[Wien] multipole moments for cubic case

[明文美]

Dear Prof. Blaha:
     I am sorry to ask you such a question again.
 
My questions is as following:
  I have known that for cubic case, lattice harmonics are linear combinations of some distinct real spherical harmonics
  with different M,such as K(l=4,j=1)=1/2*(7/3)^1/2*y(l=4,m=0)+1/2*(5/3)^1/2*y(l=4,m=4);
  but I am confused with some codes listed below which are used to calculate multipole moments in mulfsu.f of SRC_lapw0
 
#############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)a=qq(i,jatom)*imagb=qq(i+1,jatom)*imag   qq(i,jatom)=a*c1*c1/sq1 + b*c1*c2/sq1 
qq(i+1,jatom)=a*c1*c2/sqrt2 + b*c2*c2/sqrt2i=i+2
############
   since here only linear combinations are used, in principle,there should not exist some crossed terms like 
   c1*c2 and squared terms like c1*c1, which are colored green above.I guess that some special forms to represent
   the compoents of L=4,M=0 and L=4,M=4,of the charge density are chosed, not purely decompose charge density in lattice haromic basis.
   However, I cannot figure out exactly what is going on in this transformation.
   
  thus,can you give me some ideas of this issue.
  Thanks very much !Ming Wenmei
 
 
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This is explained in eg. the KURKI-Suonio paper.For the cubic case the "lattice harmonics" are more complicatedlinear combinations (with some distinct sqrt-factors) of the complexspherical harmonics and even M=0 and M=4 terms are "added" to ONElattice harmonics.  Dear Prof. Blaha;  I am sorry that I did not express myself clearly the first time. thanks for your kind reply last time, 
but I am so sorry to ask you somewhat entry-levelqueations 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,also, it is not expanded in the another sphere set of real spherical harmonics K(l,j), because based on this following code, there exists term like a1**2,a1*a2, a1*a3 and so on, not the case of directly transfroming K(l,j) to Y(L,M).K(l,j) is linear combination of y(l,m)  ## for non-cubic caseQQ(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/sq1qq(i+1,jatom)=a*c1*c2/sqrt2 + b*c2*c2/sqrt2 +c*c2*c3/sqrt2qq(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> &nb! sp; > > &nbs p; 
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