Numerical atomic basis orbitals from H to Kr

We present a systematic study for numerical atomic basis orbitals ranging from H to Kr, which could be used in large scale $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$ electronic structure calculations based on density-functional theories (DFT). 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 ${\mathrm{C}}_{60}$ 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.