  The static/strong correlation error inherent in existing functionals has
severely limited the further application of Kohn-Sham (KS) density functional
theory (DFT). The recently developed hypercomplex KS (HCKS) theory shows great
potential to overcome the fundamental limitations of the conventional KS-DFT,
hence further development and application of HCKS will effectively guide the
construction of new functionals toward better description of strong
correlation. To this end, this work derives the working equations for the HCKS
calculation and proves that HCKS using common functionals has much lower
computational complexity than reduced density matrix functional theory (RDMFT),
while maintaining the same density search space as RDMFT. Moreover, this work
combines HCKS with hybrid functionals that are based on orbitals and their
occupations. The test on triplet-singlet gaps shows that the systematic error
of HCKS due to the lack of static correlation in approximate functionals can be
effectively reduced by including appropriate amount of static correlation
correction, while the large systematic errors of RKS and UKS rarely change with
the correction. Therefore, HCKS creates new channels for the development and
evaluation of approximate functionals, and the insights and advances gained in
this work will be helpful to reduce the static correlation error in approximate
functionals.
