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We show that using complex, spin-restricted orbitals (cR) in Kohn-Shamdensity functional theory (KS-DFT) allows one to access a new class ofdensities that is not accessible by either spin-restricted (RKS) orspin-unrestricted (UKS) orbitals. We further show that the real part of a cRKSdensity matrix can be non-idempotent when the imaginary part of the densitymatrix is not zero. Using cRKS orbitals shows significant improvements in thetriplet-singlet gaps of the TS12 benchmark set for the SPW92, PBE, BLYP, andTPSS functionals. Moreover, it was shown that RKS and UKS yield qualitativelywrong charge densities and spin densities, respectively, leading to worseenergetics. We demonstrate that the modern functionals SCAN, MN15-L, and B97M-Vshow surprisingly no improvement even with a qualitatively more accuratedensity from cRKS orbitals. To this end, our work not only paves the way toescape the symmetry dilemma whenever there exists a cRKS solution, but alsosuggests a new route to design better approximate XC functionals.

Kohn-Sham Density Functional Theory with Complex, Spin-Restricted Orbitals: Accessing a New Class of Densities without the Symmetry Dilemma