Spin-Free Formalism of Spin-Density Functional Theory

The spin-free approach greatly simplifies the mathematical structure of spin-density functional theory (SDFT). With this in mind, a new spin-free constrained-search formulation of SDFT will be presented (Phys. Rev. A 100, 062507 (2020)). A rigorous spin decomposition of the SDFT energy components naturally arises from this spin-free formalism of SDFT (Phys. Rev. A 104, 022815 (2021)). In addition, new spin-dependent coordinate-scaling relations are found and proven with this formalism. Exact mathematical constraints are instrumental for the construction of new density functional approximations.