caseGS.and (e.g. Ni2GS.and) is input file for and.GS, calculating the ground state (or a few excited states with non-negligible contributions in the thermal average at the simulation temperature). The ground state is stored in EX_State.dat file which will be used later (step2) for calculating spectral intensities. caseGS.clu is the input file for the cluster model (basically the same entries with the caseGS.and).

What does caseGS.and (caseGS.clu) input file define?

1. Configuration diagonal energies (Coulomb energy Udd, charge-transfer energy Δ)
For configurations defined in caseGS.ham, here we give diagonal energies (which depend only on the electron filling in these configurations). For the initial-state calculation (without a core hole), only two energies are concerned: Coulomb energy (isotropic part) Udd, and charge-transfer energy Δ. Core-hole potential energy Udc (Coulomb interaction between valence electrons and a core-hole) appears in x-ray excited final states, see case.and. Conventionally, the charge-transfer energy Δ is defined as a (diagonal-)energy cost by an electron transfer from the neighboring ligands to the impurity site, starting with the configuration with the formal valence (i.e. with number of d electrons in the formal valence (e.g. d8 for Ni2+) at the impurity site+ filled ligand orbitals). The diagonal energies of higher configurations are calculated using the charge-transfer energy Δ and the Coulomb energy Udd, see case.and for general cases (including configurations with a core hole in final states)

Note for Anderson impurity model (when combined with DFT+DMFT calculation)
In the Anderson impurity model, the molecular (ligand) orbital (in the cluster model) is extended to the continuum bath to represent the valence/conduction bands in the crystal. There the ligand level is not well defined (though it could be represented by the ligand state in the DFT (wannierization) result which is extracted from e.g. tight-binding model constructed from the DFT bands, assuming that the ligand orbitals (wannier functions) is fully occupied in the DFT results. In our code for the Anderson impurity model, the energies of bath levels taken into account explicitly in their Hamiltonian matrix elements, and thus their energies should be excluded in the definition of the CT energy above provided by users, i.e. εL=0 in the equation above is inputted in the Anderson-model calculation.

There are two ways to provide the CT energy: as bare d-energy (εd0) or as renormalized d-energy (εdCT), see explanation in caseGS.ham. In the latter way, the εdCT value can be found in dc_info.dat which is the standard output file of the DMFT code implemented in opw2x package. To get εdCT, in general, one just computes averaged Coulomb interaction and add the Coulomb energies (nUdd) to the bare energy, see the equation above. Thus, we recommend the former way for defining the CT energy for not only the cluster model but also Anderson impurity model. To work with the former way, users can provide the bare energy (in caseGS.ham) which is obtained by extracting the double-counting corrections from the d-level in the LDA result. Importantly, in this case, the contributions of the Udd term must be added to diagonal energies in caseGS.and since this term is not included in the Hamiltonian generated in ham.GS.

About double-counting correction (for using DFT+DMFT results as input for core-level spectroscopy calculations):
In DFT+X methods, the double-counting correction is introduced to avoid double counting the effect of the electron-electron interaction which is already included in the DFT result on a static mean-field level. The orbital energies given by subtracting the double-counting correction from the DFT results serve their bare energies. No unique definition exists though several ad-hoc schemes for guessing the double-counting correction are proposed. Since the double-counting value renormalizes the energy levels of the relevant subset of orbitals (e.g. 3d orbitals in transition metals) with respect to others (e.g. uncorrelated oxygen 2p orbitals in case of transition-metal oxides), a comparison to experimental photoemission and inverse photoemission spectra will be valued for accessing the double-counting value used in the DFT+X methods.

2. Select configurations to be included in actual computation for initial states (and mixing paths).
Here the users can choose configurations and mixing paths between them (following their definitions in caseGS.ham) to be included in the (actual) initial-state calculations. For standard calculations, this part is just copy of caseGS.ham file created in previous step. Here, the users can reduce the strength of the mixing (for each path independently). This reduction is (for standard analyzes) not necessary for initial states.

3. (For Anderson model only) Define how to treat the bath (valence/conduction bands).
For the Anderson model, the users specify how to treat the bath states (i.e. how to approximate valence/conduction states in the real crystal). The code supports some simple band shapes (rectangular, semi-ellipse for a given band width W), which have been employed in conventional Anderson-model analyzes of core-level spectra. Alternatively, the users can provide the bath levels obtained by realistic band calculations combined with dynamical mean-field theory (DMFT). To discretize the continuous hybridization function obtained from the DFT+DMFT scheme, call opw_speclevel. The discretized bath levels for above/below EF are provided in Valence.dat and Conduction.dat file respectively.

caseGS.and

```            ==========     Input for Ander     ==========
DLT  Uvv  Ucv (eV)  : Charge-transfer energy, Coulomb energy, Core-hole potential (not used in the ground-state calculation)
-0.2250 6.5 7.8
CF-factors    / Mix-factors (for D-L and OP) : multiplication  factor for the crystal-field and hybridization interaction
1   1.00           1  1.00
Basis series (2*Mj)   Emitted electron in PE_Shell (EL1-EL2) : In the ground-state calculation, basis series = 0 and 1 for systems with even and odd electrons, respectively.
0                   0  0

nconf : number of configurations
4
average energy ( DLT,UVV,UCV )   shift(eV) : configuration diagonal energies
1  0.0  0.0  0.0                   0.0  d8
2  1.0  0.0  0.0                   0.0  d9L
3  2.0  1.0  0.0                   0.0  d10L2
4  2.0  1.0  0.0                   0.0  d10LL

0  0  3      : only the last one (3) is important which species no.of excited states to be computed in each 2mj block

ground               energy level   iteration   GS-Character(0/1) : choose configuration and mixing paths to be included in practical ground state calculation
4  1 2 3 4             0            150              1
mix / mix type               reduction : reduction factor for mixing (hybridization) paths
3   2 1 3 2 4 2            1.0 1.0 1.0
1   1   1
reduction (S-O,Uvv,Ucv,Hmf)
1.0 1.0 1.0 1.0```

Only for Anderson impurity model

```===========   Input for Valence and Conduction Band f90   ============
##### Valence (below Fermi level for metal)
Band Shape(1:Data,2:Rectangle,3:Semiellipse,0:Omit(Delete follows))
1
Descritization (1:Liner, 2:Two-step, 3:c-Ratio) for (0:Debug, 1:Ins, 2:Mtl)
1  2
NWtot, Wtot, c-Ratio( or W1), NW1, : Valence band levels for Band Shape 2-4
8  3.0  1.2  5
No of Valence Band kinds
4
Total Density for Bands (T1+T2 should be 2.0 for Spin_Dep_Ander) for BS 2-4
1.0 1.0 1.0 1.0
Grouping Levels for conf. with two or more Valence holes
(0:ungrouping, or No_Group (grouping unit, No of Unit))
0  or 3  1 N1 2 N2 3 N3(N3 is ignored)
##### Conduction (above Fermi level for metal)
Band Shape(1:Data,2:Rectangle,3:Semiellipse,0:Omit(Delete follows))
0
Descritization (1:Liner, 2:Two-step, 3:c-Ratio) for (0:Debug, 1:Ins, 2:Mtl)
1  2
NWtot, Wtot, c-Ratio( or W1), NW1, : Valence band levels for Band Shape 2-4
8  3.0  1.2  5
No of Valence Band kinds
4
Total Density for Bands (T1+T2 should be 2.0 for Spin_Dep_Ander) for BS 2-4
1.0 1.0 1.0 1.0
Grouping Levels for conf. with two or more Valence holes
(0:ungrouping, or No_Group (grouping unit, No of Unit))
0  or 3  1 N1 2 N2 3 N3(N3 is ignored)
========================   end of input   ============================```