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Approximate normalizations for approximate density functionals
Adam Clay, Kiril Datchev, Wenlan Miao, Adam Wasserman, Kimberly J. Daas, Kieron Burke·April 4, 2025·DOI: 10.1103/nc2l-yynf
physics.chem-phQuantum Physics
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Abstract
It seems self-evident that a density functional calculation should be normalized to the number of electrons in the system. We present multiple examples where the accuracy of the approximate energy is improved (sometimes greatly) by violating this basic principle. In one dimension, we explicitly derive the appropriate correction to the normalization. Beyond one dimension, Weyl asymptotics for energy levels yield these corrections for any cavity. We include examples with Coulomb potentials and the exchange energy of atoms to illustrate relevance to realistic calculations.