Errors in Hellmann-Feynman Forces due to occupation number broadening, and how they can be corrected

In ab initio calculations of electronic structures, total energies, and forces, it is convenient and often even necessary to employ a broadening of the occupation numbers. If done carefully, this improves the accuracy of the calculated electron densities and total energies and stabilizes the convergence of the iterative approach towards self-consistency. However, such a boardening may lead to an error in the calculation of the forces. Accurate forces are needed for an efficient geometry optimization of polyatomic systems and for ab initio molecular dynamics (MD) calculations. The relevance of this error and possible ways to correct it will be discussed in this paper. The first approach is computationally very simple and in fact exact for small MD time steps. This is demonstrated for the example of the vibration of a carbon dimer and for the relaxation of the top layer of the (111)-surfaces of aluminium and platinum. The second, more general, scheme employs linear-response theory and is applied to the calculation of the surface relaxation of Al(111). We will show that the quadratic dependence of the forces on the broadening width enables an efficient extrapolation to the correct result. Finally the results of these correction methods will be compared to the forces obtained by using the smearing scheme, which has been proposed by Methfessel and Paxton.Comment: 6 pages, 5 figures, Scheduled tentatively for the issue of Phys. Rev. B 15 15 Dec 97 Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Computation of Scanning Tunneling Microscope Images of Nanometer-Sized Objects Physisorbed on Metal Surfaces

This communication deals with the application of a transfer-matrix strategy for the quantitative evaluation of the tunnel current in a scanning tunneling microscope (STM). The image given by a simple atomic-size object deposited on a metal surface is specifically examined in both modes of STM operation namely the constant-height and the constant-current modes. The two-dimensional corrugation induced at low temperature by Xe atoms physisorbed on an otherwise clean, unreconstructed Ni (110) surface is studied in detail. It is shown that the simple consideration of the elastic scattering of electrons by the three-dimensional potential barrier between the tip and the metal substrates provides a quantitative description of the images produced by the instrument: (1) the Xe atom appears as a conic protrusion, approximately 7 A wide, with a corrugation 1.3 A high; (2) in Xe clusters, each adjoining atom is resolved, with a shape in full agreement with experiment. In order to obtain correct quantitative results, image-charge corrections to the potential cannot be neglected