Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States

The lack of particle–hole attraction and orbital
relaxation
within time-dependent density functional theory (TDDFT) lead to extreme
errors in the prediction of K-edge X-ray absorption spectra (XAS).
We derive a linear-response formalism that uses optimized orbitals
of the n – 1-electron system as the reference,
building orbital relaxation and a proper hole into the initial density.
Our approach is an exact generalization of the static-exchange approximation
that ameliorates the particle–hole interaction error associated
with the adiabatic approximation and reduces errors in TDDFT XAS by
orders of magnitude. With a statistical performance of just 0.5 eV
root-mean-square error and the same computational scaling as TDDFT
under the core–valence separation approximation, we anticipate
that this approach will be of great utility in XAS calculations of
large systems.