Unity of Kohn-Sham density-functional theory and reduced-density-matrix-functional theory

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.