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

Stefano de Gironcoli degironc at sissa.it
Wed Apr 20 10:12:29 CEST 2011

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>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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>>
>
>
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