Strong Correlation and Charge Localization in Kohn-Sham Theories with Fractional Orbital Occupations

We study static correlation and delocalization errors and show that even methods with good energies can yield significant delocalization errors that affect the density, leading to large errors in predicting, e.g., dipole moments. We illustrate this point by comparing existing state-of-the-art approaches with an accurate exchange-correlation functional based on a generalized valence-bond ansatz in which orbitals and fractional occupations are treated as variational parameters via an optimized effective potential (OEP). We show that the OEP exhibits step and peak features that, similar to the exact Kohn-Sham potential of density functional theory (DFT), are crucial to prevent charge delocalization. We further show that the step is missing in common approximations within reduced density matrix functional theory, resulting in delocalization errors comparable to those found in DFT approximations. Finally, we explain the delocalization error as coming from artificial mixing of the ground state with a charge-transfer excited state that is avoided if the occupation numbers exhibit discontinuities.