Improving Exchange-Correlation Potentials of StandardDensity Functionals with the Optimized-Effective-Potential Methodfor Higher Accuracy of Excitation Energies

We present a general scheme to improve the exchange-correlation potential of standard Kohn–Sham methods, like the PBE (Perdew, Burke, Ernzerhof) or PBE0 method, by enforcing exact conditions the exchange-correlation potential has to obey during their calculation. The required modifications of the potentials are enabled by generating the potentials within the optimized-effective-potential (OEP) framework instead of directly taking the functional derivative with respect to the electron density on a real-space grid as usual. We generalize a condition for the exact exchange potential that involves the eigenvalues of the highest occupied molecular orbital such that it is applicable to arbitrary approximate exchange potentials. The new approach yields strongly improved exchange-correlation potentials which lead to qualitatively and quantitatively improved KS orbital and eigenvalue spectra containing a Rydberg series as required and obeying much better the Kohn–Sham ionization energy theorem. If the resulting orbitals and eigenvalues are used as input quantities in time-dependent density-functional theory (TDDFT) to calculate excitation energies then the accuracy of the latter is drastically improved, e.g., for TDDFT with the PBE functional the accuracy of excitation energies is improved by a factor of roughly three. This make the introduced approach highly attractive for generating input orbitals and eigenvalues for TDDFT but potentially also for high-rung correlation functionals that are typically evaluated in a post-SCF (post self-consistent-field) manner. We apply the new approach to calculate exchange-correlation potentials to the PBE and PBE0 functionals but the approach is generally applicable to any functional.