7.12 Core Ionization Energies and Core-Excited States

7.12.1 Calculations of Core-Level States with (TD)DFT

TDDFT is not suited to describe the extended X-ray absorption fine structure (EXAFS) region, wherein the core electron is ejected and scattered by the neighboring atoms. The core-excited states can be computed by using truncated excitation space within TDDFT/TDA (activated by TRNSS and TRTYPE keywords), but the resulting core-excitation energies computed with standard hybrid functionals are many electron volts too low compared with experiment. Exchange-correlation functionals specifically designed to treat core excitations are available in Q-Chem. These short-range corrected (SRC) functionals are a modification of the more familiar long-range corrected functionals (discussed in Section 5.6). However, in SRC-DFT the short-range component of the Coulomb operator is predominantly Hartree-Fock exchange, while the mid to long-range component is primarily treated with standard DFT exchange. These functionals can be invoked by using the SRC_DFT rem. In addition, a number of parameters (OMEGA, OMEGA2, HF_LR, HF_SR) that control the shape of the short and long-range Hartree-Fock components need to be specified. Full details of these functionals and appropriate values for the parameters can be found in Refs. Besley:2009a, Besley:2010. An example of how to use these functionals is given below (examples 7.3.7 and 7.3.7 illustrate the setup for XAS calculations). For the K-shell of heavy elements (2nd row of the periodic table) relativistic effects become increasing important and a further correction for these effects is required. Also calculations for L-shell excitations are complicated by core-hole spin orbit coupling.

TDDFT can also be used to compute XES by employing core-ionized reference state computed with MOM; in these calculations, using SRC functionals is also recommended.