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Bonding and interaction of oxygen atoms on nickel (001) from self-consistent electronic structure
651
Surface Science 152/153 (1985) 651-653 North-Holland, Amsterdam
BONDING AND INTERACTION (001) FROM SELF-CONSISTENT R.W. GODBY,
V. HEINE
OF OXYGEN ATOMS ON NICKEL ELECTRONIC STRUCTURE *
and R. HAYDOCK
**
Theory of Condensed Matter, Cauendish Laboratory, Madingley Road, Cambridge CB3 OHE, UK
Received 27 March 1984
We have calculated self-consistently the electronic structure of c(2 X 2) and p(1 x 1) oxygen overlayers on the nickel (001) surface using the LAPW (linearised augmented plane wave) method. Our aim has been to analyse our calculated charge densities, band structures and wave functions to obtain a physical picture of the bonding of the oxygen atoms to the nickel surface and of the interaction between oxygen atoms. We show how an “optimal local orbital” (OLO) description of the oxygen 2p-nickel4s4p hybridised states can explain both the oxygen-oxygen repulsion which prevents the formation of the p(1 X 1) overlayer structure, and the low increase in work function caused by oxygen. We compare the degree of hybridisation with both the nickel 4s4p bands and the 3d bands and conclude that the former contributes more to the oxygen binding and vibration on the surface and to the spatial character of the wave functions. Oxygen molecules dissociate on nickel (001) forming, with increasing exposure, p(2 X 2) and then c(2 X 2) overlayers, with the oxygen atom centred in the four-fold site, its nucleus 0.9 A above the surface nickel nuclei [l-3]. The p(1 X 1) structure is never formed, but we can usefully study it computationally. As models of the c(2 X 2) and p(1 X 1) overlayer structures we have taken a three-atom-thick film of nickel with oxygen overlayers on each face in the observed positions, and have used the LAPW method [4] to calculate the electronic structure of these models by solving self-consistently the equations of density functional theory, using a local density approximation for the exchange-correlation potential. The calculated band structure of c(2 x 2) oxygen on nickel (001) shows the appearance of a set of bands with p-like dispersion at about E, - 5.5eV. Their width is 1.2 eV, about twice that of an unsupported oxygen monolayer with the * Extended abstract; full details will be included in a future paper. ** Permanent address: Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403. USA
0039-6028/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
652
R.W. Godhy et al. / Oxygen atoms on nickel (001)
same lattice spacing. In order to study the details of the hybridisation that produces these states, we have projected the wave functions onto the “LAPW orbital? of different symmetries within the “muffin tin” spheres. As expected from the dispersion of the bands, most of the weight is oxygen p; also, the nickel sp-weight is not negligible and in fact exceeds the nickel d-weight. The radial nature of the 2p-like wave functions would be displayed by the optimally localised orbitals which span these bands (in the tight-binding sense). In this case, such optimal local orbitals are essentially p,, pJ and p= orbitals, centred on the oxygen atom, whose radial part is extractable from the contribution to the total c(2 x 2) electronic charge density from the 2p-like bands, which is found to be remarkably spherically symmetric about the oxygen nucleus. Our main result is that these optimal local orbitals are very much more extended radially than atomic 2p wave functions. This “expansion of the oxygen p-orbital?, caused by their hybridisation with the nickel 4s4p free-electron-like electron gas, was originally suggested by Gallagher et al. [5,6], though the exact form and size of their orbitals were sensitive to the details of their model non-self-consistent “single site” potential. Our picture of the oxygen-nickel hybridisation is then as follows. Oxygen 2p-nickel4s4p hybridisation gives rise to a narrow resonance, whose states are described by the large p-like optimal local orbitals. After hybridisation with the d-states the tail of the resonance is partially expelled from the energy range of the d-bands (leading to a small OLO-nickel 3d antibonding peak in the density of states just above Er). The 0 2p-Ni 4s4p and 0 2p-Ni 3d antibonding states have been identified by calculating the phase relationship of orbitals in sampled wave functions. Adding neighbouring oxygen atoms then causes the resonance peak to broaden into the broad 2p-like bands of resonance states. We suggest that a major contribution to the difference between the vibration frequencies in the p(2 x 2) and c(2 x 2) overlayers comes from the slightly greater degree of d-hybridisation in the c(2 x 2) with the nickel atom directly below the oxygen atom (in the second atomic layer), as the oxygen 2p-nickel 3d interaction at the distance has negative curvature and so tends to reduce the effective medium oxygen 2p-nickel 4s4p frequency. By fitting the 2p-like bands to tight-binding form we deduce that the oxygen-oxygen interaction can be described as a direct closed-shell interaction between the extended p-orbitals (although the interaction is indirect to the extent that it is the oxygen-nickel hybridisation which gives rise to the large orbitals), supporting the suggestion [5,6] that it is this closed shell repulsion that prevents the formation of the p(1 X 1) structure. In order to discuss charge transfer effects we have calculated charge density difference plots, [0 on Ni(OOl)]-([O] + [Ni(OOl)]). The spread-out nature of the 2p-like orbitals means that although they are fully occupied, as opposed to the four p-electrons in atomic oxygen, the total electronic charge in the vicinity of the oxygen atom very nearly cancels the nuclear charge. Moreover, the small
R W. Godby et al. / Oxygen atoms on nickel (001)
653
excess of electronic charge flows nearly equally from all directions. Both these effects result in only a small increase in the work function of nickel when oxygen is chemisorbed. This work was supported in part (R.H.) by the National Science Foundation - Condensed Matter Theory - grant DMR 81-22004. One of us (R.W.G.) thanks the UK Science and Engineering Research Council for a studentship.
References [l] [2] [3] [4] [5] [6]
J.E. Demuth, D.W. Jepsen and P.M. Marcus, Phys. Rev. Letters 31 (1973) 540. J.E. Demuth and T.N. Rhodin, Surface Sci. 45 (1974) 249. K.H. Rieder, Phys. Rev. B27 (1983) 6978. H. Krakauer, M. Postemak and A.J. Freeman, Phys. Rev. B19 (1979) 1706. J.M. Gallagher and R. Haydock, Surface Sci. 83 (1979) 117. J.M. Gallagher, R. Haydock and V. Heine, J. Phys. Cl2 (1979) L13.
Surface Science 152/153 (1985) 651-653 North-Holland, Amsterdam
BONDING AND INTERACTION (001) FROM SELF-CONSISTENT R.W. GODBY,
V. HEINE
OF OXYGEN ATOMS ON NICKEL ELECTRONIC STRUCTURE *
and R. HAYDOCK
**
Theory of Condensed Matter, Cauendish Laboratory, Madingley Road, Cambridge CB3 OHE, UK
Received 27 March 1984
We have calculated self-consistently the electronic structure of c(2 X 2) and p(1 x 1) oxygen overlayers on the nickel (001) surface using the LAPW (linearised augmented plane wave) method. Our aim has been to analyse our calculated charge densities, band structures and wave functions to obtain a physical picture of the bonding of the oxygen atoms to the nickel surface and of the interaction between oxygen atoms. We show how an “optimal local orbital” (OLO) description of the oxygen 2p-nickel4s4p hybridised states can explain both the oxygen-oxygen repulsion which prevents the formation of the p(1 X 1) overlayer structure, and the low increase in work function caused by oxygen. We compare the degree of hybridisation with both the nickel 4s4p bands and the 3d bands and conclude that the former contributes more to the oxygen binding and vibration on the surface and to the spatial character of the wave functions. Oxygen molecules dissociate on nickel (001) forming, with increasing exposure, p(2 X 2) and then c(2 X 2) overlayers, with the oxygen atom centred in the four-fold site, its nucleus 0.9 A above the surface nickel nuclei [l-3]. The p(1 X 1) structure is never formed, but we can usefully study it computationally. As models of the c(2 X 2) and p(1 X 1) overlayer structures we have taken a three-atom-thick film of nickel with oxygen overlayers on each face in the observed positions, and have used the LAPW method [4] to calculate the electronic structure of these models by solving self-consistently the equations of density functional theory, using a local density approximation for the exchange-correlation potential. The calculated band structure of c(2 x 2) oxygen on nickel (001) shows the appearance of a set of bands with p-like dispersion at about E, - 5.5eV. Their width is 1.2 eV, about twice that of an unsupported oxygen monolayer with the * Extended abstract; full details will be included in a future paper. ** Permanent address: Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403. USA
0039-6028/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
652
R.W. Godhy et al. / Oxygen atoms on nickel (001)
same lattice spacing. In order to study the details of the hybridisation that produces these states, we have projected the wave functions onto the “LAPW orbital? of different symmetries within the “muffin tin” spheres. As expected from the dispersion of the bands, most of the weight is oxygen p; also, the nickel sp-weight is not negligible and in fact exceeds the nickel d-weight. The radial nature of the 2p-like wave functions would be displayed by the optimally localised orbitals which span these bands (in the tight-binding sense). In this case, such optimal local orbitals are essentially p,, pJ and p= orbitals, centred on the oxygen atom, whose radial part is extractable from the contribution to the total c(2 x 2) electronic charge density from the 2p-like bands, which is found to be remarkably spherically symmetric about the oxygen nucleus. Our main result is that these optimal local orbitals are very much more extended radially than atomic 2p wave functions. This “expansion of the oxygen p-orbital?, caused by their hybridisation with the nickel 4s4p free-electron-like electron gas, was originally suggested by Gallagher et al. [5,6], though the exact form and size of their orbitals were sensitive to the details of their model non-self-consistent “single site” potential. Our picture of the oxygen-nickel hybridisation is then as follows. Oxygen 2p-nickel4s4p hybridisation gives rise to a narrow resonance, whose states are described by the large p-like optimal local orbitals. After hybridisation with the d-states the tail of the resonance is partially expelled from the energy range of the d-bands (leading to a small OLO-nickel 3d antibonding peak in the density of states just above Er). The 0 2p-Ni 4s4p and 0 2p-Ni 3d antibonding states have been identified by calculating the phase relationship of orbitals in sampled wave functions. Adding neighbouring oxygen atoms then causes the resonance peak to broaden into the broad 2p-like bands of resonance states. We suggest that a major contribution to the difference between the vibration frequencies in the p(2 x 2) and c(2 x 2) overlayers comes from the slightly greater degree of d-hybridisation in the c(2 x 2) with the nickel atom directly below the oxygen atom (in the second atomic layer), as the oxygen 2p-nickel 3d interaction at the distance has negative curvature and so tends to reduce the effective medium oxygen 2p-nickel 4s4p frequency. By fitting the 2p-like bands to tight-binding form we deduce that the oxygen-oxygen interaction can be described as a direct closed-shell interaction between the extended p-orbitals (although the interaction is indirect to the extent that it is the oxygen-nickel hybridisation which gives rise to the large orbitals), supporting the suggestion [5,6] that it is this closed shell repulsion that prevents the formation of the p(1 X 1) structure. In order to discuss charge transfer effects we have calculated charge density difference plots, [0 on Ni(OOl)]-([O] + [Ni(OOl)]). The spread-out nature of the 2p-like orbitals means that although they are fully occupied, as opposed to the four p-electrons in atomic oxygen, the total electronic charge in the vicinity of the oxygen atom very nearly cancels the nuclear charge. Moreover, the small
R W. Godby et al. / Oxygen atoms on nickel (001)
653
excess of electronic charge flows nearly equally from all directions. Both these effects result in only a small increase in the work function of nickel when oxygen is chemisorbed. This work was supported in part (R.H.) by the National Science Foundation - Condensed Matter Theory - grant DMR 81-22004. One of us (R.W.G.) thanks the UK Science and Engineering Research Council for a studentship.
References [l] [2] [3] [4] [5] [6]
J.E. Demuth, D.W. Jepsen and P.M. Marcus, Phys. Rev. Letters 31 (1973) 540. J.E. Demuth and T.N. Rhodin, Surface Sci. 45 (1974) 249. K.H. Rieder, Phys. Rev. B27 (1983) 6978. H. Krakauer, M. Postemak and A.J. Freeman, Phys. Rev. B19 (1979) 1706. J.M. Gallagher and R. Haydock, Surface Sci. 83 (1979) 117. J.M. Gallagher, R. Haydock and V. Heine, J. Phys. Cl2 (1979) L13.