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<FONT color=#000000>Dear Prof. Blaha:</FONT><BR>
<FONT color=#000000> I am sorry to ask you such a question again.</FONT><BR>
<FONT color=#000000></FONT> <BR>
<FONT color=#000000>My questions is as following:</FONT><BR>
<FONT color=#000000> I have known that for cubic case, lattice harmonics are linear combinations of some distinct real spherical harmonics</FONT><BR>
<FONT color=#000000> 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);</FONT><BR>
<FONT color=#000000> but I am confused with some codes listed below which are used to calculate multipole moments in mulfsu.f of SRC_lapw0</FONT><BR>
<BR>
<FONT color=#000000>#############for cubic case <BR>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>a=qq(i,jatom)*imag<BR>b=qq(i+1,jatom)*imag <BR>qq(i,jatom)=a*<FONT color=#0000ff>c1*c1</FONT>/sq1 + b*<FONT color=#0000ff>c1*c2</FONT>/sq1 </FONT><BR>
<FONT color=#000000>qq(i+1,jatom)=a*</FONT><FONT color=#0000ff>c1*c2<FONT color=#000000>/sqrt2</FONT> + b*c2*c2<FONT color=#000000>/sqrt2<BR></FONT></FONT><FONT color=#000000>i=i+2</FONT><BR>
############<BR>
<FONT color=#ff0000>since here only linear combinations are used, in principle,there should not exist some crossed terms like </FONT><BR>
<FONT color=#ff0000> c1*c2 and squared terms like c1*c1, which are colored green above.</FONT><FONT color=#000000>I guess that some special forms to represent</FONT><BR>
<FONT color=#000000> 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.</FONT><BR>
<FONT color=#000000> However, I cannot figure out exactly what is going on in this transformation.</FONT><BR>
<FONT color=#ff0000> </FONT><BR>
<FONT color=#ff0000> </FONT><FONT color=#000000>thus,can you give me some ideas of this issue.</FONT><BR>
Thanks very much !<BR><BR>Ming Wenmei<BR>
<BR>
<BR>
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This is explained in eg. the KURKI-Suonio paper.<BR>For the cubic case the "lattice harmonics" are more complicated<BR>linear combinations (with some distinct sqrt-factors) of the complex<BR>spherical harmonics and even M=0 and M=4 terms are "added" to ONE<BR>lattice harmonics.<BR> <BR><BR> Dear Prof. Blaha;<BR> I am sorry that I did not express myself clearly the first time. thanks for your kind reply last time, <BR>
but I am so sorry to ask you somewhat entry-levelqueations again.now I guess the charge density in MT <BR>
sphere is expanded in the basis of real spherical harmonic.<BR>
<BR>
but I still have a question as the following: <BR><BR>
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.<BR>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 <BR>how it is expanded for cubic cases,also, it is not expanded in the another sphere set of <BR>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) <BR> <BR>## for non-cubic case<BR>QQ(LLMM,JATOM)=QQ(LLM!
M,JATOM)*fc(llmm,jatom)<BR>
<BR>## for cubic case <BR>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 + c*c1*c3/sq1<BR>qq(i+1,jatom)=a*c1*c2/sqrt2 + b*c2*c2/sqrt2 +c*c2*c3/sqrt2<BR>qq(i+2,jatom)=a*c1*c3/sqrt2 + b*c2*c3/sqrt2 + c*c3*c3/sqrt2<BR> <BR>> I have read the recommended papar in Userguide in lapw2 program about <BR>> the lattice harmonic,<BR>> but the still cannot figure out this question,so, could you give me some <BR>> your idea about this issue?<BR>> thanks very much !<BR>> <BR>> Regards!<BR>> Wenmei Ming<BR>> &nb! sp; <BR>> <BR>> &nbs p; <BR><BR><br /><hr />使用新一代 Windows Live Messenger 轻松交流和共享！ <a href='http://messenger.live.cn/' target='_new'>立即体验！</a></body>
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