19642
J. Phys. Chem. C 2008, 112, 19642–19648
First-Principles Molecular Dynamics Study of the Heterogeneous Reduction of NO2 on Soot Surfaces Antonio Rodrı´guez-Fortea*,† and Marcella Iannuzzi‡ Departament de Quı´mica Fı´sica i Inorga`nica, UniVersitat RoVira i Virgili, C/Marcel · lı´ Domingo s/n, 43007 Tarragona, Spain, and Laboratory for Reactor Physics and System BehaViour, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland ReceiVed: September 2, 2008; ReVised Manuscript ReceiVed: October 8, 2008
The heterogeneous reduction of nitrogen dioxide on the surface of atmospheric soot particles was thoroughly investigated using pristine and defective graphene layers as simple models of the soot surface. The metadynamics method, based on Car-Parrinello molecular dynamics simulations, was used to reproduce atomistic details of the reaction paths, as well as to obtain estimations of the free energy barriers of the processes. The relative energies, geometries, and electronic structures of reactants, products, and intermediates observed during the trajectories were analyzed, and the catalytic activity of the carbon vacancies concerning the reduction of nitrogen dioxide is discussed. Our study predicts the release of nitrogen monoxide and the formation of stable nitro groups on the surface of soot particles in good agreement with experiments. Introduction Carbonaceous aerosol (soot) particles produced during incomplete combustion processes are ubiquitous, both in polluted urban areas and at remote sites.1-3 The lower troposphere contains large amounts of soot, which is produced by the burning of fossil fuels and biomass at ground level. In the upper troposphere and the lower stratosphere, the only significant source of soot is known to be the exhausts of aircraft engines.4,5 Soot particles are expected to influence the radiative balance of Earth and its climate, as well as to change the composition of the gaseous atmosphere.5-10 Furthermore, they are thought to play an important role in cloud condensation processes9-11 and, in polluted populated areas, to affect human health.12 Concerning the purely chemical aspects, the catalytic properties of the surface of soot particles are of great interest. Their presence can facilitate reactions that are slow or impossible, such as the reduction of oxidized species that would not otherwise occur in Earth’s oxidizing atmosphere, for example, the reduction of NO2.7 Nitrogen oxides can be found nearly everywhere in atmospheric chemistry. The most important species are nitrogen monoxide (NO) and nitrogen dioxide (NO2), usually indicated collectively as NOx. These compounds are important for the formation and degradation of tropospheric ozone and the depletion of stratospheric ozone (ozone hole).6-8,13-15 Of these two nitrogen oxides, only NO2 reacts with soot in a significant way. Different gas-phase products have been observed from this reaction. In many investigations, NO has been observed as a product.10,16,17 In the presence of adsorbed water on the soot surface, HONO formation has also been reported.8,17,18 Much less is known about the change of the physical and chemical properties of the reacting soot surface. Surface-bound species were directly observed by infrared spectroscopy and functional groups such as carboxylic CdO, CsONO, and CsNO2 have * To whom correspondence should be addressed. E-mail: antonio.
[email protected]. † Universitat Rovira i Virgili. ‡ Paul Scherrer Institut.
been identified. These functionalities help to render hygroscopic the hydrophobic freshly emitted soot. This could result in an enhancement of water deposition and would explain the role of soot as a potential source of cloud condensation nuclei.10,11 Together with the presence of these polar functionalities, the size and geometry of soot particles can also influence the amount of water adsorbed on soot aerosols, leading to different possible mechanisms.19-22 Despite the large amount of experimental work done in this field, only a few theoretical studies addressing these problems have been performed.23-29 The main difficulty arises in modeling the soot surface. The most common choice is to model the oxidized surface by introducing oxygen-containing functionalities (such as carboxylic acids, ketones, ethers, and alcohols) in molecular polycyclic-aromatic-hydrocarbon- (PAH-) type systems, but periodic graphene layers (with or without defects) are also employed. The interactions between small inorganic oxidant species and the soot surface have been analyzed at different levels of approximation. In particular, using standard quantum chemical computations, Ghigo et al. found that NO2 shows exothermic adsorptions to vacancies in graphite regardless of the adsorption side of the molecule, the N atom or the O atom. Interestingly, they observed that adsorption on the O side is dissociative, yielding a carbonyl group on the surface and releasing a NO molecule.25 The chemisorption of NO2 on carbon nanotubes (CNTs) has also been analyzed in several theoretical studies.30-33 A single molecular adsorption on defect-free CNTs is endothermic. However, Mercuri et al. found, in a combined study using static techniques and Car-Parrinello molecular dynamics, that the vacancy-induced dissociative chemisorption of NO2 on CNTs is highly exothermic, similar to the behavior observed on graphene sheets.34 Our aim in this work was to shed light on the heterogeneous reduction of nitrogen dioxide on the soot surface. In particular, we were interested in providing a detailed dynamic picture for the heterogeneous processes that arise from the interaction between NO2 and the soot surface in dry conditions. Previously, we studied the heterogeneous decomposition reactions of HNO3 on graphite surfaces.35,36 The local, interactive portion of the
10.1021/jp807787s CCC: $40.75 2008 American Chemical Society Published on Web 11/14/2008
Heterogeneous NO2 Reduction on Soot soot surface was modeled by a defective graphene layer with carbon vacancies. These defects modify the electronic properties of these carbon-based systems dramatically and provide them with catalytic activity due to the presence of carbon atoms with dangling bonds in their structures.37-41 In the present work, we used the same model for the soot surface. Here, the catalytic role of the defective carbon layer in the reduction process of NO2 was assessed through comparison with the same process occurring in a pristine graphene layer. The metadynamics method was employed to explore the complex topology of the free energy surface (FES) and to estimate the free energy barriers of the observed processes.42-44 This methodology allows an efficient exploration of the dynamical processes, identifying different possible reaction paths. This article is organized as follows: In Computational Methodology, some technical details about the computational approach are provided. In Results and Discussion, we first describe a study of the decomposition of nitrogen dioxide on a defect-free graphene layer and then analyze the same reduction process on a graphene layer with a carbon vacancy. The most relevant structural properties of the intermediate states and the activation energies involved in the processes are also discussed. Computational Methodology The results presented in this work were obtained by density functional theory (DFT) using the CPMD program package.45 The description of the electronic structure was based on the expansion of the valence electronic wave functions into a planewave (PW) basis set that was limited by an energy cutoff of 70 Ry. The interaction between the valence electrons and the ionic cores was treated through the pseudopotential (PP) approximation. Norm-conserving Martins-Troullier PPs were employed.46 We adopted the generalized gradient-corrected Becke-LeeYang-Parr (BLYP) exchange-correlation functional47,48 in the spin-unrestricted formalism that is necessary for dealing with unpaired electrons. The nonlinear core correction (NLCC)49 and a very high-energy cutoff were employed to obtain accurate energy differences between stationary points on the potential energy surface (PES). The reliability of such a setup was tested in our previous works, and it was found that the BLYP functional somewhat underestimates the reaction barriers in this type of radical system.35,36 Some improvements might be expected from taking into consideration the self-interaction term introduced by DFT, but no correction of this kind was applied in this work. Such corrections would change the quantitative values for the barriers and the relative energies of products and intermediates to some extent, but the qualitative aspects of the mechanism would remain unaffected. In the molecular dynamics (MD) simulations, the wave functions were propagated according to the Car-Parrinello scheme, by integrating the equations of motion derived from the extended Car-Parrinello Lagrangian.50 We used a time step of 0.144 fs and a fictitious electronic mass of 900 au. A simple rescaling of the atomic velocity was used to keep the temperature within an interval of 50 K around 300 K. A unit cell containing a pristine graphite layer of 32 C atoms and one NO2 molecule with sides of lengths a ) 9.89 Å, b ) 8.57 Å, and c ) 12.0 Å was repeated periodically in space by the standard periodic boundary conditions (PBCs). For the defective layer, the unit cell, with sides of lengths a ) 12.37 Å, b ) 12.85 Å, and c ) 12.0 Å, contained 59 C atoms and one NO2 molecule. Stationary-state optimizations are performed with the pseudo-Newton-Raphson method, based on progressive updating of the initial Hessian by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm.51 The
J. Phys. Chem. C, Vol. 112, No. 49, 2008 19643
Figure 1. Collective variables along the trajectory of the metadynamics run performed for NO2 and the pristine graphene layer. The inset corresponds to the part of the curve in which COC increases and CNO decreases simulatenously (see text).
limited simulation time affordable by standard MD runs does not allow the observation of rare events such as thermally activated chemical reactions. For this reason, we employed the metadynamics technique, which is capable of efficiently reconstructing complex reaction mechanisms and providing the free energy profile, as demonstrated in previous applications.35,36,52-60 A detailed description of the metadynamics method associated with Car-Parrinello MD can be found elsewhere.42 Metadynamics simulations are based on the selection of collective variables (CVs) that are suitable to describe the process of interest. In this work, we used as CVs the coordination numbers (CNs) of certain atoms (or group of atoms), A, with respect to another atom (or group of atoms), B.42,61 The CN provides information on the interaction pattern characterizing the actual atomic configuration. The analytic definition of the CN of B with respect to A can be found elsewhere.35,36 The reconstruction of the free energy surface (FES) as a function of the CV was done by summing the repulsive Gaussian-shaped time-dependent potential added during the simulation.42-44 Other methods, such as umbrella sampling, are known to provide more accurate results but at higher computational costs.56,57,62 Results and Discussion 1. NO2 Reduction on Pristine Graphene Layers. To analyze the reduction process of nitrogen dioxide on a pristine graphene layer, we performed a 40-ps metadynamics run using the following three CVs:63 the CN of the N atom with respect to the two O atoms, CNO; the CN of the N atom with respect to the C atoms, CNC; and the average CN of the O atom with respect to the C atoms, COC. As PBCs are always used in all three dimensions, a stiff constraining potential was added to keep the molecule within 4 Å of the graphene layer. In this manner, not only were interactions with the periodic images avoided, but also the sampling of the metadynamics was restricted to configurations characterized by non-negligible interactions with graphene. Beyond this distance, the energy profile was flat. Furthermore, by keeping the molecule always in the vicinity of the surface, the effects of a finite partial pressure were mimicked. The evolution of the CVs during the 40 ps of metadynamics is depicted in Figure 1. During the first 38 ps, the NO2 molecule fluctuates back and forth over the graphene layer. The increasing amplitude of the oscillations is induced by the metadynamics time-dependent potential (Figure
19644 J. Phys. Chem. C, Vol. 112, No. 49, 2008
Rodrı´guez-Fortea and Iannuzzi TABLE 1: Relative Potential Energies, ERel, for Minima A-Ca
a
Figure 2. Reconstructed free energy surface for the system NO2 + pristine graphene as a function of CNO and COC. The energy units of the color scale are kcal mol-1.
1), and it indicates that the system explores wider regions of configuration space. When the molecule is sufficiently close to the surface, two different modes of NO2 adsorption onto the layer are observed: by the O atom (O side) and by the N atom (N side). The geometries and energies of these intermediate structures are discussed later in this article. It is interesting to point out that, when the N atom approaches the graphene surface, CNO remains unaffected; i.e., the NsO distances do not change significantly. However, when the O side of the molecule gets closer, CNO is considerably reduced; i.e., there is an increase in one (or even both) NsO distances (see inset of Figure 1). This result is in good agreement with the work of Ghigo et al., who reported an increase in the NsO distance when the O atom is chemisorbed to the carbon surface.25 After 38 ps, dissociative chemisorption of the NO2 molecule was observed, yielding an oxidated graphene layer and a NO molecule that is released, process 1.
NO2 + graphene f NO + graphenesO
(1)
As observed in a previous work, the O atom incorporated in the graphene layer adopts an epoxide configuration.36 Therefore, a reduction of NO2 to NO and oxidation of the surface occur, as seen in experiments.10,16,17 The reconstructed FES as a function of CNO and COC is represented in Figure 2. The reactants’ well is placed at the bottom right corner (CNO ≈ 1.7 and COC ≈ 0.6), and the products’ well is at the top left corner (CNO ≈ 0.8 and COC ≈ 1.5). The free energy barrier for process 1, estimated from the reconstructed FES, is 55 ( 3 kcal mol-1. This large barrier indicates that the reduction of NO2 accompanied by epoxidation of the pristine graphene layer is a very unlikely event, as already observed for gas-phase nitric acid.36 However, the significant decrease of the activation energy with respect to that needed for the dissociation of NO2 in the gas phase [around 87 kcal mol-1 at the generalized gradient approximation (GGA) level]64 confirms the expected catalytic role of the graphene layer. It is worth noting here that the depth of the products’ well in Figure 2 does not represent the relative stability of the two minima, as the metadynamics run was interrupted before any recrossing to the initial state could take place, i.e., before the complete filling of the products’ well. In the following discussion, the most interesting intermediates observed during the metadynamics trajectory are described. The potential energy differences were calculated on the optimized structures of minimum A (NO2 + graphite), B (NO + graphitesO, structure 1), and C (NO + graphitesO, structure 2), as obtained at 0 K by geometry optimization. Several other
minimum
Erel (kcal mol-1)
A B C
0.0 37.1 53.9
Energy values refer to the optimized geometries.
intermediate configurations, corresponding to chemisorption of a NO2 molecule (from both sides, the O and the N atoms), have been observed. None of them could be optimized as minimumenergy configurations, by either geometry optimization or thermal annealing at progressively decreasing temperature. The relative energies of the optimized intermediates are collected in Table 1. The minimum energy was obtained when the NO2 molecule was located at a distance greater than 3 Å from the surface, irrespective of the orientation of the molecule. At our computational level, the interaction between the pristine layer and nitrogen dioxide molecule is somewhat repulsive, as observed previously for the case of the nitric acid molecule.36 Minima B and C were found to be much more unstable than reactants (Table 1); i.e., process 1 was found to be significantly endothermic. The relative energy of the system with the epoxidated graphene (B) with respect to the minimum A was of the same order of magnitude as that found in the case of the epoxidation of graphite by means of nitric acid (29.8 kcal mol-1).36 The epoxide CsO and CsC bond distances were 1.51 and 1.50 Å, respectively. Interestingly, another structure for the oxidated surface was observed (C) that was 16.8 kcal mol-1 less stable above B. This structure showed an ether group that was not a 1,2-epoxide because the CsC bond was broken, with a C · · · C distance equal to 2.09 Å (see Figure 3). The C atoms bound to the O atom featured planar sp2 hybridization with much smaller CsO distances than in minimum B (1.39 vs 1.51 Å). In all three minima, the spin density remained on the molecules NO2 or NO, with the pristine or oxidated graphene layer showing a closed-shell electronic structure. 2. NO2 Reduction on Defective Graphene Layers. The high energy barrier associated with the oxidation of pristine graphene at ambient temperature cannot explain the generation of nitrogen monoxide observed in experiments. Defects and functionalities are expected to significantly affect the catalytic properties of the surface. The next step in our investigation was the study of the reduction of NO2 over a defective graphene layer that contained a vacancy. To this end, an 11-ps metadynamics run was performed using the same CVs as in the previous case: CNO, CNC, and COC.65 The only slight difference was that, for CNC and COC, the coordination numbers were defined with respect to only the 12 C atoms around the vacancy, rather than all of the C atoms. Also in this case, a virtual wall was applied that kept the molecule within 3.5 Å of the surface. The electronic structure of defective graphene layers has been studied previously by several authors.66,67 GGA DFT functionals predict a spin-polarized ground state. One unpaired electron of σ character is localized on one of the three unsaturated C atoms of the vacancy (sp2 dangling bond), and the unpaired electron of π character is delocalized over the graphene layer.25,35 The evolution of the CVs during the 11.4 ps of metadynamics is depicted in Figure 4. In the starting structure, the NO2 molecule is placed about 3.5 Å from the graphene (NO2 + graphene*, where the asterisk denotes that the graphene layer has a C monovacancy). The chemisorption of the NO2 molecule on an unsaturated C atom
Heterogeneous NO2 Reduction on Soot
J. Phys. Chem. C, Vol. 112, No. 49, 2008 19645
NO2 + graphene* f graphene*sNO2
(2)
In the subsequent picoseconds, the chemisorbed NO2 molecule kept rotating around the just-formed CsN bond, which, in turn, fluctuated with increasing amplitude. At around 10.5 ps, one of the fluctuations of the adsorbed NO2 group led to the formation of a NOC5 seven-membered ring, where one of the O atoms was bound to one of the remaining unsaturated C atoms. This intermediate species evolved almost instantaneously into a carbonyl group (CdO) and a NO molecule attached to the graphene. Finally, the NO molecule was released, leaving the defective layer oxidated (process 3).
graphene*sNO2 f NO + graphene*sO
Figure 3. Optimized geometries of the minima A (NO2 + graphite), B (NO + graphitesO, structure 1), and C (NO + graphitesO, structure 2).
Figure 4. Collective variables along the trajectory of the metadynamics run performed for NO2 and the defective graphene layer.
of the vacancy was observed already after 0.25 ps (process 2). The chemisorption takes place on the N side, i.e., the nitro coordination mode. This process is associated with a significant change in CNC and a moderate change in COC because the O atoms also get closer to the graphene. CNO, in contrast, does not undergo any marked changes, indicating that the NsO distances do not change significantly when NO2 chemisorbs to graphene on the N side.
(3)
The adsorption from the O side, instead, immediately induced the dissociation of the molecule, as already observed.25 The minimum-energy path generated by the metadynamics is in good agreement with previous experimental results that show (i) NO2 groups attached to the soot layer, (ii) formation of NO, and (iii) oxidation of the soot. As for the process on the pristine layer, we computed the FES by summing the repulsive Gaussians that were added during the metadynamics run. The FES as a function of CNO and CNC is represented in Figure 5. The reactant’s well is placed at the bottom right corner (CNO ≈ 1.7 and CNC ≈ 0.3), the well for NO2 chemisorbed to graphene is at the top right corner (CNO ≈ 1.7 and CNC ≈ 1.2), and the well for the oxidized graphene and the released NO molecule is at the bottom left corner (CNO ≈ 0.9 and CNC ≈ 0). Also in this case, the depth of the products’ well in Figure 5 does not represent the relative stability of the three states, as we stopped the metadynamics before any recrossing. Adsorption of NO2 to an unsaturated C atom of the vacancy required a small free energy barrier of only 5 ( 2 kcal mol-1. This result is in agreement with the fact that reactions between radical species involve small activation energies, mainly determined by entropic effects. The state in which the vacancy had chemisorbed the NO2 molecule from the N side was very stable, and 22 ( 2 kcal mol-1 was required to oxidize the vacancy and to release NO. The high stability of the graphite*sNO2 system agrees with experimental IR spectra that show the presence of NO2 groups on the surface of soot particles. The reduction of NO2 to NO and oxidation of the vacancy occur only when an O atom attaches to one of the remaining unsaturated C atoms, in a sort of dissociative adsorption process, as pointed out previously by other authors.25,34 Therefore, when a NO2 molecule is directly attached to a C atom of the vacancy by means of the O atom, the reduction of nitrogen dioxide happens immediately with the corresponding oxidation of the surface, as confirmed by another metadynamics run that we carried out with one single COC CV.68 The estimated free energy barrier for this process was 10.5 ( 0.3 kcal mol-1, a low barrier that confirms the catalytic activity of the vacancy (to be compared with the 55 ( 3 kcal mol-1 for the same process on the pristine surface). Therefore, two different pathways with low free energy barriers are available, depending on the side (N or O atom) from which NO2 approaches the surface. These two pathways lead to the same products. Finally, the most interesting intermediates observed during the metadynamics trajectory for NO2 and the defective layer are described next. The relative potential energies, as obtained from geometry optimization, of the different intermediates with respect to reactants (NO2 + graphene*) are collected in Table 2, and their structures are represented in Figure 6. Minimum D, graphene*sNO2, was calculated to be 33.8 kcal mol-1 more stable than reactants, indicating that chemisorption
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Rodrı´guez-Fortea and Iannuzzi
Figure 5. Reconstructed free energy surface for the system NO2 + defective graphene as a function of CNO and CNC. The energy units of the color scale are kcal mol-1.
TABLE 2: Relative Potential Energies, Erel, for Minima D-F with Respect to NO2 + Graphite*a
a
minimum
Erel (kcal mol-1)
D E F
-33.8 -46.6 -51.4
Energy values refer to the optimized geometries.
of NO2 from the N side is reasonably exothermic. This value compares well with that found by Ghigo et al. using a hybrid functional (B3LYP) and Gaussian orbitals as basis functions.25 The NsC distance was 1.48 Å, and the NsO distances were 1.26 Å, only slightly larger than those in the free NO2 molecule (1.22 Å, at our computational level). As far as the electronic structure is concerned, the spin density in the doublet state was mainly delocalized on the graphene layer. The unpaired electron of σ character localized at the unsaturated C atom combined with the unpaired electron of the NO2 molecule, giving rise to the CsN σ bond. The spin density of π character remained delocalized over the defective graphene layer, with a significant contribution on the saturated sp2 C atom where the NO2 was attached, as previously observed for defected carbon nanotubes with monovacancies.34 Moreover, there was also a residual spin density on the O atoms (see Supporting Information, Figure S1). Minimum E, in which a CdO bond was formed and the NO molecule was attached to another unsaturated C atom of the vacancy, was 46.6 kcal mol-1 more stable than reactants. The CsO distance of the carbonyl group was 1.25 Å, very similar to those found previously in analogous systems and to the bond length in simple ketones.69 The CsN and NsO distances were 1.44 and 1.22 Å, respectively. The electronic structure, however, showed not delocalization of the spin density over the layer, but rather localized σ spin density on the remaining unsaturated C atom. The unpaired π electron delocalized on the graphene layer in minimum D was instead forming the double CdO bond, giving rise to closed-shell π and open-shell σ electronic structures, with a dangling bond on the remaining unsaturated C atom. Some spin density was also present on the chemisorbed NO molecule (see Supporting Information, Figure S2). Minimum F, in which the graphene layer had a carbonyl group and the NO molecule had been released, was found to be the most stable configuration, being 51.4 kcal mol-1 lower in energy than the reactants. The CsO distance of the carbonyl group was 1.24 Å, and the NsO distance within the NO molecule was 1.17 Å. The NO molecule was located more than 4 Å above the surface. Interestingly, the electronic structure of this system was different from that in minima D and E because no spin polarization on
Figure 6. Optimized geometries of the minima D (graphite*sNO2), E (ONsgraphite*sO) and F (NO + graphite*-O).
the oxidized layer was found, as reported previously.35 The spin density was instead located on the NO molecule. We also analyzed the evolution of the oxidized layer. The lowest energy state was obtained when the O atom replaced the vacant C; i.e., the original structure of the graphene layer was recovered, and the vacancy was totally functionalized.35 The state with the carbonyl group and two unsaturated C atoms lay, instead, 29.9 kcal mol-1 higher. Conclusions The heterogeneous reduction of nitrogen dioxide over a graphene layer was investigated as a model for interactions with the surface of soot particles. The minimum-energy path followed by the metadynamics showed dissociative adsorption of the NO2 molecule when chemisorption took place on the O side, on both the clean and defective surfaces. The free energy barrier for the oxidation of the layer and formation of nitrogen monoxide
Heterogeneous NO2 Reduction on Soot was, however, considerably smaller in the presence of C monovacancies. The chemisorption of radical species, such as NO2, on the C atoms of the vacancies is a likely process as indicated by the small barriers of adsorption. Therefore, the presence of these defects could explain the observed formation of nitrogen monoxide with the concurrent oxidation of the surface of soot particles. Furthermore, our results support the high stability of chemisorbed NO2 groups attached to the surface from the N side, which have been detected by means of IR spectroscopy when samples of soot are in contact with NO2. The attachment of highly stable polar groups such as NO2 and CdO to the surface of fresh soot particles confers hydrophilicity on the particles to act as a source of cloud condensation nuclei, for example. Our dynamical study provides an alternative pathway for the oxidation of the surface once the NO2 molecule has been adsorbed through the N side (rotation-oxidationdissociation mechanism). The most stable state for the oxidized layer is that in which the original structure of the layer is recovered with an O atom in the place of a C atom, i.e., when the vacancy is completely functionalized. Summarizing, the presence of C monovacancies is confirmed to have an important catalytic effect on the reduction of NO2 and the concurrent oxidation of the graphene layer. Acknowledgment. A.R.F. thanks the Ministerio de Educacio´n, Cultura y Deporte (Spanish Government), for a Ramo´n y Cajal contract. Supporting Information Available: Optimized geometries for the stationary points (xyz files) and figures for the spin densities of minima D and E. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Cooke, W. F.; Jennings, S. G.; Spain, T. G. J. Geophys. Res. 1997, 102, 25339. (2) Posfai, M.; Anderson, J. R.; Buseck, P. R.; Sievering, H. J. Geophys. Res. 1999, 104, 21685. (3) Sheridan, P. J.; Schnell, R. C.; Kahl, J. D.; Boatman, J. F.; Garvey, D. M. Atmos. EnViron., Part A 1993, 27, 1169. (4) Blake, D. F.; Kato, K. J. Geophys. Res. 1995, 100, 7195. (5) Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics; John Wiley & Sons: New York, 1998. (6) Finlayson-Pitts, B. J., Jr. Chemistry of the Upper and Lower Atmosphere; Academic Press: San Diego, CA, 2000. (7) Lary, D. J.; Lee, A. M.; Toumi, R.; Newchurch, M. J.; Pirre, M. J.; Renard, J. B. J. Geophys. Res. 1997, 102, 3671. (8) Longfellow, C. A.; Ravishankara, A. R.; Hanson, D. R. J. Geophys. Res. 1999, 104, 13833. (9) Ravishankara, A. R. Science 1997, 276, 1058. (10) Rogaski, C. A.; Golden, D. M.; Williams, D. L. Geophys. Res. Lett. 1997, 24, 381. (11) Lammel, G.; Novakov, T. Atmos. EnViron. 1995, 29, 813. (12) Kaiser, J. Science 2000, 288, 424. (13) Chatfield, R. B. Geophys. Res. Lett. 1994, 21, 2705. (14) Crutzen, P. J.; Arnold, F. Nature 1986, 324, 651. (15) Gerecke, A.; Thielmann, A.; Gutzwiller, L.; Rossi, M. Geophys. Res. Lett. 1998, 25, 2453. (16) Kleffmann, J.; Becker, K.; Lackhoff, M.; Wiesen, P. Phys. Chem. Chem. Phys. 1999, 1, 5443. (17) Tabor, K.; Gutzwiller, L.; Rossi, M. J. J. Phys. Chem. 1994, 98, 6172. (18) Ammann, M.; Kalberer, M.; Jost, D. T.; Tobler, L.; Rossler, E.; Piguet, D.; Gaggeler, H. W.; Baltensperger, U. Nature 1998, 395, 157. (19) Gorbunov, B.; Baklanov, A.; Kakutkina, N.; Windsor, H. L.; Toumi, R. J. Aerosol Sci. 2001, 32, 199. (20) Moulin, F.; Picaud, S.; Hoang, P. N. M.; Partay, L.; Jedlovszky, P. Mol. Simul. 2006, 32, 487. (21) Alcala-Jornod, C.; Rossi, M. J. J. Phys. Chem. A 2004, 108, 10667. (22) Alcala-Jornod, C.; van den Bergh, H.; Rossi, M. J. Geophys. Res. Lett. 2002, 29. (23) Barco, G.; Maranzana, A.; Ghigo, G.; Causa, M.; Tonachini, G. J. Chem. Phys. 2006, 125.
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19648 J. Phys. Chem. C, Vol. 112, No. 49, 2008 perpendicular width (∆s⊥) is 0.05, and the deposition rate (∆t) is 0.007 ps. The estimated error () in the computation of the free energy is 2 kcal · mol-1. (66) El-Barbary, A. A.; Telling, R. H.; Ewels, C. P.; Heggie, M. I.; Briddon, P. R. Phys. ReV. B 2003, 68. (67) Ma, Y. C.; Lehtinen, P. O.; Foster, A. S.; Nieminen, R. M. New J. Phys 2004, 6.
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