plasmon-pole approximation and Hartree Fock convergence

[Christian Koenig]

hfgaps.pdf

hfstates.pdf

ppa.pdf

Dear all,

I'm having some issues with a GW calculation for bulk bismuth. Due to the small band gaps,
convergence has to be tight - at least 10 meV.

1) I used the plasmon-pole approximation with different values for PPAPntXp.
As you can see in the attached picture (ppa.pdf), the energies of all the shown states
do not converge to a reasonable accuracy even for quite high values of PPAPntXp.
Does this indicate that the plasmon-pole approximation can not be used in this
specific case?

2) The convergence of the Hartree Fock energies with respect to the number of
k-points seems very slow.
For comparison Aguilera et al., Phys. Rev. B 91, 125129 (2015) use a 6x6x6
k-point grid for GW without self-consistency. Of course, these authors use
a different code, but I would assume to get approximately the same number of
k-points.
Do you experienced users think that there is something wrong with this convergence,
or is there a way to improve the convergence?

Any help is appreciated.


Best,

Christian

[Daniele Varsano]

Dear Christina,
please fill your signature with your complete affiliation, you can do once for all by filling your signature in the user profile.

1) PPA: what you find it is a bit unusual, GW correction should be not that sensitive to the position of the pole in the PPA. I cannot see your input or report,
anyway be sure that you are using a reasonable value of empty bands and size of the dielectric matrix. In any case, the two plotted lines are there (valence and conduction?) if it is so, is the gap reasonably converged?
A way to check if the PPA breaks down is to have a look at the Z factor that should be not smaller of let's 0.6/0.7.

2) HF, again, I cannot see the input, but if you did not do, including the Random phase integration should improve the converge with respect the k point sampling. In order to activate you should add the -r flag when building the input file and set something like:

Code: Select all

RandQpts=3000000                     # [RIM] Number of random q-points in the BZ
RandGvec= 1            RL      # [RIM] Coulomb interaction RS components

This essentially performs a Monte Carlo integration in each region of the BZ spanned by your sampling, RandGvec= 1 means that you want to perform random integrations just for the 1st BZ which is usually enough and 3 million random points are usually enough to have well-converged integrals.

Best,
Daniele

[Christian Koenig]

ppa.txt

Dear Daniele,

First of all thanks very much for the response.

I attached the input file for the PPA calculations. BndsRnXp was set to a maximum of 600 which may
not be totally converged but doesn't appear to be particularly low.
Below are the lines from the output files which correspond to the Z factor, the real part is 0.78:

####################################################################################################
QP [eV] @ K [4] (iku): 0.434057 0.250603 -0.166667
B=30 Eo= -0.12 E= -0.55 E-Eo= -0.43 Re(Z)=0.78 Im(Z)=-.1674E-2 nlXC=-11.24 lXC=-11.26 So=-.5698
B=31 Eo= 0.02 E= -0.55 E-Eo= -0.57 Re(Z)=0.78 Im(Z)=-.1674E-2 nlXC=-11.02 lXC=-11.49 So=-1.200
####################################################################################################
QP [eV] @ K [32] (iku): 0.000000 0.000000 -0.500000
B=30 Eo= 0.05 E= -0.57 E-Eo= -0.62 Re(Z)=0.78 Im(Z)=-.1658E-2 nlXC=-11.41 lXC=-11.71 So=-1.089
B=31 Eo= 0.32 E= -0.13 E-Eo= -0.45 Re(Z)=0.78 Im(Z)=-.1689E-2 nlXC=-9.787 lXC=-11.29 So=-2.083
####################################################################################################

Not sure if this is important for the convergence here, but I did not include the Drude term in these
calculations yet, so I got also "[WARNING] The system is a metal but Drude term not included". In
more recent calculations it was included.
The gaps seem to be close to convergence, i.e. the variations are smaller than 10 meV although less
would be better.
What else could be checked to make sure the PPA is valid (except for Z)?

Regarding Hartree Fock I will try the random phase integration, thanks very much for the suggestion.


Best,

Christian

[Daniele Varsano]

Dear Christian,
the Z factor seems to be pretty ok.
The Drude term it is not a problem, as it does not take any effect in the PP approximation.
Something you can try, is to use the terminators (see https://journals.aps.org/prb/abstract/1 ... .78.085125)
for the band convergence and see if the dependence it is mitigated.
By using -V qp (o -V all) you can set:

Code: Select all

XTermKind= "BG"              # [X] X terminator ("none","BG" Bruneval-Gonze)
XTermEn= 40.00000      eV      # [X] X terminator energy (only for kind="BG")

and

Code: Select all

GTermKind= "BG"              # [GW] GW terminator ("none","BG" Bruneval-Gonze)
GTermEn= 40.81708      eV      # [GW] GW terminator energy (only for kind="BG")

The calculation will be more demanding but it should converge much faster wrt the number of bands.
You can leave the TermEn as default as they are relative energies.

Regarding Hartree Fock I will try the random phase integration

Just for sake of precision, Random integration method (e.g. Monte Carlo integration), no random phase here.

Best,
Daniele