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Optimized Unrestricted Kohn-Sham Potentials from Ab Initio Spin Densities

The reconstruction of the exchange-correlation potential from accurate ab initio electron densities can provide insights into the limitations of the currently available approximate functionals and provide guidance for devising improved approximations for density-functional theory (DFT). For open-shell systems, the spin density is introduced as an additional fundamental variable in Spin-DFT. Here, we consider the reconstruction of the corresponding unrestricted Kohn-Sham potentials from accurate ab initio spin densities. In particular, we investigate whether it is possible to reconstruct the spin exchange-correlation potential, which determines the spin density in spin-unrestricted Kohn-Sham-DFT, despite the numerical difficulties inherent to the optimization of potentials with finite orbital basis sets. We find that the recently developed scheme for unambiguously singling out an optimal optimized potential [J. Chem. Phys. 135, 244102 (2011)] can provide such spin potentials accurately. This is demonstrated for two test cases, the lithium atom and the dioxygen molecule, and target (spin) densities from Full-CI and CASSCF calculations, respectively.