<p>For the last time, no.</p>
<div class="gmail_quote">On Aug 22, 2011 3:32 PM, "Yundi Quan" <<a href="mailto:quanyundi@gmail.com">quanyundi@gmail.com</a>> wrote:<br type="attribution">> In order to get the total charge density with corrections within the sphere<br>
> r and the sphere r+dr, is it correct to sum up all terms? In the Peter's<br>> email, it says that L=0, M=0 is the radial charge density and I do not need<br>> to sum up all terms.<br>> <br>> Yundi<br>
> <br>> On Mon, Aug 22, 2011 at 7:50 AM, Laurence Marks <<a href="mailto:L-marks@northwestern.edu">L-marks@northwestern.edu</a>>wrote:<br>> <br>>> 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">quanyundi@gmail.com</a>>:<br>>> > 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">L-marks@northwestern.edu</a>><br>
>> 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">quanyundi@gmail.com</a>> wrote:<br>
>> >>> Thanks for clarifying CTO. I just want to find out the charge within<br>>> 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.<br>>> the<br>>> >>> charge within the sphere r and r+dr. So I should sum up all the<br>
>> 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">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<br>
>> 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,<br>
>> 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>>> >>>>> Wien mailing list<br>>> >>>>> <a href="mailto:Wien@zeus.theochem.tuwien.ac.at">Wien@zeus.theochem.tuwien.ac.at</a><br>
>> >>>>> <a href="http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien">http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</a> <<br>>> >>> <a href="http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien">http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</a>><br>
>> >>>><br>>> >>>> --<br>>> >>>><br>>> >>>> P.Blaha<br>>> >>>><br>>> >>>><br>>> --------------------------------------------------------------------------<br>
>> >>>> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna<br>>> >>>> Phone: +43-1-58801-15671 <tel:%2B43-1-58801-15671><br>>> >>>> <tel:%2B43-1-58801-15671> FAX:<br>
>> >>> +43-1-58801-15698 <tel:%2B43-1-58801-15698> <tel:%2B43-1-58801-15698><br>>> >>>> Email: <a href="mailto:blaha@theochem.tuwien.ac.at">blaha@theochem.tuwien.ac.at</a> WWW:<br>
>> >>> <a href="http://info.tuwien.ac.at/theochem/">http://info.tuwien.ac.at/theochem/</a><br>>> >>>><br>>> >>>><br>>> --------------------------------------------------------------------------<br>
>> >>>> _______________________________________________<br>>> >>>> Wien mailing list<br>>> >>>> <a href="mailto:Wien@zeus.theochem.tuwien.ac.at">Wien@zeus.theochem.tuwien.ac.at</a><br>
>> >>>> <a href="http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien">http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</a><br>>> >>>><br>>> >><br>>> > _______________________________________________<br>
>> > Wien mailing list<br>>> > <a href="mailto:Wien@zeus.theochem.tuwien.ac.at">Wien@zeus.theochem.tuwien.ac.at</a><br>>> > <a href="http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien">http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</a><br>
>> ><br>>> ><br>>><br>>><br>>><br>>> --<br>>> Laurence Marks<br>>> Department of Materials Science and Engineering<br>>> MSE Rm 2036 Cook Hall<br>>> 2220 N Campus Drive<br>
>> Northwestern University<br>>> Evanston, IL 60208, USA<br>>> Tel: (847) 491-3996 Fax: (847) 491-7820<br>>> email: L-marks at northwestern dot edu<br>>> Web: <a href="http://www.numis.northwestern.edu">www.numis.northwestern.edu</a><br>
>> Chair, Commission on Electron Crystallography of IUCR<br>>> <a href="http://www.numis.northwestern.edu/">www.numis.northwestern.edu/</a><br>>> Research is to see what everybody else has seen, and to think what<br>
>> nobody else has thought<br>>> Albert Szent-Gyorgi<br>>> _______________________________________________<br>>> Wien mailing list<br>>> <a href="mailto:Wien@zeus.theochem.tuwien.ac.at">Wien@zeus.theochem.tuwien.ac.at</a><br>
>> <a href="http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien">http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</a><br>>><br></div>