# Density Functional Calculations for Atomic Clusters

## Abstract

The density functional approach to the calculation of electronic properties of surfaces and amorphous materials has played a central role in the lectures of this school. In this approach it is possible, within a single-particle picture, to derive equations which determine the total energy of an interacting system of electrons in an external field. An approximation to the exchange-correlation energy functional is unavoidable, but can be justified to a very considerable extent /1/. Perhaps less evident is the relationship between atomic clusters and surfaces or disordered systems, and the motivation for performing cluster calculations in the context of chemisorption will be discussed in Sec. II. In Sec. III, we discuss the solution of the density functional equations for clusters using the linear muffin-tin orbital method of Andersen /2/, and note some of the advantages of the scheme. Before examining larger clusters, it is essential to perform detailed calculations for small molecules, in order to test the ability of the density functional method to describe chemical bonding in cases where extensive data, both theoretical and experimental, are available. In Sec. IV, therefore, we discuss the bonding in some s-and sp-bonded diatomic molecules. There are pronounced trends which correlate well with the form of the valence functions of the constituent atoms and shed light on the use of pseudopotentials in density functional theory.

## Keywords

Cohesive Energy Density Functional Method Constituent Atom Density Functional Calculation Density Functional Approach## Preview

Unable to display preview. Download preview PDF.

## References

- /1/.O. Gunnarsson, this volume.Google Scholar
- /2/.O.K. Andersen and R.G. Woolley, Mol. Phys. 26, 905 (1973);ADSCrossRefGoogle Scholar
- /2a/.O.K. Andersen, Phys. Rev. B12, 3060 (1975).ADSGoogle Scholar
- /3/.N.D. Lang and A.R. Williams, Phys. Rev. Lett. 37, 212 (1976).ADSCrossRefGoogle Scholar
- /4/.O. Gunnarsson, H. Hjelmberg and B.I. Lundqvist, Phys. Rev. Lett. 37, 292 (1976), Surface Sci. 63, 348 (1977).ADSCrossRefGoogle Scholar
- /5/.For early calculations in which the emphasis is on eigenvalues rather than the total energy, see I.P. Batra and O. Robaux, Surface Sci. 49, 653 (1975) and J. Harris and G.S. Painter, Phys. Rev. Lett. 36, 151 (1976).ADSCrossRefGoogle Scholar
- /6/.Discussions of embedding have been given by T.B. Grimley and C. Pisani, J. Phys. C 7 ,2831 (1974);ADSCrossRefGoogle Scholar
- /6a/.E.A. Hyman, Phys. Rev. B11, 3739 (1975);ADSGoogle Scholar
- /6b/.O. Gunnarsson and H. Hjelmberg, Physica Scripta 11, 97 (1975).ADSCrossRefGoogle Scholar
- /7/.There are numerous parametric schemes, such as the extended Hückel method, which have been applied in the present context. They lie outside the scope of the present discussion.Google Scholar
- /8/.A discussion of methods for including correlation effects in molecular calculations has been given by A.C. Wahl and G. Das, Advan. Quantum Chem. 6, 261 (1972). Chemisorption cluster calculations which include dominant correlation effects have been given by, for example, S.P. Walch and W.A. Goddard III, Surface Sci. 72, 645 (1978).Google Scholar
- /9/.J. Harris and R.O. Jones, Phys. Rev. (to be published).Google Scholar
- /10/.For more details, see O. Gunnarsson, J. Harris and R.O. Jones, Phys. Rev. B15, 3025 (1977). The spin-density functional of O. Gunnarsson and B.I. Lundqvist, Phys. Rev. Bl3, 4274 (1976) is used throughout.Google Scholar
- /11/.See J.C. Slater, Quantum Theory of Molecules and Solids, Vol. IV (McGraw-Hill, New York, 1974).Google Scholar
- /12/.J.B. Danese, J. Chem. Phys. 61, 3071 (1974).ADSCrossRefGoogle Scholar
- /13/.For density functional calculations of H2, see O. Gunnarsson and P. Johansson, Int. J. Quantum Chem. 10, 307 (1976) and Gunnarsson, Harris and Jones (Ref. 10).CrossRefGoogle Scholar
- /14/.For more details, see J. Harris and R.O. Jones, J. Chem. Phys. 68, 1190 (1978).ADSCrossRefGoogle Scholar
- /15/.J. Harris and R.O. Jones, J. Chem. Phys. (to be published).Google Scholar
- /16/.B.J. Austin and V. Heine, J. Chem. Phys. 45, 928 (1966).ADSCrossRefGoogle Scholar
- /17/.See, for example, J.A. Appelbaum and D.R. Hamann, Rev. Mod. Phys. 48, 479 (1976); H. Wendel and R.M, Martin, Phys. Rev. Lett. 40, 950 (1978).ADSCrossRefGoogle Scholar
- /18/.J. Harris and R. O. Jones, Phys. Rev. Lett. 41, 191 (1978).ADSCrossRefGoogle Scholar
- /19/.J.A. Appelbaum and D.R. Hamann, Phys. Rev. B8, 1777 (1973).ADSGoogle Scholar
- /20/.J. Harris and R.O. Jones, J. Chem. Phys. 68, 3316 (1978) and to be published.ADSCrossRefGoogle Scholar
- /2l/.T. Kagawa, Phys. Rev. A12, 2245 (1975).ADSGoogle Scholar
- /22/.V.L. Moruzzi, A.R. Williams and J.F. Janak, Phys. Rev. B15, 2854 (1977).ADSGoogle Scholar
- /23/.J. Harris and R.O. Jones, J. Chem. Phys. (to be published).Google Scholar