[Wien] density expansion for cubic case in MT sphere

[明文美]

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