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O: Fachverband Oberflächenphysik
O 79: Poster Session - Frontiers in Electronic-Structure Theory - Focus on Electron-Phonon Interaction
O 79.4: Poster
Mittwoch, 18. März 2020, 18:15–20:00, P2/EG
An efficient representation of the Kohn-Sham potential and its use in density functional calculations — •Rudolf Zeller — Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
In the standard numerical treatment, the main effort is directed at an efficient description of the density, usually by applying a judicious expansion in basis functions or a sophisticated choice of numerical grid points. The potential V(r) is then represented by its matrix elements determined by the basis functions or grid points. In view of the computational cost, this number is reduced as much as possible, often by replacing the real potential with a pseudopotential.
In my presentation, instead, the emphasis is put on
an efficient description of the potential in terms of spherical harmonics
used to expand the potential at the nuclear sites.
The potential is understood as an integral operator
V(r) δ (r−r′) approximated by
δ (r−r′) ∑lml′m′ Ylm (r) Yl′m′ (r′) Vlml′m′ (r)
with a finite number of spherical harmonics. For such potentials the density
can be evaluated practically exactly
by a mathematically rigorous expression [1].
The calculated densities converge fast with increasing number
of harmonics and excellent total energies are obtained
at low computational cost.
[1] R. Zeller, J. Phys.: Condens. Matter 27, 306301 (2015).