Electronic structure interpolation via atomic orbitals

We present an efficient scheme for accurate electronic structure interpolations based on the systematically improvable optimized atomic orbitals. The atomic orbitals are generated by minimizing the spillage value between the atomic basis calculations and the converged plane wave basis calculations on some coarse $k$-point grid. They are then used to calculate the band structure of the full Brillouin zone using the linear combination of atomic orbitals (LCAO) algorithms. We find that usually 16 -- 25 orbitals per atom can give an accuracy of about 10 meV compared to the full {\it ab initio} calculations. The current scheme has several advantages over the existing interpolation schemes. The scheme is easy to implement and robust which works equally well for metallic systems and systems with complex band structures. Furthermore, the atomic orbitals have much better transferability than the Shirley's basis and Wannier functions, which is very useful for the perturbation calculations.