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Tutorial: F K edge in LiF

First, we create a directory for the BSE calculations. All subsequent calculations with the exciting code will be performed in that directory

mkdir lif-exciting
cd lif-exciting/

F K Edge BSE in LiF

First, we need to calculate the DFT electronic structure and F K edge absorption spectrum. We do this with the following input file:

<input>
  <title>LiF F K Edge</title>
  <structure speciespath="./">
    <crystal scale="1.8897543768634038">
      <basevect>      0.00000000       2.01297060       2.01297060</basevect>
      <basevect>      2.01297060       0.00000000       2.01297060</basevect>
      <basevect>      2.01297060       2.01297060       0.00000000</basevect>
    </crystal>
    <species speciesfile="Li.xml">
      <atom coord="      0.00000000       0.00000000       0.00000000" />
    </species>
    <species speciesfile="F.xml">
      <atom coord="      0.50000000       0.50000000       0.50000000" />
    </species>
  </structure>
  <groundstate
    do="fromscratch"
    ngridk="2 2 2"
    xctype="GGA_PBE_SOL"/>
 <xs
      xstype="BSE"
      ngridk="2 2 2"
      ngridq="2 2 2"
      rgkmax="4.0" 
      vkloff="0.05 0.15 0.25"
      nempty="30" 
      gqmax="2.0" 
      broad="0.0276"
      tappinfo="true"
      tevout="true">

      <energywindow 
         intv="23.6 24.6" 
         points="1500" />
 
      <screening 
         screentype="full" 
         nempty="100"/>
 
      <BSE 
        chibar0="false"
        chibar0comp="1"
	      xas="true"
        xasspecies="2"
	      xasatom="1"
        xasedge="K"
        bsetype="singlet" 
	      nstlxas="1 2"
        brixshdf5="true"/>
 
      <qpointset>
      <qpoint>0.0 0.0 0.0</qpoint>
      </qpointset>
       <storeexcitons MinNumberExcitons="1" MaxNumberExcitons="32"/>
   </xs>
</input>

We see that we write all 32 excitonic eigenstates to file. In a converged BSE calculation, the number of eigenstates is huge and one might need to consider carefully how many are necessary for a converged RIXS spectrum. Generally, this will depend on the range of excitation energies one is interested in. The higher the excitation energy is beyond the absorption edge, the more eigenstates are required.

Executing the exciting code with this input.xml will generate a output file named bse_output.h5 which we rename by

mv bse_output.h5 core_output.h5

Renaming is important, because otherwise it will be overwritten when we calculate the valence excitation spectrum.

Momentum Matrix Elements

An important ingredient of the RIXS calculation are the momentum matrix elements between the core and conduction states. These can be calculated with low computational cost by adjusting the input files such that it looks like:

<input>
  <title>LiF F K Edge</title>
  <structure speciespath="./">
    <crystal scale="1.8897543768634038">
      <basevect>      0.00000000       2.01297060       2.01297060</basevect>
      <basevect>      2.01297060       0.00000000       2.01297060</basevect>
      <basevect>      2.01297060       2.01297060       0.00000000</basevect>
    </crystal>
    <species speciesfile="Li.xml">
      <atom coord="      0.00000000       0.00000000       0.00000000" />
    </species>
    <species speciesfile="F.xml">
      <atom coord="      0.50000000       0.50000000       0.50000000" />
    </species>
  </structure>
  <groundstate
    do="fromscratch"
    ngridk="2 2 2"
    rgkmax="4.0"
    xctype="GGA_PBE_SOL"/>
 <xs
      xstype="BSE"
      ngridk="2 2 2"
      ngridq="2 2 2"
      rgkmax="4.0" 
      vkloff="0.05 0.15 0.25"
      nempty="30" 
      gqmax="2.0" 
      broad="0.0276"
      tappinfo="true"
      tevout="true">

      <energywindow 
         intv="23.6 24.6" 
         points="1500" />
 
      <screening 
         screentype="full" 
         nempty="100"/>
 
      <BSE 
        chibar0="false"
        chibar0comp="1"
	      xas="true"
        xasspecies="2"
	      xasatom="1"
        xasedge="K"
        bsetype="singlet" 
	      nstlxas="1 2"
        brixshdf5="true"
        distribute="true"/>
 
      <qpointset>
      <qpoint>0.0 0.0 0.0</qpoint>
      </qpointset>
      <plan>
        <doonly task="writepmatxs"/>
        <doonly task="writepmatasc"/>
      </plan>
   </xs>
</input>

The input file is nearly identical to the one used for the calculation of the F K edge, with the only change being the subelement plan which triggers the calculation of the momentum matrix elements (writepmatxs) and the output to HDF5 file (writepmatasc). The matrix elements are written to the file bse_output.h5. We rename the file again

mv bse_output.h5 pmat.h5

Valence Spectrum in LiF

Following the F K edge spectrum, we now calculate the valence excitation spectrum. While many parameters (such as nstlbse and gqmax) can be different between the two BSE calculations, the parameters ngridk, ngridq, and vkloff HAVE TO BE IDENTICAL. To make sure that the wavefunctions are identical in both calculations, we do not calculate the DFT electronic structure again (a repeated diagonalization of the Kohn-Sham Hamiltonian can introduce a different global phase, which alters the results). As such, the input file looks like this

<input>
  <title>LiF Valence Spectrum</title>
  <structure speciespath="./">
    <crystal scale="1.8897543768634038">
      <basevect>      0.00000000       2.01297060       2.01297060</basevect>
      <basevect>      2.01297060       0.00000000       2.01297060</basevect>
      <basevect>      2.01297060       2.01297060       0.00000000</basevect>
    </crystal>
    <species speciesfile="Li.xml">
      <atom coord="      0.00000000       0.00000000       0.00000000" />
    </species>
    <species speciesfile="F.xml">
      <atom coord="      0.50000000       0.50000000       0.50000000" />
    </species>
  </structure>
  <groundstate
    do="fromscratch"
    ngridk="2 2 2"
    rgkmax="4.0"
    xctype="GGA_PBE_SOL"/>
 <xs
      xstype="BSE"
      ngridk="2 2 2"
      ngridq="2 2 2"
      rgkmax="4.0" 
      vkloff="0.05 0.15 0.25"
      nempty="30" 
      gqmax="2.0" 
      broad="0.0276"
      tappinfo="true"
      tevout="true">

      <energywindow 
             intv="0 1.0" 
             points="1500" />

      <screening 
              screentype="full" 
              nempty="100" />

      <BSE
        chibar0="false"
        chibar0comp="1"
        bsetype="singlet" 
        nstlbse="2 5 1 2"
        brixshdf5="true"
        distribute="true" />

      <qpointset>
                  <qpoint>0.0 0.0 0.0</qpoint>
       </qpointset>
       <storeexcitons MinNumberExcitons="1" MaxNumberExcitons="64"/>
       <plan>
         <doonly task="writepmatxs"/>
         <doonly task="scrcoulint"/>
         <doonly task="exccoulint"/>
         <doonly task="bse"/>
       </plan>
   </xs>
</input>

Once again, we write all 64 eigenstates of the BSE to file. With the plan subelement, we specify which tasks need to be performed. We re-calculate neither the KS electronic structure nor the screening. These quantities are supossed to be identical in the two BSE calculations. Finally, we also rename this file

mv bse_output.h5 optical_output.h5

From this point on, only the files core_output.h5, pmat.h5, and optical_output.h5 are required. We will move them to a different directory

mkdir ../lif-rixs
mv *.h5 ../lif-rixs
cd ../lif-rixs

RIXS Spectrum LiF

Now we have to create the file input.cfg that describes the input parameters for the BRIXS calculation. The file contains the following:

omega= 653 654 655 656
pol_in=1.0 0.0 0.0
pol_out=1.0 0.0 0.0
broad=0.15
nblocks=2
eigstates_optical=64
eigstates_core=32

Here, we specify the excitation energies (omega) and the polarizations pol_in of the incoming and pol_out of the outgoing photon. Note that the polarization should be identical to the one specified by the parameter chibar0comp in the exciting calculations.We furthermore specify the lifetime broadening (broad) of the intermediate state. With eigstates_optical and eigstates_core we specify how many eigenstates of the corresponding BSE calculations are used. Finally, nblocks defines in how many blocks the eigenvectors should be separated. More blocks will reduce the memory requirements of the calculations, but might increase the runtime. A good estimate is to use the number of k-points along a specific direction.

We then execute the first BRIXS executable with

/path/to/BRIXS/bin/rixs-pathway-serial

which creates the file data.h5. The final result is then obtained by executing

/path/to/BRIXS/bin/rixs-oscstr-serial

The final result is stored in the file rixs.h5.

Note: For calculations done with chibar0="false" it is necessary to choose pol_in and pol_out to be identical. Otherwise for calculations with chibar0="true", which is an approximation on the level of RIXS, it is possible to use different polarizations for the incoming and outgoing photon.