[Pw_forum] implementation of variation of occupations and Fermi level with perturbations

[David Strubbe]

Stefano,

Thank you for the explanation. Things are clear now. Is there a circumstance
in which Delta n_ext(q=0) is nonzero?

David Strubbe
UC Berkeley

On Wed, Apr 20, 2011 at 1:12 AM, Stefano de Gironcoli <degironc at sissa.it>wrote:

>  Dear David Strubbe,
>
> eq. 79 is a general formula; in the phonon code Delta n_ext(q=0) is always
> vanishing because the perturbation is neutral (atoms are displaced but their
> charge is not changed), still Delta Vscf is in general non zero so one has
> to do something
>
> Let's look at the scf variation of rho that is something like
>
> Delta rho(r) = sum_i  f_i (phi_i* Delta_phi_i +cc) + d f_i/de *(Delta e_i -
> Delta e_F) |phi|^2
>
> As said, eq. 79 is the condition of charge neutrality of the perturbation
> which is due ONLY to the last term involving changes in occupation of states
> (remember that Delta phi is always orthogonal to the unperturbed phi so in
> no case Delta phi can contribute to the total charge variation)
>
> if you work out the expression ...
>
> total charge = Delta n_ext + Delta_n induced by Delta e_i (defined in terms
> of the potential change) + Delta_n induced by the Fermi energy shift..
>
> and the neutrality condition reads
>
> 0 = Delta_n_ext + \int n(e_F,r) Delta Vscf - n(e_F) * Delta e_F
>
> which is eq. 79.
>
> HOWEVER, delta rho that enters ef_shift has been computed without the
> contribution coming from the (then unknown) Fermi energy shift Delta e_F
> that is (see above)
>
> - n(e_F,r) * Delta e_F
>
> this is how ef_shift routine icomputes Delta e_F:  it calculates the G=0
> component of Delta rho before the shift ( which amount to be \int n(e_F,r)
> Delta Vscf ) and define Delta e_F in such a way that after the term  -
> n(e_F,r) * Delta e_F is added the final Delta rho is neutral.
>
> I hope the procedure is a bit clearer now.
>
> stefano
>
>
>
> On 04/20/2011 12:08 AM, David Strubbe wrote:
>
> Paolo,
>
> Thanks for the response. This gives me some more insight into what is going
> on, but I still don't understand.
>
> As far as I can tell, the drhoscf in ef_shift is still the change in the
> density rather than the change in the potential, because the calls in
> solve_linter to dv_of_drho are using a copy of the density response rather
> than drhoscf itself:
>
>         call zcopy
> (nrxx*nspin_mag,drhoscfh(1,1,ipert),1,dvscfout(1,1,ipert),1)
>         call dv_of_drho (imode0+ipert, dvscfout(1,1,ipert), .true.)
>
> The heart of the matter is the lines in ef_shift:
>
> delta_n = delta_n + omega*drhoscf(nl(1),is,ipert)
> def (ipert) = - delta_n / dos_ef
>
> delta_n does not seem to refer to \Delta n_{ext} or the integral of the LDOS
> with \Delta V_{SCF}, as in the numerator of Eq. 79. Do those quantities
> exist in the calculation here?
>
> Thanks,
> David Strubbe
> UC Berkeley
>
> On Tue, Apr 19, 2011 at 1:44 PM, Paolo Giannozzi <giannozz at democritos.it> <giannozz at democritos.it>wrote:
>
>
>  On Apr 8, 2011, at 20:39 , David Strubbe wrote:
>
>
>  Eq. 79 refers to a quantity \Delta n_{ext} and an integral of the LDOS
> with \Delta V_{SCF} to calculate the shift in Fermi level. However in
> ef_shift it appears that the density response drhoscf is used instead
> of these quantities in the numerator, which doesn't seem like the
> same thing.
>
>  it doesn't, but it is. The (dirty) trick is well hidden in the call
> to routine dv_of_drho:
> it accepts in input the variation of the charge density, returns in
> output the
> variation of the potential, overwritten on the former. It was done a
> looong time
> ago in order to spare some memory, when machines had much less ram and
> the code was much simpler and smaller (occasional dirty tricks were
> under
> control, sort of). A comment in the code would have spared you (and me)
> some time. Unfortunately comments in code tend to belong to one of the
> following categories: 1) useless, 2) misleading, 3) obsolete, 4)
> nonexistent
>
> P.
> ---
> Paolo Giannozzi, Dept of Chemistry&Physics&Environment
> Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
> Phone +39-0432-558216, fax +39-0432-558222
>
>
>
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