[Wien] Bad formation energies for the charged vacancies

[Laurence Marks]

I think the issue is that at present Wien2k does not really add a
constant charge background and calculate the self-energy of this
charge (in a given potential), it instead add the potential associated
with this charge. If one has N-1 electrons, a nuclear charge of N,
only N-1 eigenvalues are calculated, no "eigenvalue" for a flat
background (of course one would not get a flat eigenvalue).

You can see this by doing a calculation of an H+ ion in a cell with no
electrons. The results one will get is -ve, i.e. it is the energy of a
H+ ion in the background potential. This is not the same as the energy
of an H+ ion in vacuum.

The question is then how to do a realistic charged cell calculation
with meaningful energies taking account of the effect of a potential
shift? If vacuum is available one can determine the potential shift
and correct; one can also calibrate the value of a core level and use
this to determine the shift (with reservations) but it would be nice
to have a more elegant method......

On Fri, Feb 26, 2010 at 5:30 PM, John Pask <pask1 at llnl.gov> wrote:
>
> Hi Peter,
>
>> In the integrals below, \rho is just the electronic charge density
>> (without nuclei).
>> Thus c \int{\rho] does NOT vanish and gives c * NE (number of electrons).
>> However, if rho comes from electronic states, each eigenvalue is shifted
>> by the constant c
>> and thus the sum of eigenvalues cancels the  c * NE term
>>
>> However, when I add a "background charge" to neutralize the unit cell,
>> this does not come
>> from any eigenvalue, so if I handle this in the "usual" way, \rho will now
>> integrate to
>> NE + Q, and I get an extra c * Q term, which is not compensated by an
>> eigenvalue.
>
> Actually, in the integrals below, \rho is the *total* (electronic + nuclear)
> charge, which must be net neutral to have a well-defined total energy
> (otherwise energy diverges).
>
> With regard to the present question on charged-cell calculations, the point
> is just that the calculation must be performed on a neutralized cell in
> order to have well-defined total energy. So the Kohn-Sham calculation is
> performed on a neutral cell, whether or not the physical system is charged,
> and the corrections for non-neutrality, if any (e.g., Makov-Payne, Eq.
> (15)), are added after.
>
> So as long as the neutralizing charge enters all potential and energy
> expressions along with the "physical charge", so that all expressions
> operate on a net-neutral total, the Kohn-Sham total energy must be invariant
> to arbitrary constants in V (because the total Coulomb energy is).
>
> John
>
>>
>> John Pask schrieb:
>>>
>>> Dear Peter,
>>> Yes, the background charge must be taken into account as part of the
>>> net-neutral total charge in order to have well-defined total energy. Then as
>>> long as the compensation charge is then in exactly the same way as the
>>> remaining "physical" charge (i.e., enters all the same integrals), then the
>>> arbitrary constant in potential should not matter since:
>>> \int{ \rho (V + c)}  = \int{ \rho V}  + c \int{ \rho} = \int {\rho V},
>>> independent of arbitrary constant c.
>>> John
>>> On Feb 24, 2010, at 11:54 PM, Peter Blaha wrote:
>>>>>
>>>>> Is the question regarding the computation of total energy per unit
>>>>>  cell in an infinite crystal with non-neutral unit cells? If so, then  the
>>>>> total energy diverges -- and so is not well-defined. (So  neutralizing
>>>>> backgrounds must be added in such cases to obtain  meaningful results, etc.)
>>>>
>>>> Yes, this is the question and yes, of course we add a positive or
>>>> negative background.
>>>> We are quite confident that the resulting potential is ok, but the
>>>> question is if there
>>>> is a correction to the total energy due to the background charge.
>>>> I believe: yes (something like Q * V-col_average / 2), but my problem is
>>>> that V-coul
>>>> is in an infinite crystal only known up to an arbitrary constant and
>>>> thus this correction
>>>> is "arbitrary".
>>>>
>>>> --
>>>> -----------------------------------------
>>>> Peter Blaha
>>>> Inst. Materials Chemistry, TU Vienna
>>>> Getreidemarkt 9, A-1060 Vienna, Austria
>>>> Tel: +43-1-5880115671
>>>> Fax: +43-1-5880115698
>>>> email: pblaha at theochem.tuwien.ac.at
>>>> -----------------------------------------
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>>
>> --
>> -----------------------------------------
>> Peter Blaha
>> Inst. Materials Chemistry, TU Vienna
>> Getreidemarkt 9, A-1060 Vienna, Austria
>> Tel: +43-1-5880115671
>> Fax: +43-1-5880115698
>> email: pblaha at theochem.tuwien.ac.at
>> -----------------------------------------
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>>
>
>
>
>
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-- 
Laurence Marks
Department of Materials Science and Engineering
MSE Rm 2036 Cook Hall
2220 N Campus Drive
Northwestern University
Evanston, IL 60208, USA
Tel: (847) 491-3996 Fax: (847) 491-7820
email: L-marks at northwestern dot edu
Web: www.numis.northwestern.edu
Chair, Commission on Electron Crystallography of IUCR
www.numis.northwestern.edu/
Electron crystallography is the branch of science that uses electron
scattering and imaging to study the structure of matter.