Ab Initio Studies of ClO
xReactions. 3. Kinetics and Mechanism for the OH + OClO
Reaction
Zhen-Feng Xu, Rongshun Zhu, and M. C. Lin*
Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322 ReceiVed: May 9, 2002; In Final Form: NoVember 11, 2002
The mechanism for the OH + OClO reaction on the singlet and triplet surfaces and its rate constants for formation of various products have been investigated by means of ab initio molecular orbital theory and variational RRKM theory calculations. The geometric parameters of stationary points were optimized at the B3LYP level of theory with the 6-311G(d,p) and 6-311+G(3df,2p) basis sets, and the potential energy surfaces were evaluated at the G2M(CC2)//B3LYP/6-311+G(3df,2p) level of theory. Three main product channels, all located on the singlet PES, have been identified: (1) HOO + ClO, (2) HOCl +1O
2, and (3) HOClO2, the
association product. The predicted results show that the rate constants for channels 1 and 2 are pressure-independent up to 1000 atm and that for channel 3 is strongly pressure dependent. Below 1000 K, all rate constants were found to vary negatively with temperature. The individual and total rate constants in the temperature range from 200 to 1000 K at 1 Torr He pressure can be represented by k1(T) ) 1.22× 10-22T2.75
exp(1682/T), k2(T) ) 5.47 × 10-20T2.07 exp(2064/T), k3(T) ) 1.37 × 104T-6.61exp(-536/T) (200-500 K)
and 4.99× 1054T-22.36exp(-9807/T) (500-1000 K), and k
tot(T) ) 1.78× 10-20T2.25exp(2100/T) in units of
cm3molecule-1s-1. The predicted rate constant, with the HOCl +1O
2as the major products in the 300-500
K range, agrees well with available experimental data obtained at 1 Torr He pressure. The high- and low-pressure limits of k3can be effectively given by k3∞(T) ) 3.24× 10-11T0.28exp(-18/T) cm3molecule-1s-1
in 200-2500 K and k3°(T) ) 1.28× 10-13T-6.36 exp(-635/T) for 200-800 K, 7.37× 1084T-36.02
exp(-22134/T) for 800-1000 K, and 2.91× 10-13T-8.42exp(11500/T) for 1000-2500 K in units of cm6molecule-2
s-1 with N2as the third body.
1. Introduction
Chlorine dioxide, OClO, is a key reactive intermediate in the combustion of ammonium perchlorate (AP); it may be formed by the decomposition of ClO31and by the reaction of OH with
ClO3, which has been predicted to yield HO2 + OClO very
effectively.2In the stratosphere, OClO may be formed by the
reaction of ClO with XO (where X ) Br, Cl, or O2).3,4In both
media, OH radicals are known to be present and play a key role in the global kinetics. Poulet, Zagogianni, and Le Bras5
investigated experimentally the kinetics of reaction of OH with OClO by electron paramagnetic resonance and laser-induced fluorescence in 1986. They obtained total rate constants at pressures 0.5-1.4 Torr and over the temperature range from 293 to 473 K and suggested the following reaction mechanism:
to explain an unusually high HOCl + O2product yield with its
branching ratio approaching unity, according to the result of their kinetic modeling.5In addition to the above processes, the
association reaction,
which has not been considered under the low-pressure conditions employed,5 may become competitive under the stratospheric
condition.
In the present work, we investigate the kinetics and mecha-nism of the title reaction by high-level molecular orbital and statistical theory calculations using a similar approach as we have recently employed in our studies of analogous systems, OH + ClO,6O + OClO,7OH + ClO
3,2and ClO + ClO.8The
results from our latest study of this series, OH + OClO, is presented herein.
2. Computational Methods
The geometric parameters of the reactants, products, inter-mediates, and transition states on the potential energy surfaces of the OH + OClO system at singlet and triplet electronic states were optimized at the B3LYP level of theory9,10(i.e., Becke’s
three-parameter nonlocal exchange functional with the nonlocal correlation functional of Lee, Yang, and Parr) with the standard Gaussian basis sets 6-311G(d,p) and 6-311+G(3df,2p). All the stationary points have been identified for local minima and transition states by vibrational analysis. Intrinsic reaction coordinate analyses11 have been performed to confirm the
connection between transition states and designated reactants, products, or intermediates. The higher level single-point energy calculations of the stationary points were performed by the G2M(CC2) method12based on the optimized geometries at the
B3LYP/6-311+G(3df,2p) level. The G2M method calculates the base energy at the PMP4/6-311G(d,p) level of theory and improves it with the expanded basis set and coupled cluster * Corresponding author. E-mail: chemmcl@emory.edu. National Science
Council Distinguished Visiting Professor at the National Chiaotung University, Hsinchu, Taiwan.
OH + OClO f HOO + ClO OH + OClO f HOCl + O2 HOO + ClO f HOCl + O2
OH + OClO f HOClO2
10.1021/jp021183+ CCC: $25.00 © 2003 American Chemical Society Published on Web 01/25/2003
corrections as well as a “higher level correction”. All electronic structure calculations were performed with the GAUSSIAN 98 program.13
The rate constant for the association reaction producing HOClO2was calculated by the VARIFLEX program14based
on the microcanonical Rice-Ramsperger-Kassel-Marcus (RRKM) theory.15The component rates were evaluated at the
E/J-resolved level and the pressure dependence was treated by the one-dimensional master equation calculations using the Boltzmann probability of the complex for the J-distribution. For the barrierless transition state process, the Morse functional
was used to represent the minimum potential energy path for the association reaction. Here, De is the bonding 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 Reis the equilibrium value of R at
the stable intermediate structure.
For the coupling of different accessible reaction paths, we have employed the ChemRate program of NIST16to evaluate
product branching ratios under different T, P conditions. The predicted rate constants and product branching ratios will be compared with experimental values.5
3. Results and Discussion
A. Potential Energy Surfaces and Reaction Mechanism.
The geometries of the intermediates optimized at the B3LYP/ 6-311G(d,p) and B3LYP/6-311+G(3df,2p) level are shown in Figure 1 whereas those of the transition states optimized at the same levels are displayed in Figure 2. The singlet and triplet potential energy diagrams obtained at the G2M level are presented in Figure 3a,b. Tables 1 and 2 display the calculated geometry parameters and frequencies, comparing with available
experimental values for the reactants and products. The total and relative energies of the singlet and triplet species involved in the reaction are compiled in Table 3, and the vibrational frequencies and moments of inertia are summarized in Table 4 for the intermediates and transition states. Table 5 compares the experimental and calculated heats of formation for some known species.
By inspection of Table 1, one can see that the structural parameters of the all species obtained at the B3LYP/6-311+G-(3df,2p) level are in better agreement with experimental values than those at the B3LYP/6-311G(d,p) level. The largest errors in bond length and angle are 0.075 Å and 1.2°at the B3LYP/ 6-311G(d,p) level, and 0.011 Å and 1.2° at the B3LYP/6-311+G(3df,2p) level. For the predicted frequencies listed in Table 2, the largest deviation from experimental values is 8%. The intermediates and transition states on the singlet and triplet paths will be discussed in the following sections.
(a) Singlet reaction channels. (i) 1HOOClO-1 and 1
HOO-ClO-2 (Two Isomers of Peroxychlorous Acid) and1HOClO 2
(Chloric Acid). It is readily seen that the interaction between the O atom of OH and the O or Cl atom of OClO directly forms different intermediates, HOOClO and HOClO2. HOOClO has
both isomers as shown in Figure 1. Checking the structure parameters of1HOOClO-1 and 1HOOClO-2 we find that the
Cl2-O3 bond lengths (see Figure 1) for both intermediates are sensitive to the size of the basis set. At the B3LYP/6-311+G-(3df,2p) level, this bond in 1HOOClO-1 and 1HOOClO-2
decreases by 0.171 and 0.521 Å, respectively, comparing with those obtained at the B3LYP/6-311G(d,p) level; meanwhile, the dihedral angles O4O3Cl2O1 and H5O4O3Cl2 in1HOOClO-1
increase by about 5° when the basis set increases from 6-311G(d,p) to 6-311+G(3df,2p). In1HOOClO-2, however, the
dihedral angle changes are more significant, they increase by 70.5°and 11.3°from the 6-311G(d,p) to the 6-311+G(3df,2p) for the O4O3Cl2O1 and H5O4O3Cl2 dihedral angles, respec-tively. The absolute values of the Cl2-O3 bond and the O4O3Cl2O1 and H5O4O3Cl2 dihedral angles in1HOOClO-1
obtained at the B3LYP/6-311+G(3df,2p) level, 1.750 Å, 80.4°, and 93.1°, respectively, are close to those of 1.758 Å, 78.2°, and 93.8°obtained at the MP2/6-311G(2df,2p) level by Fran-cisco and Sander.24
For the HOClO2 intermediate, with the basis set size
increasing, significant structural changes also occur in the bond lengths and dihedral angles. The O1-Cl2, O3-Cl2, and Cl2-O4 bonds decrease by 0.034, 0.047, and 0.051 Å, respectively; whereas the dihedral O1Cl2O4H5 increases from -59.9° to +21.7°and the dihedral O3Cl2O4H5 increases from 59.4°to 140.7°, when the basis set increases from 6-311G(d,p) to 6-311+G(3df,2p). Similar trends were found in the structures obtained from the MP2/6-31G(d) to MP2/6-311G(2df,2p) levels by Francisco and Sander.24
1HOOClO-1, 1HOOClO-2, and 1HOClO
2 lie below the
reactants by -12.1, -13.9, and -32.6 kcal/mol, respectively, at the G2M//B3LYP/6-311+G(3df,2p) level. Among these, chloric acid is the most stable one, which is also consistent with the results obtained by Francisco and Sander.24Because the
structures optimized using larger basis sets are more reliable, in the following text, the cited geometric parameters are those obtained at the B3LYP/6-311+G(3df,2p) level and the G2M energies on the basis of the structures at this level.
(ii) Isomerization among1HOOClO-1,1HOOClO-2, and1
-HOClO2. The transition states (TS1 and TS2) and energy
diagram for isomerization of1HOOClO-1 to1HOOClO-2 and 1HOClO
2, are shown in Figures 2 and 3a, respectively. For the
TABLE 1: Optimized Geometric Parameters of the Reactants and Products (Bond Lengths in Ångstroms and Angles in Degrees) species B3LYP/ 6-311G(d,p) B3LYP/ 6-311+G(3df,2p) expt OH (2Π) R OH 0.975 0.974 0.971a OClO (2B 1) ROCl 1.546 1.479 1.471a θOClO 118.1 117.3 117.6 HOO (2A′′) R HO 0.976 0.975 0.971b ROO 1.328 1.324 1.331 θHOO 105.5 105.5 104.3 ClO (2Π) R ClO 1.626 1.576 1.570a HOCl (1A′) R HO 0.968 0.966 0.964c ROCl 1.738 1.700 1.689 θHOCl 102.1 103.7 103.0 1O 2(1∆g) ROO 1.207 1.203 1.216d 3O 2(3Σg-) ROO 1.206 1.203 1.208
aReference 17.bReference 18.cReference 19.dReference 20.
TABLE 2: Moments of Inertia and Vibrational Frequencies of the Reactants and Products Predicted at
B3LYP/6-311+G(3df,2p)
species Ia, Ib, Ic(au) frequencies (cm-1)
OH (2Π) 3.2, 3.2 3722 (3735)a OClO (2B 1) 35.3, 182.4, 217.7 451, 966, 1117 (447, 945, 1110)b ClO (2Π) 97.3, 97.3 861 (853)a HOCl (1A′) 2.9, 120.3, 123.2 739, 1262, 3786 (725, 1267, 3794)c HOO (2A′′) 2.9, 53.2, 56.1 1172, 1443, 3612 (1098, 1392, 3436)d 1O 2(1∆g) 41.3, 41.3 1634 (1509)b 3O 2(3Σg-) 41.3, 41.3 1645 (1580)b
aReference 20.bReference 17.cReference 21.dReference 22.
V(R) ) De{1 - exp[-β(R - Re)]}2
isomerization between1HOOClO-1 and1HOOClO-2, it occurs
mainly through the rotation of the OH group along the O3-O4 bond. One can see from Figure 2 that there is only minor variation in the bond lengths and bond angles from1HOOClO-1
via TS1 to 1HOOClO-2; however, the dihedral angles
H5O4O3Cl2 in these three species are +93.1°, -1.0°, and -91.9°, respectively, with significantly larger changes as expected. The isomerization barrier for this process is 5.1 kcal/ mol. For the isomerization from1HOOClO-1 to1HOClO
2, the
corresponding transition state TS2, has a three-center config-uration. Inspecting the structures of1HOOClO-1 and TS2, we
see that the forming Cl2-O4 bond length in TS2 is 0.305 Å shorter than that in1HOOClO-1 and the breaking O3-O4 bond
in TS2 lengthens by 0.656 Å, comparing with those in
1HOOClO-1; meanwhile, the O4O3Cl2 bond angle bends from
111.1°in 1HOOClO-1 to 83.1°in TS1. Because of the larger
configuration changes during the isomerization process, TS2 has a higher barrier, which lies above the reactants by 3.8 kcal/ mol at the G2M level.
(iii) HOO + ClO Formation. The fragmentation of the Cl2-O3 bond in 1HOOClO-1 via TS3 results in the formation of
HOO + ClO. In TS3, the breaking Cl-O bond increases 0.175 Å whereas the forming O-O bond decreases 0.053 Å, compar-ing with those in1HOOClO-1. TS3 lies above the intermediate, 1HOOClO-1, and the products HOO + ClO by 9.4 and 3.6 kcal/
mol, respectively (see Figure 3a). This dissociation mechanism is different from that of HOOCl f HOO + Cl, which is a barrierless process and is the dominant channel in the HO + ClO reaction.6
(iv) HOCl +1O
2Formation. There are two reaction channels
producing HOCl and1O
2, as shown in Figure 3a. In the first
channel, the configuration of1HOOClO-2 rotates, accompanied Figure 1. Optimized geometries of the intermediates (lengths in ångstroms and angles in degrees). The top numbers were optimized at the B3LYP/
by H atom migration to O1 to form the molecular complex
1OOHOCl via a twisted five-membered ring transition state TS4,
followed by the decomposition of the complex into HOCl and
1O
2through a barrierless process. The imaginary frequency of
TS4 is 789 cm-1, and its vector points to1OOHOCl positively
and to1HOOClO-2 negatively. At the G2M level, the forward
and reverse potential barriers of this reaction channel are 5.7 and 21.0 kcal/mol, respectively. Apparently, it is quite favorable to the forward reaction. 1OOHOCl is a hydrogen-bonded
complex formed by the association of HOCl with1O 2; it lies
only 2.2 kcal/mol below HOCl and1O
2. For the second channel,
the two terminal O atoms of HOClO2form O2and eliminate
via TS5. This process involves the breaking of two Cl-O bonds and the formation of one O-O bond. Expectably, this reaction path has large forward and reverse potential barriers, 67.8 and 62.2 kcal/mol, respectively. Apparently, this channel is kineti-cally unimportant and will have no contribution to the formation of HOCl +1O
2.
(b) Triplet Reaction Channels. (i) HOO + ClO Formation. Three channels were found to form HOO + ClO over the triplet electronic state potential surface. TS6, TS7, and TS8 correspond
to one of the O atoms in OClO being abstracted by OH through cis,cis, trans,trans, and trans,cis structures (see Figure 2) to form loose complexes,3HOOClO-1,3HOOClO-3, and3HOOClO-2,
respectively. The potential barriers of TS6, TS7, and TS8 at the G2M level are 41.0, 33.0, and 34.4 kcal/mol, as shown in Figure 3b. Similarly, high barriers on the triplet potential energy surface were also found in the HO + ClO6and ClO + ClO8
reactions. For the HO + ClO f3HOOCl and ClO + ClO f 3ClOOCl reactions; however, their barriers are comparatively
lower, at 17.26 and 28.0 kcal/mol,8 respectively. These
phe-nomena may be attributed to the interaction between the two parallel spin electrons on the two radicals, the repulsive interaction results in the energy interval of frontier molecular orbitals being quite large.
(ii) HOCl +3O
2Formation. The formation of HOCl and3O2
involves three loose complexes and two tight transition states. This process can be expressed as HO + OClO f3OHOClO-1 f TS9 f3OHOClO-2 f TS10 f3OOHOCl f HOCl +3O2,
as shown in Figure 3b. For TS9, it mainly undergoes the transfer of the H atom in the HO group to one of the terminal O in OClO (see Figure 2) to form complex3OHOClO-2. In TS10, Figure 2. Optimized geometries of the transition states (lengths in ångstroms and angles in degrees). The top numbers were optimized at the
B3LYP/6-311+G(3df,2p) level; the bottom numbers were optimized at the B3LYP/6-311G(d,p) level. x
the forming O1-O5 bond length is 0.640 Å shorter than that in3OHOClO-2 and the breaking O1-Cl2 bond lengthens 0.183
Å compared with that in3OHOClO-2. As the reaction proceeds,
O2eliminates from3OHOClO-2 to form3OOHOCl, which is a
hydrogen-bonding complex formed by 3O
2 and HOCl. The
complex lies below3O
2and HOCl by only 1.2 kcal/mol at the
G2M level. The forward and reverse potential barriers for TS9 are 37.4 and 9.7 kcal/mol, respectively, and those for TS10 are 19.5 and 101.3 kcal/mol, respectively.
On the basis of the above discussion, we may conclude that the products HOO, ClO, HOCl, and1O
2are mainly produced
by singlet reaction channels. Due to their high entrance barriers, the contribution of triplet channels to the overall reaction of the HO + OClO reaction can be neglected in kinetic modeling. To establish the reliability of this calculation, the predicted heats of formation of some species are compared in Table 5 with the experimental and theoretical values reported previously by other authors. It can be seen that the values of HOCl and HOO calculated at the G2M level agree reasonably with experimental data and the absolute differences between the experimental and calculated values are less than 1.8 kcal/mol. However, for the heats of formation of HOClO2and
HOOClO-TABLE 3: Total and Relative Energies of the Reactants, Intermediates, Transition States, and Products for the OClO + OH Reaction with ZPE Correction
energies (kcal/mol)
species B3LYP/6-311G(d,p) B3LYP/6-311+G(3df,2p) G2M//B3LYP/6-311+G(3df,2p)
∆rH°(0K) exptb(kcal/mol) OH (2Π) + OClO(2B 1) -686.22180a -686.30066a -685.48534a HOO(2A′′) + ClO(2Π) -32.7 -10.1 -6.3 -7.3 HOCl(1A′) +1O 2(1∆g) -39.9 -13.8 -27.0 -27.3 HOCl(1A′) +3O 2(3Σg-) -78.9 -52.3 -53.4 -49.8 1HOOClO-1 -18.6 -6.2 -12.1 1HOOClO-2 -23.2 -7.8 -13.9 3HOOClO-1 -35.3 -11.4 -8.4 3HOOClO-2 -35.1 -11.4 -7.9 3HOOClO-3 -34.6 -10.9 -8.3 1HOClO 2 -17.4 -25.3 -32.6 3OOHOCl(3A′′) -79.7 -52.4 -54.6 1OOHOCl(1A′) -42.5 -15.3 -29.2 3OHOClO-1(3A′′) -3.1 -1.3 -0.5 3OHOClO-2 31.2 30.8 27.2 TS1 -14.1 -3.7 -7.0 TS2 18.8 18.1 3.8 TS3 -18.3 -3.5 -2.7 TS4 -23.3 -0.1 -8.2 TS5 53.3 59.5 35.1 TS6 (3A′′) 15.0 28.7 41.0 TS7 14.0 26.4 33.6 TS8 (3A′′) 15.1 27.5 34.4 TS9 18.8 28.4 36.9 TS10 (3A′′) 24.2 43.4 46.7
aUnit in au.bReferences 17, 20, and 23.
TABLE 4: Moments of Inertia and Vibrational Frequencies of the Intermediates and Transition States at the B3LYP/ 6-311+G(3df,2p) Level
species Ia, Ib, Ic(au) frequencies (cm-1)
1HOOClO-1 103, 466, 515 137, 255, 356, 432, 489, 871, 1008, 1402, 3736 1HOOClO-2 109.8, 446.0, 506.6 125, 271, 356, 452, 503, 874, 995, 1411, 3732 3HOOClO-1 70.4, 881.4, 951.9 76, 79, 96, 207, 349, 845, 1188, 1462, 3523 3HOOClO-2 40.9, 1083.3, 1124.2 43, 69, 78, 106, 200, 852, 1177, 1446, 3614 3HOOClO-3 37.3, 1107.2, 1144.5 28, 78, 85, 122, 185, 846, 1179, 1446, 3604 1HOClO 2 194.9, 214.8, 362.1 97, 373, 409, 534, 619, 1059, 1137, 1237, 3742 3OOHOCl(3A′′) 136.0, 1063.9, 1199.9 4, 18, 64, 87, 177, 743, 1281, 1647, 3763 1OOHOCl(1A′) 78.5, 1160.3, 1238.8 22, 40, 75, 168, 294, 743, 1327, 1631, 3690 3OHOClO-1(3A′′) 136.1, 830.6, 966.7 23, 26, 108, 287, 352, 458, 967, 1114, 3681 3OHOClO-2 218.2, 372.8, 534.5 86, 140, 202, 336, 490, 660, 944, 1270, 3622 TS1 101.6, 452.8, 499.4 300i, 169, 320, 392, 550, 813, 1010, 1359, 3763 TS2 145.5, 385.2, 462.4 417i, 174, 277, 364, 478, 798, 973, 1184, 3748 TS3 136.0, 395.6, 516.4 134i, 198, 348, 468, 542, 964, 1021, 1432, 3676 TS4 145.4, 369.5, 508.9 789i, 230, 250, 505, 526, 854, 1205, 1465, 2023 TS5 104.1, 356.8, 454.7 912i, 238, 300, 361, 462, 658, 877, 1009, 3796 TS6 (3A′′) 79.5, 662.2, 741.8 881i, 63, 175, 266, 352, 430, 1015, 1019, 3758 TS7 35.1, 671.8, 700.9 844i, 122, 133, 227, 351, 575, 851, 1006, 3767 TS8 (3A′′) 32.6, 716.7, 749.3 823i, 36, 90, 154, 326, 495, 939, 1033, 3762 TS9 169.4, 443.3, 524.9 689i, 115, 148, 388, 689, 818, 1027, 1127, 2011 TS10 (3A′′) 166.7, 350.8, 517.6 903i, 127, 233, 369, 543, 638, 682, 1411, 2830
TABLE 5: Heats of Formation of Four Species (kcal/mol) at 0 K Predicted at the G2M(CC2)//B3LYP/6-311+G(3df,2p) Level
species this worka literature
HOCl (1A′) -16.8 -17.1 ( 0.5,b-16.7 ( 0.6c
HOO (2A′′) 2.2 1.2 ( 2.0,b4.0 ( 0.8,d3.5 ( 0.5e
HOClO2 0.1 4.2f
1HOOClO-1 20.6 25.3f aHeats of formation of OH, OClO, O
2(1∆g), and ClO are 8.8 ( 0.1,
23.9 ( 1.9, 22.5, and 24.2 kcal/mol, respectively, as standard values taken from refs 23, 17, and 20, respectively.bReference 17.cReference
1, the G2M values are 4.1 and 4.7 kcal/mol less than those calculated by Francisco and Sander24at the G2 level, presumably
due to the smaller basis set employed in geometry optimization with the latter method.
B. Rate Constant Calculations. From the above analysis of
the reaction mechanism, key product channels of the HO + OClO reaction system can be determined as
The rate constants for these reaction channels were calculated by using variational TST and RRKM rate theory with parabolic barrier tunneling correction.28 In fact, the tunneling effect is
very small and unimportant because of the low-lying barriers
below the reactants and the flat PES in the TS’s involving H-atom migration. The increase in the rate constant due to tunneling is less than 2% at 200 K.
The relative energies given in Table 3 and the vibrational frequencies and moments of inertia in Table 4 are used to calculate the rate constants. The L-J (Lennard-Jones) param-eters required for the RRKM calculations for the HOOClO isomers (assumed to be the same for all three), ) 230 K and σ ) 4.2 Å, were derived from deconvoluting the L-J potential of the He-HOOClO system obtained by our ab initio calculation at the B3LYP/6-311G(d,p) level using the approximation, 12 ) (12)1/2andσ12) (σ1+σ2)/2, for the collision pair. The 12
andσ12parameters for the He-HOOClO collision pair were
predicted to be 48.0 K and 3.4 Å by fitting the He-HOOClO potential energy curve using the L-J function,29 V ) 4[(σ/ r)12- (σ/r)6]; here r represents the distance between atom He
and the center of the mass of the intermediate. The L-J Figure 3. Schematic energy diagram of the OH + OClO system calculated by means of the G2M(CC2) method with the geometry parameters
optimized at the B3LYP/6-311+G(3df,2p) level. x
parameters for He, ) 10 K andσ ) 2.56 Å, were taken from the literature.30
The back-dissociation of 1HOOClO-1, 1HOOClO-2, and
HOClO2 intermediates to HO + OClO occurs barrierlessly,
without a well-defined transition state. Their dissociation potential energy curves were calculated by varying the O3-O4, O3-O3-O4, and Cl2-O4 bond distances with an interval of 0.1 Å for1HOOClO-1,1HOOClO-2, and HOClO
2from their
equilibrium values, 1.386, 1.314, and 1.783 Å, to 3.3, 3.2, and 3.5 Å, respectively. Other geometric parameters were fully optimized at the B3LYP/6-311G(d,p) level of theory. For each process, the B3LYP/6-311G(d,p) calculated total energy at each point along the reaction path was used to evaluate the Morse potential energy function and then scaled to match the dissocia-tion energy predicted at the G2M level of theory. For the above processes, Morse’s parameters β, obtained by fitting the predicted V(r) curves, are 5.38, 4.07, and 3.71 Å-1, respectively. The fitting deviations are less than 4% for the disassociation energy and 8% forβ, which have no noticeable influence on the predicted rate constants.
The rate constant for the association reaction channel 3 was calculated in the temperature range from 200 to 2500 K and the pressure range from 1× 10-5to 7.6× 107Torr with the
VARIFLEX code,14whereas those for channels 1 and 2 were
computed with the ChemRate code16coupling all intermediates
involved in the forward and reverse reactions, as shown in Schemes 1 and 2. To perform the ChemRate calculation, we first evaluated the transition state structures for the barrierless association/decomposition processes by the much-practiced canonical variational method.31-33 The Gibbs free energy of
activation,∆G(T,s), was calculated along the reaction path, s, using the energies given by the Morse functions and the optimized molecular structures and vibrational frequencies evaluated above. The transition state at the dividing surface s ) s#was defined by the maximum value of ∆G(T,s)s#) ) ∆G#(T) for each temperature.32,33For both barrierless association
processes, the O(3)-O(4) separations of the variational transition states were determined to be 1.9 Å below 1500 K and 1.8 Å above 1500 K. Namely, the positions of the variational transition state for these two barrierless association processes are not sensitive to the variation of temperature.
The individual and total rate constant curves are presented in Figure 4 as a function of reciprocal temperature. From the
result, it is evident that all rate constants exhibit negative temperature dependences at temperatures below 1000 K, and the rate constants for reaction channels 1 and 2 are pressure independent up to 1000 atm, whereas the rate constant for channel 3 is strongly positive-pressure dependent. Under the 1 Torr condition employed by Poulet et al.,5 k
3is far less than
those of other channels and its contribution to total rate constant is negligible. Total rate constant calculated at 1 Torr pressure is shown in Figure 4d. The predicted rate constant is in good agreement with the available experimental data. The upswing in the total rate constant above 1000 K results from the increase in both k1and k2(see Figure 4a,b and Table 6). The predicted
rate constants over the temperature range 200-1000 K at 1 Torr He pressure for the three product channels can be expressed in units of cm3molecule-1s-1by
For AP combustion applications, the high- and low-pressure limits of the rate constant for the formation of HClO3from OH + OClO, k3, with N2as the third-body are given as
and
At atmospheric N2 pressure, k3 can be represented by the
expressions
In contrast to the results above, the rate constants of the triplet reaction channel via the lowest barrier at TS7 shown in Figure 5 are many orders of magnitude smaller. Accordingly, the reactions via all triplet paths cannot compete with those via the singlet paths, as one would expect. As the absolute error of energies predicted by the G2M method for the second row compounds was estimated to be in the range 0.9-1.2 kcal/mol,12
we have examined the sensitivity of the predicted total rate
SCHEME 1 SCHEME 2 k1(T) ) 1.22× 10-22T2.75exp(1682/T) k2(T) ) 5.47× 10-20T2.07exp(2064/T) k3(T) ) 1.37× 104T-6.61exp(-536/T) 200-500 K k3(T) ) 4.99× 1054T-22.36exp(-9807/T) 500-1000 K ktot(T) ) 1.78× 10-20T2.25exp(2100/T) k3∞(T) ) 3.24× 10-11T0.28exp(-18/T) cm3molecule-1s-1in 200-2500 K k30(T) ) 1.28× 10-13T-6.36exp(-635/T) cm6molecule-2s-1in 200-800 K k30(T) ) 7.37× 1084T-36.02exp(-22134/T) cm6molecule-2s-1in 800-1000 K k30(T) ) 2.91× 10-13T-8.42exp(11500/T) cm6molecule-2s-1in 1000-2500 K k31 atm(T) ) 1.33× 109T-7.36exp(-1182/T) cm3molecule-1s-1in 200-800 K k31 atm(T) ) 5.03× 10115T-39.55exp(-25443/T) cm3molecule-1s-1in 800-1000 K k31 atm(T) ) 3.89× 1010T-9.76exp(10860/T) cm3molecule-1s-1in 1000-2500 K
constant to the potential error in TS1 and TS4. The result of our test shows that ktotis insensitive to the increase or decrease
in the barrier at TS1 by 1.2 kcal/mol, becasuse the key intermediate leading to the formation of the major products
HOCl + O2, 1HOOClO-2, can be formed by the direct
barrierless association process. The increase or decrease in the TS4 barrier by the same amount, however, leads to a corre-sponding decrease in ktotby 10-28% or increase by 17-42%,
respectively, depending on the temperature, as shown in Figure 4d.
C. HOCl Branching Ratio. Experimentally, the branching
ratio for the formation of HOCl at∼1 Torr pressure was reported to be near unity, with the lower limit of 0.8, allowing for potential contributions from side reactions;5 this is truly an
interesting observation. The results of our calculation with ChemRate, based on the two possible entrance channels forming HOOClO-1* and HOOClO-2* as shown above, allowing for all forward and reverse reactions, are summarized in Table 6 and graphically presented in Figure 6a-d including the con-tribution from reaction 3 forming HOClO2, which is competitive
only at higher pressures. As revealed by the results, the branching ratio for the formation of HOCl + O2 under the
conditions employed by Poulet et al.5 (293-473 K, 0.5-1.4
Torr) was indeed near unity; at 300 K, about 80% derives from the reaction via 2* and about 17% from
HOOClO-Figure 4. Plots of predicted individual and total rate constants. (a) Rate constants for production of HO2+ ClO. (b) Rate constants for production
of HOCl +1O
2. (c) Rate constants for production of HOClO2. (d) Comparison of predicted total rate constants with available experimental data: (solid curve) predicted ktotat 1 Torr He; (dotted and dashed curves) predicted ktotat 1 Torr He with the TS4 energy arbitrarily decreased or increased by 1.2 kcal/mol; (circles) experimental data.5
TABLE 6: Predicted Product Branching Ratios for Channels 1 and 2 at 1 Torr He Pressure (Rate Constants in Units of cm3
molecule-1s-1)
HO2+ ClO HOCl +1O2
T/K k1′ k1′′ k1) k1′+ k1′′ k2′ k2′′ k2) k2′+ k2′′ k2/(k1+ k2)
200 2.91E-13 9.01E-13 1.19E-12 9.60E-12 8.64E-11 9.60E-11 0.988
300 6.90E-14 1.40E-13 2.09E-13 1.34E-12 6.14E-12 7.48E-12 0.973
400 4.38E-14 6.96E-14 1.13E-13 5.59E-13 1.86E-12 2.42E-12 0.955
500 3.97E-14 5.21E-14 9.18E-14 3.56E-13 9.93E-13 1.35E-12 0.936
600 4.12E-14 4.67E-14 8.79E-14 2.78E-13 7.06E-13 9.84E-13 0.918
800 5.18E-14 4.58E-14 9.76E-14 2.23E-13 5.19E-13 7.42E-13 0.884
1000 6.89E-14 5.01E-14 1.19E-13 2.11E-13 4.87E-13 6.98E-13 0.854
1500 1.36E-13 6.99E-14 2.06E-13 2.35E-13 5.81E-13 8.16E-13 0.799
2000 2.40E-13 9.70E-14 3.37E-13 2.88E-13 7.80E-13 1.07E-12 0.760
2500 3.78E-13 1.30E-13 5.08E-13 3.69E-13 1.06E-12 1.43E-12 0.738
Figure 5. Plot of the rate constants of the triplet reaction channel HO + OClO f TS7 f HOO + ClO.
1* via the isomerization process. At higher pressures, under which no experimental data are available, the branching ratio for HOCl formation was affected by pressure and temperature, due to the formation of HOClO2, which is strongly P,
T-dependent (see Figure 6c,d). It should be mentioned that in our ChemRate calculations, the reaction time used in the solution of the master equation covered the range 0.001-10 ms. The predicted absolute rate constants for the individual channels are independent of time.
4. Conclusions
The mechanism for the OH + OClO reaction over the singlet and triplet potential energy surfaces of the OH + OClO reaction have been elucidated at the G2M(CC2)//B3LYP/6-311+G(3df,-2p) level of theory. Three major product channels, (1) HOO + ClO, (2) HOCl +1O
2, and (3)1HOClO2, have been identified
on the singlet PES. The rate constants for formation of these products have been calculated in the temperature range from 200 to 2500 K and the pressure range from 1× 10-5Torr to 7.6 × 107 Torr by using variational RRKM theory with the
VARIFLEX and ChemRate programs. The predicted results show that the rate constants of channels 1 and 2 are pressure independent up to 1000 atm and that of channel 3 has a strong pressure dependence. The theoretically predicted near unity branching ratio for formation of the HOCl +1O
2products and
the total rate constant at 1 Torr He pressure in the 300-500 K range agrees well with experimental data. Because of the high entrance barriers of all triplet channels, their contributions to the OH + OClO reaction are negligible kinetically.
Acknowledgment. This work is sponsored by the Office of
Naval Research under contract no. N00014-02-1-0133, Dr. J. Goldwasser program manager. M.C.L. acknowledges
Tai-wan’s National Science Council for the distinguished visiting professorship at the National Chiaotung University in Hsinchu.
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