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# 7.13.3 Transition-Potential DFT

(July 14, 2022)

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

 $\Delta E=\epsilon_{v}-\epsilon_{c}\;,$ (7.119)

with oscillator strengths

 $f\propto|\langle\phi_{c}|\hat{\mu}|\phi_{v}\rangle|^{2}$ (7.120)

where $\phi_{c}$ is a core orbital and $\phi_{v}$ is a valence orbital, with energy levels $\epsilon_{v}$ and $\epsilon_{c}$, 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.
, 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.
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 .

Example 7.153  The calculation of the XES spectrum of water using Koopmans’ theorem within KS-DFT with a short-range corrected functional.

$molecule 0 1 C 0.0000000000 0.0000000000 0.5121520001 O 0.0000000000 0.0000000000 -0.6942567610 H 0.9377642813 0.0000000000 1.1074358558 H -0.9377642813 0.0000000000 1.1074358558$end

$rem METHOD src1r1 BASIS 6-311G** NCORE_XES 2 NVAL_XES 4 GEN_SCFMAN false$end


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.
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.
(1972), 6, pp. 1.
Only energies are implemented for TD-DFT, not gradients.

Example 7.154  This example shows a calculation using TP-DFT.

$molecule 0 1 O 0.0000000000 0.0000000000 -0.1239093563 H 0.0000000000 1.4299372840 0.9832657567 H 0.0000000000 -1.4299372840 0.9832657567$end

$rem METHOD b3lyp BASIS aug-cc-pCVQZ INPUT_BOHR true$end

@@@

$molecule read$end

$rem METHOD b3lyp BASIS aug-cc-pCVQZ INPUT_BOHR true UNRESTRICTED true TPDFT_ATOM 1 TPDFT_FRAC 50 TPDFT_LUMO 0$end


Example 7.155  This example shows a calculation using TP-DFT.

$molecule 0 1 O 0.0000000000 0.0000000000 -0.1239093563 H 0.0000000000 1.4299372840 0.9832657567 H 0.0000000000 -1.4299372840 0.9832657567$end

$rem METHOD b3lyp BASIS aug-cc-pCVQZ INPUT_BOHR true$end

@@@

$molecule read$end

$rem METHOD b3lyp BASIS aug-cc-pCVQZ INPUT_BOHR true UNRESTRICTED true TPDFT_ATOM 1 TPDFT_FRAC 50$end