7.13 Core Ionization Energies and Core-Excited States

7.13.1 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. 78, 71. 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.