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 flips, and 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) and generalized KS (GKS) orbitals, the KS potentials, and the electron density, with respect to fractional spin, in different atomic systems. We analyze seven standard exchange-correlation functionals and find two 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, as well as the related plateau in the corresponding KS potential, when using the optimized effective potential method within the KS scheme. When calculations are performed using the GKS approach, no jumps are observed, as expected. Moreover, we demonstrate that for high-spin systems, a full three-dimensional treatment is crucial; the spherical approximation commonly used in atoms causes a qualitative deviation. 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.