Quantum Chemical Prediction of Reaction Pathways and Rate

Apr 15, 2010 - E-mail: [email protected] (S.I.); [email protected] (M.C.L.)., † ... Nagoya University. , §. National Chiao Tung University. ...
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J. Phys. Chem. C 2010, 114, 8375–8382

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Quantum Chemical Prediction of Reaction Pathways and Rate Constants for Reactions of NO and NO2 with Monovacancy Defects on Graphite (0001) Surfaces S. C. Xu,† S. Irle,*,‡ 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: December 18, 2009; ReVised Manuscript ReceiVed: March 17, 2010

We present reaction pathways for adsorption reactions of NO and NO2 molecules in the vicinity of monovacancy defects on graphite (0001) based on quantum chemical potential energy surfaces (PESs) obtained by B3LYP and dispersion-augmented density-functional tight-binding (DFTB-D) methods. 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 reactions of NOx on the monodefective graphite surface are initiated by rapid association processes with negligible barriers, leading to nitridation and oxidation of the graphite surface, and eventually producing gaseous COx, NO, and CN species leaving from an even more defective graphite surface. On the basis of the computed reaction pathways, we predict reaction rate constants in the temperature range between 300 and 3000 K using Rice-Ramsperger-Kassel-Marcus theory. High-temperature 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 is being tested as surface material for rocket nozzles1 and for plasma divertors in nuclear fusion technology.2 Despite the importance of these technologies, very little is known about the hightemperature, high-pressure (high-T,P) processes causing graphite erosion due to reactions with oxidizing agents from fuel combustion, most importantly H2O and CO2.1 Recently, numerical simulations have given insight into the dynamics of reactive turbulent combustions that stress the importance of OxHy (x ) 1,2, y ) 0-2) species.3 With most modern fuels, not only OxHy, but also COx and NOx (x ) 1,2) are exhaust species that are the most likely candidates for inducing graphite erosion. In addition, an experimental investigation for nitrogen adsorption on defects of carbon black surfaces at 77 K by surface spectroscopy (secondary ion mass spectrometry (SIMS))4 was reported and compared with theoretical results obtained by grand canonical Monte Carlo simulations.4 It was found that nitrogen adsorption was sensitive to the defects and was enhanced at low temperature and high pressure. Recently, the chemical functionalization of semiconducting graphene nanoribbons (GNRs) with Stone-Wales (SW) defects by carboxyl (COOH) groups has been investigated using density functional theory (DFT).5 It was found that the geometrical structures and electronic properties of the GNRs changed significantly, and the electrical conductivity of the system could be considerably enhanced by monoadsorption and double-adsorption of COOH, depending sensitively upon the axial concentration of SW defect COOH pairs (SWDCPs). How graphite defect formation occurs * Corresponding author. E-mail: [email protected] (S.I.); [email protected] (M.C.L.). † Emory University. ‡ Nagoya University. § National Chiao Tung University.

under the high-T,P conditions is still not completely understood. Knowledge of these processes is a prerequisite for the improvement of both graphite-based nozzle lining material and the chemical composition of the fuel. Some time ago we developed a methodology that allows us to systematically investigate a priori high-T,P dissociative adsorption processes on the basal graphite surface.6 This methodology uses for the description of the graphite (0001) surface the dicircumcoronene C96H24 finite-size graphene flake, optionally stacked up to trilayers, and employs DFT as well as density-functional tight-binding7,8 augmented with London dispersion (DFTB-D)9,10 quantum chemical methods for the exploration of dissociative adsorption potential energy surfaces (PESs). Beginning from stationary points along the reaction pathways, DFTB-D-based molecular dynamics (quantum chemical molecular dynamics (QM/MD)) are then performed at constant temperature to check whether most important reaction pathways have been considered, and finally reaction rate constants are predicted for a wide range of temperatures, based on Rice-Ramsperger-Kassel-Marcus (RRKM) theory.11,12 Using this methodology, we predicted high-T,P dissociative adsorption processes and their reaction kinetics for H2O,6 COx,13,14 and NOx14 (x ) 1,2) on the defect-free graphite (0001) surface, and those of OHx15 and COx16 (x ) 1,2) species on the basal face of graphite containing monovacancy defects. In short we found that, on an intact graphene surface, H2O6 and even more so the radical species NO and NO2 can cause irreversible oxide defects on the graphite surface,14 with gaseous CO leaving as a thermodynamically highly stable and highly entropic erosion product. Likewise, the OH radical readily leaves hydrogenated monovacancy defects (model L1H1V in ref 15) behind. We further noticed a pathway for nitridation in the case of NO attack.14 In the investigation of dissociative adsorptions on various defective models, we found that attacks on the monovacancy defect have generally much lower barriers than cor-

10.1021/jp911991k  2010 American Chemical Society Published on Web 04/15/2010

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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).

responding reactions on the defect-free graphite surface.15,16 In the case of reactions of CO and CO2 with monovacancy defects, we found 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.16 In this work, we extend our studies to the reactions of NO with single-layer monovacancy defect models S1V (small, C31H14), M1V (intermediate, C65H20), and L1V (large, C95H24), and NO2 on the L1V model (see Figure 1 for the molecular structures of these small, medium, and large monovacancy defect model systems, featuring the 5/9 defect isomer with a carbenelike center in opposition to the pentagon), using the model systems with the same composition and names as in our study of the COx-monovacancy defect reaction systems.16 To the best of our knowledge, no attempt has been made to investigate the reactions of NOx species with such graphite monovacancy defect surface models. 2. Computational Methodology In this work, we select the same models and computational methods as in our previous study of the reactions of COx (x ) 1,2) on defective model surfaces.16 The PES exploration of the reaction of NO 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-binding7,8,17 plus damped London-type 1/r6 dispersion9 (DFTB-D) level of theory with the S1V, M1V, and L1V model compounds. In addition, the PES exploration of the reaction of NO2 with the L1V model was undertaken using DFTB-D. The location of transition states with the DFTB-D method is presently only possible for a finite molecular system. The single-layer monovacancy defect models S1V, M1V, and L1V are therefore of finite size and are terminated by hydrogen at the edges. For the investigation of small molecule interactions with graphite surfaces, cluster calculations were employed as well, with members of the coronene family as model systems for individual graphite layers.18,19 Our previous study6 found that the DFTB-D method with the finite graphite models was able to reproduce the experimental bulk graphite C-C bond length, interlayer distances, and binding energies of bulk graphite reasonably well. QM/MD simulations at the DFTB-D level were carried out for the dissociation product species of NOx reactions with the L1V model, using a Verlet algorithm with a 0.12 fs time step. This time interval was checked to conserve the total energy to

within 3 kcal/mol accuracy during microcanonical dynamics with temperature-adjusted initial velocities for 3000 K. In all production trajectories, 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.20 We therefore give an approximation that only the electronic ground state in our QM/ MD simulations is considered. For the quantum chemistry calculations, the GAUSSIAN 03 revision C.121 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.22 3. Results and Discussion 3.1. Dissociative Adsorption Reaction of NO on Defective Graphite. The molecular structures for the reactions of NO on defective graphite S1V, M1V, and L1V models are presented in Figure 2, and corresponding schematic PESs are presented in Figure 3. The standard deviation for geometry parameters between B3LYP/6-31+G(d) and DFTB-D in the case of the S1V model compound was 0.08 Å. As shown in Figure 1, the key structural parameters calculated with the M1V model are close to those obtained with the L1V model at the DFTB-D level, and the standard deviation between these two calculations is only about 0.02 Å, indicating convergence of defect delocalization in the M1V model. In comparison, the standard deviation is about 0.07 Å for the structural parameters between the S1V and L1V 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 similar to twodimensional (2D) graphite. Correspondingly, we found substantial out-of-plane deformations in the case of the S1V models by the reaction with NO, providing an 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 NO to the monovacancy defect, the standard deviations between the L1V and M1V models are about 2.1 kcal/mol, whereas the corresponding standard deviation of relative energies between L1V and S1V models amounts to 5.4 kcal/mol, which stems from stabilization of the defect by surrounding hexagon layers. The energy standard deviation between B3LYP/6-31+G(d) and

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Figure 2. Local structures for the dissociative adsorption of NO on the defective graphite S1V, M1V, and L1V models: the top values were calculated with the L1V model at the DFTB-D level, the values in brackets were calculated with the M1V model at the DFTB-D level, the values in parentheses were calculated with the S1V model at the DFTB-D level, and the bottom values were calculated with the S1V model at the B3LYP/6-31+G(d) level. The unit for the bond lengths is Å.

DFTB-D for the S1V model is 9.4 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 NO with the monovacancy defect, we only discuss here the results on the large L1V model in the following section. As shown in Figure 3, there are two paths for the NO radical to react directly with the L1V. In the first (the lower energy) pathway, the O atom of NO connects to the unsaturated carbenelike carbon of the 5/9 defect, and the N atom inserts itself into the C-C bond of the pentagon to form the NO-P1 adduct with a binding energy BE () negative relative energies ∆E ) Ecomplex - ∑Eireactant) of 126.1 kcal/mol. The product is low in energy because it contains a newly formed O-C and two N-C bonds, creating a fused 7/7 heteroring system with an N-O-C bridge. In a subsequent step, the NO bond breaks, and the NO-P2 adduct (N-site + O-site) is formed. This isomerization is exothermic by 12.4 kcal/mol and occurs via a 15.8 kcal/mol barrier at NOTS1, replacing the 7/7 fused ring system by two hexagons where nitrogen substitutes the missing carbon in the all-hexagon graphite carbon network. Finally, the CO group in NO-P2 can

break away from the deformed graphite to give a defective graphite L2V-N. This desorption is endothermic by 47.0 kcal/ mol and occurs with a 70.2 kcal/mol energy barrier at NOTS2. The overall result of this reaction is the nitridation of the monovacancy, replacing the carbene-like carbene atom by a nitrogen atom at the opposite side of the nine-membered ring. In the second path, the NO molecule is simply rotated by 180° in the initial attack. Here, the O atom inserts itself into the C-C bond of the pentagon, whereas the N atom connects to the carbene-like carbon of the nine-membered ring to form the NOP3 adduct with a significantly lower binding energy of only 47.4 kcal/mol. Clearly, the trivalent O and divalent N atom are overand undersaturated in this compound, which is a frustrated compound in the sense that the positions of O and N are best exchanged. Correspondingly, the barriers associated with NOP3 are low, and the NO-P3 may easily isomerize to the NO-P4 adduct by breaking the NO bond. As can be expected, this process is exothermic by 47.7 kcal/mol and occurs via a smaller barrier of 0.4 kcal/mol at NO-TS3. The NO-P4 may isomerize to the NO-P5 adduct by breaking the C-C bond connecting

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Figure 3. Schematic drawing of the PESs for the dissociative adsorption pathways of NO on the defective graphite S1V, M1V, and L1V models: the top values were calculated with the L1V model at the DFTB-D level, the values in brackets were calculated with the M1V model at the DFTB-D level, the values in parentheses were calculated with the S1V model at the DFTB-D level, and the bottom values were calculated with the S1V model at the B3LYP/6-31+G(d) level.

the N atom. However, this process is endothermic by 11.6 kcal/ mol and occurs with a 15.2 kcal/mol energy barrier at NOTS4. Finally, the CN group in NO-P5 can break away from the deformed graphite to give a defective graphite L2V-O by overcoming a dissociation energy of 82.5 kcal/mol. Therefore, the NO radical can react barrierlessly with the monovacancy defective graphite surface to produce CO or CN. Comparing the NO on the monodefective graphite surface with that on the defect-free graphite surface, the reaction of NO on the monodefective graphite surface is a fast association process with negligible barriers and can easily lead to nitridation and oxidation of the graphite surface. However, the reaction of NO on the defect-free graphite surface is an addition process with 75-88 kcal/mol barriers, which has to overcome 138 kcal/ mol for nitridation of the graphite surface.14 In general, we find that NO can much more readily react with the monodefective graphite surface than with the defect-free graphite. 3.2. Dissociative Adsorption Reaction of NO2 on Defective Graphite. The optimized molecular structures and schematic drawings of the corresponding PESs for the dissociative adsorption of NO2 on the L1V model surface are presented in Figures 4 and 5, respectively. As shown in Figure 5, the NO2 radical reacts without barrier with the carbene-like carbon atom of L1V to form a stable adduct of NO2-P1 with a binding energy of 49.5 kcal/mol. Then, NO2-P1 isomerizes to adduct NO2-P2 with a 15.8 kcal/mol exothermicity. This adduct isomer is unique in that it features a tetravalent nitrogen with a radical O center pointing away from the surface. It also features the N-O-Cbridge of a fused 7/7 ring system that was encountered in the reaction of NO, structure NO-P3. The isomerization occurs via a 5.8 kcal/mol barrier at NO2-TS1 and has a remarkably high backward barrier of 21.6 kcal/mol. As can be expected, from NO2-P2 the reaction proceeds readily via the formation of adduct NO2-P4 via cleavage of an N-O bond; this process is exothermic by 15.4 kcal/mol and occurs with a small, 1.1 kcal/ mol transition state NO2-TS3. The resulting NO2-P4 adduct isomerizes to another adduct, NO2-P5, which occurs with an 8.9 kcal/mol barrier and is endothermic by 5.5 kcal/mol. Finally, NO2-P5 can dissociate to produce gaseous CO2 and nitridation

product L2V-N or produce gaseous CO and nitridation product L2V-NO. The first dissociation process is exothermic by 33.6 kcal/mol and requires a 12.8 kcal/mol energy barrier. The second dissociation process is endothermic by 5.5 kcal/mol and requires a 39.6 kcal/mol energy barrier. In order to produce NO, a high-barrier pathway exists from NO2-P2 that involves dissociation of the ON-O bond to form a van der Waals complex NO2-P3. This step of the reaction is endothermic by 13.1 kcal/mol and occurs with a 32.4 kcal/mol barrier at NO2-TS2. Final dissociation of the NO molecule from NO2-P3 leads to the oxidized graphite monovacancy surface, and is endothermic by 42.4 kcal/mol (calculated relative to NO2P2). As seen from Figure 4, the previously discussed nitridation pathway leading to L2V-N + CO2 is energetically and kinetically the more favorable path. As described above, the reaction of NO2 on the monodefective graphite surface is a barrierless association process with subsequent low isomerization and decomposition barriers and can easily lead to nitridation and possibly oxidation of the graphite surface to produce gaseous CO2, CO, and NO products. For comparison, the reaction of NO2 on the defect-free graphite surface is an addition process with 27-37 kcal/mol barriers, which has to overcome 62 kcal/mol for oxidation of the graphite surface with gaseous NO product.14 In general, NO2 is similar to NO, which can much more easily react with the monodefective graphite surface than 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.22 The predicted rate constants of the NO dissociative adsorption reaction for the two processes

k1: NO + L1V f CO + L2V-N

(1)

k2: NO + L1V f CN + L2V-O

(2)

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

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Figure 4. Local structures for the dissociative adsorption pathways of NO2 on the defective graphite L1V model calculated at the DFTB-D level. The unit for the bond lengths is Å.

k1 ) 1.12 × 10-40T9.91 exp(-196/T) for T ) 300-1200 K 222 -64.90 ) 4.36 × 10 T exp(-90 500/T) for T ) 12003000 K k2 ) 6.90 × 10

-62 16.43

T

exp(-6300/T) for T ) 300-1600 K

270 -76.78

) 1.15 × 10

T

exp(-129 000/T) for T ) 1600-3000 K

k3 ) 5.79 × 10-7T-1.17 exp(-200/T) for T ) 300-1800 K ) 5.74 × 10271T-76.40 exp(-137 000/T) for T ) 1800-3000 K k4 ) 1.74 × 10-32T6.27 exp(-268/T) for T ) 300-1800 K ) 1.38 × 10287T-80.67 exp(-149 700/T) for T ) 1800-3000 K k5 ) 9.56 × 10-41T7.17 exp(-1400/T) for T ) 300-1800 K

The predicted rate constants of the NO2 dissociative adsorption reaction for the two processes

k3: NO2 + L1V f CO2 + L2V-N

(3)

k4: NO2 + L1V f CO + L2V-NO

(4)

k5: NO2 + L1V f NO + L2V-CO

(5)

) 1.80 × 10284T-81.38 exp(-152 000/T) for T ) 1800-3000 K The rate constants (ki) for the dissociative adsorption reactions of NOx on graphite are defined by23

d[X]surf/dt ) ki(θ/As)[X]g

in the temperature range from 300 to 3000 K can be represented, respectively, by the following expressions in units of cubic centimeters per second (cm3/s):

which has the unit of a flux (molecule/cm2 · s). 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 NOx in molecules per cubic centimeter.

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Figure 5. Schematic drawing of the PESs for the dissociative adsorption pathways of NO2 on the defective graphite L1V model calculated at the DFTB-D level.

Figure 6. The dynamics structures for the QM/MD simulations of dissociation products of NOx on the L1V model at 3000 K using the DFTB-D method. Two trajectories are shown corresponding to different initial geometries. The unit for the bond lengths is Å.

Reaction Pathways for Reactions of NOx on Graphite In comparison, the rate constant of the NO on the monodefective graphite surface at 1000 K is 1.68 × 105 times faster than that of the CO on the monodefective graphite surface, and 1.51 × 1034 times faster than that of the NO on the defect-free graphite surface. The rate constant of the NO2 on the monodefective graphite surface at 1000 K is 1.19 × 1015 times faster than that of the CO2 on the monodefective graphite surface, and 6.23 × 1015 times faster than that of the NO2 on the defectfree graphite surface. Therefore, by predicting rate constants of NOx on the graphite surface, we can learn quantitatively how fast are the reactions of NOx on the graphite surface, providing us a guideline for related experimental investigations. 3.4. QM/MD Simulations of NOx Dissociative Adsorption Products on Defective Graphite. QM/MD constant temperature simulations of the dissociative adsorption products of NOx 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. When the temperature is higher than 3000 K, the enthalpy and heat capacity of graphite increase slowly,24 so 3000 K is a standard temperature for simulating the high temperature property of graphite. In the following, we describe the details of these simulations. QM/MD simulations starting from the dissociative products of NO-P1, NO-P2, NO-P3, NO-P4, and NO-P5 for NO 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, for the first reaction path, the NO bond in NO-P1 dissociates to form NO-P2 after 48 fs. The CO in NO-P2 begins to dissociate from the surface and finally produces gaseous CO and L2V-N after 36 fs. Similarly for the second reaction path, the NO bond in NO-P3 dissociates to form NO-P4 after 36 fs. The C-C bond in NO-P4 dissociates to form NO-P5 after 24 fs. Finally, the CN in NO-P5 begins to dissociate from the surface and produce gaseous CN and L2V-O after 96 fs. In the QM/MD simulations, we observe that the reaction of NO on the monodefective graphite surface can easily lead to nitridation and oxidation of the graphite surface and produce gaseous CO and CN, and the dissociation rate for CO is faster than that for CN. Therefore, the QM/MD simulations of NO on the defective graphite surface indicates that the NO dissociative adsorption PES presented in Figure 3 contains the most important key elements for this reaction. The QM/MD simulations for the dissociative products of NO2-P1, NO2-P2 and NO2-P3 for NO2 on the defective graphite surface are also shown in Figure 6. It is found that NO2-P1 can isomerize to adduct NO2-P2 only after 2.4 fs. After 24 fs, NO in NO2-P2 dissociated and formed adduct NO2-P4. After 36 fs, NO2-P2 underwent two isomerization processes from NO2-P2 f NO2-P4 f NO2-P5. After 48 fs, CO2 in the NO2-P5 dissociated from the surface and finally produce gaseous CO2 and L2V-N. In addition, for the QM/MD simulation of NO2P3, NO dissociated from the surface and finally produce gaseous NO and L2V-CO after 3.6 fs. In summary, the results for the QM/MD simulations of NO2 on the defective graphite surface have shown that the reaction path in the simulation followed the minimum energy path shown in the NO2 dissociative adsorption PES, which finally produces L2V-N + CO2. 4. Conclusions The reactions of NO and NO2 on the monovacancy defective graphite surface were calculated using the B3LYP/6-31+G(d) and DFTB-D methods. The PESs for the adsorption reactions of NOx (x ) 1 and 2) on the defective graphite were computed, and intermediate structures, transition states, and low-lying

J. Phys. Chem. C, Vol. 114, No. 18, 2010 8381 product structures were characterized. For the adsorption of NO on the defective graphite, we found that NO radical can react directly with the L1V with a chemical adsorption energy of 47.4-126.1 kcal/mol. In addition, the reaction of NO on the monodefective graphite surface can easily lead to nitridation and oxidation of the graphite surface and produce gaseous CO and CN products. Similarly, for the dissociative adsorption of NO2 on the defective graphite, we found that NO radical can react directly with the L1V with a chemical adsorption energy of 49.5 kcal/mol. In addition, the reaction of NO2 on the monodefective graphite surface can easily lead to nitridation and oxidation of the graphite surface and produce gaseous CO2, CO, and NO products. On the basis of the transition state structures, frequencies, and energetics, we also predict the rate constants of the dissociative adsorption reactions of NOx on the defective graphite using RRKM. QM/MD simulations at the DFTB-D level of theory were also carried out for reaction products to elucidate reverse adsorption pathways and to further explore the PESs accessible at T ) 3000 K. The QM/MD simulations of NOx on the defective graphite surfaces are consistent with the PESs results. Overall, we conclude that NOx can much more easily oxidize the monovacancy defective graphite (0001) surface than the defect-free graphite, and produce gaseous COx, NO, and CN species. Chain reactions of these product species may occur afterward, leading to further erosion of the graphite surface. Acknowledgment. We gratefully acknowledge financial support from the Office of Naval Research under an 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 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 the B3LYP/6-31+G(d) and DFTB-D total energies and imaginary frequencies where applicable 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) Darmstadt, H.; Roy, C. Carbon 2001, 39, 841. (5) OuYang, F.; Huang, B.; Li, Z.; Xu, H. Los Alamos National Laboratory, Preprint Archive, Condensed Matter, 2007, 1. (6) Xu, S.; Irle, S.; Musaev, D. G.; Lin, M. C. J. Phys. Chem. A 2005, 109, 9563. (7) Porezag, D.; Frauenheim, T.; Koehler, T.; Seifert, G.; Kaschner, R. Phys. ReV. B 1995, 51, 12947. (8) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Phys. ReV. B 1998, 58, 7260. (9) Elstner, M.; Hobza, P.; Frauenheim, T.; Suhai, S.; Kaxiras, E. J. Chem. Phys. 2001, 114, 5149. (10) Kumar, A.; Elstner, M.; Suhai, S. Int. J. Quantum Chem. 2003, 95, 44.

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