3800
J . Phys. Chem. 1993,97, 3800-3805
Theoretical Study of the Binding Energy and Bonding of Benzene to the Ni (1 1 l), (loo), and (1 10) Surfacest F. A. Grimm University of Tennessee, Knoxville, Tennessee 37996- 1600. and Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -6201
D. R. Huntley' Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -6201 Received: November 10, 1992; In Final Form: January 18, I993
The atomic superposition electron delocalization molecular orbital (ASED-MO) method has been applied to a study of the favored bonding sites for benzene adsorbed on the (1 1 1). (loo), and (1 10) crystal faces of nickel metal. The different faces were represented in the calculations by clusters, which contained 30 nickel atoms. By using the same size clusters and parameters, it was possible to compare the results among the three different crystal faces. The most favored (highest binding energy) sites for the benzene ring parallel to the surface were found to be the highest coordination site for the (1 11) and (100) planes and the atop site for the (1 10) plane. These results are compared with both experimental and other theoretical calculations on these crystal planes. In addition, the bonding of the benzene to the Ni surfaces has been investigated by using "bonding plots", which are graphical representations of the Mulliken population matrix. By use of these bonding plots, a picture of the bonding of the benzene to the nickel surface is developed and an explanation for the increase of the binding energy with increased cluster size is discussed.
Introduction While experimental studies of chemisorption of organic molecules on metal surfaces abound, theoretical descriptions are considerably rarer. Chemists have found great utility in the intuitively simple extended Hiickel method in understanding bonding and chemical properties of a wide variety of molecules. In this paper, the value of a similar method for studying the adsorption of organic species, specifically benzene, on nickel surfaces is investigated. The computational technique used in this study is the atomic superposition and electron delocalization (ASED) method of Anderson,'.*which is essentially an extended Hiickel theory. The critical differences include the inclusion of a pairwise repulsion term, based on the Hellmann-Feynman force theorem. This repulsive term allows the possibility of modeling structures. In addition, the off-diagonal terms, Hi,, in the Hiickel matrix are multiplied by an exponential, exp[-0.13RiJ], which allows these terms to decrease with interatomic spacing and leads to a more localized calculation for the adsorbate on a small cluster. The ASED method has been used previously to predict adsorption sites on clusters representing Ag( 11 l), Pt( 1 1 l), Ni(1 l 1),j.4and Ni( 1oO)4.5surfaces. The general conclusion of those studies was that the benzene molecule was adsorbed in the highest coordination site in all of thosecases. However, no computational results were available for benzene adsorbed on the Ni( 1 10) surface, which has been the subject of recent and no fully consistent study of all three surfaces had been made to allow reasonable comparisons of the computational predictions between the three surfaces and with experimental results. This paper presents such a study for nickel clusters constructed to mimic the structure of the (1 1 l), (loo), and (1 10) surfaces of the fcc nickel lattice. In addition, the effects of cluster size on the binding energies and the bonding interactions between the metal clusters and the benzene ring are discussed. The chemisorption of benzene on nickel has been studied
' Research sponsored by the Division of Chemical Sciences, Office of Basic Energy Sciences, U S . Department of Energy under Contract DE-ACOS8 4 0 1 2 1 4 0 0 with Martin Marietta Energy Systems, Inc.
experimentally for all three low index surfaces.6-12 In all cases, the benzene is thought to lie parallel (ring flat) to the surface and, at temperatures below 300 K, be associatively adsorbed. When these calculations were started, little was known about the adsorption site or symmetry for benzene on these three surfaces. Recently the azimuthal orientation of the benzene ring on Ni(1 10)' and on Ni( l l 1)9 has been studied by angle-resolved photoemission spectroscopy. Above 300 K, benzene decomposition competes with molecular benzene desorption. While qualitatively similar, the details of the molecular desorption/ decomposition competition are very structure sensitive. For example, on Ni(110)'j about 75% of the adsorbed benzene ultimatelydecomposes, whileon Ni( 111) only 39% of the benzene decomposes.I0 The desorption temperatures of the molecular benzene also vary substantially between surfaces. One of the purposes for undertaking this computational study was to aid in the interpretation of these differences in chemical reactivity. The reactivity of benzene seems to be related to a combination of metal/benzene and benzene/benzene interactions. The localized nature of the ASED method only assesses the former and so does not adequately account for differences in the chemistry where benzene/benzene interactions would be important, such as at medium to high coverage. However, we did obtain considerable information on the nature of the ASED method and its use in calculations for energetics and bonding of adsorbates on small clusters. The paper is divided intosections, which cover the major topics (1) Calculated Adsorption Geometries, (2) Comparison with Calculations, (3) Comparison with Experiment, (4) Bonding Plots, and ( 5 ) Effect of Cluster Size on Binding Energies.
Calculated Adsorption Geometries The adsorption geometries for benzene on 30-atom nickel clusters were predicted on the basis of the calculated binding energies [Etenzcnc/cluster - (&luster + E t e n z e n e ) l - The parameters used in the ASED calculations are shown in Table I. These correspond to those used by Anderson et al.) for H, C, and Ni. Since there are several structural parameters to be considered, including adsorption site, azimuthal orientation, tilt angle, benzene
This article not subject to U S . Copyright. Published 1993 by the American Chemical Society
The Journal of Physical Chemisrry, Vol. 97, No. 15, 1993 3801
Bonding of Benzene to Ni Surfaces
TABLE I: SIater Atomic Orbital Parameters' atom/orbital
H/ls c/2s CpP N1/4S Nj/4P N1/3d
VSIP,h eV 12.600 19.000 10.260 8.635 4.990 11.000
CI
1.0 1.0 1.0 1.0 1.0 0.5683
(I
c2
1.200 1.685 1.618 1.800 1.500 5.750
0 0 0 0 0 0.6290
c2
0 0 0 0
[OlOI
f
0 2.0000
Parameters from ref 3. h Valence-state ionization potential.
ring distortion, and height above the cluster surface, certain assumptions were made. The structuresof the clusters were fixed and corresponded to the structures of the unreconstructed crystal faces. Discreet azimuthal orientations along low index lattice directions were tested. A few calculations were done on expanded benzene rings and with hydrogen atoms tilted out of the plane of the aromatic ring, but no stabilization was predicted so, in general, the benzene ring was held rigid with its gas-phase structure. No Kekule ring distortions were examined. The height above the cluster surface was optimized on smaller clusters (1 3 atoms for Ni(100) and N i ( l l 0 ) and 10 atoms for Ni(ll1)). Binding energies were calculated for heights above the surface in 0.05-Aincrements and the height resulting in the energy minimum was chosen for calculations on larger clusters. Figure 1 depicts the sites and orientations considered in these calculations. The calculated binding energies for benzene adsorbed on the three surfaces in various sites are summarized in Table 11. In all cases, the results are for 30-atom clusters to minimize cluster size effects (vide infra). Included in Table I1 is some information on the interaction of benzene with the metal surface. The column labeled Hintgives the Hiickel electronic contribution to the interaction energy between the surface and the adsorbate and is calculated as the difference in Hiickel energies, Hbenzcnc/cIuster - (Hc~uster + Hbenzenc) The column labeled ERint gives the similar difference for the repulsion terms between the benzene-cluster complex and the sum of the individual repulsion energies of benzene and the bare cluster. The different adsorption sites vary in the relative contributions to the total binding energy of the Hiickel electronic energy (bonding energy) and the repulsion energy. The most stable adsorption site for benzene on the Ni( 1 1 1) surface is predicted to be the 3-fold hollow site at a height of 2.0 A. The slight preference (0.1 1 eV) for the hcp site over the fcc site is not significant. Adsorption in the Cju-.d hollow sites ( H l , Hl') clearly maximizes the Hiickel electronic energy. The respulsive terms are also relatively low, with only the atop site having smaller repulsive interactions. The azimuthal preference for the C 3 ( , 4( H l ) site over the C3,-,, (H2) site is quite large, due to substantially less favorable electronic and repulsive terms. Benzene is predicted to adsorb on Ni(100) surfaces on the hollow site at a height of 2.0 A. Two different azimuthal orientations were considered ( H l , H2), one with the carboncontaining C2 axis aligned with the [Oll] azimuth ( H l ) and one with the C2 axis aligned with the [OlO] azimuth (H2). The calculations predict that these two configurations are essentially equally favorable. Interestingly, the equivalence of these two sites is due to cancellation of differences in repulsive and electronic terms. The H2 hollow site has a somewhat less favorable electronic energy but also a substantially lower repulsive term than the H1 hollow site. The situation is quite different on the N i ( l l 0 ) surface. Here the most favorable adsorption site is a low coordination site, either the atop site (Al) at a height of 1.75 A or the short bridge site (Sl) at a height of 1.90 A. The calculation predicts a strong preference for the orientation with the benzene carbon-containing C2 axis along the [OOl] azimuths. Here, the atop site has both a large Hiickel electronic energy and a small repulsive energy. A comparison of the energetics of the benzene in its preferred siteoneach ofthe threeclustersshows that thebondingof benzene
---+ 10111
riioi
-W
c
r11i1
riioi
t -bLWlI
-
Figure 1. Sites and orientations modeled for each of the three faces. The actual clusters were constructed as follows: Ni(100) (top) and Ni( 1 IO) (bottom) three-layer slabs with 12 nickel atoms in the first and third layers and six in the second layer; Ni( 1 1 1) (middle): two-layer slab with 18 nickel atoms in the first layer and 12 in the second layer.
on the Ni( 1 11) cluster is stronger than to the other surfaces. The binding energies on the Ni( 1 10) and (100) clusters are comparable to each other.
Comparison with Other Calculations Three calculations that model the adsorption of benzene on the N i ( l l 1 ) face have been reported in the l i t e r a t ~ r e . ~ .A~ ' ~ comparison of the results of these authors with our results are presented in Table 111. As expected, our results are in agreement with those of Anderson et al.,3 since the only difference is in the size of the Ni cluster (30 atoms vs 17 atoms for Anderson et al.). There are, however, some small differences, as can be seen in the table, which are due to either the size of the cluster or the exact positioning of the benzene relative to the edges of the cluster. This latter possibility has not been extensively studied, but in the few cases in which we changed the relative position we did not see any significant changes in the binding energies. Most importantly, wedoagree with Andersonet al.on thelowestenergy site (highest binding energy). We also agree with Jing and Whitten13 on the lowest energy site. Our results do not agree with those of Myers, Schoofs, and Benziger? which predict the high coordination site, but with a different azimuthal orientation.
3802 The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 TABLE 11: Calculated Binding Energies' for Benzene on Nickel site height, A -Eeh -HIn1 ' ER'"'
Grimm and Huntley
troughs.l5 The ARUPS measurements7 did not determine the actual adsorption site, but our calculations predict either an atop site or a short bridge site is preferred. The height of the benzene molecule was not determined experimentally, but the distances Benzene on Ni( 100) calculated here (e.g., 1.75 A for the atop site) compare favorably hollow, H2 2.00 5.228 6.984 1.756 with those of nickel arene complexes such as ($-metisy1ene)hollow, H 1 2.00 5.157 7.188 2.031 bridge, B2 2.00 5.066 6.633 1.567 bis(pentafluorophenyl)nickel(II)I6 where the nickel +arene 1.95 4.673 6.985 2.285 bridge, BI distance is 1.693 A. The recent ARUPS7study also demonstrated 1.90 4.445 6.355 1.910 atop, A 1 that, at high coverage, the benzene reorients on the surface. This reorientation is attributed to benzene/benzene interactions, which Benzene on Ni( 1 11) hollow (hcp), HI, C,, od 2.00 5.770 7.435 1.665 are not reflected in our calculations. hollow (fcc), HI', CI,n,/ 2.00 5.664 7.328 1.664 A recent ARUPS study of benzene on Ni( 1 11) has indicated 2.00 5.358 7.260 1.902 bridge, 82, C~,(X+X) a C3r-ad symmetry of the adsorption complex benzene/Ni( 11 1) bridge, BI, C?,(x-y) 2.00 5.258 6.965 1.707 2.05 5.050 6.900 1.850 as we predict. However, the azimuthal orientation of the benzene hollow (hcp), H2, C,, ", hollow (fcc), H2', C,, nl 2.05 4.901 6.742 1.841 ring is such that the carbon-containing C2 axis points along the atop, A2, Co' 1.90 4.740 6.155 1.415 [211] azimuths, in contradiction to our calculation^.^ Further2.00 4.196 5.835 1.639 atop, A I , Co more, the ARUPS seemed to favor the atop site, which we find Benzene on Ni( 1 IO) to be much less stable then the hollow sites. Our calculations do atop, A I 1.75 5.375 6.974 1.599 agree with the theoretical results of Anderson et ala3and Jing and 1.90 5.256 6.983 1.727 short bridge, SI WhittenI3 for Ni( 111) and do reflect the experimentally deteratop, A2 1.80 4.952 6.794 1.842 mined adsorption geometry for other fcc metal (1 11) faces such short bridge, S2 1.90 4.794 6.441 1.647 as AgI7 and Pd.I8 A recent diffuse LEED structural study of 2.00 4.8 I4 6.525 1.7 1 1 short bridge, S2', tilted 1 So hollow, HI 1.95 4.805 6.407 1.602 benzene on Pt(l1 1)19suggests the benzene adsorbs on a bridge atop, A2', tilted 15' 1.90 4.599 6.212 1.613 site with the same azimuthal orientation as predicted by our hollow, H2 2.00 4.302 5.619 1.317 calculations ( C z j + y ) . Anderson et aL3 have calculated the long bridge, L2 1.90 4.263 6.704 2.441 adsorption geometries for benzene on Pt( 11 1) and Ag( 1 11) and long bridge, L I 2.05 4.122 5 319 1.197 predict the C3u-ad geometry for Ag( 11 I), in agreement with the " All energies are given in electronvolts. E B= Eclu*lcr+rd\orbrle - (EcIuItcr conclusions of the experimental studies. The computational results + E,,d,urb.,lc), where E, is the total energy. HIn1 = Hclu\ter+rdwrbrtc- ( H C I U , ~ for the Pt( 1 11) surfaceindicate only a slight (0.07 eV) preference + H,l~rorb.nu). where H, is the electronic Huckel energy. E R ' "is~ the for the C3o4 geometry over the C2, geometry determined repulsion energy between the cluster and the adsorbate. experimentally. Unfortunately, there is no experimental information on the The only other molecular orbital calculations for benzene on orientation and/or site preference for benzene on the Ni( 100) Ni that we found in the literature were those by Myers and face. Our low-coverage prediction is in agreement with a Benzigers for three sites on the Ni( 100) face. Although our values for the binding energies are larger than those reported by Myers calculation of Myers and BenzigerSfor a hollow site. We obtained and Benziger, we do agree on the relative order of the three sites, a slight preference for the orientation along the [OlO] direction with the hollow site having the highest binding energy and the as they did. atop site as having the lowest binding energy. We find little The calculations predict that, of the three surfaces, chemidifference in the equilibrium perpendicular height above the sorption is strongest on Ni( 11 1) if the benzene is in the hollow surface for the three sites (1.9-2.0 A), whereas, Myers and site. It is desirable to try to relate this to experimental reactivity Benziger find as much as 0.4 A with the on-top site having the and desorption patterns. However, this comparison is complicated largest distance of 2.6 A. This difference probably arises from by the fact that on all three surfaces at low benzene coverages twosources. Myers et al. used different coefficients for the Slater much of the chemisorbed benzene decomposes below the deorbitalsand different orbital energies, chosen so that the calculated sorption temperature. Molecular desorption only occurs at high energies better match experiment but resulting in interactions at coverage, where repulsive lateral interactions between benzene larger distances than is reasonable. Second, Myers et al. did not molecules are very important. The importance of such lateral multiply the off-diagonal terms of the Huckel matrix by exp(interactions is apparent in the ARUPS experiments on Ni( 1 1 1)9 0.13Rl,), which also results in an optimization at longer bond and Ni(llO)', where the benzene molecules were found to lengths. Recently, a molecular mechanics calculation of benzene rearrange in order to minimize repulsions on the surfaces at high on Ni(ll0) was p~b1ished.l~However, the method proved coverage. We have tried to model the high-coverage case by insufficient to distinguish bonding geometries of the benzene putting two benzene molecules on a large cluster, at positions adsorbates. dictated by the observed LEED patterns. Thecalculated energies were simply the sum of two chemisorbed molecules; the interComparison with Experiment molecular repulsive terms calculated by the ASED calculation were not affected by the close benzene-benzene spacings. Huber et al.7-9have recently published two papers on benzene Experimentally, it was found that the benzene has the highest adsorbed on Ni( 110) and Ni(ll1) in which they used angledesorption temperature on the Ni(100) surface.I2 This is resolved ultraviolet photoelectron spectroscopy (ARUPS) to seemingly in contrast to our results, which would predict stronger extract information on the orientation of adsorbed benzene. For chemisorption on Ni( 1 1l), but can be understood in terms of Ni( 1lo), they determined that the orientation of the benzene steric crowding at high coverage. On the Ni( 11 1) and Ni( 110) molecule is coverage dependent. At low coverage, where a surfaces, the benzene adsorbates are more tightly packed than comparison with our calculations is most appropriate, the benzene on the Ni( 100) surface and, hence, repulsive lateral interactions is oriented parallel to the surface with the carbon-containing C2 dominate the desorption behavior and lower the desorption axispointingalong the [OOl] directionofthecrysta1,in agreement temperatures. Based on observed LEED patterns, the surface with our calculations. Our calculations indicate no stabilization area per benzene molecule is only 35.1 and 37.7 A2 on Ni( 110) upon tilting the benzene molecule 1 5 O , which is consistent with and Ni( 11l), respectively, but is 49.5 Az on Ni( lOO).'O This is recent experiments but not with earlier studies on Pd( 110) where the molecule was thought to be tilted about 10-20° into the consistent with bonding dominated by repulsive interactions on ~~
~~
The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 3803
Bonding of Benzene to Ni Surfaces
TABLE 111: Comparison of Theoretical Results for Benzene Adsorbed on Ni(ll1)' present authors site
-EB
height
hollow (hcp), HI,CJ,od hollow (fcc), H 1; Cl, bridge, B2, Cl,(x-x) bridge, BI, C2,(x-y) hollow (hcp), H2,C3, ", hollow (fcc), H2; C3, ", atop, A2 Ch' atop, A1
5.77 5.66 5.36 5.26 5.05 4.90 4.14 4.20
2.00 2.00 2.00 2.00 2.05 2.05 I .90 2.00
Anderson3 -E0
height
4.58 4.51 4.38 4.12
2.0 2.0 2.0 2.0
4.00 3.73 4.01
2.1 2.0 2.0
BenzigerJ -E0
Whitten"
height
0.705
2.2
0.860 0.622 0.871
2.4 2.4 2.5
0.415 0.674
2.5 2.5
height
-E0
1.2 1 .o 0.32 0.40 0.90
2.15 2.2 2.4 2.4 2.15
All binding energies, EB, in electronvolts and all heights in angstroms.
Ni(ll0) and Ni(ll1) at high coverages, but on Ni(100), the metal-adsorbate bonding plays a bigger role in the desorption behavior. Ni( 110) is apparently more reactive toward benzene decomposition than is Ni( 111).6.10A comparison of bonding plots (vide infra) suggests the reason for this. The benzene a orbitals are destablized relative to the gas phase on both surfaces, but more so on Ni( 110). The destabilization of the a orbitals suggests a reduction in the aromaticity of the benzene ring and hence a greater reactivity for decomposition. A reduction of aromaticity has been observed on other metal surfaces such as Rh,I9 where Kekule distortions have been observed.
Bonding Plots Mulliken overlap populations from extended Hiickel calculation have been widely used as means of investigating the bonding in molecules and have been extended to solids in the development of the COOP plots as discussed by Hoffmann.*O In the case of cluster calculations as reported in this paper, the Mulliken overlap populations provide information similar to the COOP plots for the solid. The MO bonding-antibonding plots (referred to as bonding plots) we use in this paper have been obtained by separately summing the positive (bonding) and negative (antibonding) off-diagonal A,, = c,*c,*S,, terms for each M O over the atomic orbitals of interest. The results of these separate sums provide information on the relative bonding and antibonding contributions to each M O and, from the relative magnitude of LA,,, an indication of the localization of the overall contribution (for example, a value of zero would be obtained for an atomic lone pair). Any pairs of atoms or orbitals can be examined and the contribution to the overall bonding can be determined. For clarity of plotting and interpretation, we have normalized the magnitude for each M O by multiplying both the bonding and antibonding contributions by a constant, C,where
Thus, for a nondegenerate M O the absolute height for all bonding and antibonding contributions would be equal to 1. In addition, each M O was broadened by a Gaussian of width 0.25 eV, which gives some indication of the solid-state broadening one would expect for very large clusters or an infinite solid calculation. From these plots, the relative bonding vs antibonding contribution to the molecular orbitals for the filled valenceorbitals and thevirtual orbitals for any combination of selected atomic orbitals can be easily visualized. The contribution from selected atomic orbitals can becompared to the result when all atomic orbital contributions are included for a surface. In addition, the bonding for selected atomic orbitals and energy position differences of the molecular orbitals for bonding to different surfaces can be identified. The disadvantage of the normalization is the loss of the information on the localized nature of the individual MO's, but this can be readily obtained from a comparison of the normalization values, C, for each MO.
4
n
%
v
x
E? al c
W
-2-1
0
1
2
3
Amp lit ude Figure 2. Bonding plots (see text): (a) gas-phase benzene, all atomic orbitalsincluded; (b) gas-phase benzeneonly C 2p,contributionconsidered (r-molecular orbitals); (c) benzene on Ni(l IO) most stable site; outer curve (light line) all atomic orbitals included, inner curve (bold line) only contributions from the atomic orbitals on benzene included; (d) benzene on Ni(l10) most stable site; outer curve (light line) all atomic orbitals included, inner curve (bold line) only C 2p: contribution considered (benzene r orbitals).
To aid in an understanding of the bonding plots for the cluster calculations, we discuss the plot for gas-phase benzene shown in Figure 2a. Although it would be more appropriate to use a single energy for each M O rather than a Gaussian function, we have used the Gaussian representation to aid in the later comparison with the cluster calculations. In the range from -10 to -30 eV are all of the filled valence molecular orbitals, and above -10 eV are two of the virtual orbitals. The lowest energy orbital (bottom of the Figure 2a) is the ring bonding orbital composed of the C 2s orbitals. This is the totally bonding, 2al,, orbital and the band representing this orbital extends only to the right, reflecting its total bonding character. The next orbital at 24 eV is the degenerate, 2el",orbital, which is predominantly bonding but does show some antibonding contribution. The method used for normalization leads to the doubly degenerate orbital having twice the height (sum of both the antibonding and bonding heights) of the nondegenerate orbital 2al,. Jumping over the next three orbitals, there are the five molecular orbitals in the range from -10 to -1 5 eV. Only four peaks are shown in this energy range, because the width of the Gaussian functions leads to an overlap in the five M O s . The first peak below -10 eV corresponds to the lelg,bonding a, orbital and the first band above -10 eV is the antibonding a* orbital as indicated by the extent to the left in the figure. By selecting the benzene atomic orbitals in the
3804
Grimm and Huntley
The Journal of Physical Chemistry, Vol. 97, No. 15. 1993 Ni( 1 10) Ni(1 11)
1
-10
-5
15
-
A
2
W
-25: -30 -2
, -1
6: 0
1
-25
1
2
Amplitude
-30
Figure 3. Bonding plot: comparison of benzene atomic orbitals for Ni( I IO) and Ni( l l l ) . Ermarks the top of the occupied molecular orbitals.
later plots for benzene-nickel cluster calculations, we will be able to observe how these orbitals are effected by the presence of the nickel surface. An example of atomic orbital selection for gasphase benzene is provided in Figure 2b. Here we have plotted only the contributions from the C 2p, atomic orbitals of benzene, which can only contribute to themolecular rorbitals. Comparison with Figure 2a readily identifies which of the molecular orbitals are A orbitals. Clearly, the first peak below -10 eV is a a orbital and the third peak has contributions from both a a orbital and a u orbital. To illustrate our use of the bonding plots for the cluster calculations we will discuss just a few of the many plots that we produced in our effort to better understand the bonding of the benzene adsorbate to the Ni clusters. In Figure 2c a bonding plot is presented for benzene on Ni(ll0) that includes all atomic orbitals, outer line. All of the occupied orbitals are shown and a line is drawn to show the energy position of the highest occupied MO, Ef.Only the virtual orbitals with energies below zero are shown. Around -10eV is theNid band, which has been truncated in order to better see the MO’s associated with the benzene adsorbate. This expansion of the plots also leads to truncation of the Ni 4p virtual orbitals around -5 eV. A comparison with Figure 2a for gaseous benzene confirms that the benzene orbitals are still discernible in the benzene/Ni( 110) complex. The differences in the benzene orbitals can be seen by comparing the inner curve (bold line) in Figure 2c, which shows only the benzene atomic orbitals for all MOs in the benzene/Ni( 110) complex, with Figure 2a. One aspect of the bonding that has received attention is the interaction of the a orbitals of the carbon ring with the Ni in the region of the Ni d band. This can be readily observed in our bonding plots as shown in Figure 2d. The inner curve (bold line) is for only the C 2pl orbitals and should be compared with Figure 2b to see the effect of the A interaction. One immediatelyobvious result is how the lelg,highest occupied A, orbitals now extend over a much larger energy range, having spread mostly to higher energies. The Ni cluster-benzene ring A interaction is easily identified by these bonding plots. In Figure 3 we illustrate theeffect ofdifferent surface structures on the bonding of the benzene adsorbate. The plot is for the benzene atomic orbitals for benzene adsorbed on the Ni( 11 1) surface for the most stable site and on the Ni( 1 10) surface, again for the most stable site. We see a difference in the region near E(,indicating mostly a difference in the benzene ring a-bonding interaction. Slight energy shifts for the two deepest valence orbitals are observed, but the middle orbitals are almost identical for the two surfaces. It is interesting that the energy positions
-2
0
-1
1
2
Amplitude Figure 4. Bonding plot: comparison of the benzene orbitals for two hollow site orientations on N i ( l 1 I). The dashed line represents the H I (c3{.,,d) site and the solid line is the H2 ( C J ~ , .site. ~~) 6
X
Ef
’
t .-ol
w 4 -
z E
3 -
0
P 10
.
“111) til(110) M(100) 0 M(ll1). *nd.rmn
20
30
40
50
60
Cluster Size(# Ni atoms)
Figure 5. Plot of binding energy vs cluster size for various sites and surfaces considered in this investigation. Solid circles show our calculated values. Line is drawn to aid in showing the trend toward a constant value above approximately 25 atom clusters.
of the deepest valence orbitals are more effected by the site than the middle valence region. Figure 4 illustrates another example of the utility of the bonding plots. The benzene occupied orbitals are shown for two different azimuthal orientations (H1 and H2) of benzene adsorbed on the hollow site on Ni( 111). These two orientations differ by 0.72 eV in calculated binding energy, due to both electronic and repulsive contributions. The energy difference between these two orientations can be viewed as a rotational energy barrier and as such seems too large. The difference in the repulsive energies between the two orientations accounts for about 25% of the calculated energy barrier. The bonding plots indicate that the major electronic differences are manifested in a shift in the lowest (primarily C 2s) orbital (40% of the barrier) and the rest in the redistribution of the benzene bonding with the Ni 3d orbitals. The C 2s shift, due to delocalization with the metal 4p orbitals (vide infra), is certainly overemphasized in these calculations, which accounts for both the large absolute energies and the large rotational barriers. The rotational barriers scale reasonably well with the binding energies, and range typically from 1 to 14% of the binding energies. These bonding plots are not limited to the extended Hiickel methods but are quite general and can be used with any of the one-electron methods which use a linear combination of atomic orbitals in the variation method with overlap. We have so far
Bonding of Benzene to Ni Surfaces
used them with CNDO, MNDO, and with simple Gaussian-90 ab initio STO wavefunctions. Effect of Cluster Size on Binding Energies The binding energy for benzene absorbed on different sized clusters and bonding sites is shown in Figure 5 . Clearly, the binding energy increases with cluster size but does appear to reach a maximum for very large clusters. The bonding plots indicate that this increase is due to the presence of the Ni 4p orbitals. The two lowest (deepest) energy valence MO’s shift 1-3 eV to lower energy when compared to gas-phase benzene (compare parts c and a of Figure 2). Additionally, the MO’s acquire antibonding character, which arises between C and the Ni surface. The energy shift is dependent on the size of the cluster and provides a lowering of the Hiickel electronic energy with cluster size due to the delocalization of the electrons into the Ni 4p orbitals of the cluster for these two lowest orbitals. This energy shift is clearly due to the Ni 4p orbitals as was determined by omitting them both from the calculation, producing no shift, and from bonding plots (not shown), that look at the Ni 4p orbitals. The effect of the delocalization on the energy position of the orbital does level out for clusters larger than about 25 Ni atoms, as might be expected as the perturbation of the adsorbate has less effect on Ni atoms far removed from benzene. The ASED calculations likely over emphasize the delocalization of electrons into the Ni cluster, which could explain the larger binding energies obtained from the calculations as compared to the experimental results.2’ The bonding picture provided by the ASED calculations is of a dual nature. The bonding plots in the region of the Ni d-band show that the benzene a orbitals interact with the Ni d orbitals over an extended energy range for all surfaces, with the major contributions at energies above the gas phase benzene a orbitals (destabilizing). However, the major contribution to the binding energy of the benzene to the Ni surface is provided by the lowering oftheenergyofthec 2sbondingringorbitalsduetodelocalization of electron density into the Ni 4p orbitals of the cluster, as discussed above. Thus, the ASED calculations would conclude that the major binding of benzene to the Ni surface is provided by the overlap of the C 2s orbitals of the benzene with the 4p orbitals of the Ni, which leads to a lowering of the energy of the lowest (deepest) valence MO’s. This unexpected shift in energy of the deeper valence M O s in benzene is confirmed by experiment22 and the shifts for C 2s orbitals have been discussed in the l i t e r a t ~ r e . ~The ~ - ~suggestion ~ was made that thelossof symmetry by the benzene in the presence of the surface could lead to the lowering of the energy of these valence orbitals. Model calculations for a Be surface were presented to support these suggestions.26 We have also done calculations on ethylene bonded to a single Ni atom with the Ni atom placed below the plane of the ethylene and centered between the C-C bond using the Gaussian-90 programs.27 These calculations, also, showed a lowering of these C 2s deep valence orbitals when compared to gas-phase ethylene. Without the experimental data confirming the lowering of these deeper valence orbitals, we would have been disposed to treating this delocalization bonding picture as being an artifact of the calculations. With this experimental confirmation and the reported ab initio results of Siegbahn,**which provide a bonding picture for Ni surfaces that confirm little bonding due to the Ni 3d orbitals, we have concluded that the ASED bonding picture is a realistic one within the one-electron approximation. The results show that in treating the bonding of adsorbates with the fourth period transition metals it is necessary to include the 4p orbitals of the transition metal in our frontier orbital picture, since they can interact strongly with the orbitals of the adsorbate. The extent of this interaction is dependent on the overlap between the transition-metal 4p and the orbitals of the adsorbate. In the case of the benzene-Ni cluster interactions,
The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 3805 at the Ni-C distances used, theoverlap matrixcontainsa relatively large matrix element for the C 2s-Ni 4p interactions, whereas the C 2p,-Ni 3d overlap is small. This relatively large overlap can compensate for the large energy separation of the C 2s-Ni 4p orbitals in the calculation of the interaction energy.
Suinmary The adsorption sites for benzene on Ni surfaces predicted by the ASED method generally agree with other calculations and experimental results. An exception to this is the adsorption of benzene on Ni( 11 l), where the experimental results9 disagree with the present and previously published calculations. The absolute values of the energies are much larger than experiment, but the structural parameters (height above the surface and prefered site) are quite reasonable. Cluster size effects were examined and found to be due to a delocalization of the C 2s orbital into theNi 4porbitals. Thisdelocalization alsocontributes to the large calculated binding energies. The use of the bonding plots has provided an intuitively satisfying method of visualizing bonding interactions. We conclude that, while limited in absolute accuracy, the ASED method does provide useful information on the expected structures and bonding of benzene to metal surfaces.
References and Notes ( I ) Anderson, A. B. J . Chem. Phys. 1975, 62, 1187. (2) Anderson, A. B.; Grimes, R. W.; Hong, Sung Y. J. Phys. Chem. 1987, 91, 4245. (3) Anderson, A. B.; McDevitt, M. R.; Urbach, F. L. Surf. Sri. 1984, 146, 80. (4) Myers, A. K.; Schoofs, G.R.; Benziger, J. 8. J . Phys. Chem. 1987. 91. 2230. (5) Myers, A. K.; Benziger, J. B. Langmuir 1987, 3, 414. (6) Huntley, D. R.; Jordan, J. L.; Grimm, F. A. J . Phys. Chem. 1992, 96. 1409. (7) Huber, W.; Weinelt, M.; Zebisch, P.; Steinruck. H.-P. Surf. Sci. 1991, 253, 72. (8) Ramsey,M.G.;Steinmiiller,D.;Netzer, F. P.;Schede,T.;Santaniello, A.; Lloyd, D. R. Surf. Sei. 1991, 251, 979. (9) Huber, W.; Zebisch, P.; Bornemann, T.; Steinriick, H.-P. Surf. Sci. 1991, 258, 16. (IO) Steinriick, H.-P.; Huber, W.; Pache, T.; Menzel, D. Surf. Sci. 1989, 218, 293. ( I I ) Huber, W.; Steinriick, H.-P.; Pache, T.; Menzel, D. Surf. Sei. 1989, 217, 103. (12) Blass, P. M.; Akhter, S.;White, J. M. Surf. Sei.1987, 191, 406. (13) Jing, Z.; Whitten, J. L. Surf. Sci. 1991, 250, 147. (14) Fox, R.; Rosch, N . Surf. Sei. 1991, 256, 159. ( 1 5) Netzer, F. P.; Rangelov, G.; Rosina, G.; Saalfeld, H. B.; Neumann, M.; Lloyd, D. R. Phys. Rev. B 1988, 37, 10399. (16) Radonovich, L. J.; Koch, F. S.; Albright, T. A. Inorg. Chem. 1980, 19, 3373. (17) Dudde, R.; Frank, K.-H.; Koch, E.-E. Surf. Sei. 1991, 225, 267. (18) Ohtani, H.; Bent, B. E.; Mate, C. M.; van Hove, M.A.; Somorjai, G. A. Appl. Surf. 1988, 33/34, 254. (19) Wander, A.; Held, G.; Hwang, R. Q.;Blackman, G. S.; Xu,M. L.; de Andres, P.; van Hove, M. A.; Somorjai, G. A. Surf. Sci. 1991, 249, 21. (20) Hoffman, R. Solids and Surfaces: A Chemist’s View of Bonding in Extended Structure; VCH Publishers, Inc.: New York, 1988. (21) For a comparison of experimental and theoretical binding energies,
see, for example, the article by: Shustrorovich, E. In Advances in Catalysis; Eley, D., Pines, H., Weisz, P., Eds.; Academic Press, Inc.: New York, 1990; Vol. 37, pp 151-155. (22) Demuth, J. E. Phys. Rev. Lett. 1978, 40, 409. (23) Rhodin, T. N.; Gadzuk, J . W. Electron Spectroscopy and Surface Chemical Bonding. In The Nature of the Surface Chemical Bond, editors T. N. Rhodin, T. N., Ertl, G.,Eds.; North Holland Publishing Company: New York, 1979, 1981; Chapter 3. (24) Demuth, J . E.; Eastman, D. E. Phys. Rev. 1976, 813, 1523. (25) BrodCn, G.; Rhodin, T. N. Chem. Phys. Leu. 1976, 40. 247. (26) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971. 54, 724. (27) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foreman, J. 9.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A,; Binkley, J. S.; Gonzales, C.;
Defrees, D. J.; Fox, D. J.; Whiteside, R. A,; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Steward, J. J . P.; Topiol, S.; Pople, J. A. Gaussian 90; Gaussian, Inc.: Pittsburgh, PA, 1990. (28) Siegbahn. P. E. M.; Wah1gren.U. Cluster ModelingofChemisorption Energetics. In Metal Surface Reaction Energetics; Theory and Applications to Heterogeneous Catalysis, Chemisorption, and Surface Diffusion; Shustorovich, E.. Ed.; VCH Publishers, lnc.: New York, 1991; Chapter 1.
