LSELFENERGY

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LSELFENERGY = [logical]
Default: LSELFENERGY = .FALSE.

Description: Controls whether the frequency-dependent self-energy is calculated or not.

If LSELFENERGY = .FALSE. (default), quasi-particle (QP) shifts are evaluated.

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 Imag(sigma)
 
      1      -7.1627      -8.3040     -14.5626     -12.7276     -21.6682       0.6219       2.0000       1.2037
      2      -2.0901      -3.4347     -15.7660     -14.2799     -21.7439       0.9048       2.0000       0.6914
      3      -2.0901      -3.4347     -15.7660     -14.2799     -21.7439       0.9048       2.0000       0.6914
      4      -2.0901      -3.4347     -15.7660     -14.2799     -21.7439       0.9048       2.0000       0.6914
      5       0.4603      -0.4663     -13.7603     -12.5200     -18.1532       0.7471       2.0000       0.2167
      6       0.4603      -0.4663     -13.7603     -12.5200     -18.1532       0.7471       2.0000       0.2167

If LSELFENERGY = .TRUE., the frequency dependent self-energy $\langle \psi _{n{\mathbf {k} }}|\Sigma (\omega )|\psi _{n{\mathbf {k} }}\rangle$ is evaluated and printed to vasprun.xml. An example output looks like the following:

<varray name="selfenergy" >                                                                                                                                                                                                                                               
  <v>    -150.00000000     -25.40060536       0.24429448 </v>                                                                                                                                                                                                              
  <v>    -149.70000000     -25.40600800       0.24673910 </v>                                                                                                                                                                                                              
  <v>    -149.40000000     -25.41141065       0.24918372 </v>                                                                                                                                                                                                              
  <v>    -149.10000000     -25.41681330       0.25162834 </v>                                                                                                                                                                                                              
  <v>    -148.80000000     -25.42221682       0.25406890 </v>                                                                                                                                                                                                              
  <v>    -148.50000000     -25.42762671       0.25647992 </v>                                                                                                                                                                                                              
  <v>    -148.20000000     -25.43303731       0.25888834 </v>

To print the self-energy is a slight extra computational effort since, within the GW algorithms, the self-energy is usually just evaluated near KS eigenenergies

\epsilon _{nk}

and not the entire frequency range.

Mind: In quartic-scaling GW the self-energy is given on the real-frequency axis, while for low-scaling GW the self-energy is given on the imaginary-frequency axis.

Format

Real frequencies

If quartic-scaling GW algorithms are selected, e.g. ALGO=EVGW0, the first column corresponds to points on the real-frequency axis (in eV). The second and third columns are the real and imaginary parts of the self-energy (in eV) at a given band index and k point. To identify the band index and k point, the ordering has to be taken from the OUTCAR: Instead of the QP shifts, a small set of self-energy points are printed to OUTCAR, similar to the following output

calculating selfenergy CALC_SELFENERGY_LINEAR between w=-150.00 150.00                                                                                                                                                                                                     
                                                                                                                                                                                                                                                                           
k-point   1 :       0.0000    0.0000    0.0000                                                                                                                                                                                     
 band No.  band energies     occupation                                                                                                                                                                                            
                                                                                                                                                                                                                                   
     1     -11.4323      2.00000  selfenergy along real axis                                                                                                                                                                       
 -150.0000000   -24.0756124     0.2065066                                                                                                                                                                                          
 -147.0000000   -24.1277845     0.2302741                                                                                                                                                                                          
 -144.0000000   -24.1803224     0.2537669                                                                                                                                                                                          
 ...
  147.0000000   -20.3498375    -2.8348252                                                                                                                                                                                          
  150.0000000   -20.2310127    -2.7491028                                                                                                                                                                                          
                                                                                                                                                                                                                                   
     2      -2.7832      2.00000  selfenergy along real axis                                                                                                                                                                       
 -150.0000000   -13.0060959     0.1938781                                                                                                                                                                                          
 -147.0000000   -13.0530569     0.2231126                                                                                                                                                                                          
 -144.0000000   -13.1030584     0.2520593 
 ...

Here, the first and second band at the Gamma point are printed. The line with selfenergy along real axis contains band No., the KS energy, and the occupation of this state. The output in vasprun.xml has the same ordering of bands and k points, i.e., the band index is always the fastest. The frequency grid cannot be controlled. It is always 1000 points in the range of -150 to 150.

Imaginary frequencies

For low-scaling GW algorithms, the QP shifts are evaluated and printed to OUTCAR for both, LSELFENERGY=T and F. For LSELFENERGY=T, the vasprun.xml file additionally contains the self-energy for a given band index and k point on the imaginary-frequency axis:

<varray name="selfenergy along imaginary axis" >                                                                                                                                                                                                                          
  <v>       0.1570801806644298    -23.7971327349915711     -0.0179645094529067</v>                                                                                                                                                                                         
  <v>       0.4718033117773284    -23.7968260788831572     -0.0537856829291801</v>                                                                                                                                                                                         
  <v>       0.8108804505648752    -23.7966749072893577     -0.0932103588740998</v>                                                                                                                                                                                         
  <v>       1.3058951128526406    -23.7949927690568188     -0.1482973553314607</v>         
...

To identify the band index and k point, the ordering has to be taken from the QP shifts block in the OUTCAR. The band index is faster than the k point. The imaginary frequency is selected by the Minimax routines^[1], and the number of points depends on NOMEGA.

Format

Real frequencies

Imaginary frequencies

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