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[Xiaohong Zheng <zheng@chips.ncsu.edu>]

Hi, Dear Dr. Giantomassi,

Thank you very much. I get better understanding now. I still have some 
doubts on several quantities. In the tutorial,  there are  the following 
exercises:

"3. Convergence on the number of planewaves in the wavefunctions to 
calculate the Self-Energy."

"4. Convergence on the number of planewaves to calculate Sigma_x."

"5. Convergence on the number of bands to calculate the Self-energy."


In 3 and 4, when calculating <i|Sigma|i> or <i|Sigma_x|i>, do the wave 
functions mean the |i> here or the wave functions entering in the 
expression of Green's function?  Which wave functions does "  the number 
of planewaves" refer to?  Which parameter determines the number of 
planwaves of |i> and which parameter determines the number of planwaves 
of the wave functions in the Green function? In 5, does "the number of 
bands" means the number of bands entering the Green function?

I am sorry to bother you again and again.

Xiaohong


Matteo Giantomassi wrote:
> 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 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