Ab Initio Study of Interlayer Interaction of Graphite: Benzene

Mehdi Shakourian-Fard , Zahra Jamshidi , Ahmad Bayat , and Ganesh Kamath ..... Lee Sin Ang , Shukri Sulaiman , Mohamed Ismail Mohamed-Ibrahim...
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J. Phys. Chem. B 2001, 105, 9541-9547

9541

Ab Initio Study of Interlayer Interaction of Graphite: Benzene-Coronene and Coronene Dimer Two-layer Models Henna Ruuska and Tapani A. Pakkanen* Department of Chemistry, UniVersity of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland ReceiVed: April 19, 2001; In Final Form: June 26, 2001

A study was made of a series of one-layer and two-layer models of graphite surface and especially of interactions in the two-layer models. Seven one-layer models, of increasing size up to seven rings, in the C6n2H6n series were calculated for reference purposes with the Hartree-Fock method. Four two-layer models with different stacking sequences (AA, ABAB, and ABCABC) were studied with second-order MøllerPlesset perturbation method using basis set 6-31G*, and one model (ABAB) was also studied with 6-311G* and 6-311G** basis sets. Properties such as charge distribution and density of energy states were compared for the different models. Optimal interlayer distance for (C24H12)2 with MP2 method and 6-31G* basis was 3.41 Å and for the three C24H12-C6H6 models of different stacking sequence about 3.5 Å, which agrees fairly well with the experimental value of 3.35 Å. The BSSE corrected MP2 interaction energy for (C24H12)2 was -78.1 kJ/mol, whereas interaction energies for the three C24H12-C6H6 models were in the range of -21.8 to -22.8 kJ/mol. The bigger basis set 6-311G** gave almost twice as strong an interaction for ABAB, -38.8 kJ/mol, as did the 6-31G* basis set. Optimal interlayer distances for ABAB model were 3.29 Å with 6-311G* and 6-311G** basis sets.

Introduction The peculiar characteristics of graphiteslamellar structure, weak interlayer interaction, and conductivityshave found for it a variety of industrial uses in lubricants, refractory crucibles, heat shields and composite materials, electrical contacts, and electrodes. Graphite is able to conduct electrons within planes via π bonds, and electrical and thermal conductivity is good in that direction. Electrons do not easily pass between the layers, however, and in the direction perpendicular to the basal plane, graphite is an insulator.1,2 Because of its ubiquity and importance for industry, graphite has been widely studied both experimentally and theoretically. Quantum chemistry provides a method for describing the electronic properties of molecular systems, and reliable information of molecular structures, reactivities, reaction mechanisms, and different physical and chemical properties can be obtained from calculations.3 With the use of a cluster model approach, QM methods can also be applied to solid surfaces.4 In QM studies on graphite, a one-layer model is often regarded as a sufficient surface model, because of the weak interlayer interaction.5,6 Hydrogen termination is usually used to saturate the boundaries of cluster models of graphite,3-5 as it is for other covalent materials.7 It is easy and reasonable to create highly symmetrical surface models for graphite. A common approach to this is to take a six-membered ring and add rings around it to form D6h symmetrical models. The smallest of these models correspond to the organic polyaromatic compounds benzene, coronene (seven rings), and circumcoronene (19 rings).5,8 When a single carbon atom is desired in the center of the model, C3V symmetrical models are formed.3 In some studies, the influence of a second (and third) layer is examined,9,10 and in certain cases, the second plane is * To whom correspondence [email protected].

should

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addressed.

E-mail:

necessary, as in studies of friction11 or graphite intercalants.4,12,13 However, two-layer graphite models and interlayer interaction have not been extensively studied with sufficiently high levels of theory. Research is still needed on the influence of both the second layer in a graphite model as well as different stacking of the layers. This study comprises ab initio QM calculations on one- and two-layer models of graphite. Charge distributions and densities of energy states of the models were determined to obtain information about the influence of the size of the model and of the second layer. Interlayer interaction and equilibrium interlayer distance as well as the dependence of these on the stacking sequence and the size of the second layer were examined for the two-layer models. Computational Methods and Models A. Methods. The single-point energies of seven graphite C6n2H6n models were calculated with the Hartree-Fock (HF) method using basis sets 3-21G, 6-31G*, and 6-311G**. Because the number of the basis function increases rapidly with the size of the model and quality of the basis set, a compromise had to be found between them. Thus, the 6-31G* basis was used only for the five smallest models, and 6-311G** was used only for three models. Two-layer models require closer consideration of the electron correlation, and these models were calculated with the second-order Møller-Plesset (MP2) method. MP2 covers a part of the correlation energy, but it overestimates the pair correlation effect and gives too large binding energies. However, MP2 is computationally simplest way to apply correlation correction, and significantly better methods such as CCSD(T) are unattainable for our models.14 In an MP2 level study of the intermolecular interaction potentials of corannulene dimer, Tsuzuki et al.15 compared the results calculated with basis sets 6-31G*, 6-311G*, 6-311G**, and 6-311G(2d) and found

10.1021/jp011512i CCC: $20.00 © 2001 American Chemical Society Published on Web 09/01/2001

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Figure 1. (a) Hexagonal and (b) rhombohedral forms of graphite.1

the choice of the basis set to have a notable effect on the calculated energies.15 We choose basis sets 6-31G*, 6-311G*, and 6-311G** for study of the two-layer models. The basis set superposition error (BSSE) was corrected by the counterpoise method. All calculations were carried out using the Gaussian 9416 program package on Silicon Graphics Origin 200 R10000 and Compaq Alpha ES40 computers. Atomic charges were obtained from Mulliken population analysis. B. Models. Lamellae are ordered according to ABABAB stacking in the hexagonal form of graphite and according to ABCABCABC stacking in the rhombohedral form (Figure 1). The latter form is less stable and seldom is referred to in the literature. Because of the staggered form of the layers in the hexagonal form, there are two types of surface atoms: one type that has a carbon atom directly underneath it in the next layer (R type) and another type that does not (β type). There are weak van der Waals forces between the basal planes, and the interplanar distance is 3.35 Å. The interatomic distance between the carbon atoms, 1.42 Å, is close to that of benzene (1.39 Å).1,2,17 The graphite surface was modeled with use of cluster models of D6h symmetry. To eliminate the border artifacts, dangling bonds were terminated with hydrogen atoms. Some properties of the surface bulk structure may be lost when a molecular cluster model is constructed. As mentioned, graphite is a semiconductor along the crystal planes, but another important property is its aromaticity. A finite model can describe the aromatic character of graphite well: the three smallest of our D6h models (C6H6, C24H12 and C54H18) are stable organic, aromatic compounds: benzene, coronene, and circumcoronene.8 The conductivity of graphite is due to the slight overlap of the π and π* bands, whereas the σ bands are below the Fermi level. A finite cluster model always has a band gap between the HOMO and LUMO orbitals, however. In addition, the symmetries of the molecular orbitals of finite clusters do not necessarily correspond to the bands of infinite periodic lattice calculations, which are another approach to the modeling of bulk structures.4 Because the conductivity of graphite is not a property of interest in this study, the cluster model is assumed to be appropriate, although critical examination is applied. One-layer models were created on the basis of information about the C-C bond length (1.42 Å) in graphite found in the literature1,2,4,17 and calculating the coordinates. A value of 1.072 Å obtained from the optimization of benzene with Gaussian 94 HF/3-21G was used for the C-H distance. The geometries of the models were kept within the geometry of the bulk structure; that is, the models were not optimized. Figure 2 presents the one-layer models in series C6n2H6n with n ) 1, 2, 3, and 7 and, thus, C6H6, C24H12, C54H18, and C294H42. Assuming a value of 1.42 Å for the C-C bond length, the diameter of the largest model is about 40 Å, which could realistically be a slice of crystallite graphite. The diameter of crystallites in disordered

Figure 2. C6n2H6n graphite models, n)1, 2, 3, and 7, i.e., C6H6, C24H12, C54H18, and C294H42.

carbon materials prepared by heat treatment of polyphenylene ranges from 20 to 30 Å.1 The diameter of C96H24 is almost 20 Å and that of C216H36 is somewhat over 30 Å. The diameter of coronene is only about 10 Å. Although the properties of graphite, except the conductivity, can be modeled with a one-layer model, it was of interest to see if the inclusion of a second layer has an influence on the calculated properties. The smallest relevant two-layer model is a coronene ring with a benzene ring. The optimum interlayer distance was determined by the method employed. For the coronene-benzene model, this was done for three different stacking sequences: benzene on top of the coronene (eclipsed), staggered 1/2 step, and staggered 1/3 step. The 1/2-step staggered model corresponds to the hexagonal packed form of graphite (AB), and the 1/3-step staggered corresponds to the rhombohedral (ABC). Two coronene rings were calculated only in the most common packed form: the 1/2-step staggered. The influence of different stacking sequences and basis sets was tested with the coronene-benzene model. The 1/2-step staggered model was calculated with basis sets 6-31G*, 6-311G*, and 6-311G**, and the other two models were calculated only with basis set 6-31G*. Figure 3 shows the two-layer eclipsed, 1/2-step staggered, and 1/ -step staggered coronene-benzene models as tube and space 3 fill forms. In the 1/3-step staggered form, none of the carbon atoms of benzene are situated on top of one another, whereas in the 1/2-step staggered form, three atoms are situated on top of one another, and in the eclipsed form, all six carbon atoms lie on top of the bottom carbons. The benzene ring does not extend over the edge of the coronene in either of the staggered

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Figure 3. Three C24H12-C6H6 models viewed from top as tube forms and from top and side as space-fill forms (vdw-radii). (a) Eclipsed C24H12C6H6. (b) 1/3-step staggered C24H12-C6H6. (c) 1/2-step staggered C24H12-C6H6. The equilibrium interlayer distance obtained from MP2/6-31G* calculations (3.5 Å) was used in the figures.

models. Figure 4 shows the dicoronene model with interlayer distance of 3.4 Å viewed from the top and side. In this model, the second coronene is not totally superimposed on the first. Results A. Interaction Energies. MP2 interaction energies and optimized interlayer distances for the two-layer models are presented in Table 1. Both counterpoise corrected and noncorrected values are shown as well as the size of the BSSE. Figure 5 shows the BSSE corrected MP2 interaction energies for the three benzene-coronene systems as a function of the interlayer distance. The bigger basis set 6-311G** gives almost twice as strong an interaction for the 1/2-step staggered model than 6-31G* basis set. The influence of polarization functions for hydrogen is not significant (2.1 kJ/mol), but the difference in interaction energy between 6-31G* and 6-311G* is noteworthy (17 kJ/mol). The optimum BSSE corrected distance was closer

to the experimental value with the 6-311G* and 6-311G** basis sets than with 6-31G* basis. At HF level, the interaction is repulsive in all models. The curves obtained with MP2/6-31G* were closely similar. The bottom of the curve was at almost the same distance in the three models. The strongest interaction was found in the 1/3step staggered form, but with the method employed, the difference is negligible. As expected, when the two layers approach very close to each other, the eclipsed form is most unfavorable energetically, because of the repulsion of the C atoms lying on top of one another. A larger basis set allows the layers to press closer to one another. As representative of a larger two-layer model, two coronene rings were used in the 1/2-step staggered form. The bottom of the BSSE corrected MP2 interaction curve occurs at the interlayer distance (Figure 6 and Table 1), agrees well with the experimental value. The interaction is much stronger for two

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Figure 5. MP2/6-31G* interaction energy (E) curves as a function of interlayer distance (R) for the three coronene-benzene systemss eclipsed, 1/2-step staggered, and 1/3-step staggeredsand MP2/6-311G* and MP2/6-311G** interaction energies for the 1/2-step staggered form. Ecl ) eclipsed, 1/2-ss ) 1/2-step staggered, and 1/3-ss) 1/3-step staggered.

Figure 4. 1/2-step staggered two-layer (C24H12)2 model of graphite with interlayer distance 3.4 Å, viewed from top as tube form and side as space-fill form (vdw-radii).

TABLE 1: MP2 Interaction Energies E (kJ/mol) and Optimized Interlayer Distances R (Å) for Two-Layer Modelsa model

basis set

R (Å)

(C24H12)2 C24H12-C6H6, ecl C24H12-C6H6, 1/3-ss C24H12-C6H6, 1/2-ss C24H12-C6H6, 1/2-ss C24H12-C6H6, 1/2-ss

6-31G* 6-31G* 6-31G* 6-31G* 6-311G* 6-311G**

3.41 3.54 3.49 3.46 3.29 3.29

E (kJ/mol) E (kJ/mol) CP no CP BSSE -78.1 -22.0 -22.8 -21.8 -36.7 -38.8

-131.0 -39.2 -41.7 -41.4 -60.5 -62.7

52.8 17.2 18.9 19.6 23.7 23.9

The experimental interlayer distance is 3.35 Å.1,2,17 Ecl ) eclipsed, 1/ -ss ) 1/ -step staggered, 1/ -ss ) 1/ -step staggered, and CP ) 2 2 3 3 counterpoise correction for BSSE. a

coronene molecules than for coronene and benzene calculated with the same level of theory. This is because two coronene molecules have a larger contact area than do coronene and benzene. On the basis of the results for the benzene-coronene models, the interlayer distance would be expected to decrease and the interaction energy to increase with use of a bigger basis set. Thus, with a bigger basis set, the interlayer distance might agree even better with the experiment. Hankinson et al.4 calculated staggered coronene dimer (ABAB stacking) by the MP2/3-21G method in their study of lithium intercalated graphite, obtaining 3.16 Å for the optimized interlayer distance and 95.0 kJ/mol for the binding energy.4 The basis sets used in this study are of intermediate size but give reliable qualitative results. A more detailed comparison of the method and the basis set could be done performing calculations on the benzene dimer, whose small size allows the use of larger basis sets. Benzene dimers have been studied extensively by, e.g., Hobza18-22 and co-workers and Tsuzuki

Figure 6. MP2/6-31G* interaction energy (E) as a function of interlayer distance (R) for (C24C12)2.

and co-workers.23,24 Tsuzuki et al.23 have performed a comprehensive comparison of the split-valence basis sets for the parallel structure of the benzene dimer. This study is useful to verify the performance of the basis sets used in present work. The (BSSE corrected) MP2 total energies were E(6-31G*) ) 0.25 kJ/mol, E(6-311G*) ) -3.59 kJ/mol, E(6-311G**) ) -5.42 kJ/mol, E(6-311++G**) ) -8.09 kJ/mol, E(6-311G(2d,p)) ) -8.22 kJ/mol, E(6-311G(2d,2p)) ) -8.92 kJ/mol, and E(6311G(2df, 2p)) ) -12.8 kJ/mol.23 The BSSE correction is significant with our basis sets, but its proportion to the uncorrected energy is rather constant (around 40%), and it scales well with the size of the system. The influence of the BSSE correction on the interaction energy is very predictable. The size of the BSSE decreases slowly with larger basis sets: Feller and Jordan24 have studied the interaction between a water molecule and various graphite models, and even with basis sets as large as aug-cc-pVTZ and aug-cc-pVQZ, the BSSE is still about 30% from the uncorrected interaction energy. The BSSE corrected interlayer distance of the benzenecoronene model at the 6-311G* level (3.29 Å) was closer to the experimental value of 3.35 Å than the noncorrected one (3.0 Å). A similar result was obtained for the coronene dimer:

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Figure 8. Comparison of DOS graphs for the C24H12 model obtained with HF/6-31G* and HF/6-311G** methods. Figure 7. 6-31G* Mulliken charges (q) of successive circles (n) for graphite models. Charges are average values for the circles in question. In the first three cases, the charge of C6H6 (-0.24) is off the scale.

the noncorrected value of 3.25 Å was further from the experimental one than the corrected value (3.4 Å). The MP2 method is known to overestimate the attractive interaction compared to the more reliable CCSD(T) method. According to Hobza et al.,21 the MP2 correlation interaction energies for benzene dimer were 25-30% larger than the CCSD(T) correlation energies with valence double-ζ basis set.21 According to Tsuzuki et al.,24 the MP2 correlation interaction energies for the benzene dimer were 21-31% larger than CCSD(T) energies, depending on the basis set and dimer configuration. In the interaction energies of the present work, underestimation due to the small basis set and overestimation due to the MP2 method partially cancel. At the level of theory and basis sets used in the present work, the method can be expected to give at least a qualitative picture of the weak van der Waals interaction. The prediction of the interaction properties of the bulk graphite is the final goal for the model system studies. This is not straightforward because of the different shapes and the limited size of the models. The simplest way to consider the interaction on a per carbon atom basis is to regard the binding energy as the sum of interactions between every surface atom with the corresponding number of atoms at the lower layer. The interaction energy per carbon atom can be thus calculated by dividing the total interaction energy by the number of carbon atoms in the smaller layer of the model. This ratio at the MP2/ 6-31G* level for the (C24H12)2 model is 78.1/24 ) 3.25 kJ/mol and for 1/2-step staggered C24H12-C6H6 model 21.8/6 ) 3.63 kJ/mol, which are rather close to each other. This rough model suggests that the MP2/6-31G* interaction is about 3.4 kJ/mol for carbon atom pairs. B. Charge Distribution. The influence of the model size on charge distribution in the middle of the model was examined for estimating the adequate size for the cluster model of graphite. Mulliken population analysis was used to evaluate the atomic charges. The result of the Mulliken analysis heavily depends on the basis set employed, and only a qualitative indication is obtained of the charge distributions. The charge distributions for four one-layer models with the HF/6-31G* method are shown in the graphs of Figure 7 as average carbon charge of successive circles (n). The variation in charges within a circle is not insignificant, due to the difference in carbon sites, but because the variation is about the same for each circle, general trends of changes in charge with model size can be seen. Moreover, the central area of the model is of greatest interest, and there the charges are smoother.

The 3-21G charge of the central carbon is almost the same for all seven one-layer models except benzene (q ) -0.24, off the scale). From model C96H24 to model C294H42, the central carbon atom is nearly neutral (0.00). With the 6-31G* basis (Figure 7), the result is almost the same, except that the charge in model C54H18 is neutral. The 6-311G** result is different: C6H6 does not differ very much from C24H12, but the charge in C54H18 is positive (0.057). The charge of the central carbon of coronene in the eclipsed coronene-benzene two-layer system was -0.020 and that of benzene was -0.199. For a single coronene, the value with the same basis set (6-31G*) was -0.032 and for a single benzene -0.2012. For the two staggered forms, the values varied slightly (e0.012 unit) because of the irregular location of the atoms. The charges of the central carbons in the dicoronene model were -0.025 and -0.037. In practice, the difference between the charges of single coronene and dicoronene is insignificant. As a conclusion, the charges at the centers of the models approach zero, the atomic value of carbon, with very small models; even the charge of coronene is close to zero. The addition of a second layer has little effect on the charges. C. Densities of Energy States. Examination of the density of orbital energy states is a useful tool for evaluating the convergence of finite cluster models of increasing size to the infinite system. DOS graphs were determined for each of the models employed. Only the valence and low-lying virtual orbital energies were included because these are the orbitals that take part in reactions and bonding. Attention was first paid to the influence of the basis set on orbital energies in one-layer models. For comparison, the HF/6-31G* result is presented together with the HF/6-311G** graphs in Figure 8. Energy states of occupied orbitals calculated with the HF/321G and HF/6-31G* methods were almost identical with those in the HF/6-311G** curve. Virtual energy states from the 6-311G** calculation were somewhat different, but because of the computational cost, that basis set was used for only three models. The 6-31G* basis did not improve the density of virtual orbital energies much from the 3-21G result. The 3-21G band gaps between occupied and unoccupied orbitals are shown in Table 2, and a DOS graph for the C294H42 model is presented in Figure 9. All models are stable, i.e., have a clear band gap. As well, the shapes of the DOS graphs were more or less the same for all models. In particular, the curves of the three biggest models, C150H30, C216H36, and C294H42, were nearly identical; C54H18 and C96H24 did not differ much. The DOS graphs of the three biggest models were also very similar to the corresponding graphs of the tight-binding plus dispersion model of graphite presented by Palser.25 Palser’s model was developed to describe the stacking of graphite planes and to study interlayer interactions of graphite and multiwalled carbon nanotubes.

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TABLE 2: HOMO and LUMO Energies and Band Gaps for Seven One-Layer Models Calculated with the HF/3-21G Method model

HOMO/ au

LUMO/ au

∆E/ au

C6H6 C24H12 C54H18 C96H24 C150H30 C216H36 C294H42

-0.332 -0.256 -0.222 -0.202 -0.188 -0.177 -0.168

0.142 0.057 0.012 -0.016 -0.037 -0.053 -0.065

0.474 0.312 0.234 0.185 0.151 0.124 0.103

layer models, as well as for benzene and coronene, calculated with HF/6-31G* method. For all three C24H12-C6H6 models, the band gap was the same as that for the single coronene model. Thus, the stacking, or the entire second layer, does not significantly influence the band gap within these models. In the previously mentioned study of Palser,25 however, the density of states at the Fermi level was greater in AAA than in ABA graphite; moreover, splitting of the π band was observed in the ABA form but not in the AAA form. An interlayer distance of 3.35 Å was used for these models. As a summary of the DOS and band gap examination, it can be stated that the DOS of the one-layer models converges to the DOS of infinite graphite models and the three largest one-layer models give a good representation of the energy states of bulk graphite. Conclusions

Figure 9. DOS graph for the C294H42 model calculated with HF/321G method.

Figure 10. DOS graph for dicoronene (HF/6-31G* method).

TABLE 3: HOMO and LUMO Energies and Band Gaps for Benzene, Coronene, and Four Two-Layer Models Calculated with the HF/6-31G* Methoda model

HOMO/ au

LUMO/ au

∆E/ au

C6H6 C24H12 (C24H12)2 C24H12-C6H6, ecl C24H12-C6H6, 1/3-ss C24H12-C6H6, 1/2-ss

-0.324 -0.247 -0.228 -0.245 -0.245 -0.245

0.141 0.062 0.063 0.063 0.063 0.063

0.466 0.308 0.290 0.308 0.308 0.308

a Ecl ) eclipsed, 1/ -ss ) 1/ -step staggered, and 1/ -ss ) 1/ -step 2 2 3 3 staggered.

The bigger the model, the narrower the band gap becomes. In the three smallest models, the band gap was located at zero energy; in other words, all occupied orbitals were negative and virtual ones positive, as is usual in stable molecules and models. In the bigger models, a few of virtual orbitals were slightly negative. DOS graphs for the two-layer models were generated at equilibrium interlayer distances obtained from MP2/6-31G* calculations, which were 3.5 Å for C24H12-C6H6 models and 3.4 Å for the (C24H12)2 model. There were no perceptible differences between DOS graphs for the different stacking forms of C24H12-C6H6. The graphs were also very similar to those of dicoronene (Figure 10) and single coronene. Table 3 presents the HOMO and LUMO energies and band gaps for the two-

Properties of seven one-layer models of D6h symmetry and four two-layer models of graphite were calculated and compared. Optimal interlayer distances were determined for the two-layer models. On the basis of the charges and DOS graphs, it can be concluded that there is no need to go to one-layer models larger than C150H30. Even a model as small as C54H18 is a realistic one-layer model of a graphite surface. This means that the center of the model is not disturbed by the cut boundary of the cluster. The two smallest models, C6H6 and C24H12, are useful at least in preliminary studies. The optimized value of the interlayer distance for the (C24H12)2 and C24H12-C6H6 two-layer systems was in accordance with the experimental value (3.35 Å). The interlayer distance is so large that the second layer does not significantly influence either charges or the density of orbital energy states, at least within such small models. The difference in interactions between the different stacking sequences in two-layer models was small, which indicates that graphite layers can slide easily. This can also be seen from the space-fill models (Figure 3), which present the spatial extent of atoms: the interlayer distance is relatively large compared with the sizes of the atoms. Although a large enough one-layer model may be more informative than a model with a second layer, the influence of the second layer should nevertheless be examined. For twolayer models, the C54H18 system becomes very large (about the same number of C atoms as in C96H24), so it should be decided whether a fourth circle in the first layer is more informative than a second layer below. Because the difference in interaction energy, the atomic charges, and so on between C24H12-C6H6 and the other models was not significant, this model might be as realistic as the hexagonal packing model, and with its higher symmetry, it might be easier to handle. However, the border effects in a larger model may be greater than those for the benzene molecule. References and Notes (1) Patric, J. W. Porosity in Carbons; Edward Arnold: London, 1995. (2) Borg, R. J.; Dienes, G. J. The Physical Chemistry of Solids; Academic Press: San Diego, 1992. (3) Chen, N.; Yang, R. T. Carbon 1998, 36, 1061. (4) Hankinson, D. J.; Almlo¨f, J. J. Mol. Struct. (THEOCHEM) 1996, 388, 245. (5) Strout, D. L.; Scuseria, G. E. J. Chem. Phys. 1995, 102, 8448. (6) Arellano, J. S.; Molina, L. M.; Rubio, A.; Alonso, J. A. J. Chem. Phys. 2000, 112, 8114. (7) Sauer, J. Chem. ReV. 1989, 89, 199. (8) Disch, R. L.; Schulman, J. M.; Peck, R. C. J. Phys. Chem. 1992, 96, 3998. (9) Duffy, D. M.; Blackman, J. A. Surf. Sci. 1998, 415, L1016. (10) Wagner, F. R.; Lepetit, M.-B. J. Phys. Chem. 1996, 100, 11050.

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