Spin migration in density functional theory: energy, potential and density perspectives

Spin is a fundamental property of any many-electron system. The ability of density functional theory to accurately predict the physical properties of a system, while varying its spin, is crucial for describing magnetic materials and high-spin molecules, spin flip, magnetization and demagnetization processes. Within density functional theory, when using various exchange-correlation approximations, the exact dependence of the energy on the spin often deviates from the exact constant or piecewise-linear behavior, which is directly related to the problem of strong (static) correlation and challenges the description of molecular dissociation. In this paper, we study the behavior of the energy, the frontier Kohn-Sham (KS) orbitals, the KS potentials and the electron density, with respect to fractional spin, in different atomic systems. We analyze five standard exchange-correlation functionals and find three main scenarios of deviation from the expected exact results. We clearly recognize a jump in the frontier orbital energies upon spin variation in the exact exchange and in hybrid functionals, and the related plateau in the corresponding KS potential. Our results are instrumental for the assessment of the quality of existing approximations from a new perspective and for the development of advanced functionals with sensitivity to magnetic properties.