= Spherical averaging versus self-consistent orbital optimization
Spherical averaging and self-consistent optimization impose different conditions on an atomic model. Spherical averaging replaces an angularly varying effective <potential energy> by one depending only on radius. It simplifies <atomic orbitals> into radial functions multiplied by angular functions, but does not determine those radial functions by itself.
Self-consistency instead requires the orbitals used to construct an effective <potential energy> to agree with the orbitals obtained by solving its <Schrödinger equation>. One can solve a prescribed spherical <potential energy> without self-consistency, or iterate a spherically averaged <Hartree method> model until it is self-consistent. Neither operation alone supplies all <electron correlation>.
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