[Wien] total charge density

[Laurence Marks]

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/
>>>>
>>>> --------------------------------------------------------------------------
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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/
Research is to see what everybody else has seen, and to think what
nobody else has thought
Albert Szent-Gyorgi