Ultra-large-scale electronic state calculations based on ab initio theory and mathematical optimization methods

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Ultra-large-scale electronic state calculations were developed, which is based on the ab initio theory and mathematical optimization methods. Optimization methods, in particular, Krylov-subspace linear-algebraic algorithms were investigated and implemented in the code. In result, massively parallel computations with one-hundred-million atoms were realized on the K computer. Moreover, optimized model (tight-binding-form) theory was obtained from ab initio calculations. Application studies were carried out for localized pi states in amourphous-like conjugated polymers and nano-domain analysis of nano-composite carbon solid.