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<FONT color=#339966>Dear Prof. Blaha;</FONT><BR>
<FONT color=#339966> thanks for your kind reply last time, but I am so sorry to ask you somewhat entry-level </FONT><BR>
<FONT color=#339966>queations again.</FONT><BR>
<FONT color=#339966> now I guess the charge density in MT sphere is expanded in the basis of </FONT><BR>
<FONT color=#339966>real spherical harmonic.but I still have a question as the following: </FONT><BR>
<FONT color=#339966> I find some different treatments of the multipole moments between cubic and</FONT><BR>
<FONT color=#339966>non-cubic cases in lapw0.F when I read the source code file in SRC_lapw0.</FONT><BR>
<FONT color=#339966>Seemingly for the non-cubic case the coefficients of density is straightly transformed </FONT><BR>
<FONT color=#339966>from real spherical haromonic representation to complex sphereical harmonic representation,</FONT><BR>
<FONT color=#339966>however, for cubic case, it go through some complex transformations distinctly from non-cubic </FONT><BR>
<FONT color=#339966>transformation as the code below indicats. I feel that for cubic case, the density is not</FONT><BR>
<FONT color=#339966>expanded according to real spherical harmonics,but I don't know exactly how it is expanded for </FONT><BR>
<FONT color=#339966>cubic cases.</FONT><BR>
<BR>
<FONT color=#0000ff>## for non-cubic case</FONT><BR>
<FONT color=#0000ff> QQ(LLMM,JATOM)=QQ(LLMM,JATOM)*fc(llmm,jatom)</FONT><BR>
<FONT color=#0000ff> </FONT><BR>
<FONT color=#0000ff> ## for cubic case </FONT><BR>
<FONT color=#0000ff> c1=c_kub(ABS(lm(1,i,jatom)),lm(2,i,jatom))<BR> c2=c_kub(ABS(lm(1,i,jatom)),lm(2,i,jatom)+4)<BR> c3=c_kub(ABS(lm(1,i,jatom)),lm(2,i,jatom)+8)<BR> qq(i,jatom)=a*c1*c1/sq1 + b*c1*c2/sq1 + &<BR> c*c1*c3/sq1<BR> qq(i+1,jatom)=a*c1*c2/sqrt2 + b*c2*c2/sqrt2 &<BR> + c*c2*c3/sqrt2<BR> qq(i+2,jatom)=a*c1*c3/sqrt2 + b*c2*c3/sqrt2 &<BR> !
+ c*c3*c3/sqrt2</FONT><BR>
<BR>
<FONT color=#339966> I have read the recommended papar in Userguide in lapw2 program about the lattice harmonic,</FONT><BR>
<FONT color=#339966>but the still cannot figure out this question,so, could you give me some your idea about this issue?</FONT><BR>
<FONT color=#339966>thanks very much !</FONT><BR>
<FONT color=#339966> </FONT><BR>
<FONT color=#339966>Regards!</FONT><BR>
<FONT color=#339966>Wenmei Ming</FONT><BR>
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<BR>
<BR>> Date: Mon, 17 Dec 2007 21:21:10 +0100<BR>> From: Peter Blaha <pblaha@theochem.tuwien.ac.at><BR>> Subject: Re: [Wien] charge density in CLM files<BR>> To: A Mailing list for WIEN2k users <wien@zeus.theochem.tuwien.ac.at><BR>> Message-ID: <4766DA36.9040605@theochem.tuwien.ac.at><BR>> Content-Type: text/plain; charset=GB2312<BR>> <BR>> 1) I hope you agree: the electron density (psi^* psi) must be a "real"<BR>> function.<BR>> The usual definition of spherical harmonics gives them as a complex<BR>> function. However, one can always form some linear combination and<BR>> obtain "real"-spherical harmonics. This is what is used here. More<BR>> specifically, we use "lattice" harmonics, i.e. a symmetry adapted<BR>> selection of some spherical harmonics.<BR>> <BR>> 2) This "syntax" is connected with the selection of "lattice harmonics".<BR>> Of course a "negative"-l does not mean that l is negative, but indicates!
<BR>> a particular form of linear combination. For more details see the UG or<BR>> the original papers (cited in the UG).<BR>> <BR>> > 1) why the density in MT sphere given in case.clmXX files are all <BR>> > real values<BR>> > rather than complex values for all radial points. Based on the <BR>> > userguide, these values<BR>> > represent the coefficients of spherical harmonic <BR>> > expansion,according to this,<BR>> > these coefficients should be complex values not real ones. so ,I <BR>> > want to know<BR>> > what the so-called "density" for MT sphere in clm file really <BR>> > mean !!<BR>> > <BR>> > 2) occasionaly,some of the lattice harmonic indexes for L listed in <BR>> > case.in2 are negative,<BR>> > and the possible LM listed in the table in the LAPW2 chapter in <BR>> > userguide <BR>> > also indicate that L can negative,furthermore, I read the <BR>> > relate!
d source codes<BR>> > and find that some programs are firmly con
nected with this <BR>> > issue. thus, I am puzzled about this,because L should not be negative (>=0)<BR>> > <BR>> > I am eager to figure out what is going on about the two issues, <BR>> > can you give me some ideas<BR>> > or let me know the details of both of them.<BR>> > <BR>> > thanks very much !<BR>> > <BR>> > Ming Wenmei<BR>> > <BR><BR>
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