Spin symmetry in thermally-assisted-occupation density-functional theory

For electronic systems with multireference (MR) character, Kohn-Sham density-functional theory (KS-DFT) with the conventional exchange-correlation (xc) energy functionals can lead to incorrect spin densities and related properties. For example, for H₂ dissociation, the spin-restricted and spin-unrestricted solutions obtained with the same xc energy functional in KS-DFT can be distinctly different, yielding the unphysical spin-symmetry breaking effects in the spin-unrestricted solutions. Recently, thermally-assisted-occupation density-functional theory (TAO-DFT) has been shown to resolve the aforementioned spin-symmetry breaking, when the fictitious temperature is properly chosen. In this work, a response theory based on TAO-DFT is developed to demonstrate that TAO-DFT with a sufficiently large fictitious temperature can always resolve the unphysical spin-symmetry breaking in MR systems. To further support this, TAO-DFT calculations with various fictitious temperatures are performed for the dissociation of H₂, N₂, He₂, and Ne₂ as well as the twisted ethylene.