Systematically improvable optimized atomic basis sets for ab initio calculations.

We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the spillage of the wavefunctions between the atomic orbital calculations and the converged plane wave results for dimer systems. The quality of the bases can be systematically improved by increasing the size of the bases within the same framework. We show that the spillage can describe the convergency of the total energy very well and the cutoff radii of the atomic orbitals are extremely important for the quality of the atomic orbitals. The scheme is easy to implement and very flexible. We have performed extensive tests of this scheme for a wide variety of systems, including semiconductors, oxides, metals, clusters, etc. The results show that the obtained atomic bases are very satisfactory for both accuracy and transferability.