Skip to Content.
Sympa Menu

forum - Re: [abinit-forum] Hartree Fock corrections

forum@abinit.org

Subject: The ABINIT Users Mailing List ( CLOSED )

List archive

Re: [abinit-forum] Hartree Fock corrections


Chronological Thread 
  • From: jacky even <jacky.even@insa-rennes.fr>
  • To: forum@abinit.org
  • Subject: Re: [abinit-forum] Hartree Fock corrections
  • Date: Mon, 26 Oct 2009 18:59:33 +0100
Dear Fabien,

- If I apply directly a GW correction (PPM) to the LDA initial calculation, the degeneracy of the initial LDA calculation is preserved (so I suppose that the chosen GW parameters are more or less sufficient for that purpose) :

LDA+GW
k = 0.000 0.000 0.000
Band E0 <VxcLDA> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E
7 1.004 -11.329 -12.249 1.644 0.809 -0.237 -10.744 0.585 1.589
8 1.004 -11.329 -12.249 1.644 0.809 -0.237 -10.744 0.585 1.589
9 1.004 -11.329 -12.249 1.644 0.809 -0.237 -10.744 0.585 1.589
10 1.366 -10.795 -7.043 -2.229 0.816 -0.225 -9.552 1.243 2.609
11 4.609 -10.411 -5.937 -3.006 0.810 -0.235 -9.222 1.189 5.799
12 4.609 -10.411 -5.937 -3.005 0.811 -0.233 -9.220 1.192 5.801
13 4.609 -10.411 -5.937 -3.006 0.810 -0.235 -9.222 1.189 5.799
14 8.260 -7.975 -2.488 -4.292 0.810 -0.235 -7.007 0.968 9.228


- If I apply the same GW correction on top of the LDA+COHSEX(corr) calculation, the degeneracy is still removed whereas a nice result is obtained for the LDA+SEX(corr) +GW case. Then i suppose again that the accuracy of the GW correction is not the problem here (and that the dielectric matrix is evaluated with a good precision).

LDA+COHSEX(corr) +GW
k = 0.000 0.000 0.000
Band E_lda <Vxclda> E(N-1) <Hhartree> SigX SigC[E(N-1)] Z dSigC/dE Sig[E(N)] DeltaE E(N)_pert E(N)_diago
1 -14.085 -7.623 -8.713 -6.562 -6.027 1.452 0.899 -0.113 -4.329 -2.179 -10.892 -12.923
2 -14.085 -7.623 -8.697 -6.531 -6.131 1.485 0.896 -0.117 -4.388 -2.222 -10.918 -11.225
3 -14.085 -7.623 -8.693 -6.515 -6.166 1.496 0.894 -0.119 -4.405 -2.227 -10.920 -11.221
4 -14.004 -7.912 -8.360 -6.132 -6.292 1.502 0.892 -0.121 -4.514 -2.286 -10.646 -11.213
5 -14.004 -7.912 -8.360 -6.132 -6.292 1.499 0.893 -0.120 -4.519 -2.292 -10.651 -10.927
6 -11.931 -11.619 -5.720 -0.321 -18.126 5.547 0.828 -0.208 -11.343 -5.944 -11.664 -10.921
7 1.004 -11.601 -0.285 12.655 -12.694 1.463 0.797 -0.254 -11.577 1.364 1.078 -0.225
8 1.004 -11.601 8.307 12.587 -12.527 -0.289 0.790 -0.265 -11.025 -6.745 1.562 -0.167
9 1.004 -11.601 8.312 12.608 -12.573 -0.268 0.789 -0.268 -11.037 -6.740 1.571 1.068
10 1.366 -12.429 9.711 13.773 -8.208 -4.518 0.726 -0.377 -10.354 -6.292 3.419 1.501
11 4.609 -11.063 12.376 15.667 -6.589 -5.231 0.709 -0.411 -9.336 -6.045 6.331 3.835
12 4.609 -11.063 12.376 15.678 -6.609 -5.231 0.711 -0.406 -9.372 -6.071 6.306 3.847
13 4.609 -11.063 12.378 15.682 -6.614 -5.229 0.710 -0.409 -9.366 -6.061 6.317 3.856

LDA+SEX(corr) +GW
k = 0.000 0.000 0.000
Band E_lda <Vxclda> E(N-1) <Hhartree> SigX SigC[E(N-1)] Z dSigC/dE Sig[E(N)] DeltaE E(N)_pert E(N)_diago
1 -14.085 -7.623 -8.701 -6.542 -6.105 1.462 0.885 -0.129 -4.359 -2.200 -10.901 -13.031
2 -14.085 -7.623 -8.701 -6.542 -6.105 1.462 0.885 -0.130 -4.359 -2.200 -10.901 -11.247
3 -14.085 -7.623 -8.701 -6.542 -6.105 1.460 0.885 -0.129 -4.361 -2.202 -10.903 -11.245
4 -14.004 -7.912 -8.360 -6.131 -6.292 1.472 0.898 -0.113 -4.556 -2.328 -10.687 -11.245
5 -14.004 -7.912 -8.360 -6.131 -6.292 1.472 0.898 -0.114 -4.556 -2.328 -10.687 -10.951
6 -11.931 -11.619 -5.720 -0.326 -18.125 5.438 0.710 -0.408 -10.574 -5.181 -10.901 -10.951
7 1.004 -11.601 8.313 12.610 -12.571 -0.332 0.767 -0.304 -10.897 -6.600 1.714 -0.239
8 1.004 -11.601 8.313 12.610 -12.571 -0.333 0.767 -0.304 -10.898 -6.601 1.712 -0.239
9 1.004 -11.601 8.313 12.610 -12.571 -0.333 0.767 -0.304 -10.897 -6.600 1.713 -0.239
10 1.366 -12.429 9.711 13.769 -8.222 -4.682 0.802 -0.247 -11.150 -7.091 2.620 0.884
11 4.609 -11.063 12.377 15.682 -6.626 -4.957 0.716 -0.396 -9.236 -5.932 6.446 4.102
12 4.609 -11.063 12.378 15.682 -6.626 -4.957 0.716 -0.396 -9.236 -5.932 6.445 4.103
13 4.609 -11.063 12.378 15.682 -6.626 -4.959 0.717 -0.394 -9.244 -5.940 6.438 4.103


- As you said, the problem seems indeed related to the SigC part of the self-energy in the COHSEX case (line 8 of the calculation below), and more precisely to the Coulomb-hole contribution in the COHSEX case (which is not present in the SEX case as far as i know from the published papers). I shall also add that E(N)_diago has a strange behaviour for line 7.

- to summarize these calculations :
the various terms E_lda, <Vxclda>, <Hhartree>, SigX, the GW correction and the screened exchange part of SigC seem to have normal behaviours with respect to the valence band degeneracy. On the contrary, the Coulomb-hole contribution, which is probably not the most complicated part of the self-energy, has a strange behaviour for GaAs and not for Si. I suppose however that convergence problems or the influence of the Ga 3d semicore electrons should affect all these terms more or less in a similar way.
I have not found in the doc files (or in the papers) a description of the Coulomb-hole implementation in abinit, so i would appreciate some further help to understand how to correct my results in a proper way,

yours sincerely,

Jacky Even
FOTON, UMR6082
INSA de Rennes, France



Fabien Bruneval a écrit :
A few points about your calculations:

1) We usually observe degeneracy lifting in the GW calculations. Fortunately, by increasing the convergence parameters, the correct degeneracy is generally recovered... up to a given accuracy.

2) All your COHSEX values are extremely weird for GaAs. Indeed the correlation part SigC is equal to the screened exchange value, except for the line that breaks the degeneracy. What could it be? Have you performed GW calculations also?

3) For gallium and arsenic, which include a noticeable 3d contribution, I guess that the semicore states 3s and 3p are crucial for the exact exchange. You can observe that already at the HF-level the top valence band has sunk below the other valence bands. I think this could be corrected using a proper pseudopotential that includes 3s3p electrons.

Have a good evening

Fabien



On 10/26/2009 04:39 PM, jacky even wrote:
Thank you Fabien for your precise and quick response, this is exactly what i expected.

I have got however another question concerning test86.in :

- when extending the number of bands "bdgw" from 4 - 5 to 1 - 8 for Si, i checked that degeneracy is preserved by the three correction procedures at gamma point for the valence (and conduction) bands

for HF :
k = 0.000 0.000 0.000
Band E0 <VxcLDA> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E
1 -5.555 -10.386 -16.930 0.000 1.000 0.000 -16.930 -6.544 -12.099
2 6.469 -11.260 -12.551 0.000 1.000 0.000 -12.551 -1.291 5.179
3 6.469 -11.260 -12.551 0.000 1.000 0.000 -12.551 -1.291 5.178
4 6.469 -11.260 -12.552 0.000 1.000 0.000 -12.552 -1.292 5.178
5 9.024 -10.046 -5.658 0.000 1.000 0.000 -5.658 4.387 13.412
6 9.024 -10.046 -5.658 0.000 1.000 0.000 -5.658 4.387 13.412
7 9.024 -10.046 -5.658 0.000 1.000 0.000 -5.658 4.387 13.412
8 9.864 -10.514 -5.519 0.000 1.000 0.000 -5.519 4.995 14.859

E^0_gap 2.555
E^GW_gap 8.234
DeltaE^GW_gap 5.679

for SEX :
k = 0.000 0.000 0.000
Band E0 <VxcLDA> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E
1 -5.555 -10.386 -16.930 12.214 1.000 0.000 -4.716 5.670 0.115
2 6.469 -11.260 -12.551 8.327 1.000 0.000 -4.224 7.036 13.505
3 6.469 -11.260 -12.551 8.327 1.000 0.000 -4.224 7.036 13.505
4 6.469 -11.260 -12.552 8.328 1.000 0.000 -4.224 7.036 13.506
5 9.024 -10.046 -5.658 3.128 1.000 0.000 -2.531 7.515 16.539
6 9.024 -10.046 -5.658 3.128 1.000 0.000 -2.530 7.515 16.539
7 9.024 -10.046 -5.658 3.128 1.000 0.000 -2.530 7.515 16.539
8 9.864 -10.514 -5.519 2.868 1.000 0.000 -2.652 7.863 17.727

E^0_gap 2.555
E^GW_gap 3.034
DeltaE^GW_gap 0.479

for COHSEX :
k = 0.000 0.000 0.000
Band E0 <VxcLDA> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E
1 -5.555 -10.386 -16.930 4.082 1.000 0.000 -12.848 -2.462 -8.017
2 6.469 -11.260 -12.551 -0.153 1.000 0.000 -12.704 -1.443 5.026
3 6.469 -11.260 -12.551 -0.152 1.000 0.000 -12.704 -1.443 5.026
4 6.469 -11.260 -12.552 -0.152 1.000 0.000 -12.704 -1.443 5.026
5 9.024 -10.046 -5.658 -4.927 1.000 0.000 -10.585 -0.540 8.485
6 9.024 -10.046 -5.658 -4.927 1.000 0.000 -10.585 -0.540 8.485
7 9.024 -10.046 -5.658 -4.927 1.000 0.000 -10.585 -0.540 8.484
8 9.864 -10.514 -5.519 -5.458 1.000 0.000 -10.977 -0.463 9.402

E^0_gap 2.555
E^GW_gap 3.459
DeltaE^GW_gap 0.904

- when turning on now to GaAs (including 3d electrons with fhi pseudopotential) with similar parameters (ecut=6, ...) , it appears to me that degeneracy (bands 7-9 below) is lifted in the valence band at gamma point by the correction procedures in the three cases. However, when performing convergence studies (ecut 40, nbandkss 100, ecutwfn 5 , ecutsigx 6, ecuteps 6,... i admit it may not be sufficient ??) , this numerical degeneracy lifting is cleanly removed except in the COHSEX case which still exhibit a pathological behaviour :

for HF :
k = 0.000 0.000 0.000
Band E_lda <Vxclda> E(N-1) <Hhartree> SigX SigC[E(N-1)] Z dSigC/dE Sig[E(N)] DeltaE E(N)_pert E(N)_diago
1 -14.085 -7.623 -14.085 -6.462 -6.197 0.000 1.000 0.000 -6.197 1.426 -12.659 -18.460
2 -14.085 -7.623 -14.085 -6.462 -6.197 0.000 1.000 0.000 -6.197 1.426 -12.659 -12.707
3 -14.085 -7.623 -14.085 -6.462 -6.197 0.000 1.000 0.000 -6.197 1.426 -12.659 -12.707
4 -14.004 -7.912 -14.004 -6.092 -6.298 0.000 1.000 0.000 -6.298 1.614 -12.390 -12.707
5 -14.004 -7.912 -14.004 -6.092 -6.298 0.000 1.000 0.000 -6.298 1.614 -12.390 -12.390
6 -11.931 -11.619 -11.931 -0.312 -18.147 0.000 1.000 0.000 -18.147 -6.527 -18.458 -12.390
7 1.004 -11.601 1.004 12.605 -12.514 0.000 1.000 0.000 -12.514 -0.912 0.091 0.136
8 1.004 -11.601 1.004 12.605 -12.514 0.000 1.000 0.000 -12.514 -0.912 0.091 0.136
9 1.004 -11.601 1.004 12.605 -12.514 0.000 1.000 0.000 -12.514 -0.912 0.091 0.136
10 1.366 -12.429 1.366 13.795 -8.378 0.000 1.000 0.000 -8.378 4.051 5.417 5.418
11 4.609 -11.063 4.609 15.673 -6.571 0.000 1.000 0.000 -6.571 4.492 9.102 9.105
12 4.609 -11.063 4.609 15.673 -6.571 0.000 1.000 0.000 -6.571 4.492 9.102 9.105
13 4.609 -11.063 4.609 15.673 -6.571 0.000 1.000 0.000 -6.571 4.492 9.102 9.105


for SEX :
k = 0.000 0.000 0.000
Band E_lda <Vxclda> E(N-1) <Hhartree> SigX SigC[E(N-1)] Z dSigC/dE Sig[E(N)] DeltaE E(N)_pert E(N)_diago
1 -14.085 -7.623 -14.085 -6.462 -6.197 3.968 1.000 0.000 -2.229 5.394 -8.691 -8.701
2 -14.085 -7.623 -14.085 -6.462 -6.197 3.968 1.000 0.000 -2.229 5.394 -8.691 -8.701
3 -14.085 -7.623 -14.085 -6.462 -6.197 3.968 1.000 0.000 -2.229 5.394 -8.691 -8.701
4 -14.004 -7.912 -14.004 -6.092 -6.298 4.030 1.000 0.000 -2.268 5.644 -8.360 -8.360
5 -14.004 -7.912 -14.004 -6.092 -6.298 4.030 1.000 0.000 -2.268 5.644 -8.360 -8.360
6 -11.931 -11.619 -11.931 -0.312 -18.147 12.745 1.000 0.000 -5.401 6.218 -5.713 -5.720
7 1.004 -11.601 1.004 12.605 -12.514 8.215 1.000 0.000 -4.298 7.303 8.307 8.313
8 1.004 -11.601 1.004 12.605 -12.514 8.215 1.000 0.000 -4.298 7.303 8.307 8.313
9 1.004 -11.601 1.004 12.605 -12.514 8.215 1.000 0.000 -4.298 7.303 8.307 8.313
10 1.366 -12.429 1.366 13.795 -8.378 4.286 1.000 0.000 -4.091 8.338 9.704 9.711
11 4.609 -11.063 4.609 15.673 -6.571 3.272 1.000 0.000 -3.298 7.765 12.374 12.377
12 4.609 -11.063 4.609 15.673 -6.571 3.272 1.000 0.000 -3.298 7.765 12.374 12.378
13 4.609 -11.063 4.609 15.673 -6.571 3.272 1.000 0.000 -3.298 7.765 12.374 12.378

for COHSEX :
k = 0.000 0.000 0.000
Band E_lda <Vxclda> E(N-1) <Hhartree> SigX SigC[E(N-1)] Z dSigC/dE Sig[E(N)] DeltaE E(N)_pert E(N)_diago
1 -14.085 -7.623 -14.085 -6.462 -6.197 3.968 1.000 0.000 -2.229 5.394 -8.691 -8.713
2 -14.085 -7.623 -14.085 -6.462 -6.197 3.968 1.000 0.000 -2.229 5.394 -8.691 -8.697
3 -14.085 -7.623 -14.085 -6.462 -6.197 3.968 1.000 0.000 -2.229 5.394 -8.691 -8.693
4 -14.004 -7.912 -14.004 -6.092 -6.298 4.030 1.000 0.000 -2.268 5.644 -8.360 -8.360
5 -14.004 -7.912 -14.004 -6.092 -6.298 4.030 1.000 0.000 -2.268 5.644 -8.360 -8.360
6 -11.931 -11.619 -11.931 -0.312 -18.147 12.745 1.000 0.000 -5.401 6.218 -5.713 -5.720
7 1.004 -11.601 1.004 12.605 -12.514 8.215 1.000 0.000 -4.298 7.303 8.307 -0.285
8 1.004 -11.601 1.004 12.605 -12.514 -0.393 1.000 0.000 -12.907 -1.306 -0.302 8.307 (strange line !!)
9 1.004 -11.601 1.004 12.605 -12.514 8.215 1.000 0.000 -4.298 7.303 8.307 8.312
10 1.366 -12.429 1.366 13.795 -8.378 4.286 1.000 0.000 -4.091 8.338 9.704 9.711
11 4.609 -11.063 4.609 15.673 -6.571 3.272 1.000 0.000 -3.298 7.765 12.374 12.376
12 4.609 -11.063 4.609 15.673 -6.571 3.272 1.000 0.000 -3.298 7.765 12.374 12.376
13 4.609 -11.063 4.609 15.673 -6.571 3.272 1.000 0.000 -3.298 7.765 12.374 12.378

Jacky Even
FOTON, UMR6082
INSA de Rennes, France

Fabien Bruneval a écrit :
Hello Jacky!

1) The only difference with a regular Hartree-Fock calculation is the basis set.
In the present implementation, we don't use the usual plane-wave basis set, but rather the basis set of Kohn-Sham orbitals:
\phi_i^{HF} = \sum_j c_{ij} \phi_j^{KS}

The size of the KS basis set is governed by the range given by keyword "bdgw"
In the limit of the complete KS basis, the result should be equivalent to the true HF result.


2) You're right: "getscr" is in principle useless. But Abinit would complain if it is not present.
I generally produce a "fake" SCR file, which is very small and not converged, just to please Abinit.

Cheers,

Fabien



On 10/26/2009 01:39 PM, jacky even wrote:
Dear all,

i have a few questions concerning Hartree-Fock corrections (test86 and test87 for Si FCC, version 4.x) :

- Is it true that Hartree-Fock corrections calculated self-consistently (like in test87.in) would lead finally to a solution equivalent (eigenvalues and wavefunctions) to a true Hartree-Fock simulation ?

- The "getscr" is set in test86.in and test.87 for this calculation : is it really used ? (and in which step of the correction ?)

yours sincerely,
Jacky Even
FOTON, UMR6082
INSA de Rennes, France








Archive powered by MHonArc 2.6.16.

Top of Page