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Manuscript Title: Green function for crystal surfaces I.
Authors: B. Wenzien, J. Bormet, M. Scheffler
Program title: fhi93g0
Catalogue identifier: AADF_v4_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 88(1995)230
Programming language: Fortran, C Preprocessor.
Computer: IBM RISC System/6000.
Operating system: AIX3.2, UNICOS 7.0, Convex OS, UTS, BSD UNIX.
RAM: 1.4M words
Word size: 64
Keywords: Green function, Liquid, Overlayer, Charge density, Density of states, Layer kkr method, Multiple scattering, Solid state physics, Condensed matter.
Classification: 7.3.

Nature of problem:
The computer code (as that of papers I (AADF) and II (AAXZ)) allows to calculate the Green function (GF) for the one-electron hamiltonian of a semi-infinite solid with two-dimensional translational symmetry parallel to the surface, within any given range of energy E. Thus, this surface Green function (SGF) satisifies the Bloch-type periodic boundary conditions parallel to the surface, for a given value of the Bloch vector k||, and the boundary condition for outgoing waves normal to the surface. The following quantities describing the electronic structure may be computed from the SGF directly: (i) the electronic charge density within an arbitrary plane or box, both for given E and k|| and totally, i.e. integrated over E and k||, and (ii) the local density of states (LDOS), either for a given k|| and projected onto a given angular momentum, L = (l,m), (partial LDOS) or totally, i.e., integrated over k|| and summed up over L. In generalization to paper II, it is now possible to treat more complex systems with any number of different atoms composing the unit cell, e.g., reconstructed or rumpled clean surfaces as well as adsorbate systems.

Solution method:
The layer Korringa-Kohn-Rostoker (KKR) approach is used. The semi- infinite crystal is composed from layers parallel to the surface, and the atomic positions within the layer unit cell at the surface may differ from their ideal (bulk) values ("rumpled" layers). The potentials are treated within the muffin-tin approximation, and non- local pseudopotentials may be used. The system may be divided into four regions of commensurable, two-dimensional lattice vectors, but with possibly different muffin-tin zeros and geometries: (i) vacuum region, (ii) overlayer, (iii) surface or subsurface region, (iv) substrate (bulk) region. The unit cell of any layer may be composed of any required number of different atoms. The intra-layer scattering is treated by the method of Kambe [1], and the inter-layer scattering is treated using the layer-doubling scheme proposed by Pendry [2]. The Green function is evaluated using the method of Kambe and Scheffler [3] in a spherical-wave expansion up to any maximum quantum number of angular momentum, with basis functions centered at the atomic sites of the layers. Beginning with the top (overlayer or surface) region, the computational procedure is repeated layer-by-layer for the specified number of layers. The bulk Green function may also be evaluated.

All substrate (bulk) layers are assumed to be identical, but, they may differ from the top layers (over-layer, surface, subsurface layers). The muffin-tin zero of the subsurface region has to equal that of the bulk region. If the Green function of the vacuum region is projected onto spherical waves, the number of centers for the expansion must not exceed the number of atomic sites per unit cell within the overlayer or top substrate layer, respectively. The two-dimensional lattice vectors of the different layers have to be commensurable to those of the corresponding (1 x 1) structure of the substrate.

Running time:
The running time for the test run, i.e., one energy and k|| point for a substitutional (sqrt(3) x sqrt(3))R30degrees overlayer on the (111) surface of a fcc crystal, using 25 plane waves and 3 phase shifts per atom, and computing the Green function and LDOS for the overlayer, the first two subsurface layers, and the bulk, is * 20 s on IBM RISC System/6000, model 350, * 4 s on CRAY Y-MP/4, * 40 s on CONVEX 220, * 60 s on Amdahl 370, * 623 s on SPECS TRITON. Remarks concerning installationof program Programming is done in a rigorous modulare structure. All of the source files contain only one program unit (PROGRAM, SUBROUTINE, FUNCTION, BLOCK DATA) and are distributed over different subdirectories, corresponding to the different generated object module libraries and installations. A pre-processor has to be available for interpreting the C-like pre-processor statements within the source files during compilation. All the source files, including also shell scripts for compilation etc., may be extracted from the MS-DOS installation diskettes. For details, see the file INSTALL.

[1] K. Kambe, Z. Naturforschg. 22 a (1967) 322, 422; 23 a (1968) 1280.
[2] J.B. Pendry, Low Energy Electron Diffraction (Academic Press, London, 1974).
[3] K. Kambe and M. Scheffler, Surf.Sci. 89(1979)262.