Quantum Chemical Prediction of Pathways and Rate Constants for

Oct 1, 2009 - Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, Georgia 30322, Institute for...
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Quantum Chemical Prediction of Pathways and Rate Constants for Reactions of CO and CO2 with Vacancy Defects on Graphite (0001) Surfaces S. C. Xu,† S. Irle,*,‡ D. G. Musaev,*,† and M. C. Lin*,†,§ Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322, Institute for AdVanced Research and Department of Chemistry, Nagoya UniVersity, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan, and Institute of Molecular Science, Department of Applied Chemistry, National Chiao Tung UniVersity, Hsichu, Taiwan 300. ReceiVed: June 17, 2009; ReVised Manuscript ReceiVed: August 3, 2009

We present reaction pathways for adsorption of CO and CO2 molecules in the vicinity of monovacancy defects on graphite (0001) based on B3LYP and dispersion-augmented density-functional tight-binding (DFTB-D) studies of the potential energy surfaces (PES) of these reactions. To model the graphite (0001) monovacancy defects, finite-size molecular model systems up to the size of dicircumcoronene (C95H24) were employed. We find that the CO molecule reacts readily with the monovacancy defects and partially “heals” the carbon hexagon network leading to the formation of a stable epoxide, whereas CO2 oxidizes the defect via a dissociative adsorption pathway following CO elimination. We predict reaction rate constants in the temperature range between 300 and 3000 K using Rice-Ramsperger-Kassel-Marcus theory. Quantum chemical molecular dynamics simulations at 3000 K based on on-the-fly DFTB-D energies and gradients support the results of our PES studies. 1. Introduction Graphite is an important surface lining material for systems operating under high temperature and high pressure and has become popular as surface material for rocket nozzles1 as well as plasma facing components.2 Despite this popularity, very little is known about the high-temperature, high-pressure (high-T,P) processes causing graphite erosion due to reactions with oxidizing agents from fuel combustion, most importantly H2O and CO2.1 Only very recently, numerical simulations have given insight into the dynamics of reactive turbulent combustions3 and stress the importance of OxHy (x ) 1, 2, y ) 0-2) species. While some ideas are currently being developed regarding the graphite erosion process by hydrogen chemical sputtering in nuclear fusion reactions,4 still nearly nothing is known about the oxidative processes related to fuel combustion, causing rocket nozzle material to fail after prolonged exposure, and how such erosion could be mitigated by improving the surface material. It is obvious that with most modern fuels, OHx, COx, and NOx (x ) 1, 2) are important exhaust species which may induce the graphite oxidation. However, if and how graphite defect formation caused by the interaction of these species with graphite lining material plays a role at the high-T,P conditions remains still unclear. We have recently developed a methodology that allows to investigate a priori high-T,P dissociative adsorption processes on graphite surfaces.5 This methodology is based on a description of the surface graphite (0001) layer using mono-, bi-, and trilayers of dicircumcoronene C96H24 as a model of graphite, employing density functional tight binding6,7 augmented plus London dispersion (DFTB-D)8,9 quantum chemical molecular * To whom correspondence should be addressed. E-mail: (S.I.) [email protected]; (D.G.M.) [email protected]; (M.C.L.) [email protected]. † Emory University. ‡ Nagoya University. § National Chiao Tung University.

dynamics (QM/MD) at constant temperature, quantum chemical (density functional theory (DFT) and/or DFTB-D) calculations for the identification and characterization of intermediate surface species along reasonable reaction pathways leading to irreversible adsorption products, and reaction rate constant predictions based on Rice-Ramsperger-Kassel-Marcus (RRKM).5 Applying this methodology, we predicted high-T,P dissociative adsorption processes and their reaction kinetics for H2O,5 COx,10,11 NOx11 (x ) 1,2), and OHx (x ) 1,2)12 species. In the investigation of the H2O-graphite system, we found that irreversible oxidation of a pristine graphite (0001) surface by the H2O reaction is virtually impossible due to associated high O-H bond activation barriers and very small reverse barriers, which stems from rapid self-healing of an intact graphene surface, leading to immediate ejection of any chemisorbed adsorbates.5 In the investigation of dissociative COx and NOx adsorption on pristine graphite (0001) surface,11 we found CO2 and even more so the radical species NO and NO2 causing irreversible defects on the graphite surface11 with CO leaving as thermodynamically highly stable, volatile erosion product species. We also noticed the incorporation of N and subsequent C/N replacement to occur in the case of attack by the NO radical.11 In the investigation of the dissociative adsorption for H2O on different defective models and OH on defect-free and defective models,12 we found that the OH radical can react with pristine graphite (0001) surfaces (model L0D in ref 12) and irreversibly lead to the formation of hydrogenated monovacancy defects (model L1H1V in ref 12) by expelling CO. We also found that the dissociative adsorptions of the OH radical on defect-free surfaces, and H2O on the defective graphite surfaces have much lower barriers than the dissociative adsorption of H2O on the defect-free graphite L0D. In this work, we extend our efforts on the studies of the reactions of CO with monovacancy single-layer defective graphite surface models S1V (C31H14), M1V (C65H20), and L1V (C95H24) models, and CO2 on the L1V model (see Figure 1 for

10.1021/jp9056994 CCC: $40.75  2009 American Chemical Society Published on Web 10/01/2009

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Figure 1. Structures for 5/9 monovacancy defective graphite (0001) surface models: small S1V (C31H14), middle M1V (C65H20), and large L1V (C95H24) model.

a the molecular structures of these small, medium, and large monovacancy defect graphite model systems which all contain fused pentagon/nonagon (5/9) structures featuring a carbenelike carbon center). To the best of our knowledge, no attempt has been made to investigate the reactions of COx species with such defective graphite surface models, and we will present the results of our investigation in Section 3. 2. Computational Methodology In our previous study of the OHx (x ) 1, 2) on defective model surfaces,12 we have compared several defective models including Stone-Wales defective (SW), monovacancy (1V) defective, hydrogenated 1V (1H1V) defective, and divacancy (2V) defective graphite (0001) surfaces. Since SW and 2V defects are almost as inert as pristine graphite, we selected for the present study only the monovacancy (1V) defective graphite (0001) surface with small S1V (C31H14), middle M1V (C65H20), and large L1V (C95H24) models shown in Figure 1. The PES exploration of the reaction of CO with defective graphite models was performed using higher level hybrid density functional B3LYP/6-31+G(d) with the S1V model, and the computationally more economical but nevertheless nearly equally accurate self-consistent-charge density-functional tight-binding6,7,13 plus damped London-type 1/r6 dispersion8 (DFTB-D) level of theory with the S1V, M1V, and L1V model compounds. In addition, the PES exploration of the reaction of CO2 with the L1 V model was undertaken using DFTB-D. QM/MD simulations at the DFTB-D level were carried out for the dissociation product species of COx reactions with the L1V model, using a Verlet algorithm with a 0.12 fs time step. This time interval was checked to conserve total energy to within 3 kcal/mol accuracy during microcanonical dynamics with temperature-adjusted initial velocities for 3000 K. A target temperature of 3000 K was maintained by using the scaling of velocities approach with 20% overall scaling probability. Although at very high temperatures electronic excitations should be abundant, internal conversion and thereby quenching of electronic excitations due to vibrational excitations is very efficient. We therefore consider it justified to consider only the electronic ground state in our QM/MD simulations. For the quantum chemistry calculations, the GAUSSIAN 03 program14 was used, and the “external” keyword was employed to perform DFTB-D with a stand-alone code. In addition, the reaction rate constants for the adsorption and dissociation reactions have been determined using the ChemRate program.15 3. Results and Discussion 3.1. Dissociative Adsorption Reaction of CO on Defective Graphite. The molecular structures for the reactions of CO on defective graphite S1V, M1V, and L1V models are presented in Figure 2, and their intersection of the PESs are presented in Figure 3. The standard deviation for geometry parameters

between B3LYP/6-31+G(d) and DFTB-D in case of the S1V model compound were 0.037 Å, which is an acceptable agreement between the two levels of theory. As shown in Figure 2, the structure parameters calculated with the M1V model are close to those obtained with the L1V model at the DFTB-D level, and the standard deviation is about only 0.003 Å, indicating convergence of defect delocalization in the M1V model. In comparison, the standard deviations are about 0.024 Å for the structure parameters between the L1V and S1V models (DFTB-D), indicating that the S1V model (the 5/9 ring system surrounded by only one layer of hexagons) experiences severe edge effects. It appears that two surrounding hexagon layers are sufficient to stabilize the 5/9 monovacancy defect and its reaction products similarly as 2D graphite. Correspondingly, we found substantial out-of-plane deformations in a case of the S1V models by the reaction with CO, providing additional indication that the S1V model is not big enough to simulate a monovacancy defective graphite surface. Correspondingly, from analysis of the relative energies listed in Figure 3 for the addition of CO to the monovacancy defect, the standard deviations between the L1V and M1V models are about 2.2 kcal/mol, whereas the corresponding standard deviation of relative energies between L1V and S1V models amounts to 7.3 kcal/mol, which stems from stabilization of the defect by surrounding hexagon layers. The energy standard deviation between B3LYP/ 6-31+G(d) and DFTB-D for the S1V model is 14 kcal/mol, and therefore on the order of the deviation found for other DFT functionals. In order to simplify our discussion of the reaction pathways of CO with the monovacancy defect, we only mention the results on the large L1V model in following section. As shown in Figure 3, there are potentially two possible pathways for CO reacting with the monodefective graphite surface. First, the O atom of CO connects to the unsaturated carbene-like carbon of the 5/9 defect to form the CO-P1 adduct. This addition is endothermic by 24.0 kcal/mol and occurs via a 28.1 kcal/mol barrier at CO-TS1. Alternatively, the C atom of CO connects at the same place to form the CO-P2 adduct. This pathway is exothermic by 18.6 kcal/mol and occurs with a 16.2 kcal/mol barrier at CO-TS2. Subsequently, the C atom of CO in either CO-P2 or CO-P1 can connect with surrounding carbon atoms of the defective 5/9 ring system to form the more stable epoxide CO-P3 adduct, which has a nearly perfect chicken-wire hexagonnetwork; the only interruption in the C-C network is the large bridge-head distance associated with the epoxide threemembered ring. The pathway from the CO-P2 to CO-P3 is hugely exothermic by -103.0 kcal/mol and occurs with a 24.7 kcal/mol barrier at CO-TS3. The other pathway from CO-P1 to CO-P3 is also exothermic by 120.9 kcal/mol and occurs with a 11.1 kcal/mol barrier at CO-TS4. Finally, the open 3-membered ring epoxide CO-P3 can isomerize to the closed 3-membered

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Figure 2. Local structures for the dissociative adsorption of CO on the defective graphite S1V, M1V, and L1V models, the upper values calculated with the L1V model at the DFTB-D level, the values in brackets calculated with the M1V model at the DFTB-D level, the values in parentheses calculated with the S1V model at the DFTB-D level, and the bottom values calculated with the S1V model at the B3LYP/6-31+G(d) level.

Figure 3. Intersection of the potential energy surfaces for the dissociative adsorption pathways of CO on the defective graphite S1V, M1V, and L1V models, the upper values calculated with the L1V model at the DFTB-D level, the values in brackets calculated with the M1V model at the DFTB-D level, the values in parentheses calculated with the S1V model at the DFTB-D level, and the bottom values calculated with the S1V model at the B3LYP/6-31+G(d) level.

ring epoxide CO-P4 by overcoming a 3.4 kcal/mol barrier at CO-TS5. Thus, finally the C atom of the reactant CO has filled in the monovacancy defective site and bonded to the three surrounding carbon atoms on the surface, healing the monovacancy defect. Therefore, overall, the reaction of CO repaired the carbon network of the monovacancy defective site while

creating an epoxide defect that may undergo further structural transformations at high temperatures. In comparison, the barriers of the reactions of CO on the monodefective graphite surface are about 70 kcal/mol lower than that of the dissociative adsorption reactions on the defect-free graphite surface,11 which means that CO can much more easily oxidize the monodefective graphite surface than defect-free graphite while at the same time partially fill into the vacancy defects of the carbon hexagon network. 3.2. Dissociative Adsorption Reaction of CO2 on Defective Graphite. The molecular structures for the dissociative adsorption of CO2 on defective graphite L1V model are presented in Figure 4, and the intersection of PES for the dissociative adsorption pathways of CO2 is presented in Figure 5. As shown in Figure 5, at the first step, CO2 reacts with two carbon atoms of the 5/9 ring system to form a lactone-like CO2-P1 adduct. This process is exothermic by 20.4 kcal/mol and occurs with an 18.5 kcal/mol energy barrier at CO2-TS1. Then, the C-O bond in CO2-P1 cleaves to form the more stable CO2-P2 adduct. This step of the reaction is calculated to be 14.2 kcal/mol exothermic and occurs via a 12.4 kcal/mol barrier at CO2-TS2. At the same time, the CO2-P1 adduct can also dissociate to produce L1V-O by expulsion of CO. This step of the reaction is endothermic by 14.9 kcal/mol and occurs with a 31.5 kcal/ mol energy barrier at CO2-TS3. Thus, the overall reaction of CO2 + L1 V is found to be only slightly, 5.6 kcal/mol, exothermic, occurs with a 18.5 kcal/mol barrier, and leads to the surface oxidation product L1V-O + CO.

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Figure 4. Local structures for the dissociative adsorption pathways of CO2 on the defective graphite L1V model calculated at the DFTB-D level.

k2(CO) ) 1.98 × 10-20T2.52 exp(-7800/T) where k1(CO) and k2(CO) are the rate constants for the addition reactions for forming CO-P4. The total rate constants ktotal(CO) is the sum of k1(CO) and k2(CO)

ktotal(CO) ) 1.96 × 10-20T2.52 exp(-7800/T) The predicted rate constants of the CO2 dissociative adsorption reaction for the two processes

Figure 5. Intersection of the potential energy surfaces for the dissociative adsorption pathways of CO2 on the defective graphite L1V model calculated at the DFTB-D level.

In comparison, the reaction barriers for producing irreversibly the expelled CO in the dissociative adsorptions of CO2 on the monovacancy defective graphite surface are about 100 kcal/ mol lower than those on the defect-free graphite,11 which means CO2 can much more easily oxidize the monodefective graphite surface than the defect-free graphite. 3.3. Reaction Rate Constants Predicted by RRKM Theory. The rate constants for these gas-surface reactions have been computed with the RRKM theory using the ChemRate code.15 The predicted rate constants of the CO dissociative adsorption reaction for the two processes

CO2 + L1V f CO2-P1 f CO + LIV-O

(3)

CO2 + L1V f CO2-P1 f CO2-P2

(4)

in the temperature range from 300 to 3000 K can be represented respectively by the expressions in units of cm3/s

k3(CO2) ) 6.23 × 10-10 exp(-43600/T) k4(CO2) ) 3.80 × 10-11 exp(-33700/T)

CO + L1V f CO-P1 f CO-P4

(1)

where k3(CO2) is the rate constant for producing gas CO + L2VCO and k4(CO2) is the rate constant for the addition reaction for forming CO2-P2. The total rate constants ktotal(CO2) is sum of k3(CO2) and k4(CO2)

CO + L1V f CO-P2 f CO-P4

(2)

ktotal(CO2) ) 6.62 × 10-11 exp(-33900/T)

in the temperature range 300-3000 K can be represented respectively by the expressions in units of cm3/s

The rate constants (ki) for the dissociative adsorption reactions of COx on graphite are defined by16

k1(CO) ) 2.17 × 10-22T2.47 exp(-13500/T)

d[X]surf/dt ) ki(θ/As)[X]g

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Figure 6. The dynamics structures for the QM/MD simulations of dissociation products of COx on the L1V model at 3000 K using the DFTB-D method. Two trajectories are shown corresponding to different initial geometries. ft denotes femtoseconds.

which has the unit of a flux, molecule/(cm2s). In the rate equation, θ represents the fraction of available surface sites, As is the surface area, and [X]g is the gas phase concentration of COx in molecules/cm3. 3.4. QM/MD Simulations of COx Dissociative Adsorption Products on Defective Graphite. QM/MD constant temperature simulations of the dissociative adsorption products of COx on the surface of the L1V defective graphite model as described above were carried out using the DFTB-D quantum chemical potential at a temperature of 3000 K. In the following, we describe the details of these simulations. QM/MD simulations starting from the dissociative products of CO-P1 and CO-P2 for CO on the defective graphite surface were carried out, and some snapshots of trajectories are shown in Figure 6. As can be seen in Figure 6, the C atom of CO in CO-P1 connects to the graphite surface after 10 fs. After 40 fs, that C atom in CO-P1 combined with the surrounding carbon atoms on the surface and CO-P1 transformed quickly to the

structure CO-P4. Similarly, the C atom of CO in CO-P2 connected to the graphite surface only after 5 fs. Only after 10 fs, that C atom in CO-P2 combined with the surrounding carbon atoms on the surface, and CO-P2 also transformed to the structure of CO-P4. CO-P4 still kept its structure during the whole simulation, which means CO can repair the monovacancy defective graphite surface even at high temperature condition by creation of an epoxide structure. In the QM/MD simulations, we observe that CO-P2 can transform to CO-P4 much faster than CO-P1, which reflects our finding reported above that the reaction barrier from CO-P2 to CO-P4 is lower than that from CO-P1 to CO-P4. Therefore, the QM/MD simulations of CO on the defective graphite surface are consistent with the CO dissociative adsorption PES result finally forming CO-P4. The QM/MD simulations for the dissociative products of CO2-P1 and CO2-P2 for CO2 on the defective graphite surface are also shown in Figure 6. It is found that the bond of O-CO in CO2-P1 was broken after 5 fs. After 10 fs, CO dissociated

Reactions of CO and CO2 with on Graphite Surfaces and left an O atom adsorbed on the surface. For CO2-P2, the OC-site combined with the O-site again to form CO2 adsorbed on the surface and therefore CO2-P2 transformed to CO2-P1, which is the reverse reaction for CO2-P1 to CO2-P2 in the PES study. Apparently, the QM/MD simulations for CO2 on the defective graphite surface are consistent with the CO2 dissociative adsorption PES result. 4. Conclusions From the above presented B3LYP/6-31+G(d) and DFTB-D studies of the reactions of CO and CO2 on the monovacancy defective graphite surface we can draw the following conclusions: 1. The rate-determining energy barrier for the adsorption of CO on the defective graphite on the monodefective graphite surface is about 70 kcal/mol lower than that for dissociative adsorption of CO on the defect-free graphite surface. 2. The reaction barriers for the dissociative adsorption of CO2 on the defective graphite, to produce the L1V-O + CO(gas) are about 100 kcal/mol lower than that on the defect-free graphite. 3. On the basis of the TS structures, frequencies, and energetics, we predicted the rate constants of the dissociative adsorption of COx on the defective graphite using RRKM. 4. Quantum chemical molecular dynamics (QM/MD) simulations (at the DFTB-D level of theory carried out at T ) 3000 K) of COx on the defective graphite surfaces provide good agreement with the PES studies. In summary, presented data show that COx can oxidize more easily the monovacancy defective graphite (0001) surface than the defect-free graphite, and that CO molecule adsorption is surprisingly capable to heal monovacancy defects via epoxide formation. Acknowledgment. We gratefully acknowledge financial support from the Office of Naval Research under a MURI grant. M.C.L. acknowledges support from the National Science Council of Taiwan for a Distinguished Visiting Professorship at the National Chiao Tung University in Hsinchu, Taiwan. S.I. acknowledges support by the Program for Improvement of Research Environment for Young Researchers from Special Coordination Funds for Promoting Science and Technology (SCF) commissioned by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, and by a Grant-in-Aid No. 20550012 from JSPS. We thank the Cherry L. Emerson Center for Scientific Computation at Emory University for valuable computer time. Supporting Information Available: Table S1 lists names, the B3LYP/6-31+G(d) and DFTB-D total energies and imagi-

J. Phys. Chem. C, Vol. 113, No. 43, 2009 18777 nary frequencies for all structures of the reaction pathways, and Table S2 lists corresponding Cartesian coordinates. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Keswani, S. T.; Andiroglu, E.; Campbell, J. D.; Kuo, K. K. J. Spacecr. Rockets 1985, 22, 396. (2) Federici, G.; Skinner, C. H.; Brooks, J. N.; Coad, J. P.; Grisolia, C.; Haasz, A. A.; Hassanein, A.; Philipps, V.; Pitcher, C. S.; Roth, J.; Wampler, W. R.; Whyte, D. G. Nucl. Fusion 2001, 41, 1967. (3) Hawkes, E. R.; Sankaran, R.; Sutherland, J. C.; Chen, J. H. J. Phys. Conf. Ser. 2006, 16, 65. (4) Ferro, Y.; Marinelli, F.; Allouche, A.; Brosset, C. J. Nucl. Mater. 2003, 321, 294. (5) Xu, S.; Irle, S.; Musaev, D. G.; Lin, M. C. J. Phys. Chem. A 2005, 109, 9563. (6) Porezag, D.; Frauenheim, T.; Koehler, T.; Seifert, G.; Kaschner, R. Phys. ReV. B 1995, 51, 12947. (7) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Phys. ReV. B 1998, 58, 7260. (8) Elstner, M.; Hobza, P.; Frauenheim, T.; Suhai, S.; Kaxiras, E. J. Chem. Phys. 2001, 114, 5149. (9) Kumar, A.; Elstner, M.; Suhai, S. Int. J. Quantum Chem. 2003, 95, 44. (10) Xu, S.; Irle, S.; Musaev, D. G.; Lin, M. C. The JANNAF 15th Nondestructive Evaluation/24th Rocket Nozzle Technology/37th Structures and Mechanical Behavior Joint Subcommittee Meeting, Hilton San Diego Mission Valley, San Diego, CA, Oct. 31-Nov. 4, 2005; 2005-0244AE, Published by the Chemical Propulsion Information Analysis Center, the Johns Hopkins University, Baltimore, Maryland 21044. (11) Xu, S. C.; Irle, S.; Musaev, D. G.; Lin, M. C. J. Phys. Chem. B 2006, 110, 21135. (12) Xu, S. C.; Irle, S.; Musaev, D. G.; Lin, M. C. J. Phys. Chem. C 2007, 111, 1355. (13) Frauenheim, T.; Seifert, G.; Elstner, M.; Hajnal, Z.; Jungnickel, G.; Porezag, D.; Suhai, S.; Scholz, R. Phys. Status Solidi B 2000, 217, 41. (14) Frisch, M. J, Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery. Jr J. A.; Vreven, T.; Kudin, K. N. , Burant, J. C.; Iyengar, S. S.; Millam, J. M.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Ehara, M.; Toyota, K.; Hada, M.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Kitao, O.; Nakai, H.; Honda, Y.; Nakatsuji, H.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J. J.; Cammi, R.; Pomelli, C.; Gomperts, R.; Stratmann, R. E.; Ochterski, J.; Ayala, P. Y.; Morokuma, K.; 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.1; Gaussian, Inc.: Pittsburgh, PA, 2004. (15) Mokrushin, W. ; Bedanov, V.; Tsang, W.; Zachariah, M.; Knyazev, V. ChemRate, version 1.20; National Institute of Standards and Technology: Gaithersburg, MD, 2003. (16) Rettner, C. T.; Ashfold, M. N. R. Dynamics of Gas-Surface Interactions; The Royal Society of Chemistry: London, 1991; Chapter 5.

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