SCF is actually based on Variational principle and Non-SCF uses Harris energy functional believed to be anti-variational to Kohn-Sham density functional theory
The self-consistent method, also referred to as the Hartree-Fock method is used to determine the energy of a many-body system in a stationary state. This method seeks self-consistency in the calculation.
The central aim is to identify the is to identify the lowest-energy arrangement of atoms. A particular electronic density is proposed, and based on that the electronic density is calculated again and again to reach an improved description, until there's negligible change in the results, so until the electronic density is "self-consistent".
The non-self consistent method applies to non-stationary systems as far as I understood.
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