Strong Correlation and Charge Localization in Kohn-Sham Theories with Fractional Orbital Occupations: The Role of the Potential

Strongly correlated electrons have been the subject of substantial theoretical interest for many years. Most work has focused on obtaining the energy in a low-cost fashion. Here, we show that even methods with good energies can yield significant "delocalization errors" that affect the orbitals and density, leading to large errors in predicting other important properties such as dipole moments. We illustrate this point by comparing existing state-of-art approaches with an accurate exchange correlation functional based on a generalised valence bond ansatz, in which orbitals and fractional occupations are treated as variational parameters via a common optimized effective potential (OEP). We show that the OEP exhibits step and peak features which, similar to the exact Kohn-Sham (KS) potential of 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 delocalisation error as coming from an artificial mixing of the ground state with a charge-transfer excited state which is avoided if occupation numbers exhibit discontinuities.