3024
J . Phys. Chem. 1988, 92, 3024-3028
Cluster Approach to Structure of Surfaces and Chemisorption D. E. Ellis,* J. Guo, and H. P. Cheng Department of Chemistry and Materials Research Center, Northwestern University, Euanston, Illinois 60201 (Received: July 14, 1987; In Final Form: November 1 1 , 1987)
The electronic structure of small transition-metal particles is studied in the local density approximation, using a discrete variational method for solving the self-consistent field equations. Both free particles and clusters embedded in a medium representative of an (hkl) face of an infinite crystal are described. Binding energies are calculated by means of the statistical total energy expression and used to study equilibrium geometries and fragments of the interatomic potential surface. Molecular dynamics techniques employing the embedded atom scheme are used to couple classical theory to the electronic densities derived from first principles. Surface relaxation and reconstruction of Ni (hkl) crystal faces are described in this approach. The approach and interaction of C,H2 with free Ni particles and simulated surfaces are described in the self-consistent framework.
I. Introduction The idea of using clusters to model chemisorption processes relies on assumptions about the locality of chemical bonding interactions. Fortunately, the wealth of new experimental data generated in molecular beam devices provides opportunities to compare cluster-admolecule and surface-admolecule properties. First-principle theoretical models can be helpful in exploring similarities and differences between finite cluster and (semi)infinite surface environments. Much of the work done to date has been performed by selfconsistent single-particle approaches, especially in the local density (LD) framework. Such static electronic structure methods can provide relative binding energies of competing sites and give some hints about dissociation and recombination pathways. However, we believe that some combination of dynamical and static approaches is needed in order to provide realistic descriptions of finite-temperature phenomena. In this paper we describe progress in using LD theory to generate descriptions of bonding and cohesion in the transition metal and transition metal-hydrocarbon systems and in using LD results as input to molecular dynamics simulations of surface properties. The self-consistent local density discrete variational (DV-Xa) method’-3 with the Kohn-Sham value a = 2 / 3 for exchangecorrelation potentials is used in ground-state electronic structure calculations. The embedded-cluster approach’ is used in surface simulations. The self-consistent charge (SCC) procedure employing Mulliken population analysis4 and the more accurate least-squares self-consistent multipolar (SCM) approximation to the cluster potentials5 are used. The variational basis functions can be optimized as part of the iteration procedure. At first a S C F potential is calculated with a basis set of conventional atomic orbitals. Then, the potential is spherically averaged around each atom out to some radius R , where it is matched to a parabolic potential. Finally, new basis functions are generated from this “atom in a well” potential and the procedure can be iterated several times. The object of this procedure is to produce, for a fixed basis set size, an optimal discription of the occupied states. It was found that the optimized near-minimal basis functions give better results than the conventional ”atom in a well” bases using the SCC configuration in the binding energy calculations of Ni clusters.6 Bader’s topological density analysis scheme’ is used to explore bond linkages and the structure of “deformed atoms” within the cluster and their interaction with an adatom and molecules. ( I ) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (2) Rosdn, A.; Ellis, D. E.; Adachi, H.; Averill, F. W. J . Chem. Phys. 1976, 65, 3629. Ellis, D. E.; Painter, G. S. Phys. Rev. B: SolidStute 1970, 2, 2887. (3) Ellis, D. E.; Benesh, G. A,; Byrom, E. J . Appl. Phys. 1978, 49, 1543. Phys. Rev. B Condens. Mutter 1979, 20, 1198. Gubanov, V.A,; Ivanovsky, A. L.; Shveikin, G. P.; Ellis, D. E.; J. Phys. Chem. Solids 1984, 45, 719. (4) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1833. 1955, 23, 1841. (5) Delley, B.; Ellis, D. E.J . Chem. Phys. 1982, 76, 1949. (6) Guo, J.; Ellis, D. E., unpublished work. (7) Bader, R. F. W. Ace. Chem. Res. 1985, 18, 9 .
Properties of a Ni tetrahedron cluster and its interaction with H, are reported elsewhere.* A topological atom is defined by a subsystem bounded by surfaces satisfying z.ap = 0
(1)
Critical points (cp) are points where
=0 (2) They are classified further by (a,b), where a is the number of nonzero curvatures and b is the sum of their signs. For example, a (3,-1) cp has two negative curvatures and one positive curvature. A bond line is the line defined by two and only two gradient paths that originate at a (3,-1) cp. Each terminates at one of the neighboring nuclei. A bond line exists only between atoms sharing a common surface. Although the structure of hydrocarbons and simple molecules has been analyzed extensively by using this approach, metal-metal and metal-ligand bonds have not previously been explored. Atomic bindtig energies are calculated in the LD framework from the statistical total energy expression9 ap
(3) where the first term is the sum of single-particle energies, the second contains electronic Coulombic and exchange-correlation corrections, and the last term is the nuclear-nuclear repulsion energy. Details of the computational procedure we use are given in ref 9. 11. Results and Discussion A . Isolated Ni Clusters. Binding energy curves for isolated
planar Ni, ( n = 2, 3, 4, 7) clusters with respect to the nearestneighbor distance are given in Figure 1. These geometries were chosen with surface simulation in mind and will not in general be the lowest energy configurations of the free molecules. The Ni, dimer is of Dmhsymmetry, Ni, of D3*symmetry, Ni4 of D4h symmetry, and Ni, of D6h symmetry, each with a single parameter, the nearest-neighbor distance. In accordance with expectations, we found that dissociation energy per atom increases with the number of Ni atoms, and the bond length generally relaxes with increasing cluster size. The binding energy curve of the Ni dimer is sensitive to the choice of basis functions. In principle, we should optimize the bases in each internuclear distance; however, curve a in Figure 1 was calculated by using basis functions ls-4d5s optimized at a bond length of 4.16 au. The optimized basis functions for N i j at a separation of 4.02 au were used in the rest of the calculations. (8) Guo, J.; Ellis, D. E.; Bader, R. F. W.; Macdougall, P. J., manuscript in preparation. (9) Delley, B.; Ellis, D. E.; Freeman, A. J.; Baerends, E. J.; Post, D. Phys. ReL: E : Condens. Mutfer 1983, 27, 2132.
0022-3654/88/2092-3024$01.50/00 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988 3025
Structure of Surfaces and Chemisorption 0.00 A
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Under the SCC procedure with ls2s2p frozen core orbitals, our calculated bond lengths are 3.96, 4.19,4.04, and 4.31 au for Ni2, Ni3, Ni4, and Ni,, respectively. The corresponding dissociation energies per atom are 1.OO,1.47, 1.55, and 2.22 eV. The available experimental equilibrium bond lengths are 4.16 au for Ni2loand 4.71 au for bulk." The experimental dissociation energies per atom are 1.0 eV for Ni210923 and 4.44 eV for bulk.I2 Ni clusters have been studied by a variety of methods, for example, the semiempirical molecular orbital (MO) technique^,'^^'^ LD and X a methods,15-21and ab initio methods.22-26 Basch et a1.,22using the Hartree-Fock (HF) method, found a range of dissociation energies per atom for Ni, of 0.3-0.7 eV, much less than experimental values and typically 30% of what we found here. We do bear in mind that LD tends to produce overbinding, and we interpret our results primarily by comparing one system with another. Charge and spin density contour diagrams and charge density gradient V p of the Ni3 cluster are given in Figure 2a-c. The C3, reflection plane, perpendicular to the cluster, containing one Ni atom, and bisecting the opposite bond, is chosen for plotting. Here the bond length of bulk Ni appropriate for (1 1 1) surface simu~
(10) Morse, M. D.; Hansen, G. P.; Langridge-Smith, P. R. R.; Zheng, L . 4 . ; Geusic, M. E.; Michalopoulos, D. L.; Smalley, R. E. J . Chem. Phys. 1984, 80, 5400. (1 1) Donohue, J. The Structures of the Elements; Wiley-Interscience: New York, 1974. (12) Weltner, W., Jr.; Van Zee, R. J. Annu. Rev. Phys. Chem. 1984, 35, 291. (13) (a) Anderson, B. J . Chem. Phys. 1976,64,4046. (b) 1977,66, 5108. (14) Blyholder, G. Surf. Sci. 1974, 42, 249. (15) Snijders, J. G.; Baerends, E. J. Mol. Phys. 1977, 33, 1651. (16) Harris, J.; Jones, R. 0. J . Chem. Phys. 1979, 70, 1874. (17) Dunlap, B. I.; Yu, H. L. Chem. Phys. L e f f .1980, 73, 525. (18) Rosch, N . ; Rhodin, T. N. Phys. Rev. Left. 1974, 32, 1189. Rosch, N.; Menzel, D. Chem. Phys. 1976, 13, 243. (1 9) Messmer, R. P.; Knudson, S. K.; Johnson, K. H.; Diamond, J. B.; Yang, C. Y . Phys. Rev. B Solid State 1976, 13, 1396. (20) Messmer, R. P.; Salahub, D. R.; Johnson, K. H.; Yang, C. Y. Chem. Phys. Leu. 1977, 51, 84. (21) Raatz, F.; Salahub, D. R. Surf. Sci. 1986, 171, 219. (22) Basch, H.; Newton, M. D.; Moskowitz, J. W. J . Chem. Phys. 1980, 73, 4492. (23) Noell, J. 0.;Newton, M. D.; Hay, P. J.; Martin, R. L.; Bobrowicz, F. W. J. Chem. Phys. 1980, 73, 2360. (24) Shim, 1.; Dahl, J. P.;Johansen, H. Int. J . Quantum Chem. 1979,15, 311. (25) Upton, T. H.; Goddard, W. A., 111 J . Am. Chem. SOC.1978, 100, 5659. (26) Melius, C. F.; Moskowitz, J. W.; Mortola, A. P.; Baillie, M. B.; Patner, M. A. Surf. Sci. 1976, 59, 279.
lations is used. In Figure 2a, the left loop is the cross section of the Ni-Ni bond between two Ni atoms off the plane, showing the charge accumulation along the bond. In Figure 2b, positive spin density mainly from Ni 3d orbitals is localized around the Ni nucleus and the small negative spin density from Ni 4s, 4p orbitals appears around the bonding region and away from the cluster plane. In Figure 2c, point A where the gradient lines originate is a (3,-1) critical point. The bond line is perpendicular to the plane. Point B is a (3,+1) cp and a local maximum of the charge density along the vertical line on the plane. B. Ni, Embedded in a Ni (111) Surface. The Ni (1 11) surface is simulated by embedding the Ni, triangular cluster in the potential field of the surrounding semiinfinite crysta1.j The host atoms are fixed at the experimental bulk distance. The cluster binding energy curve for relaxation with respect to the isolated case, under the influence of the surrounding crystal potential, was calculated. It was found, as expected, that the equilibrium bond length relaxed to a value near the bulk value as compared with the isolated case. Charge and spin density contour diagrams of the simulated Ni (1 1 1) surface on the same plane as the previously displayed for isolated Ni3 case are shown in Figure 2d,e. The Ni atom on the surface layer at the right side belongs to the cluster; the other four atoms shown are host atoms. The charge density near the (1 11) surface around the cluster Ni atom is nearly the same as the isolated Ni3 case, but the positive spin density is less localized. From the partial density of states, it was found that the splitting between positive and negative spin states, mainly from 3d, 4s orbitals, increases by 0.5 eV, with the positive spin states moving down 0.5 eV with respect to the Fermi level, as compared with the isolated case. Our calculated magnetization (nt - ni) is 2 for the embedded Ni3 triangular site, giving a surface atom magnetic moment of 0.67 pB on the simulated (1 1 1) surface. Wimmer and Freeman:' by solving the LD equations on a seven-layer Ni (001) film using the full-potential linearized-augmented plane wave method, found a surface atom magnetic moment of 0.68 K~ which is enhanced by almost 20% compared with the bulklike atoms in the interior of the film. C. Chemisorption ofCzH2on a Ni (11 1 ) Surface. Our purpose in applying the LD theory to hydrocarbon adsorption on metals is to determine the chemical nature, the location relative to the surface, and the geometry of the adsorbed species. We hope to obtaine a fundamental understanding of the properties of different metals and different exposed sites with respect to their activities for scission or rearrangement of C-C and C-H bonds. This may provide a better knowledge of processes in heterogeneous catalysis.28 The adsorption of C2H2 on nickel has been studied widely. Early works on well-defined surfaces were reported about 10 years ag0.29-31 More extensive data are now available concerning the (1 11) surface, with which we are now concerned. Up to 300 K, at low exposures, associative adsorption of C2H, is found. Information useful in constructing structural models for the geometry of adsorbed CzH2has been obtained by ultraviolet photoelectron spectroscopy (UPS)32-36and electron energy loss spectroscopy (ELS).37-39By examining the separation of 20" and 30, levels (27) Wimmer, E.; Freeman, A. J.; Krakauer, H. Phys. Rev. B Condens. Mutter 1984, 30, 3 1 13. (28) Bertolini, J. C.; Massardier, J. In The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, 3B; King, D. A,, Woodruff, D. P., Eds.; Elsevier: New York, 1984; p 106. (29) Whalley, L.; Davis, B. J.; Moss, R. L. Trans. Faraday SOC.1970, 66, 3143. 1971, 67, 2445. (30) Dalmai-Imelik, G.; Bertolini, J. C. C.R . Seances Acad. Sci., Ser. A. 1970, 270, 1079. (31) Ertl, G. Chem.-Ing. Tech. 1969, 41, 289. (32) Demuth, J. E.; Eastman, D. E. Phys. Rev. Lett. 1974.32, 1123. Phys. Rev.B: Solid State 1976, 13, 1523. (33) Demuth, J. E. Chem. Phys. Lett. 1977, 45, 12. (34) Demuth, J. E. Int. Vac. Congr., 7th, 1977, 779. (35) Demuth, J. E. Surf. Sci. 1979, 84, 315. (36) Demuth, J. E. Phys. Rev.Lett. 1978, 40, 409. (37) Bertolini, J. C.; Massardier, J.; Dalmai-Imelik, G . J . Chem. Soc., Faraday Trans. 1 1978, 74, 1720.
3026 The Journal of Physical Chemistry, Vol. 92, No. 11, I988 co>
Ellis et al. cc>
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Figure 2. (a) Charge, (b) spin density contour diagrams, and (c) charge density gradient V p of the N i j cluster on the C,, reflection plane. (d) and (e) are the corresponding charge and spin density contour diagrams on the same plane for the Ni (1 11) surface. The atom at the right on the surface layer is one of the cluster atoms; the remaining ones are host atoms. The units of charge and spin densities are 1.0 X lo-' and 1.6 X lo4 au, respectively. The adjacent contours differ by 0.005 au in (a, d) and by a factor of 2 in (b, e). Dashed lines represent negative values of spin density.
in gas-phase and adsorbed molecules, Demuth proposed a weakly distorted geometry.34 On the other hand, the ELS data were interpreted in terms of a strongly coupled Ni,CzH2 surface comp l e ~ Among . ~ ~ these and others surface sites and geometries which have been proposed, we have chosen to examine first thetriangular strongly coupled site discussed by Bertolini and R o u ~ s e a u . ~ * In order to establish reference energies for comparison with surface studies, we calculated binding energies for the free molecule at different geometries. The atomic binding energy curve of an isolated linear CzH2was calculated, with the C-H bond length fixed at the value of 2.04 au.& Under the SCM procedure with 1s-3d numerical atomic basis functions for both C and H, our calculated dissociation energy is 17.87 eV and the equilibrium C-C bond length is 2.27 au. The Hartree-Fock calculation of Krishnan and co-workers using a 6-31 1G** basis set, including the second-order Maller-Plesset perturbation corrections, found the dissociation energy of 16.91 eV (390.0 kcal/mol), the C-C bond length of 2.300 au, and the C-H bond length of 2.01 1 au.43 The experimental dissociation energy is 17.53 eV (404.3 kcal/ mol)," and the C-C bond length is 2.268 au.40-4zOur calculated dissociation energies for C-C-H angles of 165O, 155O, and 145' are 17.76, 17.66, and 17.44 eV, respectively. Here the C-C and C-H bond lengths are fixed at the calculated equilibrium values. Binding energy curves of the adsorption of C2H2on a Ni (1 11) surface were calculated for a number of distances and angles. Here the SCC procedure was used with basis functions of the Ni 1s-4p (1s-3s frozen) optimized in Ni,, C ls-3p, and H 1s-2p (38) Bertolini, J. C.; Rousseau, J. Sur5 Sci. 1979, 83, 131. (39) Demuth, J. E.; Ibach, H . Surf. Sci. 1979, 89, 467. (40) Wingrove, A. S.; Caret, R. L. Organic Chemistry; Harper & Row: New York, 1981; p 39. (41) Plyler, E. H.; Tidwell, E. D. J . Opr. SOC.Am. 1963, 53, 589. (42) Lafferty, W. J.; Thibault, R. J. J . Mol. Spectrosc. 1964, 14, 19. (43) Krishnan, R.; Binkley, J. S . ; Seeger, R.; Pople, J. A. J . Chem. Phys. 1980, 72, 650. (44) Table VI1 in ref 43.
n
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Figure 3. A typical strongly coupled adsorption configuration for C2H2 on the triangular site of a N i (111) surface. The molecular plane is parallel to the surface and 3.20 au above the surface. The C-C bond length is relaxed to 2.86 au and the C-C-H angle is 155'.
orbitals. Here the C and H orbitals are generated from the usual "atom in a well" potentials. The CzH, plane is held parallel to the surface. Reflection symmetry through a plane which is perpendicular to the surface and bisecting the C-C bond is maintained. The C-H bond length is fixed a t the value of 2.04 au, and a family of curves is generated by varying the C-C bond length with height as
Rcc = 2.27
+ k/h
(4)
where k is a parameter and h is the height of the molecule above the surface. The C-C-H angle is varied at each height. A typical strongly coupled adsorption configuration is shown in Figure 3, where k = 1.9, h = 3.20 au, the C-C-H angle is 155O, and the dissociation energy is 3.5 eV relative to the one when h m. Consistent with experiment, associative adsorption of C2Hzon a Ni (1 11) surface is found, at least for the range of the geometries considered. The calculated charge and spin density contour diagrams for the configuration shown in Figure 3 are given in Figure 4a-f for
-
Structure of Surfaces and Chemisorption
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988 3027 Cb>
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1 7 Figure 4. (a-c) Charge and (d-f) spin density contour diagrams for the adsorption configuration shown in Figure 3 . The plane for (a) is the same as the one in Figure 2d. The plane for (b) is the Ni (1 11) surface, and the one for (c) is the CzHzmolecular plane. The units are the same as those in Figure 2. The adjacent contours differ by 0.005 au in (a, b), by 0.020 au in (c), and by a factor of 2 in (d-f). Dashed lines represent negative values of spin density
three different planes. In Figure 4a the loop at the top is the C-C bond cross section; charge accumulates between Ni atoms on the surface and the C-C bond. Upon adsorption the C2H2becomes polarized, with positive spin density appearing at the cross section of the C-C bond as shown in Figure 4d the negative spin density occurs on the molecule plane as shown in Figure 4f. The charge density on the molecule plane as shown in Figure 4c is similar to the isolated case except that the molecule receives 0.4 e charge from the surface Ni atoms by the Mulliken population analysis. In Figure 4b the three marked Ni atoms on the top are the cluster atoms and the rest are host atoms. In Figure 4e the spin density around the two Ni atoms on the bottom of the triangular cluster site, which is close to C2H2,is smaller than that around the top one. As in a previous study on the C O a d ~ o r p t i o nwe , ~ ~find the local metal magnetic moment is reduced by forming bonds to diamagnetic ligands. From the Mulliken population analysis, we also found that the adsorption of C2H2on the Ni surface reduces the spin of Ni atoms on the surface and the Ni atoms closer to the molecule lose more spin. Details of our results will be published el~where.~~ (45) Holland, G. F.; Ellis, D. E.; Trogler, W. C. J . Chem. Phys. 1985, 83, 3507.
D . Surface Relaxation and Effective Potentials. The semiempirical embedded atom method (EAM) has been used in molecular dynamics (MD) simulations of fcc nickel low-index surfaces. The use of a MD scheme permits a uniform treatment of both static (equilibrium) and thermal properties. The first step of our research program, reported here, is to construct effective potentials and to test their validity on the experimentally wellcharacterized nickel surfaces. The total potential energy is written as
where ph,i is the “host” electron charge density at the atom site i and c&(ril) is the “core-core” two-body interaction. In the EAM Fi(p) is a characteristic function of the atomic number 2 and independent of details of the environment. The many-body interactions are included in the embedding energy F(p,Z) which can be determined by (i) jellium model appr~ximation,~’ (ii) empirical fitting to experimental data,48and (iii) first-principle (46) Guo, J.; Ellis, D.E., work in preparation. (47) Stott, M. J.; Zaremba, E. Phys. Rev. B: Condens. Mutter 1980, 22, 1564.
3028 The Journal of Physical Chemistry, Vol, 92, No. 11, 1988 1 .E
inf:nite distance. In our simulation E is derived from the energy difference between bulk energy and film. The results are 2805 erg/cm2 for (loo), 8745 erg/cm2 for (1 10) and 1200 erg/cm2 for (1 1 1 ) surfaces, compared to the experimental average value of 2380 erg/cm for the three surface^.^' It is remarkable such a simple model potential is capable of reproducing both bulk and surface properties. A second major goal is to develop effective potentials for alloy and impurity systems; some work has already been done in this area.53 We are particularly interested in structural materials and magnetic alloys such as the heterogeneous system Ni-Fe. One of the unresolved problems is the choice of proper two-body interaction. Let 4 A B represent the pair potentials for a multicomponent system. In previous works, these were sometimes taken as algebraic or geometric means of the pure material potentials
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Figure 5. Surface relaxation obtained by molecular dynamics simulations on (a) Ni (loo), (b) Ni (1 lo), and (c) Ni (1 11). The horizontal axis represents positions of layers in a finite-thicknessfilm; the vertical axis gives percentage deviation from the bulk value.
calculations. We will discuss results obtained via (ii) and new potentials obtained via (iii) in the following section. In the MD method we used,49metal atoms are considered as Newtonian particles in a variable size and shape "box". Such a box is made periodic to cover the entire space. At each time step the positions (X,,Y,,Z,) and velocities (V,,,V,,[,V,,)are evaluated by using Lagrangian equations of motion, generated from L=T-U with T equal to kinetic energy and U given in eq 5. We first adopted the model potential of Daw et aLso and found that the simulation reproduces bulk sublimation energy and lattice constant satisfactorily. We next applied this model to studies of surface relaxation and reconstruction of Ni (loo), (1 lo), and ( 1 11) surfaces, using a unit cell of 992 atoms in 31 layers. We found very little evidence for reconstruction, consistent with experimental reports on nickel low-index surfaces. Figure 5 shows the oscillatory relaxation of interlayer spacing. The (110) surface has a 3.5% contraction with respect to bulk spacing for the first layer, with the second layer expansion of 0.1%. This compares well with the experimental results of 4 4 . 7 % and 2.3%.51 The relaxation of the other two surfaces considered, (100) and (1 1 l), is very small as is also consistent with experiments. The slight systematic shift calculated for interlayer spacing is found to be due to finite film thickness effects in our model. We also calculated the surface energy E which is defined as the energy per unit area needed to separate two half-crystals to (48) Daw,M.S.; Baskes, M. I. Phys. Rev. B: Condens. Matter 1983, 29, 6443. (49) Cheng, H . P.; Dutta, P.; Ellis, D.E.; Kalia, R.J . Chem. Phys. 1986. 85, 2232. (50) Foil, S. M.; Baskes, M. I.; Daw,M.S . Phys. Rev. B Condens. Mutter 1986, 33, 7983. (51) Adams, D. L.; Peterson, L. E.; Sorensen, C. S. J . Phys. C 1985, 18, 1753.
where dLD is the dimer interaction from LD calculations and @em is the empirical potential. With the suitable empirical 4 and F A ( p ) for element A, one can obtain the pair interactions of A-B and B-B by eq 6, and it remains to determine F B ( p ) for element B. In the literature F(p) and cp are both found by fitting to experiment. However, F(p) can also be derived from the empirical universality relation of transition metalss4 E ( a ) = E(a,)(l
+ a*)e-"*
a* = ( u / u , - ~ ) / ( E ( U , ) / ~ B Q ) ' / ~
(7)
where a. is the lattice constant at 0 K, B the bulk modulus, Q the volume of the crystal cell, and E(a) the crystal sublimation energy as a function of lattice constant. E(a) should be equal to the total potential energy defined by eq 5, that is
and F,(p)can thus be determined. By following the above analysis, we extracted a model &+Fe as well as dFe-Feand FFe(p). These potentials are being used to simulate diffusion, segregation, and impurity motion in a nickel host. 111. Conclusions In this brief paper we have reported our progress in applying LD theory under the cluster approach to study the Ni clusters, the simulated surfaces, and adsorption of C2H2on a Ni (1 11) surface and in using LD results as input to molecular dynamics simulations of surface properties. Our calculated results yield interesting information about these complex systems and compare well with available experimental ones and other accurate theoretical calculations. Our approach is also feasible and seems to be reliable to generate the energy surfaces for adsorption of molecules on metal surfaces and to study the finite-temperature phenomena by coupling with the M D methods. (52) Blakely, W. R.; Somorjai, G. A. Sur. Sci. 1977, 62, 267. (53) Foiles, S. M. Phys. Rev. 5: Condens. Matter 1985, 32, 7685. (54) Rose, J. H.; Smith, J. R.: Guinea, F.; Ferrante, J. Phys. Rec. 5: Condens. Matter 1984, 29, 2963.
