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. <div>
<br></div><div>Yundi<br><br><div class="gmail_quote">
On Mon, Aug 22, 2011 at 7:50 AM, Laurence Marks <span dir="ltr"><<a href="mailto:L-marks@northwestern.edu" target="_blank">L-marks@northwestern.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
No. The L,M terms are harmonics of the charge density, period. The<br>
L=0,M=0 term is the appropriate sum of the squares of the<br>
eigensolutions, i.e. quasi-wavefunctions. Similarly the other LM terms<br>
come from other harmonics from squares of the quasi-wavefunctions --<br>
squares of harmonics are a series of single harmonics.<br>
<br>
2011/8/22 Yundi Quan <<a href="mailto:quanyundi@gmail.com" target="_blank">quanyundi@gmail.com</a>>:<br>
<div><div></div><div>> Is it correct to say that the L=0, M=0 term in the clmsum file is charge<br>
> density due to the sum of all the harmonics while higher terms in clmsum<br>
> file is due to the corresponding terms in the wave function?<br>
><br>
> On Monday, August 22, 2011, Laurence Marks <<a href="mailto:L-marks@northwestern.edu" target="_blank">L-marks@northwestern.edu</a>> wrote:<br>
>> No, clmsum is already a density.<br>
>><br>
>> On Aug 22, 2011 4:24 AM, "Yundi Quan" <<a href="mailto:quanyundi@gmail.com" target="_blank">quanyundi@gmail.com</a>> wrote:<br>
>>> Thanks for clarifying CTO. I just want to find out the charge within the<br>
>>> sphere r and the sphere r+dr.<br>
>>> The wavefunction is given as u=the sum of (u*YLM)<br>
>>> So the spatial charge density \rho(r, solid angle) =|u|^2.<br>
>>> Now, I just want to find out the radial distribution of charge, i. e. the<br>
>>> charge within the sphere r and r+dr. So I should sum up all the harmonics<br>
>>> term. Is this correct?<br>
>>><br>
>>><br>
>>><br>
>>><br>
>>> On Sunday, August 21, 2011, Peter Blaha <<a href="mailto:pblaha@theochem.tuwien.ac.at" target="_blank">pblaha@theochem.tuwien.ac.at</a>><br>
>>> wrote:<br>
>>>>> According to userguide, the case.clmsum file contains the charge<br>
>>>>> density<br>
>>>>> in harmonics representation. For l=0, m=0, charge density is given as<br>
>>>>> 4*pi*r^2*\rho(r). For others, charge density is given as r^2*\rho(r).<br>
>>>>> My<br>
>>>>> understanding is that the total charge density should be the sum of all<br>
>>>>> the harmonics. Therefore, I summed up all the lms ( I multiplied 4pi<br>
>>>>> with<br>
>>>>> higher harmonics before summation). Is this a correct way of finding<br>
>>>>> out<br>
>>>>> the radial charge density within the Muffin-tin sphere?<br>
>>>><br>
>>>> No. The radial charge density is just the LM=0,0 component. In fact, the<br>
>>>> :CTO values are obtained by a simple 1D integretion of this component.<br>
>>>><br>
>>>> The higher LM describe the non-spherical components as plus/minus<br>
>>> corrections<br>
>>>> to the radial average (and you have to multiply them with the<br>
>>> corresponding<br>
>>>> spherical harmonics. See lapw5 on how it works in detail.<br>
>>>><br>
>>>>> Another question is how is total charge (CTO) within the Muffin-tin<br>
>>> sphere<br>
>>>>> calculated in scf file.<br>
>>>>><br>
>>>>> Thanks a lot.<br>
>>>>> _______________________________________________<br>
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>>>><br>
>>>> --<br>
>>>><br>
>>>> P.Blaha<br>
>>>><br>
>>>> --------------------------------------------------------------------------<br>
>>>> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna<br>
>>>> Phone: <a href="tel:%2B43-1-58801-15671" value="+4315880115671" target="_blank">+43-1-58801-15671</a> <tel:%2B43-1-58801-15671><br>
>>>> <tel:%2B43-1-58801-15671> FAX:<br>
>>> <a href="tel:%2B43-1-58801-15698" value="+4315880115698" target="_blank">+43-1-58801-15698</a> <tel:%2B43-1-58801-15698> <tel:%2B43-1-58801-15698><br>
>>>> Email: <a href="mailto:blaha@theochem.tuwien.ac.at" target="_blank">blaha@theochem.tuwien.ac.at</a> WWW:<br>
>>> <a href="http://info.tuwien.ac.at/theochem/" target="_blank">http://info.tuwien.ac.at/theochem/</a><br>
>>>><br>
>>>> --------------------------------------------------------------------------<br>
>>>> _______________________________________________<br>
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>>>><br>
>><br>
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><br>
><br>
<br>
<br>
<br>
</div></div><div>--<br>
Laurence Marks<br>
Department of Materials Science and Engineering<br>
MSE Rm 2036 Cook Hall<br>
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Northwestern University<br>
Evanston, IL 60208, USA<br>
Tel: <a href="tel:%28847%29%20491-3996" value="+18474913996" target="_blank">(847) 491-3996</a> Fax: <a href="tel:%28847%29%20491-7820" value="+18474917820" target="_blank">(847) 491-7820</a><br>
email: L-marks at northwestern dot edu<br>
Web: <a href="http://www.numis.northwestern.edu" target="_blank">www.numis.northwestern.edu</a><br>
Chair, Commission on Electron Crystallography of IUCR<br>
<a href="http://www.numis.northwestern.edu/" target="_blank">www.numis.northwestern.edu/</a><br>
Research is to see what everybody else has seen, and to think what<br>
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