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We implement and benchmark the frozen core approximation, a techniquecommonly adopted in electronic structure theory to reduce the computationalcost by means of mathematically fixing the chemically inactive core electronstates. The accuracy and efficiency of this approach are well controlled by asingle parameter, the number of frozen orbitals. Explicit corrections for thefrozen core orbitals and the unfrozen valence orbitals are introduced,safeguarding against seemingly minor numerical deviations from the assumedorthonormality conditions of the basis functions. A speedup of over two-foldcan be achieved for the diagonalization step in all-electron density-functionaltheory simulations containing heavy elements, without any accuracy degradationin terms of the electron density, total energy, and atomic forces. This isdemonstrated in a benchmark study covering 103 materials across the periodictable, and a large-scale simulation of CsPbBr3 with 2,560 atoms. Our studyprovides a rigorous benchmark of the precision of the frozen core approximation(sub-meV per atom for frozen core orbitals below -200 eV) for a wide range oftest cases and for chemical elements ranging from Li to Po. The algorithmsdiscussed here are implemented in the open-source Electronic StructureInfrastructure software package.

Accurate Frozen Core Approximation for All-Electron Density-Functional Theory