Quasi-Classical Trajectory Study of the HO + CO â H + CO2 Reaction

Article pubs.acs.org/JPCA

Quasi-Classical Trajectory Study of the HO + CO → H + CO2 Reaction on a New ab Initio Based Potential Energy Surface Jun Li,† Changjian Xie,†,‡ Jianyi Ma,† Yimin Wang,§ Richard Dawes,∥ Daiqian Xie,‡ Joel M. Bowman,§ and Hua Guo*,† †

Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, China § Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, Georgia 30322, United States ∥ Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, United States ‡

ABSTRACT: We report extensive quasi-classical trajectory calculations of the HO + CO → H + CO2 reaction on a newly developed potential energy surface based on a large number of UCCSD(T)-F12/AVTZ calculations. This complex-forming reaction is known for its unusual kinetics and dynamics because of its unique potential energy surface, which is dominated by the HOCO wells flanked by an entrance channel bottleneck and a transition state leading to the H + CO2 products. It was found that the thermal rate coefficients are in reasonably good agreement with known experimental data in both low and high pressure limits. Excitation of the OH vibration is shown to enhance reactivity, due apparently to its promoting effect over the transition state between the HOCO intermediate and the H + CO2 product. On the other hand, neither CO vibrational excitation nor rotational excitation in either CO or OH has a significant effect on reactivity, in agreement with experiment. However, significant discrepancies have been found between theory and the available molecular beam experiments. For example, the calculated translational energy distribution of the products substantially underestimates the experiment. In addition, the forward bias in the differential cross section observed in the experiment was not reproduced theoretically. While the origin of the discrepancies is still not clear, it is argued that a quantum mechanical treatment of the dynamics might be needed.

I. INTRODUCTION The reaction HO + CO → H + CO2 (ΔHrxn = −24.5 kcal/mol) is of great importance in various gas phase environments.1 For example, it is considered to be the “second most important” elementary reaction in combustion, serving as the last and heatreleasing step in the combustion of hydrocarbons.2 In Earth’s atmosphere, this reaction represents the major route for CO oxidation and it also controls the atmospheric OH concentration.3 Its kinetics have been extensively investigated at various temperatures and pressures, revealing some very unusual characteristics.4−8 Specifically, the rate coefficient is almost constant at low temperatures, but it increases sharply with temperature above 500 K. This non-Arrhenius behavior is indicative of intricate reaction pathway(s) on a complicated potential energy surface (PES). The reaction also shows strong pressure dependence, which was attributed to a complex-forming mechanism. 4 Various kinetic isotope effects have been observed,6,8−12 although the interpretation of these observations is not always straightforward. It was also found that excitation of the OH vibration enhances the rate coefficient,10,13,14 while the CO vibrational excitation reduces the reaction rate.15 Finally, © 2012 American Chemical Society

absolute reaction cross sections have been measured for the reaction at several energies,16,17 albeit with less precision. It is well established that the title reaction proceeds on the ground (X2A′) state,1 which is dominated by the cis- and transHOCO minima. These two species, which have been identified and characterized experimentally,18−24 are separated by a relatively low isomerization barrier. As shown in Figure 1, two pathways are present for the formation of the HOCO intermediate from the HO + CO reactants, each gated by a transition state (trans- or cis-TS1). In this entrance channel, there also exist two collinear hydrogen-bonded van der Waals complexes, one of which has been detected experimentally.25 On the other hand, decomposition of the two HOCO species to the H + CO2 products is controlled by two transition states, namely TS2 and TS4. A key feature of the HOCO PES is that the minimum energy paths toward both the reactants and products have roughly isoenergetic barriers, which is largely responsible for the unusual kinetic behaviors of the reaction. Both transition Received: March 8, 2012 Revised: May 8, 2012 Published: May 10, 2012 5057

dx.doi.org/10.1021/jp302278r | J. Phys. Chem. A 2012, 116, 5057−5067

The Journal of Physical Chemistry A

Article

prototype for complex-forming reactions with four atoms.72−74 Very recently, we have reported a chemically accurate PES for the title reaction at the level of CCSD(T)-F12/AVTZ.75 As opposed to all previous ones, this PES was developed by fitting a large number (∼35 000) of ab initio points distributed throughout the relevant configuration space. The PES thus provides a globally balanced description of the reaction pathways, with good representation of the stationary points and minimum energy paths. In this work, we report an improvement of the PES and an extensive QCT study of the title reaction on the new PES. This publication is organized as follows. Section II describes the ab initio calculations and the fitting method, as well as the QCT method. The results are presented and discussed in section III. A final summary is given in section IV. Figure 1. Energetics of reaction pathways for the HO + CO → H + CO2 reaction. The ab initio energies (E0) of the stationary points are given in kcal/mol relative to the trans-HOCO minimum. The wavy lines are for zero point energy (ZPE) corrected energies (E0 + ZPE) of the relevant species. All species are planar, except tor-TS.

II. METHODS AND CALCULATION DETAILS A. Ab Initio Calculations. Ab initio calculations of the HOCO(X2A′) PES were performed using the F12b version of the unrestricted coupled-cluster method with singles, doubles, and perturbative triples based on restricted open-shell Hartree−Fock reference wave functions (ROHF-UCCSD(T)-F12b).76,77 The augmented correlation-consistent polarized valence triple-zeta (aug-cc-pVTZ, or AVTZ) basis set of Dunning was used,78,79 with the frozen-core approximation for the 1s electrons of the non-hydrogen atoms in the correlation calculations. The F12 scheme was adapted because it has been shown to yield atomization energies, electron affinities, ionization potentials, equilibrium geometries, and harmonic frequencies for both closed- and open-shell systems better than CCSD(T) with the augmented correlation-consistent polarized valence quintuple-zeta basis set (AV5Z).77 All calculations have been carried out using MOLPRO 2010.1.80 To make sure of the applicability of the CCSD(T) method, the T1 diagnostics test81 was employed to determine the quality of the calculations. Those points with T1 values larger than 0.05, which constitute only a small percentage of points calculated, were discarded. B. Fitting the PES. The PES was fit using the permutation invariant polynomial method of Bowman and co-workers.82,83 The following expansion of symmetrized polynomials was used to represent the PES:

states in the entrance and exit channels are important for the kinetics in the low pressure limit, while the former dominates the kinetics in the high pressure limit. Several kinetic models have been developed,8,26−30 and they provide a reasonable description of the existing kinetics data, but often with adjustable barrier heights. More detailed experimental investigations have been reported recently, shedding further light on the dynamics of the reaction.31−38 For example, real-time measurements have revealed that the HOCO intermediate is not particularly longlived.31,32 This is corroborated by molecular beam experiments, in which asymmetry was found in the differential cross sections (DCSs) for the reaction in both the forward35,36 and reverse directions.37,38 However, no state-to-state experiment of the HO + CO → H + CO2 reaction has been reported yet. In addition to the scattering experiments, this reaction has also been probed by photodetachment of HOCO−,39 which indicated strong tunneling from the HOCO wells to the H + CO2 products.40,41 The aforementioned experimental observations underscore the complexity of the reaction dynamics and its underlying PES. A global PES is essential to advance our understanding of this important bimolecular reaction, as other approaches such as direct dynamics42 without a PES are expected to be quite expensive due to the complex-forming nature of the reaction. Much of the earlier work on the development of the global PES for the title reaction has been pioneered by Schatz and coworkers.43−45 Because of the large configuration space, these authors have concentrated on key areas such as the transition states and entrance channels, where the PES was fit to a small number of ab initio points. Subsequent improvements have been reported, notably by Yu, Muckerman, and Sears (YMS),46 and by Lakin, Troya, Schatz, and Harding (LTSH).47 In addition, a different PES by Valero, van Hemert, and Kroes (VvHK) was reported using an interpolation method to fit 1250 ab initio points and their first and second derivatives.48 However, dynamical studies on these PESs, which include both quasiclassical trajectory (QCT) and quantum mechanical methods,43−45,47−71 have not been able to reproduce the experimental observations in a satisfactory fashion. Given the shortcomings of earlier PESs, it has been argued by many that a globally reliable PES is desired if an accurate description of the reaction dynamics is to be achieved. This is particularly important because the title reaction serves as a

M

V (y1 , ..., y6 ) =

∑

cn1,..., n6y1n1 y6 n6 [y2 n2 y3n3 y4 n4 y5n5

n1,..., n6

+

y2 n5 y3n4 y4 n3 y5n2 ]

(M ≤ 7)

(1)

where yi = e−ri/α, i = 1, 2, ..., 6, ri is the internuclear distance between two atoms, and α = 2.0 bohr. The distances are defined as follows: r1 = rOO′, r2 = rCO, r3 = rHO, r4 = rHO′, r5 = rCO′, and r6 = rCH. The symmetrized multinomial basis functions in eq 1 are invariant with respect to interchange of the two O atoms, as can be easily verified by the reader. The total order of polynomials M = n1 + n2 + n3 + n4 + n5 + n6 did not exceed 7 (a total of 918 terms). The expansion coefficients were determined by a weighted least squares method. In order to provide a globally accurate PES with reasonable computational costs, it is vital to choose the distribution of the ab initio points prudently. Our strategy is briefly described below. First, stationary points and minimum energy paths (MEPs) were surveyed to determine the ranges of configurations and energies. As shown in Figure 1, all important transition states for the reaction are below 100 kcal/mol, relative to the global transHOCO minimum. Hence, we discarded points with energies 5058



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higher than 100 kcal/mol. Second, we divided the system into three regions and used different coordinates to define grids in these regions. In the reactant region, for example, it is reasonable to use the diatom−diatom (OH−CO) Jacobi coordinates. On the other hand, the product region is best described by the H + CO2 Radau−Jacobi coordinates. In the HOCO region, however, several different coordinates were needed in various configuration spaces. Ab initio points were first computed on small grids in these regions, near the stationary points and minimum energy paths. Additional points were added from direct dynamics trajectories at the B3LYP level of theory, which sampled dynamically accessible regions. To better fit the low energy regions of the PES, all ab initio points were weighted by the factor w = 0.1/(0.1 + E), where E is the energy in hartrees relative to the trans-HOCO minimum. In addition, points close to stationary points are further weighted by a factor of 3 to make sure of a faithful representation of these important regions. Finally, the asymptotic regions are specially treated to guarantee angular isotropy in the PES when the two reactants or products are sufficiently far apart. This was done by placing a grid in the angular coordinates at large separations and assigning the same ab initio value calculated at some representative points. These artificial points were included in the fitting. The resulting PES was then checked by comparing with key ab initio properties of stationary points and asymptotes, such as geometry, energy, and harmonic frequencies. MEPs connecting the stationary points were computed and compared with ab initio points. Furthermore, batches of trajectories at various energies were dispatched to search for unphysical regions of the PES resulting from lack of ab initio points. New points were then added to patch up these regions. This procedure was iterated multiple times until the results converged. This improved PES is denoted “CCSD-2/d”. C. QCT Calculations. Standard QCT calculations, as implemented in VENUS,84,85 were performed on the newly fitted CCSD-2/d PES. Reactions with various rovibrational states of the OH and CO reactants were investigated. The trajectories were initiated with a 7.5 Å separation between reactants, and terminated when products (or reactants for nonreactive trajectories) reached a separation of 5.5 Å. The propagation time step was selected to be 0.11 fs. Exceptionally long trajectories were halted if the propagation time reached a prespecified value (9.9 ps). The maximal impact parameter (bmax) was determined using small batches of trajectories with trial values. The scattering parameters (impact parameter, vibrational phases, and spatial orientation of the initial reactants) were selected with a Monte Carlo approach. The gradient of the PES was obtained numerically by the central-difference algorithm. The total integral cross section (ICS) for the title reaction is computed according to the following formula: σr(Ec) = πbmax 2(Ec) Pr(Ec)/2

and the scaling factor 1/2 in eq 2 is due to the electronic partition function.86 The standard error is given by Δ=

(4)

The corresponding thermal rate coefficients can be obtained as follows: k(T ) =

1/2 1 ⎛ 8 ⎞ ⎜⎜ ⎟⎟ kBT ⎝ πμR kBT ⎠

∫0

∞

σr e−Ec / kBT Ec dEc (5)

where μR is the reduced mass of the reactants, kB is the Boltzmann factor, and T is the temperature in Kelvin. A similar set of equations can be used for capture ICSs and rate coefficients. The scattering angle θ is given by

⎛ ν ⃗ ·ν ⃗ ⎞ θ = cos−1⎜ i f ⎟ ⎝ |νi⃗ ||νf⃗ | ⎠

(6)

Here, ν⃗ is the relative velocity vector and the subscripts “i” and “f” denote “initial” and “final”, respectively; ν⃗i = ν⃗HO − ν⃗CO and ν⃗f = ν⃗H − ν⃗CO2. The signs of the relative velocity vectors have been designed such that θ = 0° corresponds to forward scattering and θ = 180° corresponds to backward scattering. The reactive differential cross section (DCS) is then computed by dσr σrPr(θ ) = dΩ 2π sin(θ )

(7)

where Pr(θ) is the normalized probability for the scattering products at the angle θ.

III. RESULTS AND DISCUSSION A. HOCO PES. Approximately 67 000 ab initio points were calculated as described above, but only ∼48 000 satisfied our energy and T1 criteria. The distribution of these points is shown in Figure 2, where a large peak found in the energy range

Figure 2. Distribution of ab initio points used in the fit (energies in kcal/ mol relative to the trans-HOCO minimum).

(2)

28−47 kcal/mol corresponds to the many points generated in the entrance channel and near TS2. These ab initio points plus those artificial points in the dissociation asymptotes, totaling ∼68 000, were fit to the form in eq 1. The total root-mean-square deviation (rmsd) of the fitting is 1.09 kcal/mol, but the rmsd for points below 50 kcal/mol is significantly smaller (0.66 kcal/mol).

where the reaction probability at the specified collision energy Ec is given by the ratio between the number of reactive trajectories (Nr) and total number of trajectories (Ntotal):

Pr(Ec) = Nr /Ntotal

(Ntotal − Nr)/NtotalNr

(3) 5059



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Table 1. Geometric Parameters (in Å and deg) of the Stationary Points along the HO + CO Reaction Pathway Given in the Internal Coordinates with O′ Initially Bonded to C in CO′ species HO + CO OH···CO OH···OC trans-TS1 cis-TS1 trans-HOCO tor-TS cis-HOCO cis-TS2 trans-TS4 HCO2

C2v-TS3 TS5 H + CO2

level

RHO

ab initioa PESb ab initio PES ab initio PES ab initio PES ab initio PES ab initio PES ab initio PES ab initio PES ab initio PES ab initio PES ab initioc ab initiod PES ab initio PES ab initio PES ab initio PES

0.9703 0.9701 0.9722 0.9729 0.9706 0.9697 0.9699 0.9711 0.9724 0.9719 0.9631 0.9620 0.9659 0.9657 0.9726 0.9719 1.3394 1.3594 1.2501 1.2739 1.9942 1.9403 1.9240 2.0489 2.0323 1.3407 1.2642

ROC

RCO′

θHOC

θOCO′

3.3134 3.2819 4.4014 4.3287 2.1384 2.2791 2.0475 2.1232 1.3423 1.3454 1.3626 1.3733 1.3293 1.3303 1.2097 1.2063 1.2962 1.2873 1.2069 1.2390 1.2232 1.1872 1.1882 1.2525 1.2910 1.1622 1.1624

1.1309 1.1303 1.1288 1.1288 1.1320 1.1329 1.1313 1.1284 1.1350 1.1328 1.1783 1.1779 1.1771 1.1796 1.1836 1.1856 1.1669 1.1679 1.1758 1.1767 1.2450 1.2390 1.2232 1.1872 1.1882 1.2525 1.2910 1.1622 1.1624

0.0 0.0 0.0 0.0 93.24 92.12 90.94 93.11 107.88 107.69 108.93 110.17 108.17 108.40 115.05 116.56 62.34 62.05 31.94 35.32 35.68 44.96 46.00 68.55 67.13

180.0 180.0 0.0 0.0 123.48 124.77 122.19 127.69 127.00 126.38 129.38 130.83 130.23 129.91 157.42 157.18 143.48 141.84 143.97 145.89 146.31 159.43 162.69 117.16 111.06 180.0 180.0

ϕHOCO′

180.0 180.0 0.0 0.0 180.0 180.0 86.70 82.83 0.0 0.0 0.0 0.0 180.0 180.0 180.0 180.0 180.0 180.0 180.0 0.0 0.0

a ROHF-UCCSD(T)-F12b/AVTZ. bCCSD-2/d PES. cOnly a Cs HCO2 minimum was located at the ROHF-UCCSD(T)-F12b/AVTZ level of theory; see details in text. dCASPT2/AVDZ.

coupled electronic states.91 As a result, our PES in this region might not be as reliable as in other regions. Interestingly, a previously unknown transition state (TS5) of C2v symmetry has been located during our surveys (not shown in Figure 1). This transition state is for an H-transfer process, in which the hydrogen atom is shifted directly from one oxygen atom to the other:

As a result, this CCSD-2/d PES can be considered to be chemically accurate for this complex reaction systems. For most part, the CCSD-2/d version is quite similar to the original CCSD-1/d PES,75 as most of the new points added were used to remove unphysical features. The key stationary points on the HOCO PES are depicted in Figure 1, along with their ab initio energies and zero point energy (ZPE) corrected energies at the level of ROHF-UCCSD(T)F12b/AVTZ. A comparison of the geometries and energies of these ab initio stationary points with those on the fitted CCSD2/d PES is given in Table 1. The geometries are given in internal coordinates with O′ initially bonded to C in CO′. As shown in Table 1, the global fit is quite good, with bond distances generally within 0.02 Å and bond angles within 3.0°. The geometries are also in good agreement with experiment23,24 and previous high level ab initio calculations.24,46,87−90 The geometries of the OH···CO and OH···OC minima and the trans-TS1 and cis-TS1 transition states are less well reproduced because of the floppy nature of these stationary points. The HCO2 minimum and associated TS3 require some discussion. At the UCCSD(T)-F12b/AVTZ level, no planar C2v minimum was found for the HCO2 species. Instead, a Cs minimum was found, which is listed in Table 1. This is interesting because a C2v minimum was reported by several previous authors,26,46 and we have also found it at the CASPT2/ AVDZ level. It is well-known that the electronic structure is quite complicated in this region, due to several nonadiabatically

TS5

cis‐HOCO′ ←→ cis‐HO′CO

Its geometry, energy, and harmonic frequencies are given in Tables 1 and 2. The existence of TS5 has been confirmed by calculations at several different levels of theory. This transition state is included in the current PES, and as discussed below, trajectories have been observed to undergo the hydrogen exchange reaction through TS5. We also performed normal-mode analysis for all of these stationary points. Harmonic frequencies of the stationary points on the PES are given in Table 2 and compared with those from ab initio calculations. As shown, the quality of the fit is satisfactory. Also in Table 2, the energies of all stationary points on the fitted PES are compared with the ab initio values. It is readily seen that the ab initio energies are reproduced quite well by the PES. In our earlier report,75 the MEPs and overall reactive potentials have already been reported for CCSD-1/d, and no significant changes were found in CCSD-2/d. To illustrate the asymptotic regions of the PES, we plot in Figure 3 contours for the HO−CO interaction. In the left column, HO is placed along the Y-axis with 5060



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Table 2. Electronic Energies (kcal/mol) and Harmonic Frequencies (cm−1) of the Stationary Points along the HO + CO Reaction System frequency species HO + CO OH···CO OH···OC trans-TS1 cis-TS1 trans-HOCO tor-TS cis-HOCO cis-TS2 trans-TS4 HCO2

C2v-TS3 TS5 H + CO2

level

energya

1

2

3

4

ab initiob PESc ab initio PES ab initio PES ab initio PES ab initio PES ab initio PES ab initio PES ab initio PES ab initio PES ab initio PES ab initiod ab initioe PES ab initio PES ab initio PES ab initio PES

29.594 29.853 27.331 27.650 28.368 28.702 29.008 29.414 32.714 32.881 0 0 9.299 9.764 1.769 1.653 32.002 32.136 38.371 37.997 16.750 − 16.495 20.882 20.831 49.995 48.758 6.971 7.253

− − 71.0, 72.7 71.98f 37.7, 35.2 77.0f −210.9 −100.9 −344.0 −260.5 534.9 660.1 −582.3 −554.7 575.80 550.00 −2005.9 −1570.9 −1802.0 −1657.2 400.4 630.9 589.9 −1099.9 −925.4 −2222.5 −1753.8 − −

− − 104.7 119.2 83.0 84.6 186.1 199.8 −68.7 −226.1 620.6 725.51 646.1 656.4 604.37 650.2 519.9 567.1 550.9 503.5 750.5 809.2 632.3 613.6 655.1 835.3 833.4 − −

− − 284.6 314.1 176.4 288.5 198.0 199.9 181.4 272.1 1087.6 1060.4 997.6 975.7 1081.68 1109.9 644.5 612.6 676.3 800.1 840.7 1138.1 748.0 710.2 661.0 1014.8 946.9 673.1 668.1

2163.5 2154.3 345.8 314.1 208.9 288.5 640.6 601.3 758.5 732.7 1257.0 1261.1 1118.5 1243.1 1310.47 1369.6 934.3 968.8 1145.5 1123.5 1149.6 1202.2 1264.3 805.0 1058.2 1314.2 1325.8 673.1 668.1

5

6

2182.1 2163.3 2155.0 2137.5 2151.3 2159.1 2109.8 2098.9 1897.2 1855.7 1871.5 1840.3 1857.53 1808.6 1294.4 1261.6 1856.6 1775.0 1689.7 1840.9 1479.8 1338.0 1380.9 1632.3 1700.2 1352.2 1350.7

3740.9 3725.9 3714.3 3757.8 3746.2 3804.8 3751.6 3824.8 3710.9 3846.9 3823.8 4042.7 3784.8 3896.3 3655.11 3890.7 2175.9 2165.6 2162.2 2136.7 2337.6 2326.0 2330.2 2104.9 2057.3 2012.8 2227.0 2393.1 2396.8

Energies of the optimized geometries (see Table 1) on the fitted CCSD-2/d PES, relative to the energy of the trans-HOCO minimum. bRHFUCCSD(T)-F12b/AVTZ. cCCSD-2/d PES. dOnly a Cs HCO2 minimum was located at ROHF-UCCSD(T)-F12b/AVTZ; see details in text. e CASPT2/AVDZ. fDoubly degenerate. a

in Figure 4a with both experimental data17 and those on the LTSH, YMS, and VvHK PESs, as reported in ref 67. The cross sections computed on our new PES are smaller than those on the YMS PES, but comparable to those on the LTSH and VvHK PESs. The experimental cross sections, particularly the ones at 18.9 kcal/mol, are larger than our results. In Figure 5a, the thermal rate coefficient for the reaction was computed from the energy dependent cross sections. It is clear that our calculated rate coefficient is in reasonably good agreement with the experimental values at the low pressure limit.5,8 The agreement with the low temperature data is not as good, due presumably to the fact that much of the low temperature reactivity is due to tunneling, which is not included in the QCT method. The circumstantial evidence for tunneling includes the large H/D kinetic isotope effect for the title reaction8 and the observation that OH vibrational excitation increases the reaction rate.10 The rate coefficient is also quite close to that in our preliminary report using the CCSD-1/d PES.75 The good agreement with the experimental rate coefficient suggests that the calculated cross sections should also be reasonable, thus raising questions about the accuracy of the experimental cross sections shown in Figure 4. Due to the topography of the HOCO PES, a reactive trajectory has to overcome at least two bottlenecks to reach the product. First, it has to be captured by the HOCO well, and second, it has

H up. On the right column, on the other hand, CO is placed along the Y-axis with C up. The upper contour plots depict CO or HO approaching its counterpart with C or O, while the lower ones correspond to CO or HO with O or H approaching its counterpart. It is shown in Figure 3d in particular that the interaction potentials are attractive for H directed to the C or O of CO, corresponding to the collinear OH···CO and OH···OC van der Waals wells. They are qualitatively similar to refs 49 and 92; a similar CCSD method was used in the latter paper. It should be pointed out that cis-TS1 is not a true first-order saddle point, as it has two imaginary frequencies, as shown in Table 2. As pointed out by an earlier CCSD(T) work,92 the relaxation of the planarity constraint leads the MEP directly to the trans-TS1. B. QCT Calculations. B.1. Total Cross Sections and Rate Coefficients. The total reaction integral cross section (ICS) has been calculated using the QCT method on the CCSD-2/d PES for the HO(v1=0,j1=0) + CO(v2=0,j2=0) → H + CO2 reaction with collision energies (Ec) from 1.0 to 35.0 kcal/mol. The maximal impact parameter (bmax) ranges from 2.30 Å at 1.0 kcal/ mol to 2.18 Å at 35.0 kcal/mol. For Ec >14.1 kcal/mol, 105 trajectories were used. However, more ((2−5) × 105) trajectories were used at lower energies due to small reactivity. The standard errors of these cross sections are typically around 3%, except for the energies 2.0 and 1.0 kcal/mol, where the errors are about 6.9 and 17.7%, respectively. The results are compared 5061



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Figure 3. Contour plots of CCSD-2/d PES when HO and CO approach each other at different orientations. In (a) and (b), HO was placed along the Y-axis with the Cartesian origin at the center of mass of HO, Y = R cos θHO, X = R sin θHO, and for (a) C of CO points always toward the origin, namely θCO = 180.0°; for (b) O of CO points always toward the origin, namely θCO = 0.0°. (c) and (d) are similar, but for (c) θHO = 180.0° and (d) θHO = 0.0° as a function of Cartesian coordinates of the center of mass of CO, i.e., Y = R cos θCO, X = R sin θCO. The zero of the energy corresponds to the separated reactants; thus attractive regions are in red and repulsive ones are in blue. The top well of (d) corresponds to the OH···CO van der Waals complex, while the low well corresponds to the OH···OC van der Waals complex.

barrier. Such a “nonreactive-without-well” trajectory is shown in Figure 6a. For those that do enter the well, there is also a possibility to reenter the reactant channel, as illustrated in Figure 6b, where a “nonreactive-with-well” trajectory is shown.

to overcome a dissociation transition state, such as TS2. Many trajectories do not enter the HOCO well, because HO and CO approach each other in unfavorable orientations or because they do not have sufficient kinetic energy to surmount the

Figure 4. Integral cross sections for (a) reaction and (b) capture calculated on the CCSD-2/d PES as a function of collision energies. Results of LTSH and YMS PESs and Expt. were extracted from ref 66.

Figure 5. Calculated thermal rate coefficients for (a) reaction and (b) capture on the CCSD-2/d PES, and comparison with available literature results. 5062



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starts at cis-HOCO′ and ends up with cis-HO′CO. Two such trajectories are shown in Figure 8. Experimentally, the oxygen

Figure 6. Key geometric evolution of (a) “nonreactive-without-well” and (b) “nonreactive-with-well” trajectories. R3 is the center-of-mass distance between HO and CO. Figure 8. Key geometric evolution of (a) “exchange-TS4” and (b) “exchange-TS5” trajectories.

From the HOCO intermediate, the products can be formed via two pathways. The cis-HOCO species can reach the products via TS2, where the O−H bond is strongly coupled to the reaction coordinate. Alternatively, the trans-HOCO species can overcome a higher barrier (TS4), which can be characterized as H migration from O to C, leading to the HCO2 species. The final H−C bond cleavage over TS3 results in the H + CO2 product. In our calculations, the majority of reactive trajectories are via TS2 and there are only a very small portion of trajectories reacting via TS4. At 35.0 kcal/mol, for example, the fraction through TS4 is only 2.5%. Two representative trajectories in these two pathways are given in Figure 7.

exchange reaction was observed by Kurylo and Laufer in the absence of inert diluents (1 Torr of CO, 5 Torr of 18OH).93 However, Greenblatt and Howard found no significant exchange for 18OH and CO at 298 and 400 K in their experiments and gave an estimate of the upper limits to the exchange rate coefficients as 10−15 cm3 molecule−1 s−1, which is smaller than 0.5% of the rate coefficients of the reaction HO + CO → H + CO2.94 Our results suggest that such an exchange reaction is rare in the energy range we have studied. To understand the high pressure kinetics, we have also computed the HOCO capture cross section as a function of collision energy. These cross sections were computed by counting the total number of trajectories that reached the capture radius, which is defined by the HO−CO distance of 1.8 Å. As shown in Figure 4b, these capture cross sections are approximately 1 order of magnitude larger than the reactive ones. Nevertheless, the capture is by no means complete: many trajectories do not enter the HOCO wells. As discussed above, this is apparently due to the bottleneck in the entrance channel, despite the fact that the minimum energy path is barrierless. This phenomenon has been noted in previous theoretical studies of this reaction using other PESs.47,71 In Figure 5b, the thermal rate coefficients for HOCO capture are compared with the experimental values in the high pressure limit, where the reaction is dominated by TS1. The calculated capture rate coefficient reproduces the experimental temperature dependence reasonably well at high temperatures, although the theoretical values overestimate. The overestimation can presumably be attributed to the fact that there are conceivably nonreactive trajectories from the HOCO wells, which are assumed to be negligible in the capture model. The experiment− theory discrepancy is large at low temperatures, presumably due to tunneling near TS2, as in the low pressure limit. We note here in passing that the energy conservation of our trajectories is excellent. Almost no trajectories were observed to exceed the 0.04 kcal/mol convergence limit, which testifies to the smoothness of the CCSD-2/d PES. On the contrary, the LTSH PES has been shown to have instabilities in numerical integration of Newton’s equations, leading to poor conservation of the total energy.47,61,67,68 As a result, a large fraction of trajectories have to be discarded, which disproportionally affects the reactive ones

Figure 7. Key geometric evolution of (a) “reactive-TS2” and (b) “reactive-TS4” trajectories.

Interestingly, we have observed a very small number of trajectories that have undergone the hydrogen exchange reaction: OH + CO′ → O′H + CO. The total number of such trajectories depends on energy. For example, at 35.0 kcal/mol, there are 19 exchange reactive trajectories out of 105. Since the statistics is rather poor, we choose not to report the cross sections. This reaction may occur along two different pathways. First, the trans-HOCO′ is converted to HCOO′ via TS4, in which H migrates to the center C, followed by its further migration to O′ before it reverses to trans-HO′CO. Another pathway is via the newly discovered and higher energy transition state TS5, which 5063



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because of its small percentage.67 In addition, the evaluation of the potential energy and forces is very fast, thanks to the analytical form of our PES. This is in contrast to the slowness reported for the VvHK PES.66,67 We have also carried out QCT calculations with rotationally and vibrationally excited reactants. Since we are interested in trends, only 50 000 trajectories were used at each energy. The cross sections of OH(v=1,j=0) + CO(v=0,j=0), OH(v=0,j=0) + CO(v=1,j=0), and OH(v=0,j=2) + CO(v=0,j=7) are plotted in Figure 9. It is clear that rotational excitation in the reactants has a

Figure 10. Product translational energy distributions at Ec = 8.6 and 14.1 kcal/mol. Distributions are normalized to the maximum. The results for the LTSH and YMS PESs were extracted from ref 66.

The lower translational energy in theoretical calculations is reasonable as TS2 features a cis-HOCO structure, which is expected to deposit a significant amount of energy into the vibrational modes of the linear CO2 product, as shown below. On the other hand, the experimental distributions peak near the highest accessible translational energy, implying that little energy is imparted into the CO2 internal degrees of freedom. Although the origin of the experiment−theory discrepancy is still unclear, the experimental distributions seem to be inconsistent with the TS2 structure. In Figure 11, the vibrational energy distribution of the CO2 product is plotted in the two energies. Although the vibrational

Figure 9. Excitation functions for several rovibrationally excited reactants.

limited impact. On the other hand, excitation of the OH vibration substantially enhances the reaction, while the CO vibrational excitation has only a small enhancement effect. These observations are largely consistent with both experimental observations10,13−15 and previous theoretical results.44,47,53,62,63,71 However, the increase due to CO vibrational excitation is significantly smaller in our case than that reported in some earlier work using different PESs.47,62,63 Interestingly, the capture cross section for OH(v=0) is slightly larger than that for OH(v=1), indicating that the vibrational excitation does not help in the formation of the HOCO intermediate. It follows that the vibrational excitation must be effective in overcoming TS2, where the O−H vibrational coordinate is strongly coupled to the reaction coordinate. Due to its high frequency, the O−H bond is essentially local and energy transfer to other degrees of freedom is typically slow. As a result, the energy deposited into the OH reactant is largely preserved in the O−H bond of HOCO, leading to enhancement of reactivity. This observation suggests that the energy randomization in the HOCO wells is not complete, due presumably to its relatively short lifetime (vide infra). B.2. Final State Distributions. The product distributions serve as sensitivity tests of the PES. Here, we focus on the two collision energies of 8.6 and 14.1 kcal/mol, where molecular beam experiments have been reported.35,36 To obtain good statistics, we have run ∼7 × 105 trajectories, which are significantly more than those used in calculating the ICSs. In Figure 10, the calculated product translational energy distributions are compared with the experimental data35,36 and previous theoretical distributions on the LTSH and YMS PESs.67 However, it is clear that none of the theoretical distributions resembles the experimental distribution. At 8.6 kcal/mol, our distribution is the lowest. At 14.1 kcal/mol, our result is close to that obtained on the YMS PES.

Figure 11. CO2 vibrational energy distributions at Ec = 8.6 and 14.1 kcal/mol. Distributions are normalized to the maximum.

quantum numbers were not assigned for this triatomic product, we have evidence that the bending mode of the molecule is excited. This is consistent with the geometry of TS2, in which the CO2 moiety is bent. Furthermore, the ZPE-violating fraction in the distribution seems to be small, due apparently to the exothermic nature of the reaction and the smallness of the ZPE for CO2. As the collision energy increases, the vibrational excitation in CO2 increases as well. The CO2 rotational state distribution is displayed in Figure 12. The reaction produces the entire range of rotational states, and peaks near J = 45 at 8.6 kcal/ mol and J = 55 at 14.1 kcal/mol. Figure 13 presents the calculated product angular distributions, or DCSs, at collision energies of 8.6 and 14.1 kcal/mol. 5064



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It is well-known that DCS serves as a clock of the reaction time. Indeed, our results showed that trajectories emerging first from the HOCO well are dominated by forward scattering. It is thus interesting to compute the lifetime of the HOCO intermediate. To this end, we computed the survival probability using the geometry criterion proposed by Kudla et al.44 to determine the lifetime. Specifically, the time starts when the system passes through TS1, and ends when it passes through an exit channel saddle point (TS2). Figure 14 shows the lifetime distributions of

Figure 12. Rotational distributions for CO2 at Ec = 8.6 and 14.1 kcal/ mol. Distributions are normalized to the maximum.

Figure 14. Semilog plot of survival probability of reactive trajectories at collision energies of 8.6 and 14.1 kcal/mol. Points are original HOCO lifetime distribution, while solid lines are least-squares fits (R2 = 0.982, 0.978).

the HOCO intermediate for reactive trajectories at Ec = 8.6 and 14.1 kcal/mol. Both curves show approximately linear time dependence in the semilog plots, implying exponential decay for HOCO. Lifetimes of HOCO obtained from Figure 14 are 1.60 and 0.78 ps at 8.6 and 14.1 kcal/mol, respectively. To compare with those on the LTSH PES, we have carried out QCT calculations on that PES at 14.1 kcal/mol. The HOCO lifetime for reactive trajectories is 0.685 ps, which is somewhat shorter than the value obtained on our new PES. However, it is unclear if the small difference in lifetime is responsible for the large difference in the calculated DCSs. To determine the statistical nature or the lack thereof, we have computed the lifetimes based the microcanonical RRKM model,96 which assumes complete energy randomization in the HOCO complex. The RRKM lifetimes at 8.6 and 14.1 kcal/mol are 2.56 and 1.00 ps, respectively. Comparing them with the QCT lifetimes, it is clear that the HOCO complex is shorter lived, resulting in incomplete energy randomization. In other words, the dissociation of the HOCO complex is most likely nonstatistical. It should also be pointed out that the lifetime of the HOCO complex depends sensitively on several quantum mechanical properties of the system. The decomposition of the HOCO complex backward to the OH + CO reactant channel is expected to be overestimated by QCT because of the large number of ZPE-violating trajectories. While ZPE also plays a role in overcoming TS2, the magnitude is different, as shown in Figure 1. Another important factor is the tunneling over TS2, which is not accounted for in the QCT calculations. The tunneling is expected to further shorten the lifetime of the HOCO intermediate, perhaps leading to the forward bias in the DCS. Furthermore, the classical dynamics in the HOCO well might be more chaotic than the corresponding quantum dynamics.97 As a result, it is highly

Figure 13. Product angular distribution for HO + CO → H + CO2 reaction at (top) Ec = 8.6 kcal/mol and (bottom) Ec = 14.1 kcal/mol. Distributions are normalized to the maximum.

Also included in Figure 13 are the experimental results35,36 and those obtained on the LTSH and YMS PESs.67 Our calculated DCS is much more isotropic than those obtained on earlier PESs, which are dominated by forward and backward scattering. (We have reproduced the reported DCS on the LTSH PES.) As a result, our product angular distribution is closer to the overall shape of the experimental angular distribution. However, the forward bias in the latter was not reproduced. Very recently, Garciá et al. have reported detailed QCT calculations on YMS, LTSH, and VvHK PESs.68 Interestingly, an isotropic angular distribution was also found on the VvHK PES. Although the VvHK PES used a much smaller number of ab initio points at roughly the same level of theory,48 the similarity in the DCSs can almost certainly be attributed to the ab initio nature of the two PESs. Because of the large number of ab initio points included in fitting the CCSD-2/d PES, it is somewhat surprising that there are still significant discrepancies between the experimental and theoretical results. We note that it has recently been argued that the comparison with experimental center-of-mass (CM) angular distributions is not advisable because of the uncertainties associated with their conversion from the laboratory (LAB) frame due to experimental conditions. Lagana et al.95 have reported simulations of the LAB frame angular distribution from QCT calculations on several PESs and found that the differences are not as pronounced as in Figure 13. 5065


The Journal of Physical Chemistry A desirable to perform quantum dynamical calculations on this reaction using the new PES.

ACKNOWLEDGMENTS

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REFERENCES

This work was funded by the U.S. Department of Energy (DEFG02-05ER15694 to H.G. and DE-FG02-97ER14782 to J.M.B.), the National Natural Science Foundation of China (21133006 to D.X.), and the Missouri Research Board (R.D.). We thank Al Wagner for several useful discussions on kinetics, Bob Continetti for discussions on photodetachment of HOCO−, and Mike McCarthy for discussions on the oxygen exchange reaction.

IV. SUMMARY AND CONCLUSIONS The lack of high-quality PESs has been a major bottleneck in understanding dynamics of polyatomic reactions. To better understand a prototypical tetratomic reactive system, we reported here a chemically accurate PES for the HO + CO → CO2 + H reaction based on a permutation invariant polynomial fit to ∼48 000 ab initio points at the level of ROHF-UCCSD(T)-F12b/AVTZ. This global PES (CCSD-2/d) has more points than its predecessor (CCSD-1/d) and provides a faithful representation of not only stationary-point structures, energies, and harmonic frequencies, but also reaction pathways. In addition, a new transition state has been found for the exchange reaction cis-HO′CO ↔ cis-HOCO′, and incorporated in the new PES. This transition state could be responsible for the oxygen isotope exchange reaction HO′ + CO → HO + CO′ at high energies. QCT calculations were performed with various initial rovibrational states of HO and CO and collision energies of 1.0−35.0 kcal/mol on the CCSD-2/d PES. This PES is numerically stable for trajectory propagation and conserves energy very well. The calculated total capture and reaction ICSs yielded rate coefficients that are in reasonably good agreement with experimental values in both the low and high pressure limits. However, significant differences still exist with reported experimental product translational and angular distributions. The experimentally obtained translational energy distributions are substantially underestimated. In addition, the calculated DCSs fail to reproduce the observed forward bias. The discrepancies are somewhat surprising given the accuracy of the PES. One possible reason is the quantum effects of the reaction, which include both ZPEs and tunneling. The effects of the former are shown in Figure 1 along the reaction pathways. In addition, tunneling over TS2, which is evidenced by the large H/D isotopic effect8 and the latest photodetachement experiments,40,41 would significantly reduce the lifetime of the HOCO intermediate. When these factors are considered, it is conceivable that the calculated product distributions will be in much better agreement with experiment. Hence, it is highly desirable to perform quantum dynamics studies on the title reaction on the new PES. Another important issue concerning the title reaction is whether the reaction, particularly the decomposition of the HOCO intermediate, is statistical or not. This issue is related to the intramolecular vibrational energy redistribution (IVR) in the intermediate complex. The relatively short lifetime of the HOCO complex determined by our QCT calculations and the OH vibrational enhancement of the reaction rate seem to suggest nonstatistical components, but a rigorous statement on this issue will have to await further statistical calculations, preferably with tunneling corrections.98 Work in this direction will be reported in a future publication.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 5066



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Quasi-Classical Trajectory Study of the HO + CO â H + CO2 Reaction

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