<DIV>Dear Prof. Blaha,</DIV>
<DIV> </DIV>
<DIV>Thanks a lot. It is not difficult but it is somehow confusing because I never notice that there are no negative m. Now I know, when I follow Table7.39, I have to get rid of those with negative m.</DIV>
<DIV> </DIV>
<DIV>Thanks again.</DIV>
<DIV> </DIV>
<DIV>Stargmoon<BR><BR><B><I>Peter Blaha <pblaha@zeus.theochem.tuwien.ac.at></I></B> wrote:</DIV>
<BLOCKQUOTE class=replbq style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #1010ff 2px solid">I'm not sure if it is really that difficult, but anyway:<BR><BR>For general symmetry, for l=1 there are 3 (complex) spherical harmonics <BR>with m=0,+ and -1, right ? <BR><BR>Of course, also "real spherical hamonics" must have EXACTLY 3 combinations.<BR><BR>They are called (1 0); (1 1) and (-1 1).!! A combination (1 -1) would be<BR>a fourth combination and thus some redundend linear combination.<BR><BR>So without any symmetry (pointgroup 1) the list contains all possible<BR>combinations (but not redundand ones!), namely 3 for l=1; 5 for l=2;...<BR>lm: 0 0 1 0 1 1 -1 1 2 0 2 1 -2 1 2 2 -2 2<BR><BR>You never see any negative m!<BR><BR>For pointgroup m (that's yours!?) the LM list starts with:<BR>0 0 1 1 -1 1 2 0 2 2 -2 2 3 1 -3 1 3 3 -3 3 4 0 4 2 -4 2 4 4 -4 4<BR><BR>and already from this list it is obvious that for "odd" l you should remove<BR>all "even" m values (1 0; 3 0; 3 !
2; -3 2;
guess what comes for l=7 ?)<BR><BR>On the other hand for even l you must remove the "odd" m; (2 1; -2 1; ...)<BR><BR><BR><BR>> Thanks a lot to your patient explanations. However, I still have problems with it. According to Table7.39 in the UG, for example, there are four possible choices for l=1 with point group "M", (+-l,l-2m), they are (1,1),(-1,1) for m=0 and (1,-1),(-1,-1) for m=1. It is obvious that only (1,1) and (-1,1) are listed in the case.in2 file. I don't understand why (1,-1)(-1,-1) are not included? I think I have to understand this first before I try to translate the lm definitions up to higher combinations given in Table7.39.<BR><BR><BR>P.Blaha<BR>--------------------------------------------------------------------------<BR>Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna<BR>Phone: +43-1-58801-15671 FAX: +43-1-58801-15698<BR>Email: blaha@theochem.tuwien.ac.at WWW:
http://info.tuwien.ac.at/theochem/<BR>--------------------------------------------------------------------------<BR><BR>_______________________________________________<BR>Wien mailing list<BR>Wien@zeus.theochem.tuwien.ac.at<BR>http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien<BR></BLOCKQUOTE><p>
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