Test convergence of GW process

[sdwang]

Dear all:
I have performed the GW calculation for my 2 dimensional rectangle unitcell with 4C and 2O. I test FFTGvecs and EXXRLvcs from 2000 to 1000, when they are 6000, the result is convergence, so I chose it 7000 in all my calculation. but for NGsBlkXp, I used 200 to 1000, I get some different value and it do not converge ,and my results as following:(I only give the value of the first kpoint)

[08.02] Q(uasi)P(article) properties
====================================

Legend (energies in eV):
- B : Band - Eo : bare energy
- E : QP energy - Z : Renormalization factor
- So : Sc(Eo) - S : Sc(E)
- xx/Vxc : Sx/Vxc - dSp : Sc derivative precision
NGsBlkXp= 195
QP [eV] @ K [1] (iku): 0.166667 0.250000 0.000000
B=12 Eo= -1.83 E= 1.46 E-Eo= 3.28 Z=0.57 So= -7.50431 xx=-23.91940 Vxc=-18.78779
B=13 Eo= -1.00 E= 4.32 E-Eo= 5.31 Z=0.58 So= -9.20674 xx=-19.35795 Vxc=-16.69009
B=14 Eo= 0.00 E= 3.34 E-Eo= 3.34 Z=0.62 So=-7.380 xx=-24.43 Vxc=-19.49
B=15 Eo= 3.03 E= 1.59 E-Eo= -1.44 Z=0.70 So= 7.03507 xx= -8.20239 Vxc=-13.36181
B=16 Eo= 4.20 E= 2.40 E-Eo= -1.81 Z=0.62 So= 8.49217 xx=-10.69838 Vxc=-16.07968

NGsBlkXp= 301
QP [eV] @ K [1] (iku): 0.166667 0.250000 0.000000
B=12 Eo= -1.83 E= 1.60 E-Eo= 3.43 Z=0.60 So= 0.72235 xx=-23.91940 Vxc=-18.78779
B=13 Eo= -1.00 E= 4.14 E-Eo= 5.13 Z=0.57 So= -1.32342 xx=-19.35795 Vxc=-16.69009
B=14 Eo= 0.00 E= 4.54 E-Eo= 4.54 Z=0.56 So=0.8014 xx=-24.43 Vxc=-19.49
B=15 Eo= 3.03 E= 0.26 E-Eo= -2.77 Z=0.63 So= 0.35725 xx= -8.20239 Vxc=-13.36181
B=16 Eo= 4.20 E= 1.59 E-Eo= -2.61 Z=0.59 So= 1.27998 xx=-10.69838 Vxc=-16.07968

NGsBlkXp= 505
QP [eV] @ K [1] (iku): 0.166667 0.250000 0.000000
B=12 Eo= -1.83 E= -0.56 E-Eo= 1.27 Z=0.73 So= 0.77667 xx=-24.25345 Vxc=-18.91546
B=13 Eo= -1.00 E= 0.74 E-Eo= 1.74 Z=0.76 So= -1.29206 xx=-19.47138 Vxc=-16.74104
B=14 Eo= 0.00 E= 1.25 E-Eo= 1.25 Z=0.72 So=0.7965 xx=-24.82 Vxc=-19.64
B=15 Eo= 3.03 E= 3.53 E-Eo= 0.50 Z=0.80 So= 0.33173 xx= -8.30944 Vxc=-13.42133
B=16 Eo= 4.20 E= 5.10 E-Eo= 0.90 Z=0.77 So= 1.22343 xx=-10.83877 Vxc=-16.16137
NGsBlkXp=807
QP [eV] @ K [1] (iku): 0.166667 0.250000 0.000000
B=12 Eo= -1.83 E= -2.15 E-Eo= -0.32 Z=0.72 So= -0.86580 xx=-24.25345 Vxc=-18.91546
B=13 Eo= -1.00 E= -0.42 E-Eo= 0.58 Z=0.76 So= -3.02655 xx=-19.47138 Vxc=-16.74104
B=14 Eo= 0.00 E= 0.00 E-Eo= 0.00 Z=0.73 So=-.8054 xx=-24.82 Vxc=-19.64
B=15 Eo= 3.03 E= 4.62 E-Eo= 1.60 Z=0.81 So= 1.81973 xx= -8.30944 Vxc=-13.42133
B=16 Eo= 4.20 E= 6.21 E-Eo= 2.00 Z=0.78 So= 2.77682 xx=-10.83877 Vxc=-16.16137
NGsBlkXp=909
QP [eV] @ K [1] (iku): 0.166667 0.250000 0.000000
B=12 Eo= -1.83 E= -2.17 E-Eo= -0.34 Z=0.73 So= -1.16158 xx=-24.26364 Vxc=-18.91546
B=13 Eo= -1.00 E= -0.59 E-Eo= 0.41 Z=0.77 So= -3.33240 xx=-19.47402 Vxc=-16.74104
B=14 Eo= 0.00 E= -0.22 E-Eo= -0.22 Z=0.73 So=-1.095 xx=-24.83 Vxc=-19.64
B=15 Eo= 3.03 E= 4.80 E-Eo= 1.77 Z=0.81 So= 2.08079 xx= -8.31260 Vxc=-13.42133
B=16 Eo= 4.20 E= 6.34 E-Eo= 2.13 Z=0.78 So= 3.06300 xx=-10.84301 Vxc=-16.16137
NGsBlkXp=1011
QP [eV] @ K [1] (iku): 0.166667 0.250000 0.000000
B=12 Eo= -1.83 E= -2.30 E-Eo= -0.48 Z=0.73 So= -1.20856 xx=-24.26364 Vxc=-18.91546
B=13 Eo= -1.00 E= -0.69 E-Eo= 0.30 Z=0.77 So= -3.37930 xx=-19.47402 Vxc=-16.74104
B=14 Eo= 0.00 E= -0.33 E-Eo= -0.33 Z=0.74 So=-1.145 xx=-24.83 Vxc=-19.64
B=15 Eo= 3.03 E= 4.91 E-Eo= 1.88 Z=0.82 So= 2.12065 xx= -8.31260 Vxc=-13.42133
B=16 Eo= 4.20 E= 6.50 E-Eo= 2.29 Z=0.78 So= 3.11083 xx=-10.84301 Vxc=-16.16137

and my input is :
.-Input file : yambo.in
| xxvxc # [R XX] Hartree-Fock Self-energy and Vxc
| em1d # [R Xd] Dynamical Inverse Dielectric Matrix
| ppa # [R Xp] Plasmon Pole Approximation
| gw0 # [R GW] GoWo Quasiparticle energy levels
| FFTGvecs= 7003 RL # [FFT] Plane-waves
| EXXRLvcs= 7003 RL # [XX] Exchange RL components
| % QpntsRXp
| 1 | 14 | # [Xp] Transferred momenta
| %
| % BndsRnXp
| 1 | 100 | # [Xp] Polarization function bands
| %
| NGsBlkXp= 1011 RL # [Xp] Response block size I chose different value to test the convergence ,the results as above.
| % LongDrXp
| 0.1000E-4 | 0.000 | 0.000 | # [Xp] [cc] Electric Field
| %
| PPAPntXp= 27.21138 eV # [Xp] PPA imaginary energy
| % GbndRnge
| 1 | 100 | # [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



Is my test process right? And which one is the convergent,or I do not access it at all??If that is true, how can I do the test for it??
Thanks!
S D Wang

[Daniele Varsano]

Dear Shudong,
looking at your last results (909 and 1011 NGsBlkXp) they start to have a
reasonable behaviour (even if it's something that you should understand).
They are not yet at convergence, and you should push the number of NGsBlkXp
forward and see if they reach the convergence.


Best,

Daniele

[sdwang]

Thank you!
I will try it.

[Conor Hogan]

Bear in mind also that the value of the gap will often converge quicker than the absolute value of the HOMO or LUMO state eigenvalue, so it depends really on what you are trying to calculate and with what precision.

[sdwang]

Dear developers:
If I used Coulomb cut off , I should test the convergence with box sides. In this case, waht is the test sequence of NGsBlkXp and box sides ? I fixed the
NGsBlkXp at some value and keep it when I test box sides, but the gap can not get the step as the box sides increasing. Does this relate the value of NGsBlkXp? I mean should I firstly test the NGsBlkXp at fix box sides?
S. D. Wang

[Daniele Varsano]

Dear Shudong,
if you change the box sides, you are also changing the G vectors (2pi/L) in cubic case,
so you need more G vectors for a bigger cell to have the same energy cutoff.
If you check the convergence with respect the volume keeping fixed the Gvec cutoff,
you can do assigning the NGsBlkXp in mHa (i.e. milliHartree) instead of RL.
In this case, you can check the volume and the NGsBlkXp independently.

Cheers,

Daniele

[sdwang]

Dear Shudong,
if you change the box sides, you are also changing the G vectors (2pi/L) in cubic case,
so you need more G vectors for a bigger cell to have the same energy cutoff.
If you check the convergence with respect the volume keeping fixed the Gvec cutoff,
you can do assigning the NGsBlkXp in mHa (i.e. milliHartree) instead of RL.
In this case, you can check the volume and the NGsBlkXp independently.

Cheers,

Daniele

Thank you for your reply!
The Gvec cutoff G^2/2 < E_cut(Ry). In order to do that I can replace the RL unit in the yambo input
with mHa (i.e. milli Hartree), is it right?
In my box sides test process, I used the fixed Gvec cutoff at evry time, I am confused why it changing?
I guess the unit RL relate to the volume size in my case but the unit mHa do not, am I right?
If I used NGsBlkXp=500 RL, I should set 500^2/2=125000 Ry =62500 Ha= 6.25X10^7 mHa in input file?

[Daniele Varsano]

In order to do that I can replace the RL unit in the yambo input
with mHa (i.e. milli Hartree), is it right?

Yes!

I guess the unit RL relate to the volume size in my case but the unit mHa do not, am I right?

Using the cutoff in energy, the number of Gvec will change accordingly to the volume (the same that happen when
you do a SCF calculation in plane wave. The bigger the cell, the bigger the number of G vector for a fixed cutoff.

If I used NGsBlkXp=500 RL, I should set 500^2/2=125000 Ry =62500 Ha= 6.25X10^7 mHa in input file?

Absolutely not. 500RL is the number of Gvector and not its value. In all the report files you have the correspondence
between number of Gvector and cutoff nergy in mHa: check it and use that numbers.
Cheers,
Daniele

[sdwang]

Thank you!
I see it :
[02.03] RL shells
=================

Shells, format: [S#] G_RL(mHa)

[S12344]:89195(0.1414E+5) [S12343]:89187(0.1414E+5)...

S. D. Wang