A FORTRAN-90 Low-Energy Electron Diffraction program (LEED90 v1.1)

Abstract

We describe a FORTRAN-90 program to compute low-energy electron diffraction I(V) curves. Plane-waves and layer doubling are used to compute the inter-layer multiple-scattering, while the intra-layer multiple-scattering is computed in the standard way expanding the wavefield on a basis of spherical waves. The program is kept as general as possible, in order to allow testing different parts of multiple-scattering calculations. In particular, it can handle non-diagonal t-matrices describing the scattering of non-spherical potentials, anisotropic vibrations, anharmonicity, etc. The program does not use old FORTRAN flavours, and has been written keeping in mind the advantage for parallelism brought forward by FORTRAN-90. Program summary Title of program: LEED90 Catalogue number: ADUE Program summary URL: http://cpc.sc.qub.ac.uk/summaries/ADUE Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland. Computers: Alpha ev6-21264 (700 MHz) and Pentium-IV. Operating system: Digital UNIX V5.0 and Linux (Red Hat 8.0). Programming language: FORTRAN-90/95 (Compaq True64 compiler, and Intel Fortran Compiler 7.0 for Linux). High-speed storage required for the test run: minimum 64 Mbytes, it can grow to more depending on the system considered. Disk storage required: None No. of bits in a word: 64 and 32 No. of lines in distributed program, including test data, etc.: 17 953 No. of bytes in distributed program, including test data, etc.: 100 051 Distribution format: tar.gz Nature of problem: We describe the FORTRAN-90 program LEED90 (v1.1) to compute dynamical I(V) curves using layer-doubling. The program has been designed to be able to take, as an option, input from non-diagonal t-matrix, e.g., representing a molecule, temperature corrections for anisotropic/anharmonic vibrations, or non-spherical muffin-tin potentials. Method of solution: The intra-layer multiple-scattering problem is solved by adding self-consistently spherical wave amplitudes originated all throughout a Bravais layer. A general non-diagonal structure for the t-matrix describing the scattering by the potentials is assumed. The inter-layer multiple-scattering is computed by the layer-doubling technique. Therefore, the reflection matrix of the substrate is obtained by an iterative procedure. This is subsequently combined with the adsorbed layer diffraction matrices, to give the total reflected intensities. For the overlayer, the program can read a molecular t-matrix (e.g., as supplied by the companion program TMOL) including all the intra-molecular scattering. These matrices can be translated and rotated efficiently by using Green's function propagators and Wigner operators. Typical running time: A single I(V) curve for a fixed atomic configuration takes a few seconds/minutes depending on the two key parameters controlling the convergence: the maximum angular momentum quantum number, l max, and the number of beams, n b . Running time scales as l max 4 and n b 3. Typical values for energies up to 300 eV are 7 to 10 for l max for single atoms 10 to 15 for molecular adsorbates, and a few hundreds for n b .