Difference in spin up and spin down energies in sigma

Kostas Fykouras

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Jun 12, 2023, 3:48:45 AM6/12/23

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Hello group,

I am doing GW calculations on a magnetic semiconductor. I am examining a unit cell containing 20 atoms with 2 Fe atoms and I am studying the antiferromagnetic configuration.

On the DFT level the spin up and spin down energies are the same up to some decimal place. When i perform the sigma calculation it seems that they are no longer the same. Below I am posting the energies from the eqp1.dat file

0.000000000 0.000000000 0.000000000 16
1 91 3.312551338 1.768421716
1 92 3.312551338 1.768421716
1 93 3.316462906 1.896403609
1 94 3.714314695 2.906787073
1 95 4.444682809 2.877071388
1 96 4.796312298 6.417409337
1 97 4.846282199 6.427893605
1 98 4.846282199 6.427893605
2 91 3.312590909 1.612746447
2 92 3.312590909 1.612746447
2 93 3.316328509 1.514959804
2 94 3.714090595 3.348710622
2 95 4.445061357 3.418095886
2 96 4.795683380 8.220989438
2 97 4.845674777 8.254823767
2 98 4.845674777 8.254823767

The 95th band is the last occupied band. It seems that I also get a different QP bandgap on the GW level for the spin up and the spin down channel.

Has anyone experienced something like this before?

Any help would be appreciated.

Thanks in advance.

Zhenglu Li

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Jun 12, 2023, 12:32:38 PM6/12/23

to Kostas Fykouras, BerkeleyGW Help

Dear Kostas,

Could you post your sigma_hp file?

Best,

Zhenglu

From: Kostas Fykouras <kostasf...@gmail.com>
Sent: Monday, June 12, 2023 12:48 AM
To: BerkeleyGW Help <he...@berkeleygw.org>
Subject: Difference in spin up and spin down energies in sigma

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Kostas Fykouras

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Jun 12, 2023, 12:48:50 PM6/12/23

to BerkeleyGW Help, Zhenglu Li

Hello Zhenglu,

thank you for you reply. Please find attached sigma_hp file

frequency_dependence 3

band_index 91 98
sigma_matrix 0 0

finite_difference_form 2
finite_difference_spacing 1.000000

symmetries
ntran = 16
mtrx01 = 1 0 0 0 1 0 0 0 1
mtrx02 = -1 0 0 0 -1 0 0 0 1
mtrx03 = -1 0 0 0 1 0 0 0 -1
mtrx04 = 1 0 0 0 -1 0 0 0 -1
mtrx05 = 0 1 0 1 0 0 0 0 -1
mtrx06 = 0 -1 0 -1 0 0 0 0 -1
mtrx07 = 0 1 0 -1 0 0 0 0 1
mtrx08 = 0 -1 0 1 0 0 0 0 1
mtrx09 = -1 0 0 0 -1 0 0 0 -1
mtrx10 = 1 0 0 0 1 0 0 0 -1
mtrx11 = 1 0 0 0 -1 0 0 0 1
mtrx12 = -1 0 0 0 1 0 0 0 1
mtrx13 = 0 -1 0 -1 0 0 0 0 1
mtrx14 = 0 1 0 1 0 0 0 0 1
mtrx15 = 0 -1 0 1 0 0 0 0 -1
mtrx16 = 0 1 0 -1 0 0 0 0 -1

k = 0.000000 0.000000 0.000000 ik = 1 spin = 1

n Emf Eo X SX-X CH Sig Vxc Eqp0 Eqp1 CH` Sig` Eqp0` Eqp1` Znk
91 3.312551 3.312551 -19.322196 9.817707 -7.334147 -16.838636 -14.896553 1.370468 1.768422 -7.334147 -16.838636 1.370468 1.768422 0.795089
92 3.312551 3.312551 -19.322196 9.817707 -7.334147 -16.838636 -14.896553 1.370468 1.768422 -7.334147 -16.838636 1.370468 1.768422 0.795089
93 3.316463 3.316463 -18.726964 10.095981 -7.618781 -16.249763 -14.455999 1.522698 1.896404 -7.618781 -16.249763 1.522698 1.896404 0.791664
94 3.714315 3.714315 -24.589204 8.447559 -6.462009 -22.603655 -21.558376 2.669037 2.906787 -6.462009 -22.603655 2.669037 2.906787 0.772548
95 4.444683 4.444683 -26.240375 9.681547 -6.734927 -23.293755 -21.341188 2.492116 2.877071 -6.734927 -23.293755 2.492116 2.877071 0.802846
96 4.796312 4.796312 -13.530027 0.886089 -7.849471 -20.493408 -22.954534 7.257438 6.417409 -7.849471 -20.493408 7.257438 6.417409 0.658681
97 4.846282 4.846282 -13.550284 0.859760 -7.909879 -20.600403 -23.017221 7.263101 6.427894 -7.909879 -20.600403 7.263101 6.427894 0.654419
98 4.846282 4.846282 -13.550284 0.859760 -7.909879 -20.600403 -23.017221 7.263101 6.427894 -7.909879 -20.600403 7.263101 6.427894 0.654419

k = 0.000000 0.000000 0.000000 ik = 1 spin = 2

n Emf Eo X SX-X CH Sig Vxc Eqp0 Eqp1 CH` Sig` Eqp0` Eqp1` Znk
91 3.312591 3.312591 -19.322957 9.262805 -6.953455 -17.013606 -14.897335 1.196320 1.612746 -6.953455 -17.013606 1.196320 1.612746 0.803226
92 3.312591 3.312591 -19.322957 9.262805 -6.953455 -17.013606 -14.897335 1.196320 1.612746 -6.953455 -17.013606 1.196320 1.612746 0.803226
93 3.316329 3.316329 -18.726902 8.824988 -6.777620 -16.679534 -14.456014 1.092808 1.514960 -6.777620 -16.679534 1.092808 1.514960 0.810143
94 3.714091 3.714091 -24.589215 8.936903 -6.372818 -22.025130 -21.558765 3.247726 3.348711 -6.372818 -22.025130 3.247726 3.348711 0.783463
95 4.445061 4.445061 -26.241062 11.700060 -8.108301 -22.649303 -21.341846 3.137605 3.418096 -8.108301 -22.649303 3.137605 3.418096 0.785468
96 4.795683 4.795683 -13.530861 0.134512 -5.074293 -18.470643 -22.954548 9.279588 8.220989 -5.074293 -18.470643 9.279588 8.220989 0.763911
97 4.845675 4.845675 -13.551347 0.110066 -5.105154 -18.546435 -23.017131 9.316371 8.254824 -5.105154 -18.546435 9.316371 8.254824 0.762554
98 4.845675 4.845675 -13.551347 0.110066 -5.105154 -18.546435 -23.017131 9.316371 8.254824 -5.105154 -18.546435 9.316371 8.254824 0.762554

================================================================================

n = band index.
Emf = "inner" mean-field energy eigenvalue used to construct Sigma(E),
read from WFN_inner.
Eo = "outer" mean-field energy eigenvalue where we center the evaluation
frequency grid {E} of Sigma(E). Defaults to Emf, unless
you use WFN_outer and eqp_outer.dat / scissors_outer.
Vxc = exchange-correlation pot., calculated from VXC or read from vxc.dat.
KIH = Kinetic energy + Ionic potential + Hartree, read from kih.dat.
X = bare exchange.
SX = screened exchange contrib. to Sigma(E) at energy E=Eo
CH = Coulomb hole contrib. to Sigma(E) at energy E=Eo
Cor = SX-X + CH = correlation portion of Sigma(E) at energy E=Eo.
Sig = X + Cor = self energy, Sigma(E), at energy E=Eo.
Eqp0 = on-shell QP energy = Emf - Vxc + Sig(Eo)
Eqp0 is *not* the recommended quantity to use for QP properties.
Eqp1 = off-shell solution to the linearized Dyson`s equation
= Eqp0 + (dSig/dE) / (1 - dSig/dE) * (Eqp0 - Eo),
or a full linear interpolation if more freq. points where computed.
Eqp1 is the recommended quantity to use for QP properties.
Znk = quasiparticle renormalization factor

Notes on the finite_difference_form from sigma.inp file:
none : -2 => dSig/dE = 0 (skip the expansion)
backward: -1 => dSig/dE = (Sig(Eo) - Sig(Eo-dE)) / dE
central : 0 => dSig/dE = (Sig(Eo+dE) - Sig(Eo-dE)) / (2*dE)
forward : 1 => dSig/dE = (Sig(Eo+dE) - Sig(Eo)) / dE
default : 2 => forward for diagonal and none for off-diagonal
dE is finite_difference_spacing from Sigma.inp file.
We are using the form #2 with dE = 1.000 eV.

General notes:
- All energies are reported here in eV.
- Both Emf and Vxc contain the average pot. Vxc0, so Vxc0 doesn`t affect Sigma.
- Eqp1 and Eqp0 are Eqs. (36-37) from Hybertsen & Louie PRB 34 5390.
- We recommend you use Eqp1 for QP properties of materials.

================================================================================

All the best,

Kostas

Zhenglu Li

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Jun 12, 2023, 12:56:09 PM6/12/23

to Kostas Fykouras, BerkeleyGW Help

Hi Kostas,

Which pseudopotentials are you using?

Best,

Zhenglu

From: Kostas Fykouras <kostasf...@gmail.com>
Sent: Monday, June 12, 2023 9:48 AM
To: BerkeleyGW Help <he...@berkeleygw.org>
Cc: Zhenglu Li <zhen...@usc.edu>
Subject: Re: Difference in spin up and spin down energies in sigma

Kostas Fykouras

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Jun 12, 2023, 1:31:31 PM6/12/23

to BerkeleyGW Help, Zhenglu Li

Hi Zhenglu,

I am using the PBE standard pseudo potentials found in pseudo-dojo.org

All the best,

Kostas

Zhenglu Li

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Jun 12, 2023, 2:33:31 PM6/12/23

to Kostas Fykouras, BerkeleyGW Help

Hi Kostas,

Pseudo dojo potentials have nonlinear core corrections, which may cause some inconsistencies in the spin-polarized cases. Maybe you could try other pseudopotentials such as sg15 to see if this helps your case.

Best,

Zhenglu

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From: Kostas Fykouras <kostasf...@gmail.com>
Sent: Monday, June 12, 2023 10:31:31 AM

Kostas Fykouras

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Jun 19, 2023, 2:23:14 AM6/19/23

to BerkeleyGW Help, Kostas Fykouras

Hello Zhenglu,

sorry for the delayed reply. Thank you for your suggestion. I tried using the sg15 pseudopotentials.

The results did not change a lot.

Below I attach the results from the eqp1.dat file

1 0.000000000 0.000000000 0.000000000 16
2 1 91 3.244940409 1.805711202
3 1 92 3.244940409 1.805711202
4 1 93 3.252149038 1.945145039
5 1 94 3.626296896 2.830125163
6 1 95 4.348089923 2.866918157
7 1 96 4.707048836 6.376881094
8 1 97 4.758331077 6.394414272
9 1 98 4.758331077 6.394414272
10 2 91 3.245037157 1.655665112
11 2 92 3.245037157 1.655665112
12 2 93 3.252308614 1.561338626
13 2 94 3.626132654 3.252223212
14 2 95 4.348208997 3.391008373
15 2 96 4.706876003 8.200631631
16 2 97 4.758151807 8.227881337
17 2 98 4.758151807 8.227881337

Again the spin up and spin down energies are different on the GW level.

I have thought about this problem and I wanted to share my two working theories to why this might happening. Feel free to comment on them

1) The DFT energies of the spin up and spin down states are the same up to the 4th or 5th decimal place. Since GW is a perturbative method, is it possible that this small difference on the DFT level causes a large difference on the GW level ?

2) The system is not in the correct ground state. I am studying a double perovskite in the Fm3m symmetry group. The conventional unit cell has 40 atoms and the primitive has 10. On the primitive unit cell I can only test a ferromagnetic configuration. To test the antiferromagnetic configuration I used the findsym website to create a 20 atom unit cell for computational convenience. Is it possible that I have to exclusively test the Fm3m conventional unit cell for these calculations because experimentally this is the "correct" ground state ?

In terms of convergence, for epsilon I am using the plasmon pole model, and the dielectric constant is converged within 0.01

Any suggestions would be greatly appreciated.

Thank in advance

All the best,

Kostas

Zhenglu Li

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Jun 19, 2023, 3:35:17 PM6/19/23

to Kostas Fykouras, BerkeleyGW Help

Hi Kostas,

Could you share your sigma_hp.log file? Below are my responses to your thoughts:

1) The DFT energies of the spin up and spin down states are the same up to the 4th or 5th decimal place. Since GW is a perturbative method, is it possible that this small difference on the DFT level causes a large difference on the GW level ?

GW won't cause this big difference. The numerical difference is typically to the same order.

2) The system is not in the correct ground state. I am studying a double perovskite in the Fm3m symmetry group. The conventional unit cell has 40 atoms and the primitive has 10. On the primitive unit cell I can only test a ferromagnetic configuration. To test the antiferromagnetic configuration I used the findsym website to create a 20 atom unit cell for computational convenience. Is it possible that I have to exclusively test the Fm3m conventional unit cell for these calculations because experimentally this is the "correct" ground state ?

In this case it seems irrelevant.

Best,

Zhenglu

From: Kostas Fykouras <kostasf...@gmail.com>
Sent: Sunday, June 18, 2023 11:23 PM
To: BerkeleyGW Help <he...@berkeleygw.org>
Cc: Kostas Fykouras <kostasf...@gmail.com>

To view this discussion on the web visit https://groups.google.com/a/berkeleygw.org/d/msgid/help/914ba15b-7444-4524-b9d6-177dc8bf8b8cn%40berkeleygw.org.

Kostas Fykouras

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Jun 20, 2023, 3:06:03 AM6/20/23

to BerkeleyGW Help, Zhenglu Li

Hi Zhenglu,

Below I post the content of the sigma_hp.log file. Is there anything particular that you are looking in that file ?

91 3.244940 3.244940 -19.071246 9.568920 -7.051579 -16.553905 -14.752946 1.443981 1.805711 -7.051579 -16.553905 1.443981 1.805711 0.799146
92 3.244940 3.244940 -19.071246 9.568920 -7.051579 -16.553905 -14.752946 1.443981 1.805711 -7.051579 -16.553905 1.443981 1.805711 0.799146
93 3.252149 3.252149 -18.597425 9.861721 -7.321515 -16.057219 -14.413447 1.608377 1.945145 -7.321515 -16.057219 1.608377 1.945145 0.795125
94 3.626297 3.626297 -23.985404 8.513273 -6.533306 -22.005437 -20.985337 2.606196 2.830125 -6.533306 -22.005437 2.606196 2.830125 0.780484
95 4.348090 4.348090 -25.525783 9.547692 -6.696857 -22.674948 -20.842920 2.516062 2.866918 -6.696857 -22.674948 2.516062 2.866918 0.808488
96 4.707049 4.707049 -13.100263 1.371592 -8.000333 -19.729004 -22.244355 7.222399 6.376881 -8.000333 -19.729004 7.222399 6.376881 0.663857
97 4.758331 4.758331 -13.126168 1.393661 -8.084993 -19.817501 -22.299460 7.240290 6.394414 -8.084993 -19.817501 7.240290 6.394414 0.659190
98 4.758331 4.758331 -13.126168 1.393661 -8.084993 -19.817501 -22.299460 7.240290 6.394414 -8.084993 -19.817501 7.240290 6.394414 0.659190

k = 0.000000 0.000000 0.000000 ik = 1 spin = 2

n Emf Eo X SX-X CH Sig Vxc Eqp0 Eqp1 CH` Sig` Eqp0` Eqp1` Znk

91 3.245037 3.245037 -19.072510 9.043240 -6.692965 -16.722235 -14.754199 1.277001 1.655665 -6.692965 -16.722235 1.277001 1.655665 0.807593
92 3.245037 3.245037 -19.072510 9.043240 -6.692965 -16.722235 -14.754199 1.277001 1.655665 -6.692965 -16.722235 1.277001 1.655665 0.807593
93 3.252309 3.252309 -18.597333 8.578459 -6.470401 -16.489275 -14.413447 1.176480 1.561339 -6.470401 -16.489275 1.176480 1.561339 0.814600
94 3.626133 3.626133 -23.985667 8.973588 -6.447122 -21.459201 -20.985731 3.152662 3.252223 -6.447122 -21.459201 3.152662 3.252223 0.789721
95 4.348209 4.348209 -25.526398 11.343672 -7.868482 -22.051208 -20.843432 3.140433 3.391008 -7.868482 -22.051208 3.140433 3.391008 0.792532
96 4.706876 4.706876 -13.100607 0.657925 -5.309890 -17.752572 -22.244270 9.198574 8.200632 -5.309890 -17.752572 9.198574 8.200632 0.777825
97 4.758152 4.758152 -13.126610 0.677407 -5.371297 -17.820500 -22.299357 9.237009 8.227881 -5.371297 -17.820500 9.237009 8.227881 0.774691
98 4.758152 4.758152 -13.126610 0.677407 -5.371297 -17.820500 -22.299357 9.237009 8.227881 -5.371297 -17.820500 9.237009 8.227881 0.774691

All the best,

Kostas

Zhenglu Li

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Jun 20, 2023, 1:41:16 PM6/20/23

to Kostas Fykouras, BerkeleyGW Help

Hi Kostas,

You are currently using full frequency sampling, which obscures the issue. Could you try running a generalized plasmon-pole (GPP) calculation instead? Furthermore, the Vxc for spin-up and spin-down are different from DFT. It looks still like a pseudo-potential issue. If you have already tried SG15 library (supposedly having no nlcc), you can try some other PPs without non-linear core correction. Or you can regenerate the PPs using ONCVPSP and turn off nlcc.

Best,

ZHenglu

From: Kostas Fykouras <kostasf...@gmail.com>
Sent: Tuesday, June 20, 2023 12:06 AM

Kostas Fykouras

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Jun 21, 2023, 9:02:46 AM6/21/23

to BerkeleyGW Help, Zhenglu Li

Hello Zhenglu,

Thank your reply and for your time so far.

I am already using the GGP calculation. It seems that you are correct and that the vxc is indeed different for the spin up and the spin down channels. The differences are rather small though.

Should one expect that the Vxc would be the same for spin up and spin down channels? Since the energies are different (after the 4th decimal place or so) shouldn't one also expect that the Vxc would also be different or is Vxc calculated purely from the pseudopotentials?

Thanks in advance

All the best,

Kostas

Zhenglu Li

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Jun 21, 2023, 11:38:57 AM6/21/23

to Kostas Fykouras, BerkeleyGW Help

Hi Kostas,

You are right that Vxc indeed doesn't differ much. I was looking at the wrong columns. You are using GN-GPP model though. Could you try to use Hybertsen-Louie GPP model, by setting "frequency_dependence 1", the default value? It looks like your bare X term is Okay, but other screened terms are off. It means something is strange in the screening (possibly how frequency dependence was treated).

Best,

Zhenglu

From: Kostas Fykouras <kostasf...@gmail.com>
Sent: Wednesday, June 21, 2023 6:02 AM

Kostas Fykouras

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Jun 23, 2023, 6:01:39 AM6/23/23

to BerkeleyGW Help, Zhenglu Li

Hello Zhenglu,

It seems that indeed that frequency treatment was wrong. I re did my epsilon and sigma calculation with the default frequency dependence setting for both.

k = 0.000000 0.000000 0.000000 ik = 1 spin = 1

n Emf Eo X SX-X CH Sig Vxc Eqp0 Eqp1 Znk
91 3.244940 3.244940 -19.071246 12.034680 -9.022302 -16.058867 -14.752946 1.939019 2.173631 0.820348
92 3.244940 3.244940 -19.071246 12.034680 -9.022302 -16.058867 -14.752946 1.939019 2.173631 0.820348
93 3.252149 3.252149 -18.597425 11.825468 -8.944266 -15.716224 -14.413447 1.949372 2.184595 0.819445
94 3.626297 3.626297 -23.985404 13.089402 -10.383796 -21.279798 -20.985337 3.331835 3.377396 0.845275
95 4.348090 4.348090 -25.525783 14.564366 -10.485616 -21.447032 -20.842920 3.743978 3.841285 0.838924
96 4.707049 4.707049 -13.100263 4.188968 -11.304595 -20.215891 -22.244355 6.735513 6.420393 0.844651
97 4.758331 4.758331 -13.126168 4.209846 -11.355425 -20.271747 -22.299460 6.786044 6.468621 0.843458
98 4.758331 4.758331 -13.126168 4.209846 -11.355425 -20.271747 -22.299460 6.786044 6.468621 0.843458

k = 0.000000 0.000000 0.000000 ik = 1 spin = 2

n Emf Eo X SX-X CH Sig Vxc Eqp0 Eqp1 Znk
91 3.245037 3.245037 -19.072510 12.035010 -9.022438 -16.059938 -14.754199 1.939298 2.173869 0.820354
92 3.245037 3.245037 -19.072510 12.035010 -9.022438 -16.059938 -14.754199 1.939298 2.173869 0.820354
93 3.252309 3.252309 -18.597333 11.825391 -8.944196 -15.716138 -14.413447 1.949617 2.184827 0.819443
94 3.626133 3.626133 -23.985667 13.090008 -10.384493 -21.280151 -20.985731 3.331712 3.377266 0.845275
95 4.348209 4.348209 -25.526398 14.564117 -10.485227 -21.447507 -20.843432 3.744134 3.841434 0.838927
96 4.706876 4.706876 -13.100607 4.189410 -11.304771 -20.215968 -22.244270 6.735178 6.420073 0.844646
97 4.758152 4.758152 -13.126610 4.210382 -11.355603 -20.271831 -22.299357 6.785678 6.468272 0.843451
98 4.758152 4.758152 -13.126610 4.210382 -11.355603 -20.271831 -22.299357 6.785678 6.468272 0.843451

This is the sigma_hp file I am getting now. The energies of the spin up and the spin down channel are the same as well as their screened exchange contributions.

It seems that the problem is resolved now.

Thank you very much for your help!

All the best,

Kostas

Zhenglu Li

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Jun 23, 2023, 12:30:30 PM6/23/23

to Kostas Fykouras, BerkeleyGW Help

Hi Kostas,

Great, happy to see it's working now.

Best,

Zhenglu

From: Kostas Fykouras <kostasf...@gmail.com>
Sent: Friday, June 23, 2023 3:01 AM

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