[Wien] total charge density

[Yundi Quan]

In order to get the total charge density with corrections within the sphere
r and the sphere r+dr, is it correct to sum up all terms? In the Peter's
email, it says that L=0, M=0 is the radial charge density and I do not need
to sum up all terms.

Yundi

On Mon, Aug 22, 2011 at 7:50 AM, Laurence Marks <L-marks at northwestern.edu>wrote:

> No. The L,M terms are harmonics of the charge density, period. The
> L=0,M=0 term is the appropriate sum of the squares of the
> eigensolutions, i.e. quasi-wavefunctions. Similarly the other LM terms
> come from other harmonics from squares of the quasi-wavefunctions --
> squares of harmonics are a series of single harmonics.
>
> 2011/8/22 Yundi Quan <quanyundi at gmail.com>:
> > Is it correct to say that the L=0, M=0 term in the clmsum file is charge
> > density due to the sum of all the harmonics while higher terms in clmsum
> > file is due to the corresponding terms in the wave function?
> >
> > On Monday, August 22, 2011, Laurence Marks <L-marks at northwestern.edu>
> wrote:
> >> No, clmsum is already a density.
> >>
> >> On Aug 22, 2011 4:24 AM, "Yundi Quan" <quanyundi at gmail.com> wrote:
> >>> Thanks for clarifying CTO. I just want to find out the charge within
> the
> >>> sphere r and the sphere r+dr.
> >>> The wavefunction is given as u=the sum of (u*YLM)
> >>> So the spatial charge density \rho(r, solid angle) =|u|^2.
> >>> Now, I just want to find out the radial distribution of charge, i. e.
> the
> >>> charge within the sphere r and r+dr. So I should sum up all the
> harmonics
> >>> term. Is this correct?
> >>>
> >>>
> >>>
> >>>
> >>> On Sunday, August 21, 2011, Peter Blaha <pblaha at theochem.tuwien.ac.at>
> >>> wrote:
> >>>>> According to userguide, the case.clmsum file contains the charge
> >>>>> density
> >>>>> in harmonics representation. For l=0, m=0, charge density is given as
> >>>>> 4*pi*r^2*\rho(r). For others, charge density is given as r^2*\rho(r).
> >>>>> My
> >>>>> understanding is that the total charge density should be the sum of
> all
> >>>>> the harmonics. Therefore, I summed up all the lms ( I multiplied 4pi
> >>>>> with
> >>>>> higher harmonics before summation). Is this a correct way of finding
> >>>>> out
> >>>>> the radial charge density within the Muffin-tin sphere?
> >>>>
> >>>> No. The radial charge density is just the LM=0,0 component. In fact,
> the
> >>>> :CTO values are obtained by a simple 1D integretion of this component.
> >>>>
> >>>> The higher LM describe the non-spherical components as plus/minus
> >>> corrections
> >>>> to the radial average (and you have to multiply them with the
> >>> corresponding
> >>>> spherical harmonics. See lapw5 on how it works in detail.
> >>>>
> >>>>> Another question is how is total charge (CTO) within the Muffin-tin
> >>> sphere
> >>>>> calculated in scf file.
> >>>>>
> >>>>> Thanks a lot.
> >>>>> _______________________________________________
> >>>>> Wien mailing list
> >>>>> Wien at zeus.theochem.tuwien.ac.at
> >>>>> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien <
> >>> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien>
> >>>>
> >>>> --
> >>>>
> >>>> P.Blaha
> >>>>
> >>>>
> --------------------------------------------------------------------------
> >>>> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
> >>>> Phone: +43-1-58801-15671 <tel:%2B43-1-58801-15671>
> >>>> <tel:%2B43-1-58801-15671> FAX:
> >>> +43-1-58801-15698 <tel:%2B43-1-58801-15698> <tel:%2B43-1-58801-15698>
> >>>> Email: blaha at theochem.tuwien.ac.at WWW:
> >>> http://info.tuwien.ac.at/theochem/
> >>>>
> >>>>
> --------------------------------------------------------------------------
> >>>> _______________________________________________
> >>>> Wien mailing list
> >>>> Wien at zeus.theochem.tuwien.ac.at
> >>>> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
> >>>>
> >>
> > _______________________________________________
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> > 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/
> Research is to see what everybody else has seen, and to think what
> nobody else has thought
> Albert Szent-Gyorgi
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