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Reinhold Schneider, Thu, 14.0015.00

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Density matrix computation for electronic structure calculation
Reinhold Schneider (University Kiel)
Numerical simulation of electronic structures, based on first principle
methods derived from the multiparticle Schrödinger equation,
play a fundamental role in quantum chemistry, molecular physics, solid physics
etc. We present a short introduction into mean field calculation like
HartreeFock models or KohnSham equation in density functional theory.
The computation of the ground state energy requires the
self consistent computation of the first N eigenfunctions of a single particle
Schrödinger operator. For large molecules the computational costs
scale normaly like O(N^{3}). Instead of computing the
eigenfunctions one computes the projector onto the space spanned by these
eigenfunctions.
This projector is represented by the socalled density matrix. We present few
possibilities to compute the density matrix. These algorithms require
subsequent matrixmatrix multiplications or operator products. Most operators
are nonlocal, which demands necessarily for fast matrix calculus.
The analytical setting for density matrices will be established
and the use of wavelet basis as systematic basis functions for the
discretization will be discussed.




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