Research of nanostructures requires ab initio materials simulations to compute ground state energy and single-particle many-electron atomistic system wave functions. Simulation cores, which are typically based on Self-Consistent Field iteration, may fail if a particular surrogate minimizer increases total energy. We propose an optimization that minimizes the Kohn-Sham total energy directly. A trust region technique is introduced to restrict wave function updates within a small neighborhood of an
approximate solution.