Density functional theory (DFT) is the most widely used ab initio method in computational chemistry and material simulations. Using DFT codes, one can calculate the electronic structure, the charge density, and the total energy of an electronic system. And with the advance of new algorithms and supercomputers, we can now study many thousand-atom systems, with applications including the study of solar cells for renewable energy, biomedical imaging, and the design of novel materials. At the heart of many of these codes, one typically finds a Self Consistent Field (SCF) iteration for solving the Kohn-Sham equations. In this talk, I will discuss an alternative approach based on an optimization method that minimizes the Kohn-Sham total energy directly. I will also discuss a trust region technique as a way to improve convergence of the overall method. Numerical experiments demonstrate that the combination of these approaches is more efficient and robust than SCF alone, which can be shown to fail in certain cases.
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