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 >>>> ----------------------------------------- >>>> _______________________________________________ >>>> Wien mailing list >>>> Wien at zeus.theochem.tuwien.ac.at >>>> http://**zeus.theochem.tuwien.ac.at/mailman/listinfo/wien >>>> >>> _______________________________________________ >>> Wien mailing list >>> Wien at zeus.theochem.tuwien.ac.at >>> http://*zeus.theochem.tuwien.ac.at/mailman/listinfo/wien >> >> -- >> ----------------------------------------- >> 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 >> http://*zeus.theochem.tuwien.ac.at/mailman/listinfo/wien >> > > > > > _______________________________________________ > Wien mailing list > Wien at zeus.theochem.tuwien.ac.at > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien > -- 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.