View source for Dielectric properties of Si using BSE

{{Template:BSE - Tutorial}}

== Task ==

Description: Calculate the dielectric function of Si including excitonic effects by solving the Bethe-Salpeter equation (BSE) on top of GW0.

== Input ==

=== {{FILE|POSCAR}} ===
 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 

=== {{FILE|INCAR}} ===
*This is the {{TAG|INCAR}} file for the basic DFT calculation:
 {{TAGBL|System}}  = Si
 {{TAGBL|PREC}} = Normal ; {{TAGBL|ENCUT}} = 250.0
 {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.01
 {{TAGBL|KPAR}} = 2
 {{TAGBL|EDIFF}} = 1.E-8

=== {{FILE|KPOINTS}} ===
 Automatic
  0
 Gamma
  6 6 6 
  0 0 0

== Calculation ==

*The workflow of GW0+BSE calculations is given in doall.sh and consists of the following consecutive steps:
# "Standard" DFT groundstate calculation.
# Obtain virtual orbitals: needs {{TAG|WAVECAR}} file from step 1.
# The GW0 calculation: need {{TAG|WAVECAR}} and {{TAG|WAVEDER}} from step 2.
# Optional step: use {{TAG|LOPTICS}}=''.TRUE.'' to plot dielectric function in the independent particle approximation (IPA) using GW0 quasiparticle energies instead of DFT energies.
# The BSE calculation: needs {{TAG|WAVECAR}} from step 3 and {{TAG|WAVEDER}} from step 2.

=== Step 1: DFT groundstate calculation === 
*We perform standard DFT calculation using the INCAR.DFT file.

=== Step 2: Obtain DFT "virtual" orbitals (empty states) ===
*This step uses the INCAR.DIAG file:
 {{TAGBL|System}}  = Si
 {{TAGBL|PREC}} = Normal ; {{TAGBL|ENCUT}} = 250.0
 {{TAGBL|ALGO}} = EXACT ; {{TAGBL|NELM}} = 1
 {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.01
 {{TAGBL|KPAR}} = 2
 {{TAGBL|NBANDS}} = 128
 {{TAGBL|LOPTICS}} = .TRUE. ; {{TAGBL|LPEAD}} = .TRUE.
 {{TAGBL|OMEGAMAX}} = 40
*We use exact diagonalization for this step ({{TAG|ALGO}}=''EXACT'') and keep 128 bands after diagonalization ({{TAG|NBANDS}}=128).
*With {{TAG|LPEAD}}=''.TRUE.'' we use an alternative way of computing the derivates of the orbitals with respect to the Bloch wave vectors.
*It is important that this calculations needs the orbitals ({{TAG|WAVECAR}} file) written in step 1.

=== Step 3: RPA quasiparticles with single-shot GW (G0W0) ===
*This step uses the INCAR.GW0 file:
 {{TAGBL|System}}  = Si
 {{TAGBL|PREC}} = Normal ; {{TAGBL|ENCUT}} = 250.0
 {{TAGBL|ALGO}} = GW0  
 {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.01 
 {{TAGBL|ENCUTGW}} = 150 ; {{TAGBL|NELM}} = 1 ;  {{TAGBL|NOMEGA}} =  50 ;  {{TAGBL|OMEGATL}} = 280
 {{TAGBL|KPAR}} = 2
 #{{TAGBL|NBANDSO}}=4 ; {{TAGBL|NBANDSV}}=8 ; {{TAGBL|LADDER}}=.TRUE. ; {{TAGBL|LUSEW}}=.TRUE.
 {{TAGBL|NBANDS}} = 128
 {{TAGBL|NBANDSGW}} = 12
 {{TAGBL|LWAVE}} = .TRUE.
 {{TAGBL|PRECFOCK}} = Normal
*We select the G0W0 method by specifying {{TAG|ALGO}}=''GW0'' and {{TAG|NELM}}=1.
*The energy cut off for the response function is select by {{TAG|ENCUTGW}}.
*The number of point used in the frequency integration is given by {{TAG|NOMEGA}}.
*Use the same number of bands ({{TAG|NBANDS}}) as in step 2, otherwise the {{TAG|WAVEDER}} file is not read correctly.
*The quasiparticle energies are calculated for the first few bands given by {{TAG|NBANDSGW}}.
*It is important that this calculation needs the orbitals ({{TAG|WAVECAR}} file) and the derivatives of the orbitals with respect to the Bloch vectors ({{TAG|WAVEDER}} file).
*The quasiparticle energies can be found in the {{TAG|OUTCAR}} file (saved as OUTCAR.GW0 in this example):
   QP shifts <psi_nk| G(iteration)W_0 |psi_nk>: iteration 1
 for sc-GW calculations column KS-energies equals QP-energies in previous step
 and V_xc(KS)=  KS-energies - (<T + V_ion + V_H > + <T+V_H+V_ion>^1  + <V_x>^1)
  
 k-point   1 :       0.0000    0.0000    0.0000
  band No.  KS-energies  QP-energies   sigma(KS)   V_xc(KS)     V^pw_x(r,r')   Z            occupation

=== Step 4 (optional): Plot IPA dielectric function using GW0 quasiparticle energies ===
* This step uses the INCAR.NONE file:
 {{TAGBL|System}}  = Si
 {{TAGBL|PREC}} = Normal ; {{TAGBL|ENCUT}} = 250.0
 {{TAGBL|ALGO}} = Nothing ; {{TAGBL|NELM}} = 1
 {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.01
 {{TAGBL|KPAR}} = 2
 {{TAGBL|NBANDS}} = 128
 {{TAGBL|LWAVE}} = .FALSE.
 {{TAGBL|LOPTICS}} = .TRUE. ; {{TAGBL|LPEAD}} = .TRUE.
 {{TAGBL|OMEGAMAX}} = 40  
*By specyfing {{TAG|ALGO}}=''Nothing'' we do nothing except reading the {{TAG|WAVECAR}} file.
*Using {{TAG|LOPTICS}}=''.TRUE.'' and {{TAG|LPEAD}}=''.TRUE.'' we compute the dielectric function in the IPA.

=== Step 5: The BSE calculation ===
* This step uses the INCAR.BSE file:
 {{TAGBL|PREC}} = Normal ; {{TAGBL|ENCUT}} = 250.0
 {{TAGBL|ALGO}} = BSE 
 {{TAGBL|ANTIRES}} = 0
 {{TAGBL|ISMEAR}} = 0 ; {{TAGBL|SIGMA}} = 0.01
 {{TAGBL|ENCUTGW}} = 150
 {{TAGBL|EDIFF}} = 1.E-8
 {{TAGBL|NBANDS}} = 128
 {{TAGBL|NBANDSO}} = 4
 {{TAGBL|NBANDSV}} = 8
 {{TAGBL|OMEGAMAX}} = 20
 {{TAGBL|PRECFOCK}} = Normal
*By specifying {{TAG|ANTIRES}}=0 we use the Tamm-Dancoff approximation.
*{{TAG|ENCUTGW}}=150 specifies the energy cut-off of the response function.
*{{TAG|NBANDSO}} and {{TAG|NBANDSV}} define the number of valence and conduction bands in the calculations.
*This calculation needs the orbitals ({{TAG|WAVECAR}} file) from step 3 and the derivative of the orbitals with respect to the Bloch vectors ({{TAG|WAVEDER}} file) written in step 2.
*By using the script ./plotall.sh we get the absorption spectra within the independent particle picture and with BSE:
[[File:Fig BSE example1 2.png|600px]]
*The calculated dielectric function of Si is at this point (GW+BSE) already in much better agreement with experiment. However we can do even better as shown in the following figure:
[[File:Fig BSE example1 4.png|400px]]
*The problem comes from the coarse k-point grid that we have used. A denser grid samples more (direct) transitions between the bands. 
[[File:Fig BSE example1 3.png|200px]]
*Simply using a denser grid is mostly not an option because of the computational expense.

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== Download ==
[[Media:Si BSE.tgz| Si_BSE.tgz]]

{{Template:BSE}}

[[Category:Examples]]