Ionization potential optimized double-hybrid density functional approximations.

Double-hybrid density functional approximations (DH-DFAs) provide an accurate description of the electronic structure of molecules by semiempirically mixing density functional and wavefunction theory. In this paper, we investigate the properties of the potential used in such approximations. By using the optimized effective potential approach, the consistent Kohn-Sham (KS) potential for a double-hybrid functional (including the second-order perturbational contribution) can be generated. This potential is shown to provide an improved description of orbital energies as vertical ionization potentials (IPs), relative to the perturbation-free KS potential typically used. Based on this observation, we suggest that DH-DFAs should be constructed in such a way that the potential provides accurate orbital energies. As a proof of principle, the B2-PLYP functional is reparameterized to obtain the IP-optimized B2IP-PLYP functional, using a small set of vertical IPs and atomization energies as reference data. This functional is shown to outperform B2-PLYP in a wide range of benchmarks and is en par with the related B2GP-PLYP. In particular, it is shown to be the most reliable choice in electronically difficult and multireference cases.