Quantum Chemical Prediction of Reaction Pathways and Rate

J. Phys. Chem. B 2006, 110, 21135-21144

21135

Quantum Chemical Prediction of Reaction Pathways and Rate Constants for Dissociative Adsorption of COx and NOx on the Graphite (0001) Surface 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 ReceiVed: July 4, 2006; In Final Form: August 21, 2006

We present predictions of reaction rate constants for dissociative adsorption reactions of COx (x ) 1, 2) and NOx (x ) 1, 2) molecules on the basal graphite (0001) surface based on potential energy surfaces (PES) obtained by the integrated ONIOM(B3LYP:DFTB-D) quantum chemical hybrid approach with dispersionaugmented density functional tight binding (DFTB-D) as low level method. Following an a priori methodology developed in a previous investigation of water dissociative adsorption reactions on graphite, we used a C94H24 dicircumcoronene graphene slab as model system for the graphite surface in finite-size molecular structure investigations, and single adsorbate molecules reacting with the pristine graphene sheet. By employing the ONIOM PES information in RRKM theory we predict reaction rate constants in the temperature range between 1000 and 5000 K. We find that among COx and NOx adsorbate species, the dissociative adsorption reactions of CO2 and both radical species NO and NO2 are likely candidates as a cause for high temperature oxidation and erosion of graphite (0001) surfaces, whereas reaction with CO is not likely to lead to long-lived surface defects. High temperature quantum chemical molecular dynamics simulations (QM/MD) at T ) 5000 K using on-the-fly DFTB-D energies and gradients confirm the results of our PES study.

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 in combustion chambers as well as plasma-facing components. Despite its popularity, very little is currently known about the high-temperature, highpressure chemistry occurring on the graphite surface with oxides produced in fuel combustion, which is thought to be the leading cause for surface erosion processes. Previously, we have studied the dissociative adsorption of water molecules on a graphene surface using mono-, bi-, and trilayers of dicircumcoronene C94H24 as graphite model system in finite-size quantum chemical investigations1 and have found that defect creation on the graphite (0001) surface by H2O f H + OH dissociation and chemisorption of radical species is virtually impossible due to high forward barriers of more than 70 kcal/mol, which are associated with very small reverse barriers for the self-healing of the graphene surface and ejection of the adsorbates. In that work, we have devised and thoroughly tested a general methodology for a priori investigations of graphite defect formation, employing a combination of integrated ONIOM2,3 electronic structure calculations and quantum chemical molecular dynamics (QM/MD) simulations. Using this methodology, in the present study we investigate the interactions of carbon monoxide (CO) and dioxide (CO2), as well as open-shell radical species nitrogen monoxide (NO) and dioxide (NO2) as important exhaust species with graphite and compare their reactivities and corresponding defect formation. It can be expected that the closed-shell carbon oxides are much less likely than radical nitrogen oxides to react with the graphite surface, but on the other hand, the C-C bond formed during a potential CO addition is much stronger than a C-N bond (the C-C bond * Corresponding authors. E-mail: [email protected]; [email protected].

energy in benzaldehyde is 98 kcal/mol,4 the C-N bond energy in nitrosobenzene is 54.0 kcal/mol5). Until now, all studies on COx interactions with graphite reported in the literature have been carried out at extremely low temperatures, due to the weak interactions responsible for physisorption. In the case of CO adsorption on graphite, LEED techniques at around 35 K were used to clarify the structure of the CO monolayer.6-9 More recently, IR vibrational spectra of physisorbed CO on graphite were recorded in the low-temperature range between 20 and 40 K,10 and the measured C-O stretch frequency of the CO monolayer was found to be redshifted by merely 5 cm-1. Yet, earlier studies on the electron stimulated desorption of C+, C-, O+, and O- ions from physisorbed CO films on graphite11,12 have shown a remarkable dependence of the CO-graphite interaction on the nature of the graphite surface. The physisorption of CO2 on carbon nanotubes and graphite has also been investigated;13-15 for instance, thermodynamic properties including adsorption isotherms, isosteric heats, and the temperature dependence of the monolayer heat capacity of carbon dioxide on graphite at low temperatures have been studied extensively.16,17 Vibrational spectra of adsorbed CO2 on different sites of single walled carbon nanotube (SWNT) bundles have been recorded by Johnson et al., and the frequency shifts of CO2 adsorption on chemically different single-walled carbon nanotube (SWNT) sites have been obtained accordingly in order to elucidate the location of oxygen-containing functional groups on oxidized tubes.18 The adsorption energy of CO2 on SWNTs was experimentally determined to be 0.5 kcal/mol.19 NO and NO2 have been widely known as typical atmospheric pollutants. The adsorption reactions of NOx with various carbonaceous materials have been studied extensively because they are recognized to be very important for NO emission rates. Unfortunately, the widely varying degree of defects in com-

10.1021/jp0642037 CCC: $33.50 © 2006 American Chemical Society Published on Web 09/23/2006

21136 J. Phys. Chem. B, Vol. 110, No. 42, 2006 mercially available graphite make direct comparisons between experiments and theory very difficult. Smith et al.20,21 measured isotherms at 119 K and physically adsorption at 90 K for NO on partially graphitized carbon blacks, whereas Zarif’yants22 and Cascarini de Torre et al.23 studied adsorption of NO on freshly cleaved graphite. Brown et al.24,25 measured low-temperature adsorption isotherms of NO on carbon black and obtained isosteric heats of adsorption on graphitized carbon between 2.9 and 4.3 kcal/mol, depending on the coverage. Furthermore, the same group studied the reaction of NO with a graphite surface26 and found that NO did not react appreciably with highly graphitized carbon black at temperatures up to 670 K, while in reaction with ungraphitized carbon black graphite oxidation was observed. Moreh et al. have shown that NO2 physisorbs as dimer on graphite surfaces at temperatures between 12 and 297 K.27 More recently, the adsorption and reaction of NOx on activated carbon and carbon catalysts have been studied,28-33 and at desorption temperatures around 570 K it was found that NO adsorbs even more weakly than NO2, and needs coadsorption of O2 to make both adsorption rates similar.33 No previous theoretical studies regarding CO adsorption on graphite or SWNT surfaces are presently known to us. In the case of CO2 adsorption on carbonaceous materials, theoretical interest exists mainly due to two factors, namely to investigate the usefulness of nanoporous carbon for CO2 sequestration and to study the significant buildup of CO2 pressure during heatinduced de-oxidation of carbon nanotubes. Sandler et al. have investigated the adsorption of CO2 on a warped graphite model surface using molecular dynamics.34 Zhao et al. have studied the adsorption energies of several small gaseous molecules including CO2 on SWNTs using local density approximation (LDA) density functional theory (DFT)35 and obtained adsorption energies of CO2 on SWNTs on the order of 2 kcal/mol, larger than experimentally reported. This finding is in line with the known deficiency of LDA to overestimate weak bonding interactions. Johnson et al. used also LDA calculations to compute the adsorption energies and vibrational frequencies for CO2 adsorbed on SWNT bundles and obtained similarly too large binding energies of several kcal/mol.18 Bauschlicher et al. performed high level ab initio MP2 and CCSD(T) calculations with large basis sets of CO2 interacting with small graphene clusters and obtained a smaller interaction energy between 0.1 and 0.5 kcal/mol after elimination of the basis set superposition effect.19 In all cases, CO2 adsorption on graphite was found to be dominated by large quadrupole-quadrupole interactions. No study has investigated dissociative adsorption of CO2 on carbonaceous surfaces. Regarding the chemisorption of NOx species on carbonaceous materials, only the NO2 adsorbate species was theoretically investigated. Using periodic LDA calculations, Yim et al. found that in contrast to reactions with graphite, zigzag-type SWNTs form an almost thermoneutral C-ONO nitrite defect with a virtually nonexistent barrier, while the C-NO2 nitro defect was found to be energetically higher.36 Interestingly, multiple NO2 adsorption on SWNTs produces exothermic defects.36,37 To the best of our knowledge, no theoretical systematic investigations of the adsorption interaction and dissociative adsorption reactions of COx (x ) 1,2) and NOx (x ) 1, 2) on defect-free graphite (0001) have been reported, and therefore we have carried out hybrid ONIOM(B3LYP/6-31+G(d):DFTBD) studies on the potential energy surfaces (PES) of adsorbatedicircumcoronene model systems, using the PES data in RRKM calculations to obtain reaction rates for the dissociative adsorption reactions in analogy to our previous water-graphite

Xu et al. interaction studies.1 DFTB-D is a density functional tight binding method38-40 with dispersion energy correction41 and has recently been shown to yield excellent agreement for π-stacked systems41,42 and the water-graphite reaction system.1,43 Since we have shown that the addition of a second and third dicircumcoronene layer for simulation of vertical bulk effect influences energetics only marginally,1 we are restricting ourselves here to a monolayer graphite model. To allow a systematic study of the COx/NOx dissociative adsorption processes, we have as a first step selected single-molecule adsorbents as model systems only. Since our goal is to address high-temperature/high-pressure chemistry, the dimerization energies of 2 kcal/mol for NO44 and 14 kcal/mol for NO245 can safely be disregarded, and it can be assumed that exhaust molecules are produced mono-molecularly. As expected, weakening the adsorbate molecules double (dioxides) or triple (monoxides) bonds and breaking the π-conjugation of the graphite slab is a highly endothermic process, and therefore all reaction pathways are associated with considerable forward barriers, which are only possible to overcome under high-temperature and high-pressure conditions. In fact, high temperature will rather lead to rapid desorption of the adsorbate molecule, which is why any dissociative reaction process has to be accompanied by a directional force pushing the adsorbate molecule to the surface. Under these extreme conditions, chemical reactions do not closely follow minimum energy pathways. Such pathways can, however, shed light on the possible processes occurring under the extreme conditions of graphite erosion in combusion chambers. Yet, the high energy pathways are countless, and while we have followed some of them, we will present only selected first reaction steps on such pathways, in particular of reactions that lead irreversibly to graphite defects by means of the production of gaseous (g) species. To obtain a priori high-temperature events for the COx/ NOx-graphite adsorbate-adsorbent systems, we have performed QM/MD simulations based on DFTB-D at 5000 K target temperatures, starting from defects found on the ONIOM PESs, and analyze most stable species and frequent events under such conditions. 2. Computational Methods The exploration of the COx (x ) 1, 2) + graphite and NOx (x ) 1, 2) + graphite PESs was performed using the ONIOM(B3LYP:DFTB-D) integrated method2,3 on finite-size molecular systems. The first principles B3LYP/6-31+G(d) hybrid density functional method was selected as high-level theory for a coronene C24H12+COx/NOx model system, and the computationally less expensive self-consistent charge density functional tight binding38-40 plus London dispersion41 (DFTB-D) method was employed at the low level to include the horizontal bulk effect (mainly π-conjugation) using a larger dicircumcoronene C94H24-COx/NOx real system. We have optimized equilibrium geometries and transition states (TS) using this ONIOM approach and employed the single level DFTB-D method on respective re-optimized structures in the numerical calculation of vibrational frequencies and zero-point energy (ZPE) corrections. This ONIOM(B3LYP/6-31+G(d):DFTB-D) approach, the employed model systems, and the particular combination of DFT/DFTB-D levels of theory have been successfully tested by us in previous extensive benchmarks on the graphite-water reaction system in comparisons with higher level DFT and MP2 calculations.1 The GAUSSIAN 03 revision C.146 implementation of ONIOM was employed in all calculations, using standard convergence criteria and the “external” keyword to perform DFTB-D energy and gradient calculations with a stand-alone

Dissociative Adsorption of COx and NOx on Graphite (0001) Surface

J. Phys. Chem. B, Vol. 110, No. 42, 2006 21137

Figure 1. Molecular structures of physisorbed species and important defect structures for dissociative adsorption reactions of COx and NOx on (0001) graphite. Only relevant bonds are shown. Bond lengths are given in [Å].

code. QM/MD simulations at the DFTB-D level were carried out for the dissociation products of COx and NOx (x ) 1,2) on the surface of a graphite monolayer model, using a Verlet algorithm with a 0.12 fs time step. The target temperature of 5000 K was maintained by using the scaling of velocities approach with 20% overall scaling probability. The reaction rate constants for the adsorption and dissociation reactions have been determined using the ChemRate program,47 based on ONIOM energetics and DFTB-D vibrational frequencies. 3. Results and Discussion The dicircumcoronene C96H24 graphene slab, used as model for a perfect (0001) graphite surface, will be denoted S in the following sections, consistent with our previous water-graphite paper (see Figure 3 of ref 1). Following the methodology of that work, the adsorbate molecules are also in the present study interacting with the central hexagon of the D6h-symmetric dicircumcoronene. In ONIOM calculations, the coronene C24H12 high level model system is positioned in the center of S and surrounded by two low-level hexagon layers as before.1 All geometrical parameters mentioned in the text were obtained at the ONIOM(B3LYP/6-31+G(d):DFTB-D) level of theory while vibrational frequencies reported were obtained using the singlelevel DFTB-D method. ONIOM Cartesian coordinates of all structures presented in this study are available as Supporting Information. ONIOM interaction energies (denoted ∆E) and ONIOM interaction energies including DFTB-D ZPE-corrections (denoted ∆EZPE) are given in reference to the isolated adsorbate COx/NOx molecule and pristine S. In the remainder of the text, because of the ambiguities of the ZPE correction at high temperatures, we will discuss only ∆E values unless otherwise noted. Figure 1 shows most important optimized

geometries for all dissociative adsorption reactions, and Figures 2-5 display the associated PESs with irreversible defect creation specially marked. Complete structural information for COx and NOx species can be found in Figures S1-S4 of the Supporting Information. (a) Physisorption of COx and NOx Adsorbate Molecules on Pristine Graphite (0001). Concerning the physisorption of CO on the model system for a pristine graphite (0001) surface, we found two possible conformations of CO-RC1 and CORC2, as shown in Figure 1. CO-RC1 corresponds to the 1,2adduct, while CO-RC2 corresponds to the 1,4-adduct. In both cases, the C end is closer to the graphite surface than the O end, with C and O distances to the nearest graphite carbon optimized as 3.72 Å and 4.07 Å in CO-RC1, and 3.89 Å and 3.94 Å in CO-RC2, respectively. ∆EZPE of complexes CORC1 and CO-RC2 are almost zero with -0.1 and -0.3 kcal/ mol, respectively, the 1,4-adduct being slightly favored over the 1,2-adduct. In these very weakly bound physisorbed complexes, the frequency shifts for the CO stretch vibration on S relative to free CO are predicted by DFTB-D to be -10.7 cm-1 in CO-RC1 and -10.3 cm-1 in CO-RC2. We note that Boyd et al. gave a comparable value of about 6 cm-1 in experimental IR spectra at 20-40 K.10 The further reactions of the 1,4-adduct CO-RC2 were not investigated as no feasible pathway was apparent in ONIOM TS searches. Concerning physisorbed CO2 on graphite, we found three possible conformations of the adsorption complex, as shown in Figures 1 and S2. The C2V-symmetric 1,4-adduct complex CO2RC1 was already described by Bauschlicher et al. as lowest energy minimum due to its favorable quadrupole-quadrupole interaction at the MP2/6-31G(d) level of theory.19 The other two conformations represent minima for physisorbed CO2 on

21138 J. Phys. Chem. B, Vol. 110, No. 42, 2006

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Figure 2. Potential energy surfaces of the reaction of CO + S. Interaction energies ∆E at the ONIOM level of theory are given in kcal/mol. Numbers in parentheses include ZPEs obtained at the DFTB-D level (∆EZPE). Corresponding ONIOM(B3LYP/6-31+G(d):DFTB-D) structures are shown next to energy levels unless energy differences between consecutive stationary points are smaller than 1 kcal/mol, for which only one structure of the intermediates is shown. Only carbon atoms are shown which are significantly affected by the reaction.

graphite corresponding to the 1,2-adduct (CO2-RC2) and the T-shaped adduct (CO2-RC3), where CO2 lies vertically above one of the graphite carbon atoms. The distance of the CO2 axis in CO2-RC1 to the S plane was optimized to be 3.91 Å, while the distance of the nearest oxygen atom to the graphite surface in the T-shaped complex (CO2-RC3) was computed to be 3.49 Å, which is even slightly longer than a C-O van der Waals contact. ∆EZPE for the CO2-RCn are in fact very similar to those of CO-RCn with values around -0.5 kcal/mol, and are further reduced when ZPE’s are taken into account. Moreover, the PESs for these reaction complexes were found to be very shallow. Single-level DFTB-D calculations predict the frequency shift in the asymmetry stretching mode of CO2 on the S graphite model surface to be -6 cm-1 relative to that of the free CO2 molecule, which coincides with the experimentally observed shift of -7 cm-1 for CO2 on SWNT bundles.18 As shown in Figure 1, for physisorption of NO on graphite we found only one possible conformation NO-RC1. The alignment of the NO molecule in NO-RC1 is almost parallel to the S plane, with N and O situated roughly on top of C-C bond centers forming a four-membered ring. The distances of N and O in NO-RC1 to the nearest graphite carbons are 3.03 Å and 3.34 Å, respectively, with the radical center N slightly more tilted by 15° toward the graphene plane. The N-O bond distance is 1.152 Å, which is almost identical to that of free NO with 1.158 Å at the B3LYP/6-31+G(d) level of theory. As shown in Figure 3, ∆EZPE of NO-RC1 is almost zero with -0.2 kcal/mol. For comparison, we note that the experimental lowtemperature isosteric heats of adsorption on graphitized carbon was measured to be between 2.9 and 4.3 kcal/mol.25 As to the physisorption of NO2 on graphite, we found two possible conformations corresponding to complexes NO2-RC1 and NO2-RC2, also shown in Figure 1. NO2-RC1 corresponds to the nitrate 1,4-adduct, while NO2-RC2 corresponds to the nitrite 1,2-adduct. The distance of the O-O axis in NO2-RC1

to the parallel plane of S was predicted to be 3.52 Å, while the distances of the nearest O and N atom to the graphite surface in the NO2-RC2 were computed to be 3.79 Å and 3.28 Å, respectively, the radical center on N obviously preferring a closer interaction than O. As shown in Figure 4, ∆EZPE of complexes NO2-RC1 and NO2-RC2 are -6.7 kcal/mol and -8.0 kcal/ mol, respectively. The frequency shifts for the NO2 symmetric and anti-symmetric stretch vibrations on S are predicted by DFTB-D to be -83 and 34 cm-1 for NO2-RC1, and -89 and 29 cm-1 for NO2-RC2, respectively. These S-induced frequency shifts are much larger than in the case of CO2, in line with the much larger interaction energies. (b) Dissociative Adsorption PESs of CO on Graphite. The PESs for the dissociative adsorption pathways of CO on graphite and corresponding molecular structures are presented in Figure 2. In the dissociative adsorption of CO on graphite, the carbon monoxide molecule can either insert into a graphite C-C bond with its carbon end, forming CO-P1 with a ∆E of 71.6 kcal/ mol by overcoming an 88.6 kcal/mol barrier, or can form a highly strained four-membered ring adduct CO-P2 with 120.2 kcal/mol endothermicity by overcoming a 121.1 kcal/mol barrier. The latter barrier even vanishes when ZPE is taken into account, which is why we draw only one structure for both species on the PES plot of Figure 2. From there, further restructuring can occur only by breaking the C-O bond completely, leading to oxidized graphite with a carbon adatom defect. These processes are naturally even more endothermic and are only accessible at energies above 150 kcal/mol, and are therefore irrelevant to the CO + graphite chemistry. Since the reverse reaction barriers are very small (nonexistent for CO-P2, 17.0 kcal/mol for COP1), we therefore conclude that CO addition to graphite is reversible and that CO does not “stick” on a pristine surface at high temperatures, at least not in the absence of graphite defects, which is in agreement with experimental observations.10



Figure 3. Potential energy surfaces of the reaction of CO2 + S. Interaction energies ∆E at the ONIOM level of theory are given in kcal/mol. Numbers in parentheses include ZPEs obtained at the DFTB-D level (∆EZPE). Corresponding ONIOM(B3LYP/6-31+G(d):DFTB-D) structures are shown next to energy levels unless energy differences between consecutive stationary points are smaller than 1 kcal/mol, for which only one structure of the intermediates is shown. Only carbon atoms are shown which are significantly affected by the reaction.

(c) Dissociative Adsorption Reactions of CO2 on Graphite. Figure 3 depicts PESs and the geometries of intermediates and reaction products with corresponding TSs for the dissociative adsorption reactions of CO2 on graphite, starting from CO2RC1 and CO2-RC2. The very weakly bound T-shape complex CO2-RC3 did not lead to a dissociation reaction pathway. Potentially, the dissociative adsorption process can lead to CO (g) + O (a) and CO (a) + O (a), where (a) stands for adsorbed state and implies an oxidized graphite surface (the very reactive oxygen atom cannot leave the surface). Starting from CO2RC1 as more stable reactant complex species, CO2 can dissociate to CO (g) + O (a) with 95.7 kcal/mol ∆E endothermicity (denoted as CO+O-S in Figure 3), which we find is the lowest energy pathway for the irreversible dissociation of CO2 into gaseous CO and O (a) on graphite, leaving oxidized graphite as irreversible reaction product. The reaction occurs through CO2-TS1 with a 119.9 kcal/mol forward barrier. The symmetric O-C addition also starting from CO2-RC1 leading to CO2P2 has a reverse barrier of only abount 1 kcal/mol and is therefore irrelevant. As to the other reversible, high energy dissociative adsorption pathways, CO2-RC2 can rearrange to yield CO2-P3 with 80.1 kcal/mol endothermicity by way of CO2-TS3 with an 83.8 kcal/mol forward barrier, and then dissociate to CO2-P4 with a very large endothermicity of 201.4 kcal/mol and CO2-P5 with a still large endothermicity of 157.4 kcal/mol. As was the case for CO2-P2, due to large endothermicities and low reverse barriers, we do not expect the high energy branches CO2-P4 or CO2-P5 with subsequent isomerizations to yield CO2-P6 and CO2-P7 play any role in the high-temperature CO2 + graphite surface chemistry. We conclude therefore that graphite oxidation plus CO formation

via CO2-TS1 is the main chemical reaction process involved in the high-temperature erosion of graphite. (d) Dissociative Adsorption Reactions of NO on Graphite. The PESs for the dissociative adsorption pathways of NO on graphite plus intermediate, transition state, and reaction product molecular geometries are presented in Figure 4. In the dissociative adsorption of NO, the nitric oxide molecule can either insert into a C-C bond with its N-end, forming NO-P1 with 71.0 kcal/mol endothermicity by overcoming a 75.4 kcal/mol forward barrier, or can form a highly strained four-membered ring adduct NO-P2 as a product of a [2+2] cycloaddition reaction, with 79.0 kcal/mol endothermicity and 88.1 kcal/mol forward barrier. In both cases the reverse barriers are only fractions of the forward barriers. In particular, NO-P1 is energetically almost identical to its CO-P1 analogue structure, and in both cases the graphite defect is likely to heal by expulsion of the inserted XO fragment. On the other hand, from NO-P2, further restructuring can occur by two dissociative pathways. The first dissociative pathway involves the formation of two threemembered C-X-C defects in the 1,3-position of the central hexagon (NO-P3) by breaking the N-O bond completely. Due to ring strain, loss of N-O bond, and loss of π-conjugation, this product is 103.5 kcal/mol ∆E endothermic. Further more, both N- and O-adatoms in NO-P3 can completely insert into the C-C bonds to form NO-P4 with 85.1 kcal/mol ∆E endothermicity, the reduction of energy due to the release of ring strain. Since the reverse barrier for this N-O insertion from NO-P4 is 67.0 kcal/mol, such a defect might be possible to be reached under high temperature/high-pressure conditions. The second, even more interesting dissociative pathway starting from NO-P2 leads to an exothermic N-analogue of S with CO (g) as irreversible elimination products (CO + C95N) of a


Xu et al.

Figure 4. Potential energy surfaces of the reaction of NO + S. Interaction energies ∆E at the ONIOM level of theory are given in kcal/mol. Numbers in parentheses include ZPEs obtained at the DFTB-D level (∆EZPE). Corresponding ONIOM(B3LYP/6-31+G(d):DFTB-D) structures are shown next to energy levels. Only carbon atoms are shown which are significantly affected by the reaction.

complicated reaction pathway. Along this pathway, endothermicity is gradually reduced from NO-P5 with 99.2 kcal/mol via NO-P6 with 44.2 kcal/mol and NO-P7 with 54.9 kcal/ mol, before a CO unit irreversibly dissociates from the C95N, which is exothermic with a ∆E of -10.6 kcal/mol. Although thermodynamically stable, the irreversible N-subtitution of a carbon atom on the graphite surface introduces a reaction center that can be further attacked by oxidizing agents. As important intermediate, NO-P5 can also give rise to a novel NO-mediated Stone-Wales (SW) 6666 to 7755 condensed ring transformation via a 52 kcal/mol forward barrier to form the NO-S7755 with ∆E of only 88.4 kcal/mol. This energy is roughly the energy of an isolated SW defect48 and can be observed at high temperatures. Our QM/MD simulations have found this event, and we will discuss its dynamics further in section g). In conclusion, we find that (1) the dissociative adsorption of NO on graphite can oxidize the surface leading to an exothermic N-defect plus gaseous CO via NO-P3, or (2) can cause an NO-mediated SW defect with high reverse barrier via NO-P5. Both reaction pathways are expected to occur at high temperatures/high pressures but introduce defects that are open toward further erosion attacks of the graphite surface. (e) Dissociative Adsorption Reactions of NO2 on Graphite. The PESs for the dissociative adsorption pathways of NO2 on graphite with intermediate, transition state, and reaction product molecular structures are depicted in Figure 5. Just by visual inspection of this PES it is apparent that NO2 leads by far to the thermodynamically most stable defect species among the COx and NOx series. Starting from the physisorption complexes NO2-RC1 or NO2-RC2, NO2 can easily form a covalently bound nitrite adduct C-ONO, denoted as NO2-P1, with an endothermic 23.1 kcal/mol by overcoming a modest barrier NO2-TS1 with 34.5 kcal/mol from NO2-RC1, or alternatively

Figure 5. Potential energy surfaces of the reaction of NO2 + S. Interaction energies ∆E at the ONIOM level of theory are given in kcal/mol. Numbers in parentheses include ZPEs obtained at the DFTB-D level (∆EZPE). Corresponding ONIOM(B3LYP/6-31+G(d): DFTB-D) structures are shown next to energy levels. Only carbon atoms are shown which are significantly affected by the reaction.

by overcoming a slightly higher barrier NO2-TS2 with 44.7 kcal/mol barrier from NO2-RC2. The NO2-P1 complex is remarkably low in energy compared to all other covalently bound immediate reaction products of adsorbate additions, and we attribute this low energy to the delocalization of the radical

Dissociative Adsorption of COx and NOx on Graphite (0001) Surface electron, which is now located mainly on the π-network, with a nearly closed-shell OdN-O-Csp3 system at the defect site. The nitrite configuration was also predicted by Lee et al. as nearly thermoneutral species on the curved surface of carbon nanotubes.37 From NO2-P1, further restructuring can occur by breaking one of the N-O bond, leading to an oxidized graphite surface with NO adduct typically in the 1,3 position at NO2P2 and NO2-P3, however, with reaction energies around 100 kcal/mol. The local molecular structures of the NO-adducts are in fact similar to those of NO, but in this case are stabilized by the oxygen, causing a second defect, which induces favorable bond length alternations on the graphite surface. Remarkably, NO2-P1 can also irreversibly dissociate to NO + O-S with a ∆E of 62.3 kcal/mol via a barrierless association process. This effectively oxidizes the graphite surface, as has been observed by Mochida et al.,29 who, however, make a disproportionation reaction 2NO2 f NO3(a) + NO(g) responsible for their observation of NO evolution on activated carbon fibers. Based on the overall low-energy reaction profiles and the ease of graphite oxidation, we conclude that graphite oxidation plus NO formation plus possibly other reaction channels are feasible pathways for the high-temperature erosion of graphite (0001). (f) Rate Constants of the COx and NOx Dissociative Adsorption Reactions Predicted by RRKM Theory. The rate constants for these gas-surface reactions have been computed with the RRKM theory using the ChemRate code.47 The predicted rate constants of the CO dissociative adsorption reactions for the four processes


in the temperature range 1000-5000 K can be represented respectively by the expressions in units of cm3/s as

k5(CO2) ) 7.3 × 10-10 × exp(-87600/T) k6(CO2) ) 4.3 × 10-11 × exp(-106600/T) k7(CO2) ) 5.0 × 10-11 × exp(-69600/T) k8(CO2) ) 1.7 × 10-11 × exp(-139300/T) k9(CO2) ) 9.9 × 10-11 × exp(-110900/T) The predicted rate constants of the NO dissociative adsorption reactions for the three processes

NO + S f NO-P1

(10)

NO + S f NO-P2

(11)

NO + S f NO-P3

(12)

NO + S f CO + C95N

(13)


k10(NO) ) 1.22 × 10-12 exp(-43100/T)

CO + S f CO-P1

(1)

k11(NO) ) 3.74 × 10-13 exp(-49000/T)

CO + S f CO-P2

(2)

k12(NO) ) 4.13 × 10-13 exp(-67500/T)

CO + S f CO-P3

(3)

CO + S f CO-P4

k13(NO) ) 1.22 × 10-12 exp(-75000/T)

(4)


The predicted rate constants of the NO2 dissociative adsorption reactions for the three processes

NO2 + S f NO2-P1

(14)

k1(CO) ) 1.09 × 10-12 exp(-48600/T)

NO2 + S f NO2-P2

(15)

k2(CO) ) 6.00 × 10-13 exp(-64900/T)

NO2 + S f NO2-P3

(16)

k3(CO) ) 1.46 × 10-13 exp(-98700/T)

NO2 + S f NO + O-S

(17)

k4(CO) ) 9.12 × 10-14 exp(-102500/T)


where k1(CO) and k2(CO) are the rate constants for the addition reactions, and k3(CO) and k4(CO) are the rate constants for the dissociative adsorption reactions of CO on graphite. The rate constants of the CO2 dissociative adsorption reactions via RC1 to CO + O(a), P2, RC2 to P3 and then dissociate to give P4 and P5 on C96H24 graphite have been predicted. The predicted rate constants for the five processes

CO2 + S f CO + O-S

(5)

CO2 + S f CO2-P2

(6)

CO2 + S f CO2-P3

(7)

CO2 + S f CO2-P4

(8)

CO2 + S f CO2-P5

(9)

k14(NO2) ) 7.26 × 10-12 exp(-19600/T) k15(NO2) ) 8.63 × 10-14 exp(-54600/T) k16(NO2) ) 5.16 × 10-14 exp(-61000/T) k17(NO2) ) 1.61 × 10-13 exp(-37000/T) The rate constants (ki) for the dissociative adsorption reactions of COx and NOx on graphite are defined by49

d[X]surf/dt ) ki(θ/As)[X]g which has the unit of a flux, molecule/(cm2s). In the rate equation θ represents the fraction of available surface sites, As


Figure 6. The dynamics structures for the QM/MD simulations of dissociation products of CO on S at 5000 K using the DFTB-D method. Three trajectories are shown corresponding to different initial geometries.

is the surface area and [X]g is the gas-phase concentration of COx and NOx in molecules/cm3. (g) QM/MD Simulations of COx and NOx Dissociative Adsorption Products on Graphite. Preliminary QM/MD canonical ensemble simulations of the dissociative adsorption products of COx and NOx on the surface of the S C96H24 graphite model as described above were carried out using the selfconsistent charge DFTB-D quantum chemical potential at a temperature of 5000 K. Within about 40 fs, self-healing of the graphene sheet and loss of the adsorbate species was generally observed, although we note exceptions that are in remarkable agreement with the defect formation as described above. In the following, we describe a few details of these simulations. QM/MD simulations starting from the dissociative products of CO-P1, CO-P2, CO-P3, CO-P4 were carried out, and some snapshots of trajectories are shown in Figure 6. The COgraphite complexes CO-P1 and CO-P2 lost CO molecules within 40 fs. We also note that, in general, in all these simulations, the graphene sheet starts to bend considerably, since we only included a single graphene layer in these simulations. It can be expected that such bending is mitigated in bulk graphite. Moreover, we note that C-C bonds are only broken at the H-terminated graphene boundaries, where the first hexagon layer may detach and form polyacetylene-like chains with hydrogen atoms of S still attached on the carbon chains. On the other hand, the local area of the defect completely heals back to a regular all-hexagon honeycomb lattice. The dissociated C and O atoms of CO-P4 still remain on the surface because

Xu et al.

Figure 7. The dynamics structures for the QM/MD simulations of dissociation products of CO2 on S at 5000 K using the DFTB-D method. Three trajectories are shown corresponding to different initial geometries.

they possess strong bonds with para-C-C atoms on the center hexagon ring. However, CO-P4 can be produced only by COP2 or CO-P3 overcoming a very high energy barrier and, since the latter species easily dissociate, there is no time for the formation of CO-P4. Therefore, the dissociative adsorption reactions of CO have neglected contribution to erosion of graphite at high temperature. The QM/MD simulations for the three more stable products of CO2 on graphite are shown in Figure 7. The CO2-graphite complexes CO2-P2, CO2-P3, and CO2-P7 are found to dissociate easily to yield CO + O-graphite, and the CO molecules are irreversibly lost to the vacuum within 10 fs. This finding is consistent with our CO2 dissociative adsorption PES studies and previous experimental observations.50-56 QM/MD simulations for the dissociative products of NOP1, NO-P2, NO-P3, NO-P4, NO-P5, NO-P6, and NO-P7 were carried out. For NO-P1 and NO-P2 we observe the same rapid adsorbate desorption process as for CO-graphite. Similarly, the dissociated N and O atoms of NO-P4 still stay in the surface because they possess strong bonds with the para-C-C atoms, but as was the case for CO, this defect is very highly energetic. For NO-P6 and NO-P7, free CO molecules dissociate from the graphene sheet after 20 fs, where one carbon atom of S is replaced by one nitrogen atom to form C95N. For NO-P3 and NO-P5, we found that NO can irreversibly restructure the graphite honeycomb lattice. Figure 8 displays selected structures for such structural changes that were re-optimized at the DFTB-D level from snapshot geometries at simulation times indicated.



under the elimination of a thermodynamically more favorable CO species. In addition, we find that NO can induce StoneWales transformations with high reverse barriers, but this process is associated with high forward barriers. For the adsorption of NO2 on graphite, the NO + O(a) dissociation is found to be the primary dissociation path, but further structural rearrangements of some of the dissociative adsorption products might be feasible. Based on the TS structures, frequencies, and energetics, we also predict the rate constants of the dissociative adsorption reactions of COx and NOx on graphite using RRKM. Overall, we conclude that it is very difficult to attack the (0001) graphite surface even by radical species, but that we found pathways for erosion feasible at high temperatures, all involving oxidized or nitrogen-substituted species as irreversible products. At this stage it remains an open question how long durations of heat and pressure exposure would lead to amorphous carbon surfaces, and what erosion pathways would open on such highly defective surface species. Studies along this line are currently underway in our lab. Figure 8. DFTB-D optimized geometries of snapshot trajectory geometries for NO-S and NO2-S at times specified for each structure; ft denotes femtoseconds.

For NO2-graphite, QM/MD simulations for the three stable products NO2-P1, NO2-P2, and NO2-P3 were carried out. NO2-P1 and NO2-P3 quickly dissociate to NO(g) + O-graphite, and NO molecules are irreversibly lost to the vacuum within 10 fs. For NO2-P2, we show optimized snapshot structures at 5 and 10 fs in Figure 8. At first, a dissociated NO unit leaves the surface within 5 fs, after which CO(g) is lost to the vacuum within 10 fs, leaving a C95H24 graphene sheet with a nine-ring defect. We did not anticipate this event in our PES studies, but it is clearly another way of carbon erosion in the high-temperature chemistry of NO2-graphite. To summarize, the dissociative adsorption reactions of NO2 have oxidized the graphite surface by way of NO2-P1 and NO2-P3 and have irreversibly oxidized the graphite surface by way of NO2-P2 and loss of gaseous CO and NO at high temperature. Figure 8 displays selected structures for such structural changes that were re-optimized at the DFTB-D level from snapshot geometries at simulation times indicated. 4. Conclusions The physisorption and dissociative adsorption reactions of COx and NOx on a C96H24 graphene molecular fragment S as model for a graphite surface were calculated using the ONIOM(B3LYP:DFTB-D) integrated method. Quantum chemical molecular dynamics (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 ) 5000 K. The calculated adsorption parameters including the distances of the molecules to the surface, binding energies, and frequency shifts for weakly physisorbed COx and NOx molecules on the basal plane of graphite are comparable with available experimental data. The PESs for the dissociative adsorption reactions of COx and NOx on graphite are calculated, and transition states characterized. For the adsorption of CO on graphite, we cannot find a pathway leading to permanent defect creation, and CO is easily lost to the vacuum at high temperatures. For the adsorption of CO2 on graphite, the CO + O (a) dissociation (a indicating adsorbed state) is found to be the primary irreversible dissociation path. For the adsorption of NO on graphite, we find that it is possible to create an N defect on graphite with overall exothermicity

Acknowledgment. We thank Prof. Marcus Elstner, University of Braunschweig, Germany, for making the DFTB code available to us. 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. We thank the Cherry L. Emerson Center for Scientific Computation at Emory University for valuable computer time. Supporting Information Available: Table S1 lists names, ONIOM(B3LYP/6-31+G(d):DFTB-D) total energies and imaginary frequencies for all structures of the reaction pathways and Table S2 lists corresponding Cartesian coordinates. Figures S1 to S4 display all relevant structural parameters of these structures. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Xu, S.; Irle, S.; Musaev, D. G.; Lin, M. C. J. Phys. Chem. A 2005, 109, 9563. (2) Matsubara, T.; Maseras, F.; Koga, N.; Morokuma, K. J. Phys. Chem. 1996, 100, 2573. (3) Maseras, F.; Morokuma, K. J. Comput. Chem. 1995, 16, 1170. (4) Lias, S. G.; Bartmess, J. E.; Liebman, J. E.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data Suppl. 1988, 1, 17. (5) Park, J.; Dyakov, I. V.; Mebel, A. M.; Lin, M. C. J. Phys. Chem. A 1997, 101, 6043. (6) You, H.; Fain, S. C., Jr. Surf. Sci. 1985, 151, 361. (7) Jensen, E. T.; Palmer, R. E. J. Phys.: Condens. Matter 1989, 1, SB7. (8) Naba, A.; Shirakami, T.; Chihara, H. J. Chem. Thermodyn. 1991, 23, 461. (9) Hock, K. M.; Palmer, R. E. J. Chem. Phys. 1992, 97, 8736. (10) Boyd, D. A.; Hess, F. M.; Hess, G. B. Surf. Sci. 2002, 519, 125. (11) Laitenberger, P.; Palmer, R. E. Chem. Phys. Lett. 1995, 246, 79. (12) Laitenberger, P.; Palmer, R. E. J. Phys.: Condens. Matter 1996, 8, L71. (13) Cascarini de Torre, L. E.; Flores, E. S.; Llanos, J. L.; Bottani, E. J. Langmuir 1995, 11, 4742. (14) Park, S.-J.; Kim, K.-D. J. Colloid Interface Sci. 1999, 212, 186. (15) Yong, Z.; Mata, V. G.; Rodrigues, A. E. Adsorption 2001, 7, 41. (16) Bottani, E. J.; Bakaev, V.; Steele, W. Chem. Eng. Sci. 1994, 2931. (17) Montoya, A.; Mondragon, F.; Truong, T. N. Carbon 2003, 41, 29. (18) Yim, W.-L.; Byl, O.; Yates, J. J. T.; Johnson, J. K. J. Chem. Phys. 2004, 120, 5377. (19) Cinke, M.; Li, J.; Bauschlicher, W.; Ricca, J. A.; Meyyappan, M. Chem. Phys. Lett. 2003, 376, 761. (20) Smith, R. N.; Lesnini, D.; Mooi, J. J. Phys. Chem. 1956, 60, 1063. (21) Smith, R. N.; Swinehart, J.; Lesnini, D. J. Phys. Chem. 1959, 63, 544.

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Quantum Chemical Prediction of Reaction Pathways and Rate

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