LSELFENERGY: Difference between revisions
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If {{ | * If {{TAGO|LSELFENERGY|.FALSE.}} (default), quasi-particle (QP) shifts are evaluated. | ||
<div style="padding-left: {{{3|1.5em}}}"><pre>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</pre></div> | |||
If {{ | * If {{TAGO|LSELFENERGY|.TRUE.}}, the frequency dependent self-energy <math> \langle \psi_{n {\mathbf{k}}} | \Sigma(\omega) |\psi_{n {\mathbf{k}}} \rangle </math> is evaluated and printed to {{FILE|vasprun.xml}}. An example output looks like the following: | ||
<div style="padding-left: {{{3|1.5em}}}"><pre><varray name="selfenergy" > | |||
<v> -150.00000000 -25.40060536 0.24429448 </v> | <v> -150.00000000 -25.40060536 0.24429448 </v> | ||
<v> -149.70000000 -25.40600800 0.24673910 </v> | <v> -149.70000000 -25.40600800 0.24673910 </v> | ||
| Line 15: | Line 28: | ||
<v> -148.80000000 -25.42221682 0.25406890 </v> | <v> -148.80000000 -25.42221682 0.25406890 </v> | ||
<v> -148.50000000 -25.42762671 0.25647992 </v> | <v> -148.50000000 -25.42762671 0.25647992 </v> | ||
<v> -148.20000000 -25.43303731 0.25888834 </v> | <v> -148.20000000 -25.43303731 0.25888834 </v></pre></div> | ||
: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 <math>\epsilon_{nk}</math> and not the entire frequency range. | |||
{{NB|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.|:}} | |||
If quartic-scaling GW algorithms are selected, e.g. {{TAG|ALGO}}=EVGW0, the first column corresponds to points on the real-frequency axis. The second and third | == Format == | ||
=== Real frequencies === | |||
If '''quartic-scaling GW algorithms''' are selected, e.g. {{TAG|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 {{FILE|OUTCAR}}: Instead of the QP shifts, a small set of self-energy points are printed to {{FILE|OUTCAR}}, similar to the following output | |||
calculating selfenergy CALC_SELFENERGY_LINEAR between w=-150.00 150.00 | calculating selfenergy CALC_SELFENERGY_LINEAR between w=-150.00 150.00 | ||
k-point 1 : 0.0000 0.0000 0.0000 | k-point 1 : 0.0000 0.0000 0.0000 | ||
band No. band energies occupation | band No. band energies occupation | ||
1 -11. | 1 -11.4323 2.00000 selfenergy along real axis | ||
-150.0000000 - | -150.0000000 -24.0756124 0.2065066 | ||
-147.0000000 - | -147.0000000 -24.1277845 0.2302741 | ||
-144.0000000 - | -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 <code>selfenergy along real axis</code> contains band No., the KS energy, and the occupation of this state. | |||
The output in {{FILE|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 [[Practical_guide_to_GW_calculations#Low_scaling_GW_algorithms|low-scaling GW algorithms]], the QP | For [[Practical_guide_to_GW_calculations#Low_scaling_GW_algorithms|low-scaling GW algorithms]], the QP shifts are evaluated and printed to {{FILE|OUTCAR}} for both, {{TAG|LSELFENERGY}}=T and F. For {{TAG|LSELFENERGY}}=T, the {{FILE|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" > | <varray name="selfenergy along imaginary axis" > | ||
| Line 37: | Line 70: | ||
<v> 1.3058951128526406 -23.7949927690568188 -0.1482973553314607</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 {{FILE|OUTCAR}}. The band index is faster than the '''k''' point. | |||
The imaginary frequency is selected by the Minimax routines{{cite|Kaltak:PRB:2020}}, and the number of points depends on {{TAG|NOMEGA}}. | |||
== Related tags and articles == | == Related tags and articles == | ||
Latest revision as of 10:30, 20 February 2024
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 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 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.
Related tags and articles
- for a practical guide to GW calculations
- ALGO for response functions and RPA calculations
- LFINITE_TEMPERATURE finite temperature formalism
- NOMEGA number of real or imaginary frequency points