We present a systematic study for numerical atomic basis orbitals ranging from H to Kr, which could be used in large scale O(N) electronic structure calculations based on density-functional theories ͑DFT͒. The comprehensive investigation of convergence properties with respect to our primitive basis orbitals provides a practical guideline in an optimum choice of basis sets for each element, which well balances the computational efficiency and accuracy. Moreover, starting from the primitive basis orbitals, a simple and practical method for variationally optimizing basis orbitals is presented based on the force theorem, which enables us to maximize both the computational efficiency and accuracy. The optimized orbitals well reproduce convergent results calculated by a larger number of primitive orbitals. As illustrations of the orbital optimization, we demonstrate two examples: the geometry optimization coupled with the orbital optimization of a C 60 molecule and the preorbital optimization for a specific group such as proteins. They clearly show that the optimized orbitals significantly reduce the computational efforts, while keeping a high degree of accuracy, thus indicating that the optimized orbitals are quite suitable for large scale DFT calculations.

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We study the electronic states of the anisotropic triangular lattice Hubbard model at half filling, which is a simple effective model for the organic superconducting κ-BEDT-TTF compounds. We treat the effect of the Coulomb interaction by the fluctuation exchange (FLEX) method, and obtain the phase diagram of this model for various sets of parameters. It is shown that the d-wave superconductivity is realized in the wide region of the phase diagram, next to the antiferromagnetic states. The obtained phase diagram explains the characters of the experimental results very well.