Nonuniqueness of the Potentials of Spin-Density-Functional Theory

URL:http://link.aps.org/doi/10.1103/PhysRevLett.86.5546 DOI:10.1103/PhysRevLett.86.5546It is shown that, contrary to widely held beliefs, the potentials of spin-density-functional theory (SDFT) are not unique functionals of the spin densities. Explicit examples of distinct sets of potentials with the same ground-state densities are constructed. These findings imply that the zero-temperature exchange-correlation energy is not always a differentiable functional of the spin density. As a consequence, various types of applications of SDFT must be critically reexamined.K. C. thanks L. N. Oliveira, M. Lüders, and E. K. U. Gross for valuable discussions, the Physics Department at the University of Columbia, Missouri, for generous hospitality, and the FAPESP for financial support. G.V. acknowledges support from NSF Grants No. DMR 9706788 and No. DMR-0074959