Coulomb cutoff

[Daniele Varsano]

Dear Yuan,
you are right, unfortunately the box cutoff is not documented.
It is not the Ismail-Beigi cutoff, and should be nice to implement it in Yambo.
The idea of the box cutoff is to have a g-space cut coulomb potential with a box
shape, eventually infinite in one or more direction which are periodic. At difference
of the sphere/cylinder it is not build up with an analytic expression, but each G-component
is calculated numerically, and it implies a sum over G-space, and integration on Brilluoin zone.
This is the reason why the quality of the calculated potential depend in the number of G
component you include in this calculation, and why you need to perform a RIM calculation
first (in order to correct integrate in the Bz). In order to set an infinite direction, the box side
in that direction have to be set to 0. So, as you wrote,
CUTGeo= "box yz" # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere
% CUTBox
0.000 | 50.000 | 50.000 | # [CUT] [au] Box sides
%
this is the case for a 1D system along x.
Now, the box is constructed, in the range -L/2,L/2, so if your system has a linear dimension D,
you have to set at least L/2>D. Consequently the cell size have to be large enough.

If you want to know how the cutoff is technically build up, let me know, I will tell you by mail or via the forum.

Hope it helps.

Daniele

[sdwang]

Dear Yuan,
you are right, unfortunately the box cutoff is not documented.
It is not the Ismail-Beigi cutoff, and should be nice to implement it in Yambo.
The idea of the box cutoff is to have a g-space cut coulomb potential with a box
shape, eventually infinite in one or more direction which are periodic. At difference
of the sphere/cylinder it is not build up with an analytic expression, but each G-component
is calculated numerically, and it implies a sum over G-space, and integration on Brilluoin zone.
This is the reason why the quality of the calculated potential depend in the number of G
component you include in this calculation, and why you need to perform a RIM calculation
first (in order to correct integrate in the Bz). In order to set an infinite direction, the box side
in that direction have to be set to 0. So, as you wrote,
CUTGeo= "box yz" # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere
% CUTBox
0.000 | 50.000 | 50.000 | # [CUT] [au] Box sides
%
this is the case for a 1D system along x.
Now, the box is constructed, in the range -L/2,L/2, so if your system has a linear dimension D,
you have to set at least L/2>D. Consequently the cell size have to be large enough.

If you want to know how the cutoff is technically build up, let me know, I will tell you by mail or via the forum.

Hope it helps.

Daniele

Dear Daniele,
Does this mean when we construct the geometry of the unit cell, we have to make the origin of the coordinate system as the symmetry center? (because -L/2<Zcut<L/2)
Tnanks!

[Daniele Varsano]

Dear Shudong,
it is not needed. Here zcut it is the radius of action |z-z'|< zcut.

See you in Modena soon.

Daniele

[sdwang]

Thank you Daniele!
See you soon

[sdwang]

Dear Shudong,
it is not needed. Here zcut it is the radius of action |z-z'|< zcut.

See you in Modena soon.

Daniele

Sorry, Daniele, I remid something: In DFT formalism, if we deal with low dimensional system, we just need put the vacuum about 15 angstom(used to, maybe needs to convergence test) to avoid the interactions between the neighboring cell.But in GW formalism, if we use Coulomb truncation, we need to put the System<Zcut<D-System (D is the cell parameter), so the D must be larger than 2 times of our system. My point is: if the system is large, for example, 35 or more angnstrom, do we also need to set the vaccum bigger than 35 angstrom(DFT needs much less than this value) to be sure that the D>2System?
Thank you in advance!

[Daniele Varsano]

Dear Shudong,
there is not an exact rule (as in DFT, for instance if you have charged cell things are more complicate).
The condition System<Zcut<D-System it is something looks to me reasonable, in the sense that all the part of our system interact
and the interaction with the replica is avoided. Anyway, in my experience, it is not mandatory to fulfill this condition, taking
into account that the density decay exponentially, using a smaller cell does not affect too much the calculations.
As usual, convergences tests could be important. For instance, fixing the cell (big enough) and playing with the zcut value.
You should have a windows of zcut where your quantities are not affected. You can find an example of this (exaggerated as the system
was very small) in the inset of Fig.6 in the paper PHYSICAL REVIEW B 73, 205119 2006.
Cheers,

Daniele

[sdwang]

Thank you Daniele! I will check it.
Shudong

[fabio.caruso]

Dear Yambo developers,

I would like to report an issue that I encountered running RPA and BSE optical spectra calculations (without GW quasi-particle correction for now) for 1D nano-ribbons using a cylindrical Coulomb cutoff.

As a consistency check, I am comparing the optical spectra obtained from RPA and BSE with and without the cylindrical Coulomb cutoff.
I would expect that by increasing the cell size in the XY directions (assuming periodicity in the Z direction) the optical spectra should converge to the spectra obtained with the cylindrical cutoff.
In the case of BSE, the spectra obtained with and without cutoff converge as expected. For RPA, on the other hand, I see very large differences between the spectra evaluated with and without cutoff. In particular, the spectra obtained with the coulomb cutoff have a considerably lower intensity. Moreover, the RPA optical spectrum presents a spurious maximum at zero frequency, when evaluated with coulomb cutoff.
This seems to be a rather unphysical feature since the system that I am considering is non-metallic with a gap larger than 1 eV.
I attach the RPA and BSE spectra with and without cutoff.

I have run several convergence tests to see whether some unconverged parameter might be at the origin of this behaviour, but this does not seem to be the case.

Have you observed this behaviour before?

I am using Yambo v3.3.0 and the following Coulomb cutoff settings for both RPA and BSE calculations (the unit cell size is 50 a.u. in the X and Y direction):

RandQpts=0 # [RIM] Number of random q-points in the BZ
RandGvec=0 RL # [RIM] Coulomb interaction RS components
#QpgFull # [F RIM] Coulomb interaction: Full matrix
% Em1Anys
0.00 | 0.00 | 0.00 | # [RIM] X Y Z Static Inverse dielectric matrix
%
IDEm1Ref=0 # [RIM] Dielectric matrix reference component 1(x)/2(y)/3(z)
CUTGeo= "cylinder y" # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere
% CUTBox
0.00 | 0.00 | 0.00 | # [CUT] [au] Box sides
%
CUTRadius= 23.00000 # [CUT] [au] Sphere/Cylinder radius
CUTCylLen= 0.000000 # [CUT] [au] Cylinder length

Thanks in advance and any advice.

Best Regards,
Fabio Caruso

Department of Materials, University of Oxford, U.K.

[Daniele Varsano]

Dear Fabio,
thank you very much for reporting it. It looks there is something odd when using the cutoff in the RPA, and has to be investigated.
The problem now is that the 3.3 release in not developed anymore, many things are changed in the 3.4 (even if not the cutoff part),
but for debugging it would be desirable to work with the 3.4 release, can you reproduce these data with the new release?
If I well understood, your ribbon axis is in the y direction right?
Moreover the cylinder is not much used, do you observe the same effect when using the box: in order to build up a box you should set something like:

Code: Select all

RandQpts=1000000
RandGvec=1
CUTGeo = "box xz" ! assuming your ribbon axis is along y
%CUTBox				
46.000|0.000|46.000|		#		 CUT au Box sides
%	

This is because the build up of a box cutoff need an integration over the Bz and the RIM has to be used if your sampling is 1D, and the box side has double of the "real side" (this is something internal to the code that still has to be corrected).
Please note that also in the BSE calculation *without* cutoff you should use the RIM in order to properly evaluate the excitonic matrix.

Best,

Daniele

[fabio.caruso]

Hi Daniele,

thanks for your reply.
The ribbon is periodical in the y-direction.
I have downloaded and compiled yambo v3.4.1-rev51 and rerun the RPA calculations with the same input files as before.
(The version stamp in the output files produced by the new yambo version is still v3.3.0, even though I updated to yambo v3.4.1).
Moreover I have tried to employ the box Coulomb cutoff using the settings that you've suggested in your previous post. In both cases the numerical difference in the calculated RPA spectra are of the order of 10^-5.
Hence the cutoff type and the yambo version don't seem to have any appreciable effect on the RPA optical spectra .

Best,
Fabio