The ABINIT Users Mailing List ( CLOSED )

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

> Dear Colleagues,
> I try different plasmon pole models for Si clusters and I have several
> questions about models implemented in ABINIT.

 Dear Andrey,

> 1. If I understand well by default the Plasmon pole model of Godby and
> Needs is
> used for gwcalctyp=0. Could you provide a reference or a small description
> of
> this model?

 The equations used to implement the plasmon pole model of Godby-Needs are
described here:

 archives/57/gmatteo/devel-private/doc/theory/gwa.pdf


> 2. I would like to try also the models of Faleev. Is the Plasmon pole
> model of
> Godby and Needs used for gwcalctyp=8? Should I provide Plasmon frequency
> for
> Faleev model gwcalctyp=8?

  The plasmon pole model of Godby-Needs is the default method and it supports
  all the different "GW recipes" available in abinit.

  The specification of the plasmon frequency is only needed for this
particular model.
  It simply specifies the second frequency along the imaginary axis
  at which the irreducible polarizability has to be calculated.
  This second frequency is used in conjunction with the static limit to
find the
  parameters of the model (see section 3 of the pdf file).

  Ideally the QP results should not depend on the value chosen on the
imaginary frequency
  as the fit should be stable. However, one should check whether this is
the case
  Note that if "ppmfrq" is not specified in the input file then the code
will use the standard Drude
  plasma frequency during the calculation of the screening.

  The other plasmon pole models (ppmodel = 2,3,4) do not need the
specification
  of the plasma frequency since the coefficients of the model are
calculated imposing
  exact known properties. Note however that Faleev's method is only
available for ppmodel=1 and 2

> 3. The article of Faleev (S.V.Faleev et al., PRL 126406 2004) describes a
> self-consistent variant of calculation. However it seems that only one
> iteration gives the direct gap in Si (3.34 eV) close to experiment (3.40
> eV).
> Could this Faleev model be used in the one-shot GW method?

 What do you mean with one-shot Faleev?
 Faleev's method is different from the standard one-shot perturbative
approach in the sense
 that the correct self-energy is replaced by a static and hermitian
approximation.

 After the first Faleev iteration, you  have the hermitian matrix \Sigma_{nm}
 whose eigenvalues and eigenvectors define a new approximation for the
quasi-particle energies and amplitudes.
 These new quantities are used to construct a new screening and a new G
or, in case of GW0, just a new Green function.

 The procedure is iterated until convergence is reached and, at least, you
need two iterations!
 You should look at the values reported in the "DeltaE" column to
understand if the qp-energies are converged.
 Moreover you have to make sure that enough KS bands are used as basis set
to expand the quasi-particle amplitudes.

 For the particular case of Si, the off-diagonal matrix elements of
\Sigma_nm should be small
 therefore few iterations and few KS wave functions should suffice to get
converged results.

 Hope it helps,
 Best Regards
 Matteo Giantomassi