convergence behaviour with XTermKind
Moderators: Davide Sangalli, Daniele Varsano

 Posts: 34
 Joined: Mon Nov 18, 2019 10:48 am
convergence behaviour with XTermKind
Dear all,
I have a question regarding the behaviour of the X terminator in GW calculations. The attached plot BULK_Xterm_BndsRnXp shows the results of my calculations where I try to convergence a band gap.
When the X terminator is included, the band gap converges quickly with respect to BndsRnXp to a value which is independent of the terminator energy. This behaviour is as expected.
However, the calculation without the terminator shows a convergence to a different value. This is unlike the behaviour of GTermKind which I tested as well. Could someone please explain if this deviation is to be expected or what can be done to remove it if possible?
Also note that the convergence with the number of kpoints is much better without the X terminator (see the second plot BULK_Xterm_kpoints). Is this an artefact due to the problem above or is this also to be expected?
Best,
Christian
I have a question regarding the behaviour of the X terminator in GW calculations. The attached plot BULK_Xterm_BndsRnXp shows the results of my calculations where I try to convergence a band gap.
When the X terminator is included, the band gap converges quickly with respect to BndsRnXp to a value which is independent of the terminator energy. This behaviour is as expected.
However, the calculation without the terminator shows a convergence to a different value. This is unlike the behaviour of GTermKind which I tested as well. Could someone please explain if this deviation is to be expected or what can be done to remove it if possible?
Also note that the convergence with the number of kpoints is much better without the X terminator (see the second plot BULK_Xterm_kpoints). Is this an artefact due to the problem above or is this also to be expected?
Best,
Christian
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Christian Koenig
Tyndall National Institute
Cork, Ireland
Tyndall National Institute
Cork, Ireland
 Daniele Varsano
 Posts: 2992
 Joined: Tue Mar 17, 2009 2:23 pm
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Re: convergence behaviour with XTermKind
Dear Christian,
first, note that the terminator energy it is not an absolute value but it is an amount of energy added to the energy of the last occupied band considered in the calculation, usually taking to its default value it is enough.
It is important to note that bands summation enters both in X and G and they usually show a different convergence behaviour so it is important to have both under control when comparing calculations with and without terminator.
Best,
Daniele
first, note that the terminator energy it is not an absolute value but it is an amount of energy added to the energy of the last occupied band considered in the calculation, usually taking to its default value it is enough.
This should not happen, but it is not clear to me what you are plotting here, it is indicated as a gap, but it has a negative value making it hard to understand.However, the calculation without the terminator shows a convergence to a different value.
It is important to note that bands summation enters both in X and G and they usually show a different convergence behaviour so it is important to have both under control when comparing calculations with and without terminator.
Best,
Daniele
Dr. Daniele Varsano
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/

 Posts: 34
 Joined: Mon Nov 18, 2019 10:48 am
Re: convergence behaviour with XTermKind
Dear Daniele,
I varied the energies because I thought this might fix the problem but this was not the case. The convergence independent of the relative energy is in agreement with the reference given for the terminators (e.g. Fig. 1 in https://journals.aps.org/prb/abstract/1 ... .78.085125).
The plot indeed shows the band gap  the gap is very small and the ordering of the states changes with respect to the DFT calculation, therefore the negative value.
Regarding the number of bands, the way I understand it XTermKind has an effect on BndsRnXp and GTermKind on GBndRnge. In any case all the calculations use GTermKing="BG" and they are quite stable with respect to the number of bands (plot attached). I included 200 bands in GBndRnge.
Best,
Christian
I varied the energies because I thought this might fix the problem but this was not the case. The convergence independent of the relative energy is in agreement with the reference given for the terminators (e.g. Fig. 1 in https://journals.aps.org/prb/abstract/1 ... .78.085125).
The plot indeed shows the band gap  the gap is very small and the ordering of the states changes with respect to the DFT calculation, therefore the negative value.
Regarding the number of bands, the way I understand it XTermKind has an effect on BndsRnXp and GTermKind on GBndRnge. In any case all the calculations use GTermKing="BG" and they are quite stable with respect to the number of bands (plot attached). I included 200 bands in GBndRnge.
Best,
Christian
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Christian Koenig
Tyndall National Institute
Cork, Ireland
Tyndall National Institute
Cork, Ireland

 Posts: 34
 Joined: Mon Nov 18, 2019 10:48 am
Re: convergence behaviour with XTermKind
Dear Daniele,
I should probably mention that all the calculations were done with 8x8x8 kpoints.
My input file which I used as a starting point with all default parameters is attached.
Best,
Christian
I should probably mention that all the calculations were done with 8x8x8 kpoints.
My input file which I used as a starting point with all default parameters is attached.
Best,
Christian
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Christian Koenig
Tyndall National Institute
Cork, Ireland
Tyndall National Institute
Cork, Ireland
 Daniele Varsano
 Posts: 2992
 Joined: Tue Mar 17, 2009 2:23 pm
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Re: convergence behaviour with XTermKind
OK, I see.
Can you keep fixed:
Importantly, can you repeat the same tests for a different value of NGsBlkXp, note that NGsBlkXp and BndsRnXp are interlinked, the more bands are used the higher value of NGsBlkXp is needed to converge, for this reason, it is highly probable that the used value for NGsBlkXp it is not enough when using the terminator.
Best,
Daniele
Can you keep fixed:
and perform calculations varying "BndsRnXp" with and without terminator plotting the single particle levels instead of the gap? may it is easier to understand what is going on.% GbndRnge
1  200  # [GW] G[W] bands range
%
GTermKind= "BG"
Importantly, can you repeat the same tests for a different value of NGsBlkXp, note that NGsBlkXp and BndsRnXp are interlinked, the more bands are used the higher value of NGsBlkXp is needed to converge, for this reason, it is highly probable that the used value for NGsBlkXp it is not enough when using the terminator.
Best,
Daniele
Dr. Daniele Varsano
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/

 Posts: 34
 Joined: Mon Nov 18, 2019 10:48 am
Re: convergence behaviour with XTermKind
Dear Daniele,
Here are the plots:
BULK_states_BndsRnXp: state energies as a function of BndsRnXp (with and without the terminator; terminator energy is 40 eV).
BULK_gap_NGsBlkXp_BndsRnXp: gap as function of NGsBlkXp and BndsRnXp. I'll make a plot of the states as well.
Best,
Christian
Here are the plots:
BULK_states_BndsRnXp: state energies as a function of BndsRnXp (with and without the terminator; terminator energy is 40 eV).
BULK_gap_NGsBlkXp_BndsRnXp: gap as function of NGsBlkXp and BndsRnXp. I'll make a plot of the states as well.
Best,
Christian
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Christian Koenig
Tyndall National Institute
Cork, Ireland
Tyndall National Institute
Cork, Ireland
 Daniele Varsano
 Posts: 2992
 Joined: Tue Mar 17, 2009 2:23 pm
 Contact:
Re: convergence behaviour with XTermKind
Dear Christian,
actually looking at the single energy plot, even if more analysis is needed it seems that the terminator is not working badly, as I told you in the previous post the terminator need more G vectors in the screening matrix, so they cannot be compared directly and you should compare converged values (here the calculation using terminator has not yet converged wrt Gblks, and probably you should also look at the convergence without terminator that could be different!). Please note also that here you are looking at differences in the order of 20meV which I would say it is at the verge of the precision of the method.
Best,
Daniele
actually looking at the single energy plot, even if more analysis is needed it seems that the terminator is not working badly, as I told you in the previous post the terminator need more G vectors in the screening matrix, so they cannot be compared directly and you should compare converged values (here the calculation using terminator has not yet converged wrt Gblks, and probably you should also look at the convergence without terminator that could be different!). Please note also that here you are looking at differences in the order of 20meV which I would say it is at the verge of the precision of the method.
Best,
Daniele
Dr. Daniele Varsano
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/

 Posts: 34
 Joined: Mon Nov 18, 2019 10:48 am
Re: convergence behaviour with XTermKind
Dear Daniele,
Here is the plot for the individual states. No surprises there, the states themselves are not quite converged but I'm only considering the gap anyway. I don't have any calculations with a higher value for NGsBlkXp with and without the X terminator to compare in the moment.
Do you think that the convergence with respect to the number of kpoints is the same issue (i.e. that a better sampling with q on which the screening depends analogous to G and G' is required with the X terminator)? In this case I might have to get rid of the X terminator to avoid using a lot of kpoints. Unfortunately I have to converge to a few meV because the expected gap is so small.
Best,
Christian
Here is the plot for the individual states. No surprises there, the states themselves are not quite converged but I'm only considering the gap anyway. I don't have any calculations with a higher value for NGsBlkXp with and without the X terminator to compare in the moment.
Do you think that the convergence with respect to the number of kpoints is the same issue (i.e. that a better sampling with q on which the screening depends analogous to G and G' is required with the X terminator)? In this case I might have to get rid of the X terminator to avoid using a lot of kpoints. Unfortunately I have to converge to a few meV because the expected gap is so small.
Best,
Christian
You do not have the required permissions to view the files attached to this post.
Christian Koenig
Tyndall National Institute
Cork, Ireland
Tyndall National Institute
Cork, Ireland
 Daniele Varsano
 Posts: 2992
 Joined: Tue Mar 17, 2009 2:23 pm
 Contact:
Re: convergence behaviour with XTermKind
Dear Christian,
I do not know what kind of system in term of dimensionality you are dealing with (bulk, 2D etc.). In any case, in order to have more accurate integrations over the BZ, I suggest you activate the random integration method (yambo r ...). You will see the keyword rim_cut among the runlevel in the input, and you can set (RndGvec=1, RndQts=1000000). This will perform accurate integration of the coulomb potential in the BZ.
If you want to use that, you need to remove your ndb.HF* and ndb.QP databases and repeat the calculations. No need to recalculate the screeing.
Best,
Daniele
Actually, this is a bit surprising, I would not have expected such a different dependence wrt the k point sampling.Do you think that the convergence with respect to the number of kpoints is the same issue
I do not know what kind of system in term of dimensionality you are dealing with (bulk, 2D etc.). In any case, in order to have more accurate integrations over the BZ, I suggest you activate the random integration method (yambo r ...). You will see the keyword rim_cut among the runlevel in the input, and you can set (RndGvec=1, RndQts=1000000). This will perform accurate integration of the coulomb potential in the BZ.
If you want to use that, you need to remove your ndb.HF* and ndb.QP databases and repeat the calculations. No need to recalculate the screeing.
Best,
Daniele
Dr. Daniele Varsano
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/

 Posts: 34
 Joined: Mon Nov 18, 2019 10:48 am
Re: convergence behaviour with XTermKind
Dear Daniele,
Thanks a lot for your suggestions. This is a rhombohedral bulk cell, so I haven't used random integration.
The results with 1e6 random points in the first Brillouin zone are attached  the random integration method doesn't fix the problem.
I'll do the relevant convergence tests again without the X terminator but this will take a while.
Thanks very much!
Best,
Christian
Thanks a lot for your suggestions. This is a rhombohedral bulk cell, so I haven't used random integration.
The results with 1e6 random points in the first Brillouin zone are attached  the random integration method doesn't fix the problem.
I'll do the relevant convergence tests again without the X terminator but this will take a while.
Thanks very much!
Best,
Christian
You do not have the required permissions to view the files attached to this post.
Christian Koenig
Tyndall National Institute
Cork, Ireland
Tyndall National Institute
Cork, Ireland