Molecular T-matrix formalism in LEED-IV
When using traditional LEED-IV methods, adsorbed molecules are usually broken up into separate atoms, which are distributed over different layers according to their vertical positions. This does not appreciate the fact that adsorbed molecules are distinct chemical units, whose internal structure does usually not deviate much from the gas phase. From a chemical, as well as from a search strategic point of view, it would be advantageous if an adsorbed molecule could actually be treated as a single scattering object, which can be translated and rotated with respect to the substrate surface.
Keeping this in mind, we have implemented the Fortran90 code TMOL, that calculates the molecular T-matrix of a molecule for the analysis of LEED-IV spectra. The algorithm is based in a formalism put forward by Andersson and Pendry [1]. The molecular T-matrix is non-diagonal and completely describes intra-molecular multiple scattering. It is calculated before the start of the actual LEED-IV structural search. This matrix is then used to represent the entire molecule as a single scattering object in a conventional LEED-IV simulation. The approach makes it simple to model rigid vibrations, translations or rotations of adsorbed molecules in a highly efficient manner, by simply applying suitable operators to the molecular T-matrix.
This formalism has been successfully implemented in two LEED-IV calculation codes, LEED90 (Fortran90) and CLEED (C++) [2]. The accuracy of the approach is strongly dependent in l_{max,T}, the maximum angular momentum used to describe electron scattering by the molecule. This parameter, which also determines the T-matrix dimensions, can be estimated from a semiclassical approach l_{max,T} ≈ R ( 2E_{max} )^{1/2}, where E_{max} is the maximum energy in the IV curve and R is the approximate size of the molecule.
[1] S. Andersson and J.B. Pendry, J. Phys. C: Solid St. Phys. 13 (1980) 3547
[2] Available on request from Dr. G. Held
LEED-IV curves for benzene adsorbed on Ni(111) fcc site in the (&radic 7 x &radic 7) - R19^{o} reconstruction. Conventional (solid line) and T-matrix approach (dashed line) are compared for l_{max,T} = 12. |
Related publications
"A molecular T-matrix approach to calculating Low-Energy Electron Diffraction intensities for ordered molecular adsorbates"
M. Blanco-Rey, P.L. de Andres, G. Held and D.A. King
Surf. Sci. 579 (2005) 89-99
"Molecular t-matrices for Low-Energy Electron Difraction (TMOL v1.1)"
M. Blanco-Rey, P. L. de Andres, G. Held and D. A. King
Comp. Phys. Commun. 161 (2004) 166-178
"A FORTRAN-90 Low-Energy Electron Diffraction program (LEED90 v1.1)"
M. Blanco-Rey, P. L. de Andres, G. Held and D. A. King
Comp. Phys. Commun. 161 (2004) 151-165
Last updated 25/4/2009 by mb633 -at- cam.ac.uk