# 8. Spex and Fleur¶

Spex needs input data about a reference mean-field system, for example, the KS system of DFT. A self-consistent mean-field calculation must thus precede any Spex calculation. The following three steps prepare the input data for Spex.

Step 1: Self-consistent mean-field calculation. Generate special k-point set with Spex. Diagonalize mean-field Hamiltonian with the potential from step 1, which produces the eigensolutions at the new k points.

## 8.1. Fleur¶

The Fleur code is an implementation of KS-DFT based on the FLAPW method. Consult the Fleur manual for details.

We distinguish between an old (v0.26b) and a new generation (MaX releases) of Fleur versions. In the long run, the old versions will become obsolete. However, as of now, the new Fleur versions have not been completely integrated. Therefore, both are documented here.

### 8.1.1. Fleur v0.26b (2019.03)¶

In the Fleur input file there is a flag for writing out the necessary data for a Spex calculation. It is called gw and is appended to line 23 of the Fleur “inp” file:

23|vchk=F,cdinf=F,pot8=F,gw=n,numbands=N

n can take four values:

• gw=0: No output files are generated (default; the same as omitting gw and numbands altogether).
• gw=1: Some basic parameters are written to several files. Otherwise Fleur runs as usual.
• gw=2: All output files necessary for Spex are created and Fleur stops after one iteration (without updating the potential). In this case you should also set pot8=T and the maximal number of bands numbands=....
• gw=3: Self-consistent cycle for QSGW. Same as gw=1 but adds $$\Sigma^{\mathrm{xc,QSGW}}(\mathbf{r},\mathbf{r}')-v^{\mathrm{xc}}(\mathbf{r})$$ to the Hamiltonian in each iteration.

The output files are

• “gwa”: Basic parameters including the atomic numbers and positions in the unit cell, lattice parameters and basis vectors, FLAPW l cutoff, and local-orbital parameters,
• “LATTC”: FLAPW G cutoff,
• “ecore”: core-electron functions,
• “eig”: k points, wave-function coeffients (interstitial), energies,
• “abcoeff”: wave-function coefficients (muffin tins),
• “KS.hdf”: alternative to “eig” and “abcoeff” (now the default),
• “vxc”: expectation values of the xc potential (diagonal elements, obsolete),
• “vxcfull”: matrix of the xc potential,
• “qsgw”: matrix of the QSGW self-energy (only for QSGW calculations).

Furthermore, Spex needs the Fleur file “sym.out”.

### 8.1.2. Fleur MaX Release 3 v0.27¶

Spex has to be configured with --with-dft=fleurR3 to compile the interface to Fleur MaX Release 3 (and 4) (see Section 1).

In the Fleur “inp.xml” file, there is a flag for writing out the necessary data for a Spex calculation. It can be found at the following XML-path /calculationSetup/expertModes/@gw, the numbands flag can be set at /calculationSetup/cutoffs/@numbands.

When using the input generator for fleur it is adviseable to set the option -gw. This writes out additional options in the “inp.xml”, which already include the settings for an alternative k-point set (“kpts_gw”).

The following modes are available:

• gw=0: No output files are generated (default).
• gw=1: The files “basis.hdf”, “pot.hdf”, and “ecore” are written. Needed for Spex to construct the “kpts_gw” file. The broyden history is reset.
• gw=2: All output files necessary for Spex are created and Fleur stops after generating the KS eigensolutions (without updating the potential).

The output files are:

• “basis.hdf”: including all information about the basis (atoms, cell, kpts, muffin tin and planewave basis information),
• “ecore”: core-electron functions,
• “eig_gw.hdf”: energies, wave-function coeffients (interstitial), wave-function coefficients (atomic spheres),
• “pot.hdf”: potentials (pottot, potcoul, potx) and relevant information on the stepfunction and structure.

Furthermore, Spex needs the Fleur file “sym.out”, which contains the symmetry operations of the system.

Warning

Self-consistent GW calculations (also HF, PBE0, etc.) are not yet possible with the new Fleur code. Please use the old Fleur code for this feature.

A short tutorial can be found at: https://www.flapw.de/site/CECAM-2019-tut/Day_4_Hands-on_Spex/

### 8.1.3. Fleur MaX Release 5 version 33¶

Spex has to be configured with --with-dft=fleurR5 to compile the interface to the Fleur MaX Release 5 (see Section 1).

The following changes from Fleur MaX Release 3 (and 4) apply:

• The Fleur “inp.xml” file now contains a listName entry for the requested k-point set defined in “kpts.xml”. Spex writes its k-point set into “kpts.xml” with the name (listName) “spex”. This supercedes the file “kpts_gw” of Release 3 (and 4). For the “gw=2” run, the entry listName="spex" has to be set in “kpts.xml”. (Spex also writes its q-point path into “kpts.xml” with the name “spex_band”.)
• “pot.hdf” now also contains the symmetry information. Spex does not need an external symmetry file (“sym.out”) anymore.
• The lattice scaling factor (interpreted by Spex as the lattice parameter) is now undefined and generally set to 1.

The following modes are available:

• gw=0: No output files are generated (default).
• gw=1: The files “basis.hdf”, “pot.hdf”, and “ecore” are written. Needed for Spex to complement the “kpts.xml” file. The broyden history is reset.
• gw=2: All output files necessary for Spex are created and Fleur stops after generating the KS eigensolutions (without updating the potential).

### 8.1.4. Fleur MaX Release 5.1 version 34¶

Spex has to be configured with --with-dft=fleur5.1 to compile the interface to the Fleur MaX Release 5.1 (see Section 1).

The following changes from Fleur MaX Release 5 apply:

• The flag gw=... in “inp.xml” has been renamed to spex=....
• The Spex path name in “kpts.xml” has been changed from “spex_band” to “spex-path”.

Warning

Self-consistent GW calculations (also HF, PBE0, etc.) are not yet possible with the Fleur MaX versions. Please use the old Fleur code for this feature. Input data for $$G^\mathrm{SOC}W^\mathrm{SOC}$$ calculations cannot be provided by Fleur, but ITERATE can be used for that purpose.

## 8.2. Remarks about MT basis¶

### 8.2.1. Conduction states¶

As in a GW calculation the conduction states enter both the Green function and the screened interaction, they should be accurately described already in the KS system which is our starting point for the perturbation treatment. The LAPW basis, however, only guarantees well described occupied states. In order to obtain well-converged GW results, one must make the basis set more flexible, especially in the MT regions, by introducing local orbitals either at high energy parameters or as higher-order energy derivatives [Phys. Rev. B 74, 045104 (2006), Comput. Phys. Commun., 184, 2670 (2013)].

### 8.2.2. Semicore states¶

High-lying semicore states can appear as badly described “ghost bands” in the valence band region leading to a wrong DFT ground state. A possible solution is to use local orbitals and extend the energy window, such that the semicore states are treated as valence states. On the other hand if the ghost bands are above the Fermi energy, they usually pose no problem in a DFT calculation. In a GW calculation, however, the conduction states are also relevant, and one must make sure that there are no ghost bands at all in the energy spectrum. Therefore, it might be necessary to treat more (and deeper) semicore states as valence states than are needed in the DFT calculation. As an indication for such a case the overlap of core states with basis and wavefunctions calculated in the routine “checkinput” should be checked. As an example, here is the output for Strontium Titanate with a Titanium 3s ghost band:

Overlap <core|basis>
Atom type  1
u(s)    udot(s)
1s -0.001431  0.000644
2s -0.000830  0.000414
3s  0.287789 -0.878671
u(p)    udot(p)   ulo(p) ...
2p -0.000665  0.000112 -0.000494
...
Maximum overlap <core|val> at (band/kpoint)
Atom type  1
1s  0.000611 (031/ 001)
2s  0.000343 (031/ 001)
3s  0.664265 (047/ 001)
2p  0.000340 (003/ 036)  0.000481 (003/ 042)  0.000340 (003/ 036)
...