Approximate normalizations for approximate density functionals

• URL: http://arxiv.org/abs/2504.03845v1
• Date: Fri, 04 Apr 2025 18:06:07 GMT
• Title: Approximate normalizations for approximate density functionals
• Authors: Adam Clay, Kiril Datchev, Wenlan Miao, Adam Wasserman, Kimberly J. Daas, Kieron Burke,
• Abstract summary: It seems self-evident that a density functional calculation should be normalized to the number of electrons in the system.<n>We present examples where the accuracy of the approximate energy is improved (sometimes greatly) by violating this basic principle.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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