Dear All,
I want to ask a question about coulomb cutoff.
The coulomb parameters that I chose are as followings:
icutcoul 1
vcutgeo 0.0 0.0 -2.55
rcut 10.0
My supercell is rectangular and what I want to ask is: Do I need to put the positions of the atoms in the center of the supercell? Because in this way it seems that the charge density would be inside the radius of coulomb cutoff. Or abinit will deal with this problem automatically?
Thanks and Best regards,
Xueping Jiang
about coulumb cutoff
Moderators: maryam.azizi, bruneval
Re: about coulumb cutoff
Dear Jiang,
In the old mailling list, Matteo discussed this issue.
Sincerely,
Guangfu Luo
----------------------------------------------------------------------------------------------------
•From: "Matteo Giantomassi" <Matteo.Giantomassi@uclouvain.be>
•To: forum@abinit.org
•Subject: Re: [abinit-forum] cut-off technique for GW calculation
•Date: Tue, 25 Nov 2008 11:24:05 +0100 (CET)
•Importance: Normal
>Dear colleagues,
>I would like to use cutting technique (coulomb cut) to calculate Si clusters. The variable rcut gives the sphere radius in which I put my cluster. When I increase the rcut >radius the gap of cluster slightly increases. How could I optimize the rcut parameter? Could I use almost touching spheres from different cells or I have to choose the rcut >small enough to separate the spheres from different supercells?
Dear Titov,
The cutoff in the coulombian interaction is principally used to speed-up the convergence of the QP energies with respect to the size of the supercell by reducing the interaction between periodically repeated images.
In isolated systems one should perform a convergence study of the quantity of interest with respect to the size of the supercell, the same holds also when the coulombian interaction is truncated outside a spherical region. The only difference is that the GW results obtained with the cutoff technique should converge faster than that obtained with the true coulombian potential.
Once the supercell is large enough, the wavefunctions should be almost zero at the border of the simulation cell thus this portion of space should give a small contribution to the matrix elements entering the expression for the self-energy and the dielectric matrix. Unfortunately the long-range tail of the coulombian makes the converge
extremely slow because, although the density in regions far from the cluster is small, one still have a certain interaction due to the long-range tail of the coulombian.
The cutoff technique is designed to get rid of these spurious contributions.
The radius of the sphere should be chosen so that the spherical region always lies inside the unit cell and it encloses a significant part of the simulation cell. A reasonable value for the radius can be found by looking at the integrated charge density inside the sphere; most of the electronic charge should be contained within the sphere. The log file should report this information.
Once a good value for the radius has been defined, keep the sphere fixed and monitor the dependency of the quantity of interest with respect the volume of the supercell.
After a certain volume of the simulation box, the QP corrections should not change anymore.
>
> I would like also to use cylindrical shape of cut-off potential (finite cylinder). The rcut gives the radius of the cylinder; the center of the cylinder will be at zero by
> default. I guess vcutgeo variable determine the orientation of the cylinder axis and the height. Is it correct to use vcutgeo = 0 0 h/az for a vertical cylinder of height h
> (az- primitive translation vector in z direction)?
Note that two different approaches are available.
The first one is based on the work of Beigi (Phys. Rev. B 73, 233103) in which the coulombian interaction is truncated inside the projection of the Wigner-Seitz cell onto
the (say) x-y plane. The cylinder is of infinite extent along z. In Beigi's method no input variable defining the truncation region has to be specified, the cutoff region is automatically defined by the unit cell. To employ this approach with a cylinder along the z axis just add the following two lines to the input file.
icutcoul 1
vcutgeo 0 0 1 !along the z axis
Beigi's approach is the default method because I found that the Fourier component of the truncated interaction decay rapidly and smoothly as a function of |q+G|. Besides only two parameters have to be checked: the volume of the simulation box and the finite q-sampling along the z-axis defining the Born-von Karman periodic conditions. Please note that Beigi's method is implemented only in case of an orthorhombic Bravais lattice, for hexagonal lattices you have to use the approach of Rozzi described below.
In Rozzi's method (Phys. Rev. B 73, 205119) the interaction in truncated in a finite cylinder and, contrarily to the first approach, here you have to specify both the radius of the cylinder, rcut, and the lenght along the z-axis which should always be smaller that the extension of the Born-von Karman box in the z-direction. The length of the cylinder is given in terms of the primitive vector in the z direction R3. For example, to use a finite cylinder of radius 2.5 Bohr and length 3.0*R3, use
icutcoul 1
vcutgeo 0 0 -3.0 ! note the minus sign
rcut 2.5
Two additional comments:
1) First of all one should use the cutoff both in the screening and sigma calculation. In the next version of abinit it will be possible to avoid the first step by reading a file containing the polarizability and applying the cutoff only during the calculation of the QP corrections.
2) The second comment is related to the placement of the isolated system inside the simulation box. For the spherical symmetry the cluster should be centered on the origin. In case of a cylindrical cutoff the axis of the wire should pass through the origin and has to be parallel to one of the primitive vector. I will remove this constraint when I will find some spare time to work on this part of code.
Thank for reminding me
Hope it helps
Best regards
Matteo Giantomassi
In the old mailling list, Matteo discussed this issue.
Sincerely,
Guangfu Luo
----------------------------------------------------------------------------------------------------
•From: "Matteo Giantomassi" <Matteo.Giantomassi@uclouvain.be>
•To: forum@abinit.org
•Subject: Re: [abinit-forum] cut-off technique for GW calculation
•Date: Tue, 25 Nov 2008 11:24:05 +0100 (CET)
•Importance: Normal
>Dear colleagues,
>I would like to use cutting technique (coulomb cut) to calculate Si clusters. The variable rcut gives the sphere radius in which I put my cluster. When I increase the rcut >radius the gap of cluster slightly increases. How could I optimize the rcut parameter? Could I use almost touching spheres from different cells or I have to choose the rcut >small enough to separate the spheres from different supercells?
Dear Titov,
The cutoff in the coulombian interaction is principally used to speed-up the convergence of the QP energies with respect to the size of the supercell by reducing the interaction between periodically repeated images.
In isolated systems one should perform a convergence study of the quantity of interest with respect to the size of the supercell, the same holds also when the coulombian interaction is truncated outside a spherical region. The only difference is that the GW results obtained with the cutoff technique should converge faster than that obtained with the true coulombian potential.
Once the supercell is large enough, the wavefunctions should be almost zero at the border of the simulation cell thus this portion of space should give a small contribution to the matrix elements entering the expression for the self-energy and the dielectric matrix. Unfortunately the long-range tail of the coulombian makes the converge
extremely slow because, although the density in regions far from the cluster is small, one still have a certain interaction due to the long-range tail of the coulombian.
The cutoff technique is designed to get rid of these spurious contributions.
The radius of the sphere should be chosen so that the spherical region always lies inside the unit cell and it encloses a significant part of the simulation cell. A reasonable value for the radius can be found by looking at the integrated charge density inside the sphere; most of the electronic charge should be contained within the sphere. The log file should report this information.
Once a good value for the radius has been defined, keep the sphere fixed and monitor the dependency of the quantity of interest with respect the volume of the supercell.
After a certain volume of the simulation box, the QP corrections should not change anymore.
>
> I would like also to use cylindrical shape of cut-off potential (finite cylinder). The rcut gives the radius of the cylinder; the center of the cylinder will be at zero by
> default. I guess vcutgeo variable determine the orientation of the cylinder axis and the height. Is it correct to use vcutgeo = 0 0 h/az for a vertical cylinder of height h
> (az- primitive translation vector in z direction)?
Note that two different approaches are available.
The first one is based on the work of Beigi (Phys. Rev. B 73, 233103) in which the coulombian interaction is truncated inside the projection of the Wigner-Seitz cell onto
the (say) x-y plane. The cylinder is of infinite extent along z. In Beigi's method no input variable defining the truncation region has to be specified, the cutoff region is automatically defined by the unit cell. To employ this approach with a cylinder along the z axis just add the following two lines to the input file.
icutcoul 1
vcutgeo 0 0 1 !along the z axis
Beigi's approach is the default method because I found that the Fourier component of the truncated interaction decay rapidly and smoothly as a function of |q+G|. Besides only two parameters have to be checked: the volume of the simulation box and the finite q-sampling along the z-axis defining the Born-von Karman periodic conditions. Please note that Beigi's method is implemented only in case of an orthorhombic Bravais lattice, for hexagonal lattices you have to use the approach of Rozzi described below.
In Rozzi's method (Phys. Rev. B 73, 205119) the interaction in truncated in a finite cylinder and, contrarily to the first approach, here you have to specify both the radius of the cylinder, rcut, and the lenght along the z-axis which should always be smaller that the extension of the Born-von Karman box in the z-direction. The length of the cylinder is given in terms of the primitive vector in the z direction R3. For example, to use a finite cylinder of radius 2.5 Bohr and length 3.0*R3, use
icutcoul 1
vcutgeo 0 0 -3.0 ! note the minus sign
rcut 2.5
Two additional comments:
1) First of all one should use the cutoff both in the screening and sigma calculation. In the next version of abinit it will be possible to avoid the first step by reading a file containing the polarizability and applying the cutoff only during the calculation of the QP corrections.
2) The second comment is related to the placement of the isolated system inside the simulation box. For the spherical symmetry the cluster should be centered on the origin. In case of a cylindrical cutoff the axis of the wire should pass through the origin and has to be parallel to one of the primitive vector. I will remove this constraint when I will find some spare time to work on this part of code.
Thank for reminding me
Hope it helps
Best regards
Matteo Giantomassi