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# Plotting the BSE fatband structure of Si

## Contents

Visualization of BSE eigenvectors using fatbands.

## Input

Si
5.4300
0.5 0.5 0.0
0.0 0.5 0.5
0.5 0.0 0.5
2
cart
0.00 0.00 0.00
0.25 0.25 0.25


### INCAR

• This is the INCAR file for the basic DFT calculation:
System  = Si

PREC = Normal ; ENCUT = 250.0

ISMEAR = 0 ; SIGMA = 0.01
KPAR = 2

EDIFF = 1.E-8
NBANDS = 16
LOPTICS = .TRUE.  # needed for WAVEDER file
OMEGAMAX = 40


### KPOINTS

The KPOINTS file will be automatically generated in this example.

## Calculation

• In this example we will calculate and plot the first "bright" BSE eigenstates of silicon, also called fatbands[1]. In this tutorial the modelBSE setup from the previous tutorial is used in combination with a ${\displaystyle 10\times 10\times 10}$ gamma centered k-point grid (if you don't want to wait that long, a ${\displaystyle 4\times 4\times 4}$ grid takes only a minute). In principle the standard BSE method can also be used instead.

### Step 1 DFT calculation

We run a standard DFT calculation with the input files given above.

### Step 2 BSE calculation with fatbands

• The INCAR file for the modelBSE calculation looks like the following:
System  = Si

PREC = Normal ; ENCUT = 250.0

#ALGO = BSE
ANTIRES = 0
ISMEAR = 0 ; SIGMA = 0.01
ENCUTGW = 150

EDIFF = 1.E-8 # default 1.E-4
NBANDS = 16   # only bands that are used are required, prepare the same set in a forgoing DFT run
NBANDSO = 4
NBANDSV = 8
OMEGAMAX = 20

PRECFOCK = Normal

ALGO = TDHF
LMODELHF = .TRUE. #Turn model on
HFSCREEN = 1.26  # Screening lenght
AEXX = 0.088    #Inverse of epsilon_infinity
SCISSOR = 0.69  # Difference GW-DFT band gap

NBSEEIG = 10 # number of BSE eigenvectors written out in BSEFATBAND

• The important tag for fatband calculations is NBSEEIG. In this example this will write the 10 energetically lowest BSE eigenvectors to the output file BSEFATBAND.
• After the (model)BSE calculation we first look into the vasprun.xml file to have a look at the BSE eigenvalues and the oscillator strengths:

vasprun.xml (exact numbers can of course differ depending on the method you use and the density of your k-point grid):

<varray name="opticaltransitions" >
<v>      3.148           0.000 </v>
<v>      3.148           0.000 </v>
<v>      3.148           0.000 </v>
<v>      3.149   25654.244 </v>
<v>      3.149   25660.601 </v>
<v>      3.149   25665.652 </v>
<v>      3.151           0.001 </v>
<v>      3.151           0.001 </v>
<v>      3.152       423.751 </v>
<v>      3.310 216931.963 </v>
<v>      3.310 216916.814 </v>
<v>      3.310 216935.593 </v>

• The first number column shows the BSE eigenvalue and the second one the oscillator strength. We want to plot the first "bright" state, that means in this case number 4.