[QE-developers] Local-density-dependent Thomas Fermi screening mixing

[Stefano de Gironcoli]

Dear Phani,

    there is no Journal reference for the local-TF scheme.

    if one assumes that the error in self-consistency is small enough 
that the linear regime applies then

    \delta n_inp = \chi \chi_0^-1 \Delta n_I/O     or chi^-1 \delta 
n_inp = chi_0^-1 \Delta n_I/O

    where \delta n_inp is the error in the input density (the error that 
you want to correct) and \Delta n_I/O = n_inp - n_out is the difference 
between input and output densities (that one has access to in the 
calculation).

   chi_0 is the non-interacting electron density response function of 
the system and chi the interacting electron one, linked to the previous 
by the Dyson equation \chi = \chi_0 + \chi_0 ( v_c + f_xc ) \chi  or, 
equivalently, \chi^-1 = \chi_0^-1 - (v_c + f_xc) where v_c is the 
Coulomb kernel and f_xc the exchange-correlation one (neglected in the 
following).

   in the TF context chi_0^-1 =  \partial V_KS/ \partial n = - 
\partial^2 T[n]_TF / \partial n^2  \propto   n(r)^(-1/3)

   so using this approximation for \chi_0^-1 and iteratively solving 
(with some not too strict threshold) the linear system one gets an 
estimate for \delta n_inp from \Delta n_I/O

   best

stefano

On 03/04/19 09:04, Phani Motamarri wrote:
> Hi,
>
> Many thanks for the reply. I already saw the reference, but I am 
> talking of the reference for the mixing scheme which applies 
> local-density dependent TF preconditioning. (Key word: 'local-TF').
> The reference D.D. Johnson PRB 38, 12807 (1988) does not talk about 
> this local T-F.
>
> Regards
> Phani
>
>
>
> On Wed, Apr 3, 2019 at 2:54 AM Paolo Giannozzi <p.giannozzi at gmail.com 
> <mailto:p.giannozzi at gmail.com>> wrote:
>
>     The reference is in the header of file PW/src/mix_rho.f90:
>       ! ... Modified Broyden's method for charge density mixing
>       ! ...         D.D. Johnson PRB 38, 12807 (1988)
>     Paolo
>
>     On Wed, Apr 3, 2019 at 7:36 AM Phani Motamarri <phanim at umich.edu
>     <mailto:phanim at umich.edu>> wrote:
>
>         Hello Quantum Espresso Developers,
>
>         We are developing an in-house real-space DFT code and looking
>         to implement better mixing schemes beyond Anderson and Broyden
>         specifically for in-homogeneous systems. To this end, I came
>         across local-density-dependent Thomas Fermi screening mixing
>         implemented in Quantum expresso which is performing really
>         well for  in-homogeneous systems. I would like to know if you 
>         have any suitable journal article reference for understanding
>         the mixing method implemented in Quantum espresso.
>
>         Looking forward to hearing from you
>
>         Thanks
>         Phani
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>
>
>     -- 
>     Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
>     Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
>     Phone +39-0432-558216, fax +39-0432-558222
>
>
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