4 X-ray Dichroisms in Spherical Tensor and Green’s Function Formalism
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a single site quantum impurity problem, using a local screened Coulomb interaction (U ). In both GW and DMFT approaches, correlations (many-body effects) are
significantly better described than in standard DFT.
4.1.3.4 Which Approach Works Best for Core Level Spectroscopy
Calculations?
Unfortunately this is a very complex question: it depends on the chemical system
(ionic, covalent, strongly correlated, …), the edge (K -, L-edges, …) and the type
of spectroscopy (absorption, photoemission, …). Consequently, in the following we
try to provide some guiding considerations.
A good starting criterion for the choice of the method of calculation is the localization of the final state wave function. When electrons are excited into highly delocalized orbitals, they interact much less with other electrons meaning that the intraatomic interactions are expected to be small. In this case single-particle approaches
often give satisfactory results as the multi-electronic effects are small. This may be
the case for the K edge of 3d elements and the L 2,3 edges of heavy elements (e.g.,
rare earths, 5d transition metals), as well as the K edges of ligands (such as C, N, O,
S).
On the other hand, when electrons are excited into localized orbitals, they will
strongly interact with each other and the core hole. In this case, the multi-electronic
effects become significant, and description considering only the absorber atom may
be more successful such as LFM theory. This is typically the case for L 2,3 edges of
3d elements and M 4,5 edges of 4 f elements.
In intermediate cases where both intra- and inter-atomic effects are relevant, like
the K pre-edge of 3d elements, single-particle and many-body approaches may work
or fail. It may also happen that different energy ranges of a spectrum are best described
by different theoretical approaches. This is often the case when a weak pre-edge
feature is observed before the strong main edge. The pre-edges often arise from
excitations into localized orbitals while the main edge has a more delocalized character. Whether the final state is localized or not may be derived from the shape of
the absorption edge. When the edge is dominated by a step function, the final state
can be assumed to be delocalized. If it exhibits distinct peaks that decrease sharply,
this may be due (but not necessarily) to a localized final state.
4.1.4 Codes for Ligand-Field Multiplet Calculations
Regarding the practical aspects of calculating core level spectra, one faces yet another
level of complexity as the plethora of theoretical methods mentioned above are
implemented in a comparably large number of computational packages. Instead of
trying to provide an overview of all the available computational tools, we will focus
on introducing Quanty, one of the currently available software packages that can
95
a single site quantum impurity problem, using a local screened Coulomb interaction (U ). In both GW and DMFT approaches, correlations (many-body effects) are
significantly better described than in standard DFT.
4.1.3.4 Which Approach Works Best for Core Level Spectroscopy
Calculations?
Unfortunately this is a very complex question: it depends on the chemical system
(ionic, covalent, strongly correlated, …), the edge (K -, L-edges, …) and the type
of spectroscopy (absorption, photoemission, …). Consequently, in the following we
try to provide some guiding considerations.
A good starting criterion for the choice of the method of calculation is the localization of the final state wave function. When electrons are excited into highly delocalized orbitals, they interact much less with other electrons meaning that the intraatomic interactions are expected to be small. In this case single-particle approaches
often give satisfactory results as the multi-electronic effects are small. This may be
the case for the K edge of 3d elements and the L 2,3 edges of heavy elements (e.g.,
rare earths, 5d transition metals), as well as the K edges of ligands (such as C, N, O,
S).
On the other hand, when electrons are excited into localized orbitals, they will
strongly interact with each other and the core hole. In this case, the multi-electronic
effects become significant, and description considering only the absorber atom may
be more successful such as LFM theory. This is typically the case for L 2,3 edges of
3d elements and M 4,5 edges of 4 f elements.
In intermediate cases where both intra- and inter-atomic effects are relevant, like
the K pre-edge of 3d elements, single-particle and many-body approaches may work
or fail. It may also happen that different energy ranges of a spectrum are best described
by different theoretical approaches. This is often the case when a weak pre-edge
feature is observed before the strong main edge. The pre-edges often arise from
excitations into localized orbitals while the main edge has a more delocalized character. Whether the final state is localized or not may be derived from the shape of
the absorption edge. When the edge is dominated by a step function, the final state
can be assumed to be delocalized. If it exhibits distinct peaks that decrease sharply,
this may be due (but not necessarily) to a localized final state.
4.1.4 Codes for Ligand-Field Multiplet Calculations
Regarding the practical aspects of calculating core level spectra, one faces yet another
level of complexity as the plethora of theoretical methods mentioned above are
implemented in a comparably large number of computational packages. Instead of
trying to provide an overview of all the available computational tools, we will focus
on introducing Quanty, one of the currently available software packages that can