abstract:
In the first part of this talk, we give an introduction to the direct minimization tasks associated with Hartree-Fock and Density Functional Theory methods used in electronic structure calculations. In this context, we present some results from [Blauert, Neelov, Rohwedder, Schneider, 2008] concerned with the convergence of the eigenfunctions (i.e. the minimizer) and the energies (i.e. the quantity to be minimized) of the given functionals.
In the second part, we show how in a more general framework of functional minimization, the minimizer of a given functional $J$, given on a high-dimensional space $\mathcal{V} = \otimes_{i=1}^n V$ may be approximated by sums of elementary tensors of fixed rank $r$ by iterating directly in the space $V^{r\cdot d}, without truncation operations being involved [Espig, Hackbusch, Rohwedder, Schneider, 2009]. A transfer of the presented method to Tucker format is proposed. |