Overestimated gap in GW0 calculation ?

[hplan]

Dear Developers:

It seems a basic and naive question about accuracy of GW0 calculation for bandgap when compared with experimental value.
I performed a test GW0 calculation on Anatase TiO2 with 3s/3p semicore states , and found the calculated indirected gap was about 3.60 eV which was quite larger than experimental values ever reported(about 3.0 eV). This value seems quite dissatisfactory. I performed several convergence tests on relative parameters, but the GW0-gap didnot change much. Therefore, how about the accuracy of GW0 calculation for predicting some materials ? is there any guideline for us to reach some useful conclusions ?
Below is my setting for one of yambo running, related settings for abinit calculation such as k-point and ecutoff were well tested.

Code: Select all

#             GPL Version 3.2.1 Revision 392                
#               http://www.yambo-code.org                   
#
gw0                          # [R GW] GoWo Quasiparticle energy levels
ppa                          # [R Xp] Plasmon Pole Approximation
xxvxc                        # [R XX] Hartree-Fock Self-energy and Vxc
em1d                         # [R Xd] Dynamical Inverse Dielectric Matrix
FFTGvecs=  5737          RL  # [FFT] Plane-waves
EXXRLvcs=  8729          RL  # [XX] Exchange RL components
% QpntsRXp
  1 | 24 |                   # [Xp] Transferred momenta
%
% BndsRnXp
   1 | 400 |                 # [Xp] Polarization function bands
%
NGsBlkXp= 259            RL  # [Xp] Response block size
CGrdSpXp= 100.0000           # [Xp] [o/o] Coarse grid controller
% EhEngyXp
-1.000000 |-1.000000 |   eV  # [Xp] Electron-hole energy range
%
% LongDrXp
 1.000000 | 0.000000 | 0.000000 |      # [Xp] [cc] Electric Field
%
PPAPntXp= 20.10000       eV  # [Xp] PPA imaginary energy
% GbndRnge
   1 | 400 |                 # [GW] G[W] bands range
%
GDamping=  0.10000       eV  # [GW] G[W] damping
QPreport= "kpbne0ees0"       # [GW] QP info. Keys: kp/bn/xx/xc/s0/sq/e0/eq/ee/zf/ds/lm/lf
%QPkrange                    # [GW] QP generalized Kpoint/Band indices
  1| 24|  1| 32|
%
%QPerange                    # [GW] QP generalized Kpoint/Energy indices
  1| 24| 0.0|-1.0|
%

Best wishes,

Hai-Ping

[andrea marini]

Dear Developers:

It seems a basic and naive question about accuracy of GW0 calculation for bandgap when compared with experimental value.
I performed a test GW0 calculation on Anatase TiO2 with 3s/3p semicore states , and found the calculated indirected gap was about 3.60 eV which was quite larger than experimental values ever reported(about 3.0 eV). This value seems quite dissatisfactory. I performed several convergence tests on relative parameters, but the GW0-gap didnot change much. Therefore, how about the accuracy of GW0 calculation for predicting some materials ? is there any guideline for us to reach some useful conclusions ?

Dear Hai-PIng, first of all some general remarks. GW is composed by the Hartee-Fock (HF) self-energy plus correlation. If DFT yields a too small gap, HF generally overestimates it. Correlation partially shrinks the gap, by partially compensating the HF contribution.
Now, in general, the random-phase-approximation (RPA), that is the approximation that is beyond the GW, tends to overestimate the correlation. As a consequence the gap is shrunk too much, if compared to the experiment.
This general trend is not respected in your case, where the GW gap is too large. Now there are two possibilities:

1. Your correlation is not well converged.
2. GW does not apply to your system

Point 2 could perfectly be. However I notice in your input file something that I would like to ask you to see if your correlation is converged well enough.

• * You have only 24 q-points. Did you try increasing the size of your K-point mesh ?
  * In general the size of the response function is 1/10 of the RL components you included in HF (8729). So maybe NGsBlkXp= 259 is too small. Did you try increasing it ?
  * In general BndsRnXp (400 in your case) is 1/3 of the bands you include in the Green's function (GbndRnge). You are using the same number of bands for both. Did you try increasing GbndRnge ?

Cheers

[hplan]

Dear Andrea:

Thanks for your helpful response.

Now there are two possibilities:

1. Your correlation is not well converged.
2. GW does not apply to your system

Point 2 could perfectly be.

Is it just a typo ? As far as i know, GW0 approximation is widely applied to TiO2 systems.

However I notice in your input file something that I would like to ask you to see if your correlation is converged well enough.

• * You have only 24 q-points. Did you try increasing the size of your K-point mesh ?
  * In general the size of the response function is 1/10 of the RL components you included in HF (8729). So maybe NGsBlkXp= 259 is too small. Did you try increasing it ?
  * In general BndsRnXp (400 in your case) is 1/3 of the bands you include in the Green's function (GbndRnge). You are using the same number of bands for both. Did you try increasing GbndRnge ?

• * I just thought 4x4x4 MP grids should be enough for self-energy calculation , i will test some more q-points sistuation to examine this effect.
  * Thanks for telling me this empirical point. In fact, i did increase NGsBlkXp to 300 but the gap didnot change much. I'll try to increase this value .
  * Hmm, my previous tests always set BndsRnXp and GbndRnge to the same value. But I did a series tests by increaseing both BndsRnXp and GbndRnge from 200 to 400 to examine the convergence, it seemed no much effect when i included more bands in the calculations.

Thanks again for telling me the general points for convergence testings.

Best wishes,
Hai-Ping

[andrea marini]

Is it just a typo ? As far as i know, GW0 approximation is widely applied to TiO2 systems.

Dear Hai-Ping, I am not an expert of TiO2 systems. If you know of previous calculations on a system similar to yours you may try to reproduce them first. By the way, if you have reference post it here, so that we can have a look.

Regarding the GW0 approximation it is very important to remind that it is an approximation. Strictly speaking it is valid only in the limit where the Random Phase approximation (RPA) holds, homogeneous and dense system. Solids in general are not homogeneous, so GW0 may not work, especially in presence of localized s/p orbitals, if the metallic screening (like in noble and transition metals) does not make the RPA meaningful.

Tell us more about your material ... is it metallic ? If yes, what is the plasma frequency. If not, what is the LDA gap ....

Andrea

[hplan]

Dear Andrea:
Thank you for the suggestion.

Dear Hai-Ping, I am not an expert of TiO2 systems. If you know of previous calculations on a system similar to yours you may try to reproduce them first. By the way, if you have reference post it here, so that we can have a look.

I am sorry for my messed-information.
I then checked the previous works on Anatase TiO2, and found all calculated
GW gap are larger than experimental value reported.
For instance, a full-potential scQC gap was 3.78 eV in PRL 96 ,226402, and a GW0 value was given 3.79 eV by PRB 77 195112 . A preprint done by yambo by DTU group http://nano-bio.ehu.es/node/760 also gave
a 4.0 eV gap for anatase TiO2 system. I am quite confused about this fact, though some works like PRL 96 ,226402 claimed that strong electron-hole interaction should account for this large value .

Regarding the GW0 approximation it is very important to remind that it is an approximation. Strictly speaking it is valid only in the limit where the Random Phase approximation (RPA) holds, homogeneous and dense system. Solids in general are not homogeneous, so GW0 may not work, especially in presence of localized s/p orbitals, if the metallic screening (like in noble and transition metals) does not make the RPA meaningful.
Tell us more about your material ... is it metallic ? If yes, what is the plasma frequency. If not, what is the LDA gap ....

Thanks again for reminding . In fact, i want to examine a titania derivated nanosheet. It should be an insulator and my LDA-gap is about 3.0 eV for this system. But how to estimate the plasma frequency ?
I am a bit confused about GW0's prediction for this system. It seems we cannot get much predicted information for this titania derivate. An unconverged GW0-gap of this system is about 5.1 eV, which is largely overestimated over experimental values. I wonder how can we obtain some reasonable value by comparing TiO2 bulk systems with this nanosystem ?

Cheers,
Hai-Ping

[myrta gruning]

Dear Hai-Ping,

I performed a test GW0 calculation on Anatase TiO2 with 3s/3p semicore states , and found the calculated indirected gap was about 3.60 eV which was quite larger than experimental values ever reported(about 3.0 eV).

Andrea already answered on the accuracy and possible source of error of GW calculations.
I also want to point out that one should be careful when comparing with experiments. i.e What exact was measured, how, was 'really' the same system (e.g. defects) etc.
On the other hand your results seem to be close to other GW results in the literature (the differences may come from SC, pseudopotentials, convergence etc.).
Did they mention anything about the agreement with experiment?

In fact, i want to examine a titania derivated nanosheet. It should be an insulator and my LDA-gap is about 3.0 eV for this system. But how to estimate the plasma frequency ?
I am a bit confused about GW0's prediction for this system. It seems we cannot get much predicted information for this titania derivate. An unconverged GW0-gap of this system is about 5.1 eV, which is largely overestimated over experimental values. I wonder how can we obtain some reasonable value by comparing TiO2 bulk systems with this nanosystem ?

I do not understand exactly here. If your question is whether the bulk system is a good "model" to study the properties of the nanosheet so that one can calculate the electronic properties of the bulk and deduced that of the nanosheet?
My answer would be no, since there is a lot of "physics" coming from the reduced dimensionality of the sheet.
If the question is whether one can trust GW for the nanosystem, since you see a discrepancy with the experiment for the bulk, then I refer to my previous remark.
Still one think: about the unconverged GW0-gap of 5.1 eV. Are you referring to the nanosheet? Then beware that for such a system the convergence is much trickier than for the bulk. You can refer to the Yambo paper where convergence/numerical issues of less-than-3D systems are addressed. So it may be that the unconverged value is completely "off".

Cheers,
m

[hplan]

Dear Myrta:
Thank you for comments and suggestion !

Andrea already answered on the accuracy and possible source of error of GW calculations.
I also want to point out that one should be careful when comparing with experiments. i.e What exact was measured, how, was 'really' the same system (e.g. defects) etc.
On the other hand your results seem to be close to other GW results in the literature (the differences may come from SC, pseudopotentials, convergence etc.).
Did they mention anything about the agreement with experiment?

Hmm, I should recheck the literatures for GW calculations carefully. I noticed Andrea's instruction to me, which indeed gives some clues to understand GW calculations.
Yes, i didnot care much about what the experimental data were from. I should re-examine the these data ! Thanks for this point.

I do not understand exactly here. If your question is whether the bulk system is a good "model" to study the properties of the nanosheet so that one can calculate the electronic properties of the bulk and deduced that of the nanosheet?
My answer would be no, since there is a lot of "physics" coming from the reduced dimensionality of the sheet.
If the question is whether one can trust GW for the nanosystem, since you see a discrepancy with the experiment for the bulk, then I refer to my previous remark.
Still one think: about the unconverged GW0-gap of 5.1 eV. Are you referring to the nanosheet? Then beware that for such a system the convergence is much trickier than for the bulk. You can refer to the Yambo paper where convergence/numerical issues of less-than-3D systems are addressed. So it may be that the unconverged value is completely "off".

I thought that i should have some basic understandings on bulk phase of titania systems before my handling with nanosheets. I did notice the problems related to systmes' dimension when i carried out tutorials, and read related literatures of coulomb cutoff for 2D, 1D systems. Thanks for reminding this issue.

Best Wishes,
Hai-Ping