Development of Low-order Scaling DFT Methods
To further extend the applicability of first-principles electronic structure calculations based on density functional theory (DFT) to large-scale systems containing more than ten thousands of atoms, here we present development of low-order scaling DFT methods: one is a numerically exact one, the other is approximate O(N) methods. Though the conventional DFT calculations based on semi-local functionals scale as the third power of number of atoms, it will be shown that the computational complexity of DFT calculations can be reduced to a low-order scaling in a numerically exact sense [1,2]. We further discuss an efficient O(N) divide-conquer (DC) method based on localized natural orbitals (LNOs) for large-scale DFT calculations of gapped and metallic systems , where the LNOs are noniteratively calculated by a low-rank approximation via a local eigendecomposition of a projection operator for the occupied space. In addition to the low-order scaling methods, efficient parallelization methods for massively parallel computers will be presented for atom decompositions  and fast Fourier transforms [5,6]. T. Ozaki, Phys. Rev. B 82, 075131 (2010).
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