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Manuscript Title: A FORTRAN-90 Low-Energy Electron Diffraction program (LEED90 v1.1)
Authors: Maria Blanco-Rey, Pedro de Andres, Georg Held, David A. King
Program title: LEED90
Catalogue identifier: ADUE
Journal reference: Comput. Phys. Commun. 161(2004)151
Programming language: Fortran-90/95 (Compaq True64 compiler, and Intel Fortran Compiler 7.0 for Linux).
Computer: Alpha ev6-21264 (700Mhz) and Pentium-IV.
Operating system: Digital UNIX V5.0, Linux (Red Hat 8.0).
RAM: minimum 64 MBytes, it can grow to more depending on the system considered.
Word size: 32 and 64 bits
Keywords: Low-Energy Electron Diffraction, Multiple-Scattering, Full Dynamical Theory, Layer-Doubling, Molecular t-matrix, Anisotropic/Anharmonic vibrations, non-diagonal t-matrix.
Classification: 7.2.

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.

Solution method:
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.

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, lmax, and the number of beams, nb. Running time scales as l4max and n3b. Typical values for energies up to 300 eV are 7 to 10 for lmax for single atoms 10 to 15 for molecular adsorbates, and a few hundreds for nb.

[1] J.B. Pendry, Low-Energy Electron Diffraction, (Academic, 1974).
[2] S.Y. Tong, Progress in Surface Science, 7, 1 (1975).
[3] M.A. Van Hove, W.H. Weinberg and C.-M. Chan, Low-Energy Electron Diffraction (Springer-Verlag, Berlin 1986).