7.13.3 Transition-Potential DFT

A simpler alternative to TDDFT for x-ray emission is to use Kohn-Sham eigenvalue differences,

with oscillator strengths

where ${\varphi }_c$ is a core orbital and ${\varphi }_v$ is a valence orbital, with energy levels ${ϵ}_v$ and ${ϵ}_c$, respectively. The critical benefit from this approach is that only a calculation for the ground state is required, however as a consequence no account of the orbital relaxation for the core-ionized state is included. It has been shown that using this approach in conjunction with SRC functionals can lead to reasonable estimates of the transition energies and this is discussed in Ref.  445 Hanson-Heine M. W. D., George M. W., Besley N. A.
J. Chem. Phys.
(2017), 146, pp. 094106. Link , and this approach can be applied to study large systems. ⁴⁴⁶ Hanson-Heine M. W. D., George M. W., Besley N. A.
Chem. Phys. Lett.
(2018), 696, pp. 119. Link This approach to calculating XES is illustrated by Example 7.13.3 and extension of this approach to resonant x-ray emission spectroscopy is possible by using this feature together with MOM. The keywords NCORE_XES and NVAL_XES specify which transitions to compute.

Note:  This feature is only available with GEN_SCFMAN = FALSE .

Another approach of partial account of strong orbital relaxation, using only Kohn-Sham eigenvalues, is called transition potential (TP-)DFT. ¹¹⁴⁶ Stener M., Lisini A., Decleva P.
Chem. Phys.
(1995), 191, pp. 141. Link This approach uses Kohn-Sham orbital eigenvalue differences to approximate core-level excitation energies, based on a Kohn-Sham calculation with partial occupations of the orbitals involved in the transitions. This can be justified based on a Taylor expansion in terms of the orbital occupations, as originally suggested by Slater. ¹¹⁰⁸ Slater J. C.
Adv. Quantum Chem.
(1972), 6, pp. 1. Link Only energies are implemented for TD-DFT, not gradients.