Computational Studies on Metathetical and Redox ... - ACS Publications

Apr 2, 2010 - Self-Reaction and Interactions with HNOx (x ) 1-3) ... reduction reactions involving OH and NHx (x ) 1-3) in high ..... (4) Prasad, S. S...
0 downloads 0 Views 2MB Size
Download PDF
5320

J. Phys. Chem. A 2010, 114, 5320–5326

Computational Studies on Metathetical and Redox Processes of HOCl in Gas Phase. III. Its Self-Reaction and Interactions with HNOx (x ) 1-3) Z. F. Xu and M. C. Lin* Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322 ReceiVed: February 1, 2010; ReVised Manuscript ReceiVed: March 18, 2010

The gas-phase redox reactions of HOCl with its self and HNOx (x ) 1-3) have been studied theoretically by ab initio quantum chemical and statistical mechanical theories. The structures of reactants, intermediate complexes, products, and transition states were optimized at the MPW1PW91/6-311+G(3df,2p) level of theory. The potential energy surface of each reaction was refined at the CCSD(T)/6-311+G(3df,2p) level of theory. The most favorable products are predicted to be ClClO + H2O and ClOCl + H2O for the HOCl self-reaction (A), H2O + Cl + NO for the HOCl + HNO reaction (B), H2O + ClNO2 for the HOCl + HONO-t reaction (C), H2O + cis-ClONO for the HOCl + HONO-c reaction (D). For the HOCl + HONO2 reaction (E), only one dehydration reaction channel was considered to produce H2O + ClONO2. The rate constants of all above five reactions have been predicted at 300-3000 K by the VTST/RRKM theory. The calculation shows that the theoretical rate constants are within the upper limits of experimental results. In addition, we calculated the equilibrium constant for the Cl2O + H2O f HOCl + HOCl reaction, which is also in reasonable agreement with experimental data within the error of the available experimental enthalpy change. 1. Introduction Ammonium perchlorate (AP) is a practically important propellant in use today.1 Its initial decomposition and combustion products contain NHx (x ) 1-3) and HClOx (x ) 1-4) as well as ClO3 and OH in the gas phase.2 The reactive chlorine trioxide (ClO3) can be rapidly converted to ClO and HOCl by reduction reactions involving OH and NHx (x ) 1-3) in high temperature media. Consequently, the reactions of hypochlorous acid (HOCl) with other reactive radicals and molecules in the gas phase can be expected to take place and should play a significant role in the chemistry of the AP propulsion process.3 In addition, HOCl is a temporary reservoir of atmospheric chlorine in the stratosphere.4 It can react with other atmospheric radicals and molecules as happens in the combustion of AP. In our previous publications on HOCl reactions,5,6 we investigated the kinetics and mechanisms of its reactions with O, HOx (x ) 0-2), and ClOx (x ) 1-4) by ab initio quantum chemical theory and statistical reaction-rate theory. The results have been compared with available experimental and theoretical data. In the present work, we examine the HOCl self-reaction and the redox reactions with HNOx (x ) 1-3) because these molecules are present in AP combustion as well as in the atmosphere. To our knowledge there have been no experimental and theoretical studies for these reactions. However, there are several experimental works on the reverse reactions of HOCl + HOCl and HOCl + HNO3; that is, Cl2O + H2O and ClNO3 + H2O, respectively. For Cl2O + H2O f 2HOCl, Niki et al.7 determined its equilibrium constant to be 0.068 ( 0.010 at 295 K using the Fourier transform infrared method in 1979. In the same year, Knauth et al.8 investigated this reverse reaction by UV photometric measurement from 200 to 300 nm at 333 K. They obtained the equilibrium constant to be 0.132 ( 0.008, and the upper limit of the rate constant was found to be 4.48 × 10-23 cm3 molecule-1 s-1. In 1985, Ennis and Birks9 determined * To whom correspondence should be addressed. E-mail address: [email protected].

the equilibrium constant to be 0.092 ( 0.011 at 298 K with a low-pressure discharge flow system. For the reaction of chlorine nitrate (ClONO2) with water vapor, Atkinson et al.10 studied its kinetics in 1986 by the Fourier transform infrared spectrometer and they estimated the upper limit rate constant to be 2 × 10-21 cm3 molecule-1 s-1 at 298 K. In the same year, Rowland et al.11 obtained the upper limit rate constant to be 3.0 × 10-19 cm3 molecule-1 s-1 at 300 K in their experimental investigation on the hydrolysis of ClONO2. In 1989, Hatakeyama and Leu12 evaluated the upper limit rate constant to be 3.4 × 10-21 cm3 molecule-1 s-1 at 296 K, very close to the result of Atkinson et al.10 In the present paper, these experimental data will be compared with our theoretical prediction. 2. Computational Methods In the present study, the structures of the reactants, products, intermediates, and transition states have been optimized at the MPW1PW91/6-311+G(3df,2p) level of theory.13 The moments of inertia and frequencies of all the species and stationary points were calculated with the corresponding optimization method. For more accurate evaluation of energies, higher-level singlepoint energy calculations of all the species and stationary points have been carried out by the CCSD(T)/6-311+G(3df,2p) method14–16 based on the optimized geometries at the MPW1PW91/ 6-311+G(3df,2p) level. All the electronic structure calculations were preformed by the Gaussian 03 program.17 Rate constant calculations were carried out with the VARIFLEX program18 based on the microcanonical RRKM (RiceRamsperger-Kassel-Marcus) theory19–21 in the temperature range 300-3000 K. Eckart tunneling permeability coefficients22 were used to correct the rate constants for the hydrogen transfer quantum effects at low temperatures. The component rate constants are evaluated at the E/J-resolved level, and the pressure dependence is treated by one-dimensional master equation calculations using the Boltzmann probability of the complex for the J-distribution. For a barrierless association process, the

10.1021/jp100977k  2010 American Chemical Society Published on Web 04/02/2010

Metathetical and Redox Processes of HOCl

J. Phys. Chem. A, Vol. 114, No. 16, 2010 5321

Figure 1. Potential energy profiles for the reactions of HOCl with HOCl and HNOx (x ) 1-3) in units of kcal/mol at the CCSD(T)/6-311+G(3df,2p)// MPW1PW91/6-311+G(3df,2p) level of theory.

variational transition state theory (VTST)23,24 was employed with the Morse function, V(R) ) De{1 - exp[-β(R - Re)]}2, which represents the minimum potential energy path (MEP). In the V(R) equation, De is the binding energy excluding zero-point vibrational energy for an association reaction, R is the reaction coordinate (i.e., the distance between the two bonding atoms), and Re is the equilibrium value of R at the stable intermediate structure. 3. Results and Discussion The potential energy surfaces (PESs) of the HOCl reactions with HOCl and HNOx (x ) 1-3) were predicted at the CCSD(T)/6-311+G(3df, 2p) level of theory based on the geometric parameters optimized by MPW1PW91/6-311+G(3df, 2p) as alluded to above. All five reaction energy profiles are shown in Figure 1. The structures of reactants, intermediates and transition states at the MPW1PW91/6-311+G(3df, 2p) level of theory are drawn in Figure 2. All of the transition states were confirmed by vibrational analysis with only one imaginary frequency. For the kinetical calculation, the vibrational frequencies and moments of inertia for all of the reactants, products,

intermediate complexes, and transition states computed at the MPW1PW91/6-311+G(3df, 2p) level of theory are summerized in the Supporting Information. 3.1. Potential Energy Surfaces. 3.1.1. Reaction A: HOCl + HOCl. Three product channels have been identified in this reaction system, as seen in Figure 1A. The first two channels proceed by a hydrogen-bonded complex, a-LM1, which is formed by a barrierless association reaction of two HOCl molecules. At a-LM1, the hydrogen bond length is 1.921 Å, and its energy lies below that of the reactants by 4.5 kcal/mol. From a-LM1, there are two subchannels to continue this reaction. One is going through a four-membered ring transition state (a-TS1) and another hydrogen-bonded complex (a-LM2) to ClOCl + H2O. The energies of a-TS1, a-LM2, and ClOCl + H2O are 24.8, -4.9, and -3.3 kcal/mol, respectively, relative to reactants. At a-TS1, the O-Cl and H-O breaking bonds are 2.144 and 1.493 Å, respectively, and the O-Cl and H-O forming bonds are 2.525 and 1.025 Å, respectively. The imaginary frequency is i412 cm-1. For the second subchannel from a-LM1, a five-membered ring transition state (a-TS2) undertakes the reaction process with an imaginary frequency

5322

J. Phys. Chem. A, Vol. 114, No. 16, 2010

Xu and Lin

Figure 2. Geometric parameters (bond length in Å) of reactants, intermediates, and transition states optimized at the MPW1PW91/6-311+G(3df,2p) level of theory.

of i496 cm-1. Its O-Cl and H-O breaking bonds are 2.255 and 1.446 Å, respectively, and the Cl-Cl and H-O forming bonds are 2.899 and 1.034 Å, respectively. The relative energy of this transition state is 24.1 kcal/mol, which is only 0.7 kcal/ mol lower than that of a-TS1. However, the hydrogen bonded complex, a-LM3, and the products, ClClO + H2O, are higher

in energy than a-LM2 and ClOCl + H2O by 14.3, and 15.9 kcal/mol, respectively, because of the lower stability of ClClO. Also, we calculated the isomerization barrier for ClClO f ClOCl to be 26.6 kcal/mol, which cannot be readily overcome at low temperatures. So, the initial products of the HOCl + HOCl should be the mixture of ClClO and ClOCl. However,

Metathetical and Redox Processes of HOCl the former is unstable and can fragment to Cl + ClO with 16.0 kcal/mol endothermicity. In addition, the geometric parameters of a-TS1 are also optimized at the CCSD/6-311+G(3df,2p) level of theory and its Cartesian coordinates are put in Table S2 of the Supporting Information. The result shows that the structure of the transition state at the CCSD/6-311+G(3df,2p) level are in good agreement with that obtained at the MPW1PW91/6311+G(3df,2p) level of theory. The maximum deviation for the bond lengths is less than 0.05 Å. This is consistent with our previous papers.5,6 It implies that the geometry of the HOCl + HOCl system optimized at the MPW1PW91/6-311+G(3df,2p) level should be reliable. In the third product channel, the transition state, a-TS3, is a fourmembered ring structure with an imaginary frequecy of i731 cm-1. At a-TS3, the O-Cl and H-O breaking bonds are 2.448 and 1.088 Å, respectively, and the Cl-H forming bonds is 1.723 Å. Because of the much higher reaction barrier of 67.6 kcal/mol, this channel is not expected to be kinetically competitive to the above two channels, although both the hydrogen-bonded complex, a-LM4, and the products, HCl + ClOOH, are only 9.7 and 13.1 kcal/mol, respectively, higher than the reactants in energy. 3.1.2. Reaction B: HOCl + HNO. At first, this reaction system can barrierlessly form four hydrogen-bonded complexes, b-LM1, b-LM2, b-LM3, and b-LM5, as seen in Figure 1B. They lie below the reactants HOCl + HNO by 3.2, 1.7, 3.1, and 3.3 kcal/mol, respectively. The first two channels produce the same products, H2O + Cl + NO; the first one proceeds via the transition state b-TS1 with an imaginary frequency of i346 cm-1, and the second one via b-TS2 with an imaginary frequency of i363 cm-1. Both of these transition states represent the Cl atom elimination from HOCl with the H migration from the N atom of HNO to the O atom of HOCl. At b-TS1, the Cl-O and H-N breaking bonds are 2.059 and 1.307 Å, respectively, and the O-H forming bond is 1.145 Å. These bond lengths are very close to the corresponding bond lengths of b-TS2 as seen in Figure 2. It seems that b-TS1 is a cis structure and b-TS2 is a trans one. So, b-TS1 and b-TS2 have almost the same energy, 8.3 kcal/mol for the former and 8.4 kcal/mol for the latter. To confirm the feasibility of the MPW1PW91/6-311+G(3df,2p) method for HOCl + HNOx (x ) 1-3) systems, the CCSD/6311+G(3df,2p) method was employed to optimize the structures of both b-TS1 and b-TS2. The Cartesian coordinates are listed in Table S2 of the Supporting Information. The result shows that the geometric parameters optimized by the MPW1PW91/ 6-311+G(3df,2p) method and the CCSD/6-311+G(3df,2p) method are consistent and the maximum deviation for the bond lengths is less than 0.03 Å. The third reaction channel is to produce the H2O + ClNO products from the complex b-LM3 via the transition state b-TS3 and another complex b-LM4. The relative energy of b-TS3 is 21.4 kcal/mol and its imaginary frequency is i1818 cm-1. For the fourth reaction channel, we only give the isomerization process from b-LM5 to b-LM6 via transition state b-TS4. The transition state is a four-membered ring structure with the imaginary frequency of i652 cm-1. It represents the N-O bond forming and the H atom migration from one oxygen atom to another one. The energy of b-TS4 relative to that of reactants is 45.8 kcal/mol. Because of the much higher reaction barriers of b-TS3 and b-TS4 compared with those of b-TS1 and b-TS2, the contributions of the third and fourth channels to the HOCl + HNO reaction system are negligible kinetically. 3.1.3. Reaction C: HOCl + HONO-t. In the reaction of HOCl with trans nitrous acid (HONO-t), there are two hydrogen bonded complexes, c-LM1 and c-LM4, formed barrierlessly by

J. Phys. Chem. A, Vol. 114, No. 16, 2010 5323 the association of HOCl and HONO-t. As in Figure 1C, c-LM1 and c-LM4 are -4.5 and -2.8 kcal/mol, respectively, relative to the reactants in energy. From c-LM1, there are two subchannels giving rise to the H2O + ClNO2 and HOCl + HNO2 products. The former product channel occurs via the transition state c-TS1 with an imaginary frequency of i732 cm-1. This transition state structure shows that in the dehydration process, the migration of the H atom of HONO and the Cl atom of HOCl take place concurrently. At c-TS1, the breaking and the forming Cl-O bonds are 2.068 and 2.691 Å, whereas those of H-O bonds are 1.355 and 1.074 Å, respectively, as shown in Figure 2. The energies of c-TS1 and c-LM2 are 4.7 and -20.6 kcal/ mol, respectively, relative to that of the reactants. The latter subchannel contains c-TS2, c-LM3, and the products HOCl + HNO2 with the relative energies of 24.6, 2.8, and 8.5 kcal/mol, respectively. This channel is apparently much higher in energy than the H2O + ClNO2 product channel. The transition state c-TS2 with an imaginary frequency of i1706 cm-1 undergoes a hydrogen exchange structure to result in the isonitrous acid (HNO2), as indicated in Figure 2. In this reaction, hypochlorous acid acts as a catalyst in the isomerization process from HONO-t to HNO2. The next reaction channel from the hydrogen bonded complex c-LM4 to the products H2O + ClONO-t occurs through three transition states (c-TS3, c-TS4, and c-TS5) and two intermediates complexes (c-LM5 and c-LM6). c-TS3 is a four-membered ring transiton state with an imaginary frequency of i574 cm-1. c-TS4 is a rotation transition state of the hydroxyl group about the O-N bond from c-LM5 to c-LM6; c-TS5 is involved in the dehydration of c-LM6 to H2O + ClONO-t. As is evident from the energy diagram that c-TS3 and c-TS5 are 53.5 and 60.0 kcal/mol, respectively, higher than the reactants; this reaction channel is kinetically insignificant. Similarly, the final reaction channel from HOCl + HONO-t to HCl + HONO2 via the transition state c-TS6 has a very high potential barrier of 66.2 kcal/mol; it can also be ignored in kinetic consideration. 3.1.4. Reaction D: HOCl +HONO-c. As shown in Figure 1D, there are also several reaction channels involving the cisisomer of HONO. The lowest potential barrier reaction results in the hydrogen exchange, in which the products are the reactants themselves and thus kinetically irrelevant. This channel proceeds via d-LM1 and d-TS1 with the relative energies of -4.8 and 11.2 kcal/mol, respectively. The most important reaction channel produces H2O + ClONO-c via a hydrogenbonded complex d-LM2, a six membered ring transition state d-TS2, and another hydrogen-bonded complex d-LM3 of the product pair. These two complexes, d-LM2 and d-LM3, lie below the reactants by 3.8 and 9.8 kcal/mol, respectively, whereas the transition state d-TS2 lies above the reactants by 12.4 kcal/mol with an imaginary frequency of i264 cm-1. In Figure 2, the structure of d-TS2 illustrates that the Cl atom of HOCl migrates to the terminate O atom of HONO-c with the H atom transferring from HONO-c to the O atom of HOCl. The breaking and forming Cl-O bonds are 2.209 and 2.678 Å, whereas those of H-O bonds are 1.617 and 0.996 Å, respectively. The third dehydration process from the reactants to H2O + ClONO-t contains two intermediate complexes (d-LM4 and d-LM5) and two transition states (d-TS3 and d-TS4). The reactants associate barrierlessly to the hydrogen bonded complex, d-LM4, which then isomerizes to the intermediate, d-LM5, via the high energy transition state d-TS3 (52.1 kcal/mol). In fact, d-LM5 is identical to c-LM6 and d-TS4 is identical to c-TS5. The fourth product channel is very similar to the fourth channel of reaction C; it takes place via d-TS5 and a hydrogen-

5324

J. Phys. Chem. A, Vol. 114, No. 16, 2010

Xu and Lin

bonded complex d-LM6 with the relative energies of 66.7 and -20.8 kcal/mol, respectively. Apparently, with these much higher potential barriers comparing to that of the second reaction channel, both the third and fourth product channels are not expected to be kinetically relevant. 3.1.5. Reaction E: HOCl +HONO2. There are only two potential reaction channels for this reaction as seen in Figure 1E. Both occur via the hydrogen-bonded complex (e-LM1), formed barrierlessly with 7.2 kcal/mol exothermicity. From e-LM1, the first product channel occurs via the hydrogen exchange transition state e-TS1 with a 5.7 kcal/mol barrier, resulting in the formation of the reactant pair, HOCl +HONO2. The second reaction channel is a dehydration process from e-LM1 giving H2O + ClONO2 through e-TS2 and another hydrogen-bonded complex e-LM2. The reaction barrier is predicted to be 51.5 kcal/mol. As seen in Figure 2, the structure of e-TS2 is a six-membered ring configration with an imaginary frequency of i372 cm-1. The breaking and forming Cl-O bonds are 1.944 and 2.418 Å, whereas those of H-O bonds are 1.682 and 0.968 Å, respectively. e-LM2 is the association complex of H2O and ClONO2 with one hydrogen bond. Although the relative energies of e-LM2 and H2O + ClONO2 are -4.4 and -2.5 kcal/mol, respectively, this reaction could take place kinetically with a relatively small rate because of the high reaction barrier. 3.2. Thermochemistry and Rate Constants. From the above discussion about the potential energy surfaces of the five reaction systems, the most favorable reaction channels are the dehydration processes summarized as follows:

HOCl + HOCl f ClOCl + H2O

(1a)

f ClClO + H2O

(2a)

HOCl + HONO-t f ClNO2+H2O

(c)

HOCl + HNO f Cl + NO + H2O

(b)

HOCl + HONO-c f ClONO-c+H2O

(d)

HOCl + HONO2 f ClONO2+H2O

(e)

Table 1 compares the predicted heats of reaction (∆rH°) 0 with the values obtained from the experimental heats of formation 26–30 The theoretical results are, (∆fH°) 0 available in the literature. in general, in reasonable agreement with experimental values within experimental errors. The errors are distributed in the range from 0.1 to 0.9 kcal/mol, except the largest error of 1.9 kcal/ mol for the HOCl + HNO f Cl + NO + H2O reaction. The energetics predicted by the CCSD(T)/6-311+G(3df,2p)// MPW1PW91/6-311+G(3df,2p) method for the above chlorinecontaining reaction systems should be reliable for the thermochemical and kinetic applications. The rate constant calculations were carried out by the VARIFLEX code18 based on the microcanonical RRKM theory as described above; the component rate constants are evaluated at the E/J-resolved level with the treatment by one-dimensional master equation calculations using the Boltzmann probability of the complex for the J-distribution. The barrierless association process for hydrogen-bond complex formation can be described by the Morse function, V(RH-O) ) De(1 - exp (-1.449(RH-O - 1.981)))2 kcal/mol.6 However, this process is not important to the overall rate constant because of the unstable hydrogen-

TABLE 1: Comparison of the Theoretical Reaction Heats (∆rH°, 0 kcal/mol) with the Experimental Data reaction HOCl HOCl HOCl HOCl HOCl HOCl HOCl HOCl HOCl

+ + + + + + + + +

HOCl f ClOCl + H2O HOCl f ClOOH + HCl HNO f ClNO + H2O HNO f Cl + NO + H2O HONO-t f ClNO2 + H2O HONO-t f HONO2 + HCl HONO-c f ClONO-c + H2O HONO-c f HONO2 + HCl HONO2 f ClONO2 + H2O

this work

experimenta

-3.3 13.1 -52.1 -18.1 -19.2 -18.2 -8.4 -18.6 -2.5

-4.0 ( 1.8 13.8 ( 1.1 -51.7 ( 1.2 -16.2 ( 1.1 -18.4 ( 1.2 -18.3 ( 1.0 -8.6 ( 0.8 -17.8 ( 1.0 -2.3 ( 0.8

a Heats of formation from Chase25 for ∆fH°(HOCl) ) -17.1 ( 0.5 0 kcal/mol, ∆fH°(HCl) ) -22.0 ( 0.1 kcal/mol, ∆fH°(Cl) ) 28.6 kcal/ 0 0 mol, ∆fH°(H ) 21.5 kcal/mol, 0 2O) ) -57.1 kcal/mol, ∆fH°(NO) 0 ∆fH°(HONO-c) ) -16.9 ( 0.3 kcal/mol, ∆fH°(HONO-t) ) -17.4 ( 0 0 0.3 kcal/mol, ∆fH°(HONO ) 0 2) ) -29.8 ( 0.1 kcal/mol, ∆fH°(ClNO) 0 12.8 ( 0.1 kcal/mol, ∆fH°(ClNO 0 2) ) 4.2 ( 0.4 kcal/mol; from Thorn et al.26 for ∆fH°(ClOCl) ) 18.9 ( 0.8 kcal/mol; from Anderson27 for 0 ∆fH°(HNO) ) 26.3 ( 0.6 kcal/mol; from Alqasmi et al.28 for 0 29 ∆fH°(ClONO 0 2) ) 7.9 ( 0.2 kcal/mol; from Atkinson et al. for ∆fH°(ClONO-c) ) 14.5 kcal/mol; from Francisco et al.30 for 0 ∆fH°(HOOCl) ) 1.6 kcal/mol (this is a predicted value; no experimental 0 data available).

Figure 3. Predicted rate constants for the reactions as functions of temperature. k1a for reaction 1a; k2a for reaction 2a; kb for reaction b; kc for reaction c; kd for reaction d; and ke for reaction e.

bond complex and the following high barrier transition state, which is the rate control step. The pressure effect is negligible. Also, the vibrational frequencies and moments of inertia as well as Cartesian coordinates are taken from the table presented in the Supporting Information. The predicted results for these five reactions show that there is no pressure effect in the temperature range from 300 to 3000 K on account of the shallow well depths of the prereaction complexes. Figure 3 shows the predicted rate constants of the above five reactions plotted in the 300-3000 K range. All of the plots exhibit the characteristic of positive temperature dependence because of their distinct positive reaction barriers. Among these rate constants, k1a is almost same as k2a for their reaction barriers are almost equal; ke is the smallest due to the reaction’s largest potential barrier (51.5 kcal/mol). Also, the largest rate constant is kc at temperatures 800 K. The descending order of these rate constants, kc > kb > kd > ka > ke except kc∼ kb at high temperatures, reflects the ascending order of their reaction barriers. For kinetic modeling applications, the predicted rate constants for these five reactions have been fitted into modified three-parameter Arrhenius expressions in units of cm3 molecule-1 s-1 in the temperature range 300-3000 K:

Metathetical and Redox Processes of HOCl

J. Phys. Chem. A, Vol. 114, No. 16, 2010 5325

k1a ) 1.13 × 10-22T 3.03 exp(-11686/T) k2a ) 3.99 × 10-23T 3.06 exp(-11272/T) kb ) 5.78 × 10-22T 3.06 exp(-3054/T) kc ) 1.35 × 10-22T 2.86 exp(-1405/T) kd ) 5.38 × 10-21T 2.56 exp(-5902/T) ke ) 4.25 × 10-23T 3.08 exp(-25248/T) There are no existing experimental data for comparison. However, for reactions 1a and e, their reverse reactions have been investigated:

ClOCl + H2O f HOCl + HOCl

(-1a)

ClONO2+H2O f HOCl + HONO2

(-e)

We calculated the rate constants for these reverse processes as shown in Figure 4 for comparison with experimental values, available only as upper limits because of the slowness of these processes. As mentioned in the Introduction section, Knauth et al.8 gave the upper limit of the rate constant for reaction -1a to be 4.48 × 10-23 cm3 molecule-1 s-1 at 333 K from their experiment, which is consistent with our predicted value, 1.46 × 10-31 cm3 molecule-1 s-1 at that temperature. For reaction -e, the upper limits of three experimental rate constants are: 2 × 10-21, 3.0 × 10-19, and 3.4 × 10-21 cm3 molecule-1 s-1 by Atkinson et al.,10 Rowland et al.,11 and Hatakeyama and Leu,12 respectively, obtained around 298 K; these values, although consistent with our prediction, are much greater than the theoretical result. The predicted rate constants for the two reverse reactions have been fitted by three-parameter Arrhenius expressions:

k-1a ) 1.21 × 10-21T 2.82 exp(-13200/T) k-e ) 5.62 × 10-22T 2.75 exp(-26100/T) in units of cm3 molecule-1 s-1 in the temperature range 300-3000 K. Figure 5 shows the predicted equilibrium constant, K-1a, of reaction -1a including three experimental data. It can be seen that the predicted equilibrium constant is almost linear with positive temperature dependence. But, it is much smaller in the low temperature range because of the predicted higher reverse reaction endothermicity (3.3 kcal/mol at the CCSD(T) level of theory) than experimental values. Experimentally, Niki et al.,7 Knauth et al.,8 and Ennis and Birks9 reported the equilibrium constants 0.068 ( 0.010 at 295 K, 0.132 ( 0.008 at 333 K, and 0.092 ( 0.011 at 298 K, respectively, as shown in Figure 5. The deviation, however, is well within the uncertainties in the experimental values of ∆rH°0 (see Table 1). By reducing ∆rH°0 ) 3.3 kcal/mol by only 0.8 kcal/mol, the predicted K′-1a is increased by 3.8 and 1.9 times at 300 and 600 K, respectively,

Figure 4. Predicted rate constants of the reverse reactions and the experimental data with respect to temperature. k-1a for reaction -1a; k-e for reaction -e. (1) ref 7; (2) ref 10; (3) ref 11; and (4) ref 12.

Figure 5. Comparison of experimental equilibrium constant (K-1a) for the Cl2O + H2O ) HOCl + HOCl reaction with the predicted result as a function of temperature. (1) K-1a calculated with ∆rH°(Cl 0 2O + H2O f HOCl + HOCl) ) 3.3 kcal/mol; (2) K′-1a calculated with ∆rH°0 ) 2.5 kcal/mol; (3) ref 7; (4) ref 8; and (5) ref 9.

bringing about an excellent agreement with the experimental data, as seen in Figure 5. According to the relationship, log K ) -0.4343 (∆H - T∆S)/RT, we can estimate the enthalpy and entropy changes for the reverse reaction. From the slopes of the log K-1a curve, the values of the reverse reaction enthalpy are 2.7 and 1.8 kcal/mol in the temperature ranges of 400-1000 K and 1000-2000 K, respectively. From the intercepts of the extrapolation of those sections of the curve, the values of the entropy are 2.1 and 1.5 cal mol-1 K-1 in the 1000 K temperature range, respectively. 4. Conclusions The gas-phase redox reactions of HOCl with its self and HNOx (x ) 1-3) have been studied at the CCSD(T)/6311+G(3df,2p)//MPW1PW91/6-311+G(3df,2p) level of theory. The most favorable products are predicted to be ClClO + H2O and ClOCl + H2O for the HOCl self-reaction (A), H2O + Cl + NO for the HOCl + HNO reaction (B), H2O + ClNO2 for the HOCl + HONO-t reaction (C), and H2O + cis-ClONO for the HOCl + HONO-c reaction (D). For the HOCl + HONO2 reaction (E), only the dehydration reaction producing H2O + ClONO2 is identified. The rate constants for all five reactions above have been predicted in the temperature range 300-3000 K by the VTST/ RRKM theory. They all have strong positive temperature

5326

J. Phys. Chem. A, Vol. 114, No. 16, 2010

dependence with no pressure effect as one would expect. The predicted result reveals kc > kb > kd > ka > ke, except kc ∼ kb at high temperatures; the descending order corresponds to the ascending order of the five distinct reaction barriers. Also, the theoretical rate constants of the reverse reactions (k-1a and k-e) are consistent with the upper limits of the experimental results. The predicted equilibrium constant (K-1a) for the Cl2O + H2O ) HOCl + HOCl reaction is also consistent with the experimental data within the error limits of the experimental enthalpy values available in the literature. Acknowledgment. This work was supported by the Office of Naval Research under grant No. N00014-02-1-0133. Acknowledgment is also made to the Cherry L. Emerson Center of Emory University for the use of its computational resources. M.C.L. gratefully acknowledges the support from Taiwan’s National Science Council for a distinguished visiting professorship at the Center for Interdisciplinary Molecular Science, National Chiao Tung University, Hsinchu, Taiwan. Note Added after ASAP Publication. This article was published ASAP on April 2, 2010, with some errors in the text (particularly in the first paragraph of section 3.1.2). The correct version was reposted on April 6, 2010. Supporting Information Available: Table S1: Harmonic frequencies moments of inertia and Cartetian coordinates of all reactants, products, intermediates and transition states optimized at the MPW1PW91/6-311+G(3df,2p) level of theory. Table S2: Cartetian coordinates of a-TS1, b-TS1, and b-TS2 optimized at the CCSD/6-311+G(3df,2p) level of theory. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Jacobs, P. W. M.; Whitehead, H. M. Chem. ReV. 1969, 69, 551. (2) Zhu, R. S.; Lin, M. C. J. Phys. Chem C 2008, 112, 14481. (3) Zhu, R. S.; Lin, M. C. In Energetic Materials, Part 2, Detonation and Combustion; Politzer, P. Murray, J. S. Eds.; Elsevier Science Pub., 2003; Ch 11, pp 373-443. (4) Prasad, S. S. Plant. Space Sci. 1976, 24, 1187. (5) Xu, Z. F.; Lin, M. C. J. Phys. Chem. A 2009, 113, 8811. (6) Xu, Z. F.; Lin, M. C. J. Phys. Chem. A 2010, 114, 833. (7) Knauth, H.-D.; Alberti, H.; Clausen, H. J. Phys. Chem. 1979, 83, 1604.

Xu and Lin (8) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. Chem. Phys. Lett. 1979, 66, 325. (9) Ennis, C. A.; Birks, J. W. J. Phys. Chem. 1985, 89, 186. (10) Atkinson, R.; Tuazon, E. C.; Leod, H. M.; Aschmann, S. M.; Winer, A. M. Geophys. Res. Lett. 1986, 13, 117. (11) Rowland, F. S.; Sato, H.; Khwaja, H.; Elliott, S. M. J. Phys. Chem. 1986, 90, 1985. (12) Hatakeyama, S.; Leu, M.-T. J. Phys. Chem. 1989, 93, 5784. (13) Adamo, C.; Barone, V. J. Chem. Phys. 1998, 108, 664. (14) Scuseria, G. E.; Schaefer III, H. F. J. Chem. Phys. 1989, 90, 3700. (15) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796. (16) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968. (17) 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 C.02; Gaussian, Inc.: Wallingford, CT, 2004. (18) Klippenstein, S. J.; Wagner, A. F.; Dunbar, R. C.; Wardlaw, D. M.; Robertson, S. H. VARIFLEX Version 1.00; Argonne National Laboratory: 1999. (19) Hase, W. L. Acc. Chem. Res. 1983, 16, 258. (20) Wardlaw, D. M.; Marcus, R. A. Chem. Phys. Lett. 1984, 110, 230. (21) Klippenstein, S. J. J. Chem. Phys. 1992, 96, 367. (22) Eckart, C. Phys. ReV. 1930, 35, 1303. (23) Klippenstein, S. J. J. Phys. Chem. 1994, 98, 11459. (24) Klippenstein, S. J. J. Chem. Phys. 1991, 94, 6469. (25) Chase, M. W., Jr. NIST-JANAF Themochemical Tables, Fourth Edition J. Phys. Chem. Ref. Data, Monograph, 1998, 9, 1-1951. (26) Thorn, R. P., Jr.; Stief, L. J.; Kuo, S.-C.; Klemm, R. B. J. Phys. Chem. 1996, 100, 14178. (27) Anderson, W. R. Combust. Flame 1999, 117, 394. (28) Alqasmi, R.; Knauth, H. D.; Rohlack, D. Ber. Bunsen-Ges. 1978, 82, 217. (29) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampon, R. F.; Kerr, J. A.; Troc, J. J. Phys. Chem. Ref Dara 1989, 18, 881. (30) Francisco, J. S.; Sander, S. P.; Lee, T. J.; Rendell, A. P. J. Phys. Chem. 1994, 98, 5644.

JP100977K