Does the ionization potential condition employed in QTP functionals mitigate the self-interaction error?

Though contrary to conventional wisdom, the interpretation of all occupied Kohn-Sham eigenvalues as vertical ionization potentials is justified by several formal and numerical arguments. Similarly, the performance of density functional approximations (DFAs) for fractionally charged systems has been extensively studied as a measure of one- and many-electron self-interaction errors (MSIEs). These complementary perspectives (initially recognized in ab initio dft) are shown to lead to the unifying concept that satisfying Bartlett's IP theorem in DFA's mitigates self-interaction errors. In this contribution, we show that the IP-optimized QTP functionals (reparameterization of CAM-B3LYP where all eigenvalues are approximately equal to vertical IPs) display reduced self-interaction errors in a variety of tests including the He₂⁺ potential curve. Conversely, the MSIE-optimized rCAM-B3LYP functional also displays accurate orbital eigenvalues. It is shown that the CAM-QTP and rCAM-B3LYP functionals show improved dissociation limits, fundamental gaps and thermochemical accuracy compared to their parent functional CAM-B3LYP.