Description of core excitations by time‐dependent density functional theory with local density approximation, generalized gradient approximation, meta‐generalized gradient approximation, and hybrid functionals

Time‐dependent density functional theory (TDDFT) is employed to investigate exchange‐correlation‐functional dependence of the vertical core‐excitation energies of several molecules including H, C, N, O, and F atoms. For the local density approximation (LDA), generalized gradient approximation (GGA), and meta‐GGA, the calculated X1s→π* excitation energies (X = C, N, O, and F) are severely underestimated by more than 13 eV. On the other hand, time‐dependent Hartree‐Fock (TDHF) overestimates the excitation energies by more than 6 eV. The hybrid functionals perform better than pure TDDFT because HF exchange remedies the underestimation of pure TDDFT. Among these hybrid functionals, the Becke‐Half‐and‐Half‐Lee‐Yang‐Parr (BHHLYP) functional including 50% HF exchange provides the smallest error for core excitations. We have also discovered the systematic trend that the deviations of TDHF and TDDFT with the LDA, GGA, and meta‐GGA functionals show a strong atom‐dependence. Namely, their deviations become larger for heavier atoms, while the hybrid functionals are significantly less atom‐dependent. © 2007 Wiley Periodicals, Inc. J Comput Chem 2007