Surface Science Letters 255 (1991) L509-L515 L509 North-Holland

Surface Science Letters

A model calculation on the chemisorption of aluminum on graphite

Sarita Srivastava and Jan Alml~f Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA

Received 8 April 1991; accepted for publication 29 May 1991

Atomic chemisorption on the basal plane of graphite has been modelled with a finite-size cluster of carbon atoms. The interaction with an A1 atom has been studied extensively using different computational methods, involving large basis sets and electron correlation. The non-planarity of a clean graphite surface is found to be a very important factor determining the most stable chemisorption site, as well as the chemisorption bond energy. The large reconstruction of the graphite surface in the presence of an AI atom is a striking result of this study.

1. Introduction

The exposed basal plane of graphite is im- portant as an adlayer substrate for thin film growth because of its good uniformity [1] and relative chemical inertness. With the development of scan- ning tunnelling microscopy (STM) techniques in recent years [2], the early stages of thin film growth have been studied extensively, yet very fundamen- tal questions about nucleation sites and surface reactions remain unanswered. Therefore a better knowledge of the graphite surface and its interac- tion with adsorbed atoms is required both for the interpretation of the experimental results and for the development of a microscopic theory of chem- isorption.

The present Letter is a step in that direction from a theoretical and computational point of view using non-empirical methods. We have studied the chemisorption of a single aluminum atom on the surface of graphite. Aluminum was chosen because of its technological importance and because the calculations would be simpler than for transition metals due to the lack of d- electrons. Very recently, a theoretical study of A1 on graphite-like clusters was published [3], focus- ing on the necessary requirements for the cluster to bind the A1 atom. That calculation sheds light on some crucial questions with regard to the re-

quired size of a cluster to be useful as a model for graphite in chemisorption processes. However, the calculation was carried out at the SCF level of approximation, using "un-prepared" electronic states, and a planar carbon cluster was used to model the surface of graphite. As we argue below, surface reconstruction might be crucial for even a qualitative understanding of the chemisorption, and one major purpose of the present work is to investigate the importance of permanent and in- duced non-planarity on the binding energies.

Cluster models [4,5] have long been used with fair success to simulate chemisorption processes on metal surfaces and it is natural to try the same approach here. In the cluster approach, a finite number of atoms "cluster" is considered as a model of the surface. This cluster is treated as a molecule, and the reaction between the cluster and the adsorbate is studied with conventional molecu- lar electronic structure methods. As the size of the cluster increases, the procedure should converge to the results for an infinite system, i.e. to bulk values.

It should be emphasized that the purpose of these studies is not to explore the properties of the clusters but rather to understand the properties of cluster models and their relation with the bulk properties of the surface. For instance, a geometry relaxation of the cluster is usually not attempted,

0039-6028/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)

I 51 () S. Shri~,astat,a, .1. A lmli~/ / Model cah'ulation on the chemisorption o] A l on graphite

but, in analogy with the idea that a bulk system is modelled, the geometry parameters are fixed to bulk values.

Strictly speaking, this approach does not ad- dress the issue of surface reconstruction, i.e. the fact that a clean surface of any bulk system has geometry parameters which differ from those in- side the bulk. When the cluster model is applied to metal surfaces, this effect is usually assumed to be insignificant [5]. In contrast, the reconstruction of a clean graphite surface is probably one of the most crucial issues in determining the strength of the chemisorption. The graphite surface consists of two kinds of carbon atoms, differing in whether or not they have a carbon atom immediately be- low them in the adjacent layer. There is thus no reason for the surface to be perfectly planar on symmetry grounds, and a number of STM investi- gations have indeed confirmed the non-equiv- alency of the two types of carbon atoms [6], even though the actual degree of corrugation for a pure graphite surface is still unknown. There are rea- sons to assume that this puckering will be crucial in any cluster model for chemisorption. For a planar cluster, the ~r-system will be stabilized by delocalization, and no local orbital will be readily available for bonding. With increasing puckering, the local environment of a carbon atom will grad- ually change from sp 2 to sp 3 type, with the un- paired electron localized in the hybrid at the fourth, vacant coordination site. It can therefore also be assumed that additional non-planarity will be induced by the chemisorption process, i.e. a chemisorption-induced surface reconstruction.

Several rather non-intuitive measures are often taken in order to improve the cluster convergence, i.e. the rate at which the results for clusters of increasing size approach those of the infinite sys- tem. One such idea is the notion of "prepared" clusters [7-9]. In systems representing electric conductors, such as metals or graphite, there is not an obvious and unique one-to-one correspondence between the electronic structure of the bulk and a specific electronic state of a cluster modelling the bulk. Rather, it could be argued that any distribu- tion of valence electrons within the orbitals repre- senting the conduction "band" is a valid represen- tation. However, this does not suggest that the

choice is immaterial, or that any distribution o| electrons among those orbitals would provide a useful model. In order for the cluster to be able to participate in bonding, it must have available partly filled orbitals with point-group symmetry, energy, and spatial localization corresponding to the partly filled orbitals on the adsorbate. This would indeed provide a more reasonable model for chemisorption, since unpaired electrons of any symmetry can always be assumed to be available in the bulk of a conducting system. Any finite system modelling the bulk will in practice have a substantial separation between occupied and vir- tual valence orbital energies, and this can be taken as zeroth-order measure of the variation in ef- fectiveness of the various electronic states of the cluster.

The selection of shape and size for the cluster can also be done in a spirit similar to that of choosing suitably "prepared" electronic states. Since the sole purpose of the cluster is to serve as a model for the bulk, there is no reason to choose a stable molecule. On the contrary, one might argue that the open-shell nature of bulk graphite is best represented by a cluster having a small H O M O - L U M O gap a n d / o r unpaired electrons.

The nature of the metal-carbon bond in this type of complexes is another issue that needs to be addressed, and one that has important implica- tions for the way these studies should be carried out. If the bond is predominantly of charge-trans- fer character, then the electron affinity of the cluster and the ionization energy on the metal atom are crucial parameters. Cluster models of the surface for which these quantities are very differ- ent from the actual bulk values cannot be ex- pected to perform well in predicting binding en- ergies or other properties of the surface.

Normally, electron correlation is quite im- portant for the correct description of covalent bond energies. Further, the Har t ree-Fock model does not allow for the computation of full poten- tial energy curves for the dissociation of a bond. These issues become more significant if prepared states are used, and one further purpose of the present study is to explore the importance of correlation effects.

The distance between carbon layers in bulk

S. Shrivastava, J. Alml~f / Model calculation on the chemisorption of AI on graphite L511

graphite is close to 3.35 A and the interaction between layers is merely of van der Waals type [10]. Because of this weak interaction between the layers several studies have been done on a single sheet of graphite [11]. Preliminary studies [12] show that for small multi-layer clusters this inter- action is very insignificant. In the case of infinite systems the interaction is much stronger, resulting in an overlap between the valence and the conduc- tion band of approximately 0.04 eV, which is the cause of the semi-metallic character of graphite [13].

In the present study of chemisorption of Al on graphite we modelled the infinite graphite surface with a duster of 13 carbon atoms forming a single sheet of graphite. Thus, cluster convergence is not addressed here, but previous work [3,14] indicates that the effect of cluster size is not dramatic. Assuming that major interactions in the chemi- sorption process are of local nature, this small cluster would be sufficient in explaining the qualitative features of the binding. This is of course a hypothesis that must ultimately be tested, but the results of ref. [3] point in the same direction. As discussed below, the interaction between the surface and the metal is also of a very local nature, which supports this view. It must be emphasized, however, that the aim of our work at this time is not to obtain absolute values for binding energies, but rather to find general trends and to address methodological questions.

2. Calculations and results

All the external, "dangling" bonds of the clus- ter were saturated with hydrogen as was also done in ref. [3]. Previous studies have shown [14] that these dangling bonds introduce severe structural distortions, and that hydrogen saturation indeed improves the cluster convergence for single-sheet, graphite-like clusters. A number of important fea- tures relating to the binding of A1 on the graphite surface emerge from our study, as will be dis- cussed below.

A model of the cluster with AI chemisorbed on top of the central carbon atom is shown in fig. 1. While the STM results regarding non-planarity of

Fig. 1. The C13H9A1 system. Shaded and white circles denote carbon and hydrogen atoms.

the graphite surface must be taken with caution, there is no ambiguity with regard to the experi- mental preferred position of metal atoms on the surface. The chemisorption site is unequivocally "on-top" [15] rather than, e.g., on a bond or in the center of a 6-ring, contrary to the situation for most molecular complexes between metal atoms and aromatic systems. This position is also con- firmed by our calculations, see fig. 1.

Standard values of 1.42 and 1.1 ,~ were used for the carbon-carbon and the carbon-hydrogen dis- tances, respectively. As discussed above, it is im- portant to prepare the cluster for binding in such a way that it has partly filled orbitals of the same symmetry as the adsorbate. In its ground state A1 has one unpaired 3p-electron which can give rise to either an E or an A 1 state in C3v symmetry. It is reasonable to assume that the state with a p elec- tron in the al orbital is the one primarily of interest for on-top bonding to a graphite surface. However, the electronic ground state of C13H 9 is 2A 2, and has no possibility to form a bond to A1. This is very different from the situation in gra- phite, where unpaired electrons are always availa- ble. For the finite cluster, we must therefore choose a "prepared" electronic state such that the duster possesses a singly occupied orbital of a 1 symme- try. For this pu.r~ose we used the first excited state, which is of A~ symmetry. (It must be real-

1.512 S. Shrivastava, J. A lrnlhf / Model calculation on the ehemisorption of A I on graphite

Table 1 Basis sets used in the calculations

Label Primitive Reference Contraction Scheme

A AI (10s6p) [281 [3s2p] general contraction C (4s2p) [29] [2slp] to atomic orbitals H (2s) [291 [ls]

A" Al (10s6pld) ~) [28] [4s3pld] general contraction with C1 (7s3pld) bl [29] [3s2pld] the outermost function C (7s3p) [29] [3s2p] added uncontracted to the H (3s) [29] [2s] basis [30,31]

~) d exponent of 0.2 and 1.0 from ref. [28]. h) d exponent of 0.8 and 1.0 from ref. [28].

ized here that discrete electronic states has no counterpart in an infinite system like graphite, that the electronic ground state of the cluster therefore have no particular significance in the modeling of graphite, but that any state with the right number of ~r-electrons is equally justifiable.) Using this prepared state we calculated the bind- ing energy using SCF, MP2 and MCSCF methods. Basis set effects were also investigated by using two different basis sets denoted below as A (small), and A" (large). Details of the basis sets are given in table 1. Since calculation of binding energies can be strongly affected by basis set superposition errors (BSSE) [16,17], we corrected the binding energy for BSSE using a counter-poise technique [181.

The most striking result of this study is the large reconstruction of the surface in the presence of an A1 atom. Like previous investigators [3] we find that at the SCF level A1 is not bonded at all to a planar surface of this cluster, even though the half filled orbital of the cluster is quite localized at the chemisorption site. (It should be noted that this model system is not spontaneously puckered in the absence of an adatom and thus does not describe all the features of the graphite surface that it is supposed to model.) However, when the geometry of the cluster is allowed to relax in the presence of the metal atom, a substantial binding energy is found. The bonds in a planar fragment can be described in terms of s p 2 hybridization, and the carbon atoms cannot easily form ad- ditional bonds. When a carbon atom is moved out of the plane its environment corresponds more

and more to an sp 3 situation, with aluminum at the fourth coordination site. In addition, the puck- ering of the cluster brings the orbital energy of the half-filled orbital closer to that of the A1 atom (table 2) which also ought to facilitate the bond- ing.

In the calculation of binding energy we com- pare the total energy of the metal-hydrocarbon complex with the energy of the free A1 atom and the energy of the cluster in the prepared, excited state. In other words, the quoted binding energy describes the difference between the minimum and the asymptotic value on the same (excited) potential energy curve.

For an estimate of the degree of corrugation one might turn to results of scanning tunneling microscopy (STM) on clean graphite surfaces. However, despite a large amount of experimental effort to image the clean pyrolitic graphite surface the degree of puckering has not yet been estab- lished. A naive, straightforward interpretation of the STM images of graphite leads to the conclu-

Table 2 Open shell energy

Degree of puckering

(A)

of the cluster as a function of corrugation

Orbital energy (eV)

Basis set (A) Basis set (A")

0.3 -4 .01 - 4 . 1 3 0.4 - 4.80 - 4.69 0.5 - 5.54 - 5.51 0.6 - 6.30 - 6.20 0.7 - 6.84 - 6.53 0.8 - 7 . 1 7 - 6 . 9 3

S. Shrivastava, J. Almliif / Model calculation on the chemisorption orAl on graphite L513

sion of an apparent, unphysically l~ge "giant corrugation" ranging from 1 to 24 A [19-23]. There could be various possible explanations for this anomalous effect and some authors [24-26] have tried to analyze these results critically, giving estimates ranging from < 0.3 to 1 h,. On the other hand, Lawunmi and Payne [27] have argued that these explanations are not sufficient. The experi- mental results for the corrugation of graphite seem debatable, at best, and in the present calculation we decided to not rely on any of the quoted values, but rather to calculate the binding energy as a function of corrugation.

Using two different basis sets (see table 1) SCF and MP2 calculations were carried out. All va- lence orbitals were correlated in the MP2 calcula- tions. The calculations were carried out with the central carbon atom displaced out of the plane to various degrees. At the SCF level of approxima-

tion no binding is found on the planar surface which is in line with the findings of Head et al. [3] However, as the central carbon atom is allowed to relax the system shows strong binding, even though we are not considering the puckering of surround- ing atoms at this point. The maximum binding between A1 and the graphite surface occurs with the central carbon atom displaced by 0.5 ,~ out of the surface (table 3!. The equilibrium bond dis- tance (A1-C) is 2.1 A.

Calculations were also carried out with the A1 atom in "on-bond" or "hollow" positions, in order to test the assumption of on-top binding. How- ever, the system was not found to be bound in any of these conformations.

The two basis sets give remarkably different binding energies 22.0 and 43.7 kcal/mol, respec- tively for the large and small basis set. It might seem surprising to find a larger binding energy

Table 3

Chemisorption energy of AI as a function of corrugation using SCF and MP2 methodology

Method Degree of Bond Binding energy Charge on

basis set puckering (,~) distance (,~) (kca l /mol ) Al atom

SCF A" 0.3 2.1 +2.8 0.517

0.4 2.1 - 2.2 0.524

0.5 2.1 - 2 . 3 0.521

0.6 2.1 + 3.3 0.464

0.7 2.0 + 14.8 0.461

0.8 2.0 + 31.5 0.459

A 0.3 2.1 - 6.5 0.582

0.4 2.1 - 19.5 0.594

0.5 2.1 - 28.1 0.595

0.6 2.1 - 3 1 . 2 0.590

0.7 2.1 - 23.4 0.581

0.8 2.0 -18 .5 0.539

MP2 A" 0.3 2.1 - 1 7 . 0

0.4 2.1 - 21.6

0.5 2.1 - 22.0

0.6 2.1 - 17.7

0.7 2.1 - 8 . 7

0.8 2.0 + 4.5

A 0.3 2.1 - 7 . 5

0.4 2.1 - 29.9

0.5 2.1 - 39.1 0.6 2.1 - 43.7 0.7 2.1 - 4 0 . 7

0.8 2.1 - 37.1

1.314 S. Shrwastal,a, J. A Irnli~[ / Model calculatzon on the ~hemisorption of A I on graphzte

with the smaller basis. In this case however, the discrepancy does not arise from a difference in the description of the binding between C and A1, but rather from the difference in "stiffness" of the substrate. In fact, with the smaller basis the hy- drocarbon is on the verge of spontaneously lower- ing the planar symmetry, and distorting the central atom by 0.3 ~, in the free cluster requires only 0.9 kcal /mol as compared to 21.4 in the large basis. It could be argued that the small basis results are more representative for a real graphite surface which is indeed non-planar, but the results also indicate the severe lack of basis set convergence, and the results obtained with the smaller basis should therefore viewed with some caution. The distortions of the cluster geometry upon bonding are almost exclusively out-of-plane in nature, with no carbon atom shifting its projection onto the molecular plane by more than 0.01 A. Accord- ingly, it can be assumed that the additional geo- metric constraints imposed by a larger cluster would not strongly affect the surface reconstruc- tion, and that conclusions about the true graphite surface can be drawn even from studies on this small cluster model. The MP2 results show the importance of correlation in this study. The effect of correlation on the binding energy is 12.5 and 19.7 kcal /mol with basis set A and A" respec- tively. The larger basis set is showing more corre- lation, as expected. (Incidentally, the calculated equilibrium A1 . . - C bond distance is nearly equal with two basis sets.) Bond energies calculated with small basis sets are often severely affected by basis set superposition errors (BSSE), and the binding energies were therefore corrected using the coun- ter-poise technique [18]. This reduces the values substantially, to 9.1 and 29.9 kcal /mol respec- tively.

Table 3 also gives the charge on A1 in the chemisorbed state. Its obvious that at equilibrium distance A1 is donating an electron to the hydro- carbon and the nature of the bond is clearly quite ionic Accordingly, a lowering of the orbital energy for the half-filled a t orbital of the cluster would enhance the binding, which is exactly what is observed when going from the large to the small basis set. ( -5 .51 versus -6 .30 eV; in comparison the orbital energy of A1 is -5 .46 eV)

I ab le 4

Chemisorption energy of AI on the graphite surface as a function of corrugation using MCSCF methods (basis set A" was used)

Corrugation Bond distance Binding energy

(A) (AI-C) (A.) (kcal /mol)

0.3 2.l - 12.1 0.4 2.1 -- 17.4 0.5 2.1 - 1 7 . 7 0.6 2.1 -12 .1 0.8 2.0 + 21.2

We have also carried out corresponding calcu- lations on the C13H9A1 cluster using the multi- configurational SCF (MCSCF) method and the larger basis set A". These calculations on the combined system as well as on the free cluster have been done by distributing the two bonding electrons in the C-A1 bonding and anti-bonding orbitals of o-symmetry. The results of these calcu- lations are given in table 4.

Comparing the MCSCF results with those ob- tained with the MP2 method (table 2) it is obvious that the MP2 approach predicts a stronger bond. The MP2 calculation correlates all valence elec- trons, which appears to be important in this case. The pair-correlation energy for the bonding o- orbital is only 4.7 kcal /mol , so apparently there are other significant correlation contributions to the bond energy. We can thus conclude that, while MCSCF methods have some attractive features, such as giving smooth potential curves for dissoci- ation, it is more important in the current situation to correlate all the valence electrons which realisti- cally requires a more approximate correlation treatment such as MP2.

3. Conclusions

In summary, the overall picture of chemisorp- tion which emerges from our study is that the corrugation is the key factor in explaining the binding on the graphite surface.

The assumption of bonding at an on-top site is crucial in these calculations. While the on-top chemisorption is experimentally well ~stablished, any theoretical model does not necessarily repro-

s. Shrivastava, J. Alml6f / Model calculation on the chemisorption orAl on graphite L515

duce that finding, especially since it is well known that most molecular complexes between metal a toms and aromatic systems actually b ind the metal to a C - C bond or in the center of a 6-ring. However, in the cluster used here the binding in these positions is much weaker, and the on- top posit ion is actually the global min imum on the potential surface.

The question of spontaneous surface recon- struction leading to surface corrugat ion in gra- phite is still unresolved, and such effects are not included in our model. The chemisorption-in- duced non-planari ty, on the other hand, is estab- lished by our calculations and has been shown to be a crucial element in the bonding of metal a toms to a graphite surface. Allowing for this corrugat ion is likely to be much more impor tant than going to larger dusters. (It is impor tan t to realize, though, that we do not make any a priori assumption about surface puckering in our model. The geometry of the cluster model is completely relaxed, and the puckering comes as a result of the variation principle.) Another impor tan t factor is the correlation effect. I f these elements are prop- erly treated even small cluster models are suffi- cient in explaining the qualitative features of the binding.

Acknowledgements

These studies have benefited f rom extensive discussions with Wayne Gladfelter. The calcula- tions were carried out on the Cray-2 computers at the Minnesota Supercomputer Center and at NCSA, Illinois. The work was supported by the Minnesota Supercomputer Institute, the Nat ional Science Founda t ion (Grant no. CHE-89 15629), and the Center for Interracial Engineering at the Universi ty of Minnesota.

[3] J.D. Head, T.E. Meehan and S.J. Silva, Phys. Scr. 41 (1990) 874.

[41 F. Tr~iger and G. zu Putlitz, Eds., Metal Clusters (Springer, Berlin, 1986).

[5] B.C. Gates, L. Guczi and H. KntSzinger, Eds., Metal Clusters in Catalysis (Elsevier, Amsterdam, 1986).

[6] D. Tomanek, S.G. Louie, H.J. Mamin, D.W. Abraham, R.E. Thomson, E. Ganz and J. Clarke, Phys. Rev. B 35 (1987) 7790.

[7] I. Panas, J. Schiihle, P. Siegbahn and U. Wahlgren, Chem. Phys. Lett. 149 (1988) 265.

[8] T.H. Upton and W.A. Goddard, CRC Critical Reviews in Solid State and Materials Sciences (CRC Press, Boca Raton, 1981).

[9] K. Herman, P.S. Bagus and C.J. Nelin, Phys. Rev. B 35 (1987) 9467.

[10] A.D. Crowell, J. Chem. Phys. 29 (1958) 446. [111 R. Dovesi, C. Pisani and C. Roetti, Int. J. Quantum

Chem. 17 (1980) 517. [12] B.T. Chen and J. AlmlSf, unpublished results. [131 J.W. McCiure, IBM J. (1964) 255. [14] J. Almltif and H.P. Liithi, in: ACS Symposium Series:

Supercomputer Research in Chemistry and Chemical En- gineering, Eds. K. Jensen and D. Truhlar (1987) 35.

[15] E. Ganz, K. Sattler and J. Clarke, Surf. Sei. 219 (1989) 33. [16] E. Clementi, J. Chem. Phys. 46 (1967) 3851. [171 B. Liu and A.D. McLean, J. Chem. Phys. 59 (1973) 4557. [18] S.F. Boys and F. Bernadi, Mol. Phys. 19 (1970) 553. [19] G. Binnig, H. Fuchs, Ch. Gerber, H. Rohrer, E. Stoll and

E.T. Tosatti, Europhys. Lett. 1 (1986) 31. [20] V. Elings and F. Wudl, J. Vac. Sci. Technol. A 6 (1988)

412. [21] H.J. Mamin, E. Ganz, D.W. Abraham, R.E. Thompson

and J. Clarke, Phys. Rev. B 34 (1986) 9015. [22] S. Morita, S. Tsukada and N. Mikoshiba, J. Vac. Sci.

Technol. A 6 (1988) 354. [23] J.M. Soler, A.M. Baro and N. Garcia, Phys. Rev. Lett. 57

(1986) 444. [24] J. Tersoff, Phys. Rev. Lett. 57 (1986) 440. [25] A. Selloni, P. Carnevali, E. Tosatti and C.D. Chen, Phys.

Rev. B 1 (1985) 2602. [26] J. Tersoff and Lang, Phys. Rev. Lett. 65 9 (1990) 1132. [27] D. Lawunmi and M.C. Payne, J. Phys. Condens. Matter 2

(1990) 3811. [28] B. Roos and P. Siegbahn, Theor. Chem. Acta 17 (1970)

209. [29] F.B. van Duijneveldt, IBM Res. Rep. RJ (1971) 945. [30] J. AlmlSf and P.R. Taylor, J. Chem. Phys. 86 (1987) 198. [31] J. Alml6f and P.R. Taylor, J. Chem. Phys. 92 (1990) 551.

References

[1] N.J. Ignatiev and A. Wu, Phys. Rev. B 25 (1982) 2983. [2] P.K. Hansma and J. Tersoff, Appl. Phys. 61 (1987) R1.