A model calculation on the chemisorption of aluminum on graphite

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

Surface Science Letters

A model calculation on the chemisorption Sarita

and Jan Almlijf

Srivastava

Department

of aluminum on graphite

of Chemistty,

University

of Minnesota,

Minneupolis,

MN 55455, USA

Received 8 April 1991; accepted for publication 29 May 1991

Atomic chemisorption on the basal plane of grapbite has been modelled with a finite-size cluster of carbon atoms. The interaction with an Al 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 important as an adlayer substrate for thin film growth because of its good uniformity [l] and relative chemical inertness. With the development of scanning tunnelling microscopy (STM) techniques in recent years [2], the early stages of thin film growth have been studied extensively, yet very fundamental questions about nucleation sites and surface reactions remain unanswered. Therefore a better knowledge of the graphite surface and its interaction with adsorbed atoms is required both for the interpretation of the experimental results and for the development of a microscopic theory of chemisorption. 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 delectrons. Very recently, a theoretical study of Al on graphite-like clusters was published [3], focusing on the necessary requirements for the cluster to bind the Al atom. That calculation sheds light on some crucial questions with regard to the re0039-6028/91/$03.50

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 “unprepared” 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 induced non-plenty 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 molecular 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,

0 1991 - Elsevier Science Publishers B.V. (North-Holland)

S. Shrivastava,

J. Alml6f / Mode! calculation on the chemisorption

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 address the issue of surface r~onst~ction, i.e. the fact that a clean surface of any bulk system has geometry parameters which differ from those inside 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 che~so~tion. The graphite surface consists of two kinds of carbon atoms, differing in whether or not they have a carbon atom immediately below 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 investigations have indeed confirmed the non-equivalency of the two types of carbon atoms (61, even though the actual degree of corrugation for a pure graphite surface is still unknown. There are reasons to assume that this puckering will be crucial in any cluster model for chemisorption. For a planar cluster, the n-system will be stabilized by delocalization, and no local orbital will be readily available for bonding. With increasing puckering, the local en~ronment of a carbon atom will gradually change from sp’ to sp3 type, with the unpaired 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 system. One such idea is the notion of “prepared” clusters [7-91. 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 distribution of valence electrons within the orbitals representing the conduction “band” is a valid representation. However, this does not suggest that the

ofAi

on graphite

choice is immaterial, or that any distribution of 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 orbit& with point-group s~rnet~, 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 virtual valence orbital energies, and this can be taken as zeroth-order measure of the variation in effectiveness 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 HOMO-LUMO gap and/or 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 implications for the way these studies should be carried out. If the bond is predominantly of charge-transfer 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 different from the actual bulk values cannot be expected to perform well in predicting binding energies or other properties of the surface. Normally, electron correlation is quite important for the correct description of covalent bond energies. Further, the Hartree-Fock model does not allow for the computation of full potential energy curves for the dissociation of a bond. These issues become more sig~ficant 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. Almiif / Model cak

on the chemisorption

ofAl on graphite

graphite is close to 3.35 A and the interaction between layers is merely of van der Wadis type [lo]. Because of this weak interaction between the layers several studies have been done on a single sheet of graphite [ll]. Preliminary studies [12] show that for small multi-layer clusters this interaction is very insi~fic~t. In the case of infinite systems the interaction is much stronger, resulting in an overlap between the valence and the conduction band of approximately 0.04 eV, which is the cause of the semi-metallic character of graphite II31In the present study of che~so~tion of Al on graphite we modelled the infinite graphite surface with a cluster 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. Assu~g that major interactions in the chemisorption 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 meth~ological questions.

2. Calculations and results All the external, “dangling” bonds of the cluster 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 Al on the graphite surface emerge from our study, as will be discussed below. A model of the cluster with Al chemisorbed on top of the central carbon atom is shown in fig. 1. While the STM results regarding non-planarity of

Fig. 1. The &H,Al system. Shaded and while circles denote carbon and hydrogen atoms.

the graphite surface must be taken with caution, there is no ambiguity with regard to the experimental 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 &ring, contrary to the situation for most molecular complexes between metal atoms and aromatic systems. This position is also confirmed by our calculations, see fig. 1. Standard values of 1.42 and 1.1 A were used for the carbon-carbon and the carbon-hy~ogen distances, respectively. As discussed above, it is important 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 Al has one unpaired 3p-electron which can give rise to either an E or an A, state in C,, symmetry. It is reasonable to assume that the state with a p electron in the a, orbital is the one primarily of interest for on-top bonding to a graphite surface. However, the electronic ground state of C,,H9 is 2A2, and has no possibility to form a bond to Al. This is very different from the situation in graphite, where unpaired electrons are always available. For the finite cluster, we must therefore choose a “prepared” electronic state such that the cluster possesses a singly occupied orbital of a, symmetry. For this p ose we used the first excited urY state, which is of A, symmetry. (It must be real-

S. Shrivastava, J. AlmkYf / Model calculation on the chemisorption of AI on graphite

Basis sets used in the calculations

Label

Primitive

Reference

Contraction

Scheme

A

Al (10~6~) c (4~2~) H (2s)

P31

t3s2~1 12slpl PSI

general contraction to atomic orbitals

[4s3pld] [3s2pld] ~3~2~1 ]2sl

general contraction with the outermost function added uncontracted to the basis [30,31]

A”

Al (lOs6pld) a) Cl (7s3pld) b, C (7s3p) H (3s)

1291 1291

P81 1291 t291 ]291

‘) d exponent of 0.2 and 1.0 from ref. [28]. ‘) d exponent of 0.8 and 1.0 from ref. [ZS].

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 s-electrons is equally justifiably.) Using this prepared state we calculated the binding 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) 116,171, we corrected the binding energy for BSSE using a counter-poise technique 1181. The most striking result of this study is the large reconstruction of the surface in the presence of an Al atom. Like previous investigators [3] we find that at the SCF level Al 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 sp’ hybridization, and the carbon atoms cannot easily form additional bonds. When a carbon atom is moved out of the plane its environment corresponds more

and more to an sp3 situation, with aluminum at the fourth coordination site. In addition, the puckering of the cluster brings the orbital energy of the half-filled orbital closer to that of the Al atom (table 2) which also ought to facilitate the bonding. In the calculation of binding energy we compare the total energy of the metal-hydrocarbon complex with the energy of the free Al 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 established. A naive, strai~tfo~~d inte~retation of the STM images of graphite leads to the concluTable 2 Open shell energy of the cluster as a function of corrugation Degree of puckering

Orbrtal energy (eV) Basis set (A)

Basis set (A“)

-

-4.13 - 4.69 - 5.51 - 6.20 -6.53 - 6.93

(h 0.3 0.4 0.5 0.6 0.7 0.8

4.01 4.80 5.54 6.30 6.84 7.17

S. Shrivastava,

J. Alml6f / Model calculation on the chemisorption

sion of an apparent, unphysically latge “giant corrugation” ranging from 1 to 24 A [19-231. There could be various possible explanations for this anomalous effect and some authors [24-261 have tried to analyze these results @tically, giving estimates ranging from < 0.3 to 1 A. On the other hand, Lawunmi and Payne [27] have argued that these explanations are not sufficient. The experimental 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 valence orbitals were correlated in the MP2 calculations. The calculations were carried out with the central carbon atom displaced out of the plane to various degrees. At the SCF level of approxima-

of AI on graphite

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 surrounding atoms at this point. The maximum binding between Al and the graphite surface occurs with the central carbon atom displaced by 0.5 A out of the surface (table 3). The equilibrium bond distance (Al-C) is 2.1 A. Calculations were also carried out with the Al atom in “on-bond” or “hollow” positions, in order to test the assumption of on-top binding. However, 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, respectively for the large and small basis set. It might seem surprising to find a larger binding energy

Table 3 Chemisorption energy of Al as a function of corrugation using SCF and MP2 methodology Method

Degree of

Bond

Binding energy

Charge on

basis set

puckering (A)

distance (A)

(kcal/mol)

Al atom

SCF

A”

0.3 0.4 OS 0.6 0.7 0.8

2.1 2.1 2.1 2.1 2.0 2.0

+2.s -2.2 -2.3 + 3.3 + 14.8 + 31.5

0.517 0.524 0.521 0.464 0.461 0.459

A

0.3 0.4 0.5 0.6 0.7 0.8

2.1 2.1 2.1 2.1 2.1 2.0

-6.5 - 19.5 - 28.1 -31.2 - 23.4 -18.5

0.582 0.594 0.595 0.590 0.581 0.539

A”

0.3 0.4 0.5 0.6 0.7 0.8

2.1 2.1 2.1 2.1 2.1 2.0

- 17.0 -21.6 - 22.0 - 17.7 -8.7 +4.5

A

0.3 0.4 0.5 0.6 0.7 0.8

2.1 2.1 2.1 2.1 2.1 2.1

-7.5 - 29.9 - 39.1 -43.7 - 40.7 - 37.1

MP2

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 Al, but rather from the difference in “stiffness” of the substrate. In fact, with the smaller basis the hydrocarbon is on the verge of spontaneously lowering the planar symmetry, and distorting the central atom by 0.3 A in the free cluster requires only 0.9 kcalfmol 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. Accordingly, it can be assumed that the additional geometric constraints imposed by a larger cluster would not strongly affect the surface reconstruction, 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” respectively. The larger basis set is showing more correlation, as expected. (Incidentally, the calculated equilibrium Al . - . C bond distance is nearly equal with two basis sets.) Bond energies calculated with small basis sets are often severely affected by basis set s~pe~osition errors (BSSE), and the binding energies were therefore corrected using the countzr-poise technique j18]. This reduces the values substantially, to 9.1 and 29.9 kcalJmo1 respectively. Table 3 also gives the charge on Al in the chemisorbed state. Its obvious that at equilibrium distance Al is donating an electron to the hydrocarbon and the nature of the bond is clearly quite ionic Accordingly, a lowering of the orbital energy for the half-filled a, 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 Al is - 5.46 eV)

Table 4 Chemisorption energy of AI on. the graphite surface as a function of corrugation using MCSCF methods (basis set A” was used} Corrugation (A) 0.3 0.4 0.5 0.6 0.8

Bond distance (Al-C) (A)

Binding energy (kcal/mol)

2.1 2.1 2.1 2.1 2.0

- 12.1 - 17.4 -17.7 - 12.1 + 21.2

We have aIs0 carried out correspunding calculations on the C,,H,AI cluster using the multiconfigurational 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-Al bonding and anti-bonding orbitals of u-symmetry. The results of these calculations are given in table 4. Comparing the MCSCF results with those obtained with the MP2 me~od (table 2) it is obvious that the MPZ approach predicts a stronger bond. The MP2 calculation correlates all valence electrons, which appears to be impo~~t in this case. The pair-correlation energy for the bonding ororbital 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 dissociation, it is more important in the current situation to correlate all the valence electrons which realistically requires a more approximate correlation treatment such as MP2.

3. Conclusions In summary, the overall picture of chemisorption 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 cruciaI in these calculations. While the an-top chemisorption is expe~ment~ly well established, any theoretical model does not necessarily repro-

S. Shrivastava, J. Almlif / Model calculation on the chemisorption of Al on graphite

duce that finding, especially since it is well known that most molecular complexes between metal atoms and aromatic systems actually bind 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 position is actually the global minimum on the potential surface. The question of spontaneous surface reconstruction leading to surface corrugation in graphite is still unresolved, and such effects are not included in our model. The chemisorption-induced non-planarity, on the other hand, is established by our c~culations and has been shown to be a crucial element in the bonding of metal atoms to a graphite surface. Allowing for this corrugation is likely to be much more important than going to larger clusters. (It is important 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 important factor is the correlation effect. If these elements are properly treated even small cluster models are sufficient in explaining the qualitative features of the binding.

Acknowledgements These studies have benefited from extensive discussions with Wayne Gladfelter. The calculations 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 National Science Foundation (Grant no. CHE-89 15629), and the Center for Interfacial Engineering at the University of Minnesota.

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