The ABINIT Users Mailing List ( CLOSED )

[Matteo Giantomassi <gmatteo@pcpm.ucl.ac.be>]

On Mon, 29 Oct 2007, Xiaohong Zheng wrote:

> Hello, Dear Matteo,
>
> Thank you very much for your great help. In my mind, GW calculation will use 
> the wave functions and eigenvalues obtained in the SCF step.  But according 
> to your explanation, it seems that the wave functions created in the SCF step 
> will not be used in screening and sigma calculations. 
> The wave functions 
> |k-q,b1> and |k,b2> in M := <k-q,b1| e^{-i(q+T).r} |k,b2>  will be obtained 
> by another diagonalization of the the Hamiltonian matrix after the scf has 
> been reached?

  There are two methods to produce a KSS file, see the kssform input variable.

  In case of kssform=1, you do a standard GS or NSCF calculation to get a 
converged
  density then the (fixed) KS hamiltonian is diagonalized to obtain nbandkss 
states.
  The number of G vectors in the KS hamiltonian is defined by ecut not 
ecutwfn,
  thus the hamiltonian is not truncated. The diagonalization can be seen as an
  additional SCF iteration. If your density/potential is well converged, the
  wavefunctions obtained by diagonalizing the KS hamiltonian  and
  the wavefunctions coming from the SCF calculation are the same

  If kssform=3 is used, the wavefunctions of the KSS file are generated by 
solving
  the KS problem using the conjugate gradient method. Also in this case the G
  basis set is defined through ecut.

  ecutwfn and ecuteps do not play any role during the KSS run!


> And the size of Hamiltonian matrix for getting |k-q,b1> and 
> |k,b2> will be much smaller that the one in the original scf calculations? 
> And this Hamiltonian matrix is determined by self-consistent hamiltonian and 
> ecutwfn? Is ecut only used to get the self-consistent potential and charge 
> density and no wave functions of the output of the SCF step will stored or 
> used in GW calculations?
>
> In the tutorial, there several exercises, like
>
> *"Convergence on the number of planewaves in the wavefunctions to calculate 
> the Self-Energy."
> *
>
>
>     *"Convergence on the number of planewaves to calculate Sigma_x."*
>
> *"Convergence on the number of planewaves in the wavefunctions to calculate 
> the screening (epsilon^-1)."
>
> Does it mean that different wave functions will be used **and be recalculated 
> **be separate diagonalization of the Hamiltonian matrix determined by ecutwfn 
> and ecutsigx when we can calculate these quantities?

  Just to make it clearer: The functions in the KSS file are the same as the
  wavefunctions at the end of the GS calculation.
  In the simplest case (one-shot GW) these functions are only used to 
calculate the matrix elements M
  and some other stuff, without doing any kind of self-consistency!
  npwwfn just defines the number of G components to be read from the KSS file 
and used to describe
  \psi(r) while npweps defines the number of G vectors for the irreducible 
polarizability and the
  screened interaction.

  BTW : You can find a lot of useful information on the GW method and its 
implementation in this review
  http://www.physics.ohio-state.edu/~wilkins/vita/gw_review.ps

  In particular you might have a look at Eq. 101, 102, 104 and 105 to 
understand  how
  the screened interaction and the matrix elements of the self-energy are 
calculated.


  Regards,
  Matteo Giantomassi

> *Thank you again!
>
> Xiaohong
>
> Matteo Giantomassi wrote:
> > On Sun, 28 Oct 2007, Xiaohong Zheng wrote:
> >
> > > Hello, every one,
> > >
> > > what is the difference between "ecut" and "ecutwfn" in GW calculations? 
> > > They look like two cutoff energies of wave functions. What are the 
> > > difference between them? Why do we need two different sets of wave 
> > > functions in the GW calculations?
> >
> > Dear Xiaohong,
> >
> > To perform a GW calculation we need to evaluate matrix elements in the form
> >
> > M := <k-q,b1| e^{-i(q+T).r} |k,b2>
> >
> > where the number of reciprocal lattice vectors T is defined by ecuteps in 
> > case of a screening calculation (optdriver 3) or npwsigx in case of sigma 
> > calculations (optdriver 4).
> >
> > Ecutwfn (nwpwfn or nshwfn) is instead used to define the G basis set 
> > employed to describe the two wavefunctions |k-q,b1> and |k,b2>, and is 
> > usually smaller than ecut since the matrix elements M
> > converge faster that the wavefunctions, see the tutorial.
> >
> > In you particular case, the variable ecut is only used during the GS or 
> > NSCF calculation that precedes the generation of the KSS file. The value of 
> > ecut, roughly speaking, defines the number of Fourier coefficients written 
> > on the KSS file.
> >
> > Note that ecut has no meaning during a screening or sigma run, anyway you 
> > have to specify a value in the input
> > file otherwise the code crashes before entering the GW part.
> >
> > Hope this helps,
> > Best Regards
> > Matteo Giantomassi

  Matteo Giantomassi