Abstract
The Kohn-Sham formalism for the density functional theory (DFT) proposed a half-century ago has been the extensive motive force for the material science community, despite it is incomplete because of its problematic notion of eternally-unknown correlation energy functional including a separated part of kinetic energy. Here, we widely explain an alternative method recently discovered by us, i.e. the multiple grand canonical spin DFT (MGC-SDFT) in the unrestricted Hartree-Fock-Dirac (MGC-SDFT-UHFD) approximation. It is proved that the correlation energy functional consists of well-defined principal and secondary parts: the former yields the principal internal energy functional responsible for a set of the one-body quasi-particle spectra defined by the respective ground and excited states with each natural LCAO-MO as well as a set of the expected values of Heisenberg spin Hamiltonian, and the latter does a well-defined spin-dependent perturbation energy responsible for some many-body effects. An application will be made to explain why the water-splitting S1-state Mn4CaO5-clusters in photosystem II can exhibit two different EPR signals, called “g4.8” and “g12-multiline”. Moreover, the secondary correlation energy part will be shown to promote Cooper-pairings of Bloch-electrons near Fermi level in the superconductor, provided that their eigenstates might be exactly determined by the MGC-SDFT-UHFD method.