Energy components in spin-density functional theory

It has recently been shown how to replace spin-wave functions with purely spatial wave functions in the formulation of spin-density functional theory (SDFT), without any change to the resultant density functional expressions [F. Zahariev and M. Levy, Phys. Rev. A 100, 062507 (2019)]. The purely spatial wave functions that are obtained are much more convenient to use and thus allow for a relatively easy decomposition and manipulation of terms in the constrained-search formulation of SDFT. All the essential ingredients of SDFT, including the kinetic, exchange, and correlation contributions, are explicitly defined in terms of the universal functional expressed in this spin-free manner. Constrained-search derivations of the Oliver-Perdew relations for the kinetic and exchange terms are presented. The up-down spin component of the correlation term is found to contain the up-down spin component of the Hartree term. A spin-dependent generalization of the adiabatic connection is put forth and a connection with spin-dependent coordinate scaling is established for the correlation energy.