Multiresolution analysis for efficient, high precision all-electron density-functional calculations

Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying new techniques, we demonstrate for the first time that multiresolution analysis of all-electron calculations within density-functional theory can be carried out to high precision with a computational effort comparable to that of the corresponding plane-wave pseudopotential calculation, which neither captures the full core physics nor is systematically improvable. With this approach, we present calculations of paramagnetic core-level shifts where local density-functional theory is the sole uncontrolled approximation.