  Functionals that explicitly depend on occupied, unoccupied, or
fractionally-occupied orbitals are rigorously formalized using Clifford
algebras, and a variational principle is established that facilitates orbital
(and occupation) optimization as a formal implementation method. Theoretically,
these methodologies circumvent the limitations encountered in the original
Kohn-Sham and related methods, particularly when the interacting system's
electron density does not match that of any noninteracting reference system.
This work redefines orbital (and occupation) functionals from a novel
perspective, positioning them not merely as extensions of traditional density
functionals, but as superior, rigorous alternatives.
