[Wien] Bad formation energies for the charged vacancies
John Pask
pask1 at llnl.gov
Thu Mar 4 22:09:43 CET 2010
Hi Laurence,
Sorry for the delay in getting back....
> 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.
Yes, sounds like that may be the issue. Because the neutralizing
background charge is not actually being added to the remaining
physical charge, and carried along with the physical charge at all
points, the total energy is not uniquely defined.
> 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).
Right. Ideally, the N-1 states would be used to construct the physical
part of the density, then the constant neutralizing background would
be added to that to construct the total. If this is not the case, then
there will be inconsistencies/ambiguities.
> 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.
(... which we should approach in the limit of infinite cell dimension.)
> 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......
One answer (e.g., Makov-Payne and others) is to always neutralize non-
neutral cells with a constant background so that there are no
arbitrary constants in energies. Then correct the resulting energies
with multipole terms which vanish as L^-1, L^-3, etc. (L = cell dim.)
to aid convergence to the (unique) infinite-L limit.
However, some recent work, in the context of defects in condensed
matter, seeks to compute and apply potential shifts to define
meaningful energies: e.g.,
Title: Accurate prediction of defect properties in density functional
supercell calculations
Author(s): Lany S, Zunger A
Source: MODELLING AND SIMULATION IN MATERIALS SCIENCE AND
ENGINEERING Volume: 17 Issue: 8Article Number: 084002 Published:
DEC 2009
Note, though, that here too there is some arbitrariness, e.g., in
defining the "site potentials." In any case, possibly some of the
ideas could be of help?
John
> 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
>>>>> -----------------------------------------
>>>>> _______________________________________________
>>>>> Wien mailing list
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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
>>> -----------------------------------------
>>> _______________________________________________
>>> Wien mailing list
>>> Wien at zeus.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.
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