (tavg in fs) for the Transition State Decomposition into Products at 298 K reaction (1) (2) (3) (4) (7) (8)
H2S - NO3q D2S - NO3q (H2O)H2S - NO3q H2S - NO3(H2O)q (D2O)D2S - NO3q D2S - NO3(D2O)q
f f f f f f
HNO3 + SH DNO3 + SD (H2O)SH + HNO3 SH + HNO3(H2O) (D2O)DS + DNO3 SD + DNO3(D2O)
yield (%)
tavg (fs)
98
13.37
96
17.71
70
23.63
98
12.84
60
27.59
98
12.80
The H2S-NO3q decomposition into HNO3 and SH products has a yield of about 98% with an average reaction time of 13.37 fs. When the hydrogen atoms are replaced by the deuterium atom, D2S-NO3q, the yield barely decreases to 96% and the average reaction time slightly increase at 17.71 fs. Therefore, it shows that the D2S-NO3q decomposition is slower than the H2S-NO3q 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 interacting with the NO3 group, are similar to those of the H2S-NO3q decomposition, about 98% and 12.84 fs, respectively. However,
when a water molecule interacts with the H2S side, the yield of the (H2O)H2S-NO3q decomposition significantly decreases to about 70% and the average reaction time increases to 23.63 fs. These results show that the (H2O)H2S-NO3q decomposition is slower than those found for the H2S-NO3(H2O)q and H2S-NO3q decompositions. The (D2O)D2S-NO3q and D2S-NO3(D2O)q decompositions were calculated, and the results are also presented in Table 3. When all the hydrogen atoms are replaced by deuterium, the yield and the average reaction time of the D2S-NO3(D2O)q decomposition are similar to those found for the decomposition H2S-NO3(H2O)q and H2S-NO3q decompositions, about 98% and 12.80 fs, respectively. On the hand, as expected, the (D2O)D2S-NO3q decomposition is slower than those found for the (H2O)H2S-NO3q and H2S-NO3q decompositions. The yield and the average reaction time of the (D2O)D2S-NO3q decomposition were calculated in about 60% and 27.59 fs, respectively. It is important to note that the (H2O)H2S-NO3q and (D2O)D2S-NO3q decompositions occur by a nonconventional pathway, a water-assisted mechanism.29-39 In this mechanism, the hydrogen atom from the H2S molecule is transferred to the water molecule, and then the other hydrogen atom from the water molecule is transferred to the NO3 radical. There is a similar water-assisted mechanism reported previously, which
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.
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is generally known by the water-assisted proton-transfer mechanism.29-39 This mechanism usually occurs in aqueous phase. However, the mechanism presented here in this paper is unique for this system because it is a water-assisted H-atom transfer mechanism in gas phase. It is important to mention that it is a proton-transfer reaction, because the Mulliken charge distribution in the H3O group is positive, around +0.8. To the best of our knowledge, a similar mechanism is not reported previously 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-NO3q decomposition via the assisted-water mechanism. Remarkably, the H2S-NO3(H2O)q and D2S-NO3(D2O)q decompositions do not happen via the assisted-water mechanism, certainly because the H2O/D2O molecules are bound to the NO3 group, too far away from the reaction site. Experimentally, this could lead to different products from the conventional mechanism. For example, for (D2O)H2S + NO3 reaction, it would get DNO3 rather than HNO3, which may be verified experimentally. Conclusion In this study it was possible to verify that the Born-Oppenheimer molecular dynamics is a suitable method to investigate the chemical mechanism of the H2S + NO3 reaction in the presence of water molecules. Molecular dynamics simulations were performed 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 rate when D2O interacts with D2S but has no effect when D2O interacting with NO3. The yields of the H2S + NO3(H2O) and H2S + NO3(D2O) reactions are larger compared to those for the reactions (H2O)H2S + NO3 and (D2O)H2S + NO3. Furthermore, the average reaction times of the reactions H2S + NO3(H2O) and H2S + NO3(D2O) are shorter than those when H2O or D2O interacts with H2S. It was demonstrated that the (H2O)H2S + NO3 and (D2O)D2S + NO3 reactions occur via two possible pathways: the non-water-assisted and water-assisted hydrogen abstraction mechanisms. Acknowledgment. The authors are grateful to the CNPq funding (no. 485364/2007-7). A.S.P is recipient of a CNPq productivity fellowship (no. 304187/2009-7) and another one awarded by the Pontificia Universidade Cato´lica at Rio de Janeiro. M.C.L.S. and A.S.P. also thank FAPERJ for a research studentship (no. 101.673/2009) and a young scientist fellowship (no. 101.452/2010), respectively. References and Notes (1) Tyndall, G. S.; Ravishankara, A. R. Int. J. Chem. Kinet. 1991, 23, 483. (2) Wallington, T. J.; Atkinson, R.; Winer, A. M.; Pitts, J. N., Jr. J. Phys. Chem. 1986, 90, 5393. (3) Cantrell, C. A.; Davidson, J. A.; Sbetter, R. E.; Anderson, B. A.; Calvert, J. G. J. Phys. Chem. 1987, 91, 6017. (4) Dlugokencky, E. J.; Howard, C. J. J. Phys. Chem. 1988, 92, 1188.
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