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An approximate Xα functional is proposed from which the charge density fitting equations follow variationally. LCAO Xα calculations on atomic nickel and diatomic hydrogen show the method independent of the fitting (auxiliary) bases to within 0.02 eV. Variational properties associated with both orbital and auxiliary basis set incompleteness are used to approach within 0.2 eV the Xα total energy limit for the nitrogen molecule.
Dunlap et al. (Mon,) studied this question.