Calculation of the Electronic Structure of Ethylene Bonded to Diatomic Nickel and Correlation with Ni-C, H, Photo-Emis- sion Data* BY N. R~SCH AND T. N. RHODIN School of Applied and Engineering Physics, CorneIl University, Ithaca, N.Y. 14850 Receiued 30th May, 1974 The electronic structure of a model “ surface complex ” consisting of a Ni-diatom and an ethylene molecule has been calculated using the SCF-Xa scattered-wave method. Comparison of calculated n-orbital bonding shifts with recent photoemission spectra for chemisorption of ethylene of nickel favours a n-bonded over a o-diadsorbed complex. Charge distributions of various molecular orbitals indicate that the C-C double-bond is weakened more for the latter molecular arrangement suggesting such a complex as a likely intermediate in heterogeneous reactions.Reliable microscopic information on the interaction of transition metals with unsaturated hydrocarbons is becoming available. 9 Photoemission (UPS) studies of acetylene, ethylene and benzene chemisorbed on a Ni( 1 1 ])-surface have yielded the first direct observation of n-d bonding. Using the self-consistent field-Xa scattered wave (Xa-SW) m e t h ~ d , ~ a reasonably accurate calculation of the electronic structure of Zeise’s anion and especially of the Pt-ethylene bond has been given re~ently.~ We report here the first Xu-SW calculations for a Ni-ethylene ‘‘ surface complex”.’ They were undertaken in order to provide an additional test for the local bonding approach to chemisorption,6 to gain further information on the electronic structure of a chemisorbed ethylene molecule, and possibly to extract information from the photo-emission spectrum on the geometry of the “ surface complex ”.that ethylene (C,H,) binds to transition-metals through an interaction of its n electrons with the metal d-electrons. However, the geometry of the chemisorbed ethylene (neglecting for the moment possible dehydro- genation etc. after chemisorption) relative to the surface atoms is controversial. One assumption is that ethylene forms a n-complex coordinating symmetrically to a single metal atom, as suggested by Dewar 7* and found in many organometallic complexes. From various surface reactions 9 9 O and from infrared-spectra of ethyl- ene chemisorbed on silica-supported Ni,’ it has been concluded, however, that each of the two carbon atoms forms a o-bond to a different metal atom.As a model for the “surface complex” we choose a Ni-diatom with a bond length of 2.492A (4.709 a.u.) equal to the nearest neighbour distance in bulk Ni and an ethylene molecule with equilibrium geometry. Corresponding to the two possible bonding schemes, two different geometrical arrangements have been studied. In the complex representing the a-diadsorbed ethylene, the Ni-Ni bond has been taken parallel to the plane of the ethylene molecule ; in the n-complex the N i N i bond was * Supported by NSF Grant GH-31909, and by the Advanced Research Projects Agency through the Cornell Materials Science Centre. -f permanent address : Lehrstuhl fur Theoretische Chemie, Technische Universitat, Miinchen.West Germany. It is commonly accepted 7* 28N. ROSCH AND T. N. RHODIN 29 arranged perpendicular to that plane and symmetric to the C-C bond. Both model complexes exhibit Cz, symmetry. The distance of chemisorbed ethylene to the metal surface is unknown. Guided by the sum of covalent radii and by distances found in X-ray (1.9-2.2 A) crystallo- graphic studies of Ni-olefin complexes, a value of 2.0A was chosen for the distance between the two parallel bonds in the di-o-complex and for the distance from the bonding Ni atom to the centre of the C-C bond in the n-complex. (According to previous X-a calculations the results should not be sensitive to small changes in this distance.) The radii of the muffin tin spheres surrounding the various Ni atoms were chosen to be half the Ni-Ni bond length.For ethylene we have used the over- lapping sphere parameterization ' (parameter set D of ref. (12) with rout = 4.828 a.u. ; n-complex: rout = 6.283 a.u.). The atomic exchange parameters a for carbon and FIG. 1.-SCF-Xa-SW electronic energy levels for the model complex Niz-C2H4 : 7r-complex (" r ") against di-o-complex (" di-a "). Also shown are the Xot-SW levels of Niz and CzH4. The levels are filled up to the Fermi level Ef, marked by a dashed line. Other levels (not shown) are not involved in the metal-ethylene binding. hydrogen were taken from spin-polarized atomic calculations,' the U-value for nickel was taken from the tabulation by Schwarz.13 The a-values for the inter- atomic and the extramolecular region were set equal and taken as the weighted average over the atomic a values, where ethylene was given the same weight as one Ni atom.4 The core charges corresponding to the configurations C ls2 and Ni ls22p6 as determined from atomic calculations were included but kept fixed during the SCF cycle^.^ The remaining 48 electrons were fully taken into account in the iterations to self-consistency according to the usual Xa-SW procedure.3p30 BONDING OF ETHYLENE TO DIATOMIC NICKEL The resulting Xa-SW ground-state orbital energies for the two geometries are compared in fig.1. Only low-lying unoccupied and the valence-type orbitals with energies above -0.7 Ry are shown. The levels are labelled according to the irreduc- ible representations of the point group C2v and filled as marked up to the Fermi level, Ef. Also shown in fig.1 are the Xa-SW energy levels of Ni2 l4 and C2H4 l2 which fall in the displayed range; for ethylene these are the n- and +-level bSu and b2g, respectively, and the highest a-level bSg. To discuss and compare the bonding in the two model complexes we make use of the orbital charge distributions as obtained from the SCF-Xu-SW calculations as well as of contour plots of the individual orbitals (some typical ones are indicated in fig. 2 and 3). Thereby a clear assignment of the levels to the two components of each model complex is possible. The levels between -0.3 and -0.4 Ry correspond to the Ni diatom and represent the Ni d-band. They undergo some mixing and a slight upward shift due to the interaction with the ethylene.This parallels a reduction of the Ni work function A+ = -0.9 eV found after chemisorytion of ethy1ene.l Taking the differences of the highest occupied Xcc-SW orbital energies in each model complex and Ni2, we find A& = -0.60 eV in the n-complex and = -0.90 eV in the di-a-complex. The ethylene remains mostly unchanged in both complexes as can be inferred from the charge distributions of the corresponding orbitals. This is consistent with experi- mental informati~n,~. especially with the structure of the photo-emission peaks corresponding to a-1evels.l The only level found to interact strongly is the n-level b3*, again consistent with the photo-emission spectrum. l According to the Dewar- Chatt scheme for a n-complex, electrons of this level are donated to the metal forming a a-bond and donated back from the metal into the empty n*-level of C2H4 giving rise to a n-bond.Both these components of the Ni-ethylene bond may be identified from contour plots (fig. 2, (a) and (c)). As found in Zeise’s anion,4 but to a much lesser degree, the n-level also mixes into other orbitals, especially the a,-level contributing most to the Ni-Ni bond (fig. 2 (b)). The metal-ethylene bond in this n-complex is therefore expected to be weaker than in Zeise’s anion.N . ROSCH AND T . N . RHODIN r - ' I b, e = - 0.377 Ry 31 FIG. 2.-Contour plots for individual bonding orbitals of the n-complex. The contour values increase in absolute magnitude with increasing absolute values of the contour labels. The sign of the labels gives the sign of the orbital lobes.The selected set of the contour values plotted is the same for each of the three orbitals. (a) The ethylene n-orbital ; (b) the al orbital giving the main contribution to the Ni-Ni bond ; (c) the bl orbital showing significant r*-back bonding. For the di-a-complex we find essentially the same two-way interaction mechanism, giving rise, however, to two a-bonds, one from each carbon atom to the corresponding Ni atom. The charge donation out of the ethylene n-level is equally strong as in the n-complex, but divided among the two Ni atoms (fig. 3, (a) and (6)). On ths other hand, the back-donation out of a Ni2 anti-bonding level into the n::-orbital of ethylene32 BONDING OF ETHYLENE TO DIATOMIC NICKEL is approximately 50 % greater than in the n-complex, leading to a weaker C-C bond (fig.3(b)).11 The shift of the ethylene n-level due to n-d bonding has been derived from the photo-emission spectrum of chemisorbed ethylene to be = 0.9kO.1 eV.I In the Xu-SW approach, ionization potentials are normally calculated by invoking Slater's transition-state proced~re,~ and thereby taking relaxation effects into account. For comparable systems this relaxation is found to be nearly equal.12 As the ethylene subunit is preserved to a large degree in both model complexes, we estimate the shift of the ionization potential of the n-level upon chemisorption by taking the difference of the corresponding Xa-SW orbital energies. The accuracy of this procedure should be sufficient to compare with the value derived from measurements with an energy resolution de - 0.1 eV.l.l5 We find from our calculations de, = 0.72 eV for the n-complex and de, = 0.30 eV for the di-a-complex. The results of our calculation for the shift of the n-level and the change in the work function favour, when compared with the experimental values, the n-complex. The di-a-complex may play the role of a reaction intermediate for various surface reactions 9 9 lo due to its weaker C-C bond. The photo-emission spectra alone do not allow a discrimination between the two geometries for the " surface complex ", as n-d interaction is possible in both cases. These conclusions, however, have to be drawn with due caution because the model complexes are rather simple ones. First, one should increase the number of metal atoms to ensure a realistic description of the model '' surface 7 7 .Also, the geometry of the adsorbate should be varied, as it is known, for instance, that the ethylene subunit in Zeise's anion is not planar.16 (The effect on the ionization potentials is expected to be minor). As a next step, the model presented here should be tested for different adsorbate molecules, e.g., acetylene and ethane, and various other metal substrates. Such investigations are under way and will be reported elsewhere. The calculations presented here have shown how a local bonding approach to chemisorp- I I I FIG. 3 (a)N. ROSCH AND T. N . RHODIN 33 FIG. 3.-Contour plots for orbitals of the di-a-complex. The orbitals shown correspond to those of fig. 2. The contour values are the same.tion the bonding of hydrocarbons to a metallic diatom. implemented with the SCF-Xu-SW method can yield unique information on We thank Drs. J. E. Demuth and D. E. Eastman for making their results available before publication. We are particularly grateful to Prof. K. H. Johnson for providing us with the Xa-SW computer programmes and helpful advice in the use of the method. 58-B34 BONDING OF ETHYLENE TO DIATOMIC NICKEL Useful discussions with Dr. R. H. Paulsen are also acknowledged. The continued in- terest and support of Prof. Roald Hoffmann in this work is sincerely appreciated. One of us (N. R.) is also grateful to the Deutsche Forschungsgemeinschaft for a sti- pend. J. E. Demuth and D. E. Eastman, Phys. Rev. Letters, 1974, 32, 1123. E. W. Plummer et al., private communication. J. C. Slater and K. H. Johnson, Phys. Reu. B, 1972,5, 844. N. Rosch, R. P. Messmer and K. H. Johnson, J. Arner. Chem. SOC., 1974,96, 3855. T. B. Grimley, in Molecular Processes on Solid Surfaces, ed. E. Drauglis, R. D. Gretz and R. 1. J d e (McGraw-Hill, New York, 1969), p. 299. K. H. Johnson and R. P. Messmer, J. Vac. Sci. Tech., 1974, to be published. J. Chem. SOC., 1953,2939. G. C. Bond, Disc. Faraday SOC., 1966,41,200. G. C. Bond, CataZysis by Metals (Academic Press, New York, 1962), p. 234. (Academic Press, New York, 1973), vol. 23, p. 91. B. A. Morrow and N. Sheppard, Proc. Roy. SOC. A, 1969,311,391. ' (a) M. J. S . Dewar, Bull. SOC. Chim. France, 1951,18, C79 ; (b) J. Chatt and L. A. Duncanson, lo (a) G. I. Jenkins and E. K. Rideal, J. Chem. Soc., 1955, 2491 ; (6) J. H. Sinfelt, Ado. CatalysiJ I2 N. Rosch, W. G. Klemperer and K. H. Johnson, Chern. Phys. Letters, 1973, 23, 149. l3 K. Schwarz, Phys. Rev. B, 1972, 5, 2466. l4 We thank Dr. R. Paulson for kindly providing us with these results. J. M. Baker and D. E. Eastman, J. Vac. Sci. Tech., 1973, 10, 223. l6 W. C. Hamilton, K. A. Klandermann and R. Spratley, Acta Cryst. A, 1969, 25, S172.