The ABINIT Users Mailing List ( CLOSED )

["Matteo Giantomassi" <Matteo.Giantomassi@uclouvain.be>]

> 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