  This work presents a theory to unify the two independent theoretical
frameworks of Kohn-Sham (KS) density functional theory (DFT) and reduced
density matrix functional theory (RDMFT). The generalization of the KS orbitals
to hypercomplex number systems leads to the hypercomplex KS (HCKS) theory,
which extends the search space for the density in KS-DFT to a space that is
equivalent to natural spin orbitals with fractional occupations in RDMFT.
Thereby, HCKS is able to capture the multi-reference nature of strong
correlation by dynamically varying fractional occupations. Moreover, the
potential of HCKS to overcome the fundamental limitations of KS is verified on
systems with strong correlation, including atoms of transition metals. As a
promising alternative to the realization of DFT, HCKS opens up new
possibilities for the development and application of DFT in the future.

Chemical Physics;Quantum Physics