Localized Optimization: Exploiting non-orthogonality to efficiently minimize the Kohn-Sham Energy

Localized Optimization: Exploiting non-orthogonality to efficiently minimize the Kohn-Sham Energy

With the constantly increasing power of computers, the realm of experimental chemistry is increasingly being brought in contact with the field of computational mathematics. In particular, the ability to compute the charge density, i.e., the probabilistic location of a molecule’s electrons, allows numerous properties of matter to be displayed graphically, as opposed to investigated in the chemistry lab. As many current methods scale at a rate proportional to the cube of the number of atoms, such problems are still too large for direct {it ab initio} computations. This work describes a new algorithm for minimizing the Kohn-Sham energy that not only avoids local minima, but also guarantees the expensive energy function is only evaluated at sparse iterates. Preliminary results on a realistic model problem will be given.

keywords: Kohn-Sham Equations, nonlinear eigenvector problems, large- scale optimization