<DIV>Dear Prof. Blaha,</DIV>
<DIV> </DIV>
<DIV>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.</DIV>
<DIV> </DIV>
<DIV>Best regards,</DIV>
<DIV> </DIV>
<DIV>Stargmoon</DIV>
<DIV> </DIV>
<DIV>P.S. Could you please specify what kind of values "l,m" (symbols in Table7.39) can take? (l=0,1,2,...;m=0,1,2,...l or l=0,1,2...;m=-l,-l+1,...0,...l or something else?)<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">As I mentioned before, the negative l is just a method to specify <BR>one of the four possible linear combinations.<BR>To expand the LM list in case.in2, just type in manually the higher <BR>combinations. In the cubic cases (positive atomic numbers in the <BR>case.struct file) the order of LM pairs matters and higher LM values are <BR>given explicitely in the UG. For other pointgroups either take the <BR>"intelligence test" and continue the series in analogy to the l=0-6 <BR>values, or use the Table in the UG and translate the lm definitions given <BR>there. <BR>> Yes, for the spherical harmonics, "l" never takes negative values. <BR>But I don't understand why there are "plus and minus" symbols shown before "l" in <BR>Table 7.39 in the manual, and the real LM list generated used in WIEN2k has negative "l" <BR>(see Table 7.38)? Is it just an indicator of the possible combin!
ations?
<BR>How can I add the extra LM combinations beyond maximum value 6 by hand? <BR>Does the order of the LM combinations matter in the calculation?<BR>> <BR>> Best regards,<BR>> <BR>> Stargmoon<BR>> <BR>> Peter Blaha <PBLAHA@ZEUS.THEOCHEM.TUWIEN.AC.AT>wrote:<BR>> Te charge density is expanded in "real spherical harmonics". These <BR>> functions can be constructed from the (more common) "complex spherical <BR>> harmonics" by various linear combinations. As you all know, a complex <BR>> spherical harmonics is Y_lm = P_lm(cos theta) . exp(i m phi)<BR>> <BR>> The LM list defines linear combinations, which produce the required "real <BR>> harmonics".<BR>> <BR>> Obviously, when m=0, the imaginary part (exp(im.phi) is always zero, thus <BR>> there is only ONE (l 0) pair, but never a negative l.<BR>> <BR>> Of course also in the general case, negative l's do not exists, but the <BR>> notation of the 4 possible combinations to pro!
duce real
harmonics are <BR>> indicated by (l m),(-l m),(l -m) and (-l -m). The possible linear <BR>> combinations are<BR>> <BR>> Y_lm + Y_l-m<BR>> Y_lm - Y_l-m<BR>> (Y_lm - Y_l-m)*i<BR>> (Y-lm - Y_lm-m)*i<BR>> <BR>> <BR>> > I think the lm list looks okay, for (+-l,l-2m) the sets should be (1,1),(-1,1) <BR>> > for m=0 and for m=1 gives (1,-1) and (-1,-1)... I'm not an expert but I've <BR>> > negative m values are not valid and (-1,0), (-2,0),...(-n,0) never seem to be <BR>> > included in the lm-list, though I have no idea why. Maybe someone can <BR>> > explain?<BR>> > <BR>> > Javier<BR>> > <BR>> > >===== Original Message From "Jorissen Kevin" =====<BR>> > >Hello,<BR>> > >the lm-list is usually read and used explicitly, which sounds like the order <BR>> > doesn't matter, but I'm not sure (perhaps the last value is used as 'maximum' <BR>> > somehow)? Better play safe and pu!
t them in
the right order, unless someone <BR>> > else tells us it's okay not to.<BR>> > >How I got them : 1/ I remember finding something about it in the old archives <BR>> > which gave some examples; 2/ for pointgroup "1" it's not very difficult, <BR>> > obviously ;-).<BR>> > >As for the second atom, it would surprise me to find a mistake in the l=1 <BR>> > group, since I definitely took that from wien and only added l=7 tot 10 <BR>> > myself. But who knows, it's a file I haven't used in a while.<BR>> > ><BR>> > ><BR>> > ><BR>> > >Kevin Jorissen<BR>> > ><BR>> > >EMAT - Electron Microscopy for Materials Science <BR>> > (http://webhost.ua.ac.be/emat/)<BR>> > >Dept. of Physics<BR>> > ><BR>> > >UA - Universiteit Antwerpen<BR>> > >Groenenborgerlaan 171<BR>> > >B-2020 Antwerpen<BR>> > >Belgium<BR>> > ><BR>> > >!
tel +32 3
2653249<BR>> > >fax + 32 3 2653257<BR>> > >e-mail kevin.jorissen@ua.ac.be<BR>> > ><BR>> > ><BR>> > >________________________________<BR>> > ><BR>> > >Van: wien-admin@zeus.theochem.tuwien.ac.at namens stargmoon<BR>> > >Verzonden: do 20-1-2005 3:17<BR>> > >Aan: wien@zeus.theochem.tuwien.ac.at<BR>> > >Onderwerp: RE: [Wien] LMMAX again<BR>> > ><BR>> > ><BR>> > >Dear Kevin,<BR>> > ><BR>> > >First of all, thanks a lot for your reply. But I still have questions.<BR>> > ><BR>> > >In your example, the second sort has point group "m", so its LM combination <BR>> > should take (+-l,l-2m). As "l" takes value 1, there are supposed to have four <BR>> > sets of LM, that is, (1,0),(1,1),(-1,0) and (-1,1), I think. However I can't <BR>> > find (-1,0) in the corresponding line (second line) in your .in2 file. Am I <BR>> !
>
right?<BR>> > ><BR>> > >By the way, how do you get the LM combinations up to L=10? Do you just change <BR>> > the default value 6 to 10 in the source code directly? If I add it by hand, <BR>> > does the order of the LM list matter?<BR>> > ><BR>> > >Looking forward to your reply!<BR>> > ><BR>> > >Best,<BR>> > ><BR>> > >Stargmoon<BR>> > ><BR>> > ><BR>> > ><BR>> > ><BR>> > ><BR>> > >Jorissen Kevin wrote:<BR>> > ><BR>> > > Did you enter them in 'fixed format'?<BR>> > > Here's an example for TiO:<BR>> > > 0 0 4 0 4 4 6 0 6 4 8 0 8 4 8 8<BR>> > > 0 0 4 0 4 4 6 0 6 4 8 0 8 4 8 8<BR>> > ><BR>> > > And this is a (working) example for KC60 :<BR>> > > tsm2.cmi.ua.ac.be> more vijf.in2<BR>> > > TOT (TOT,FOR,QTL,EFG,FERMI)<BR>> > > -9.0 249.0 0.50 0.05 EMIN, NE,
ESEPERMIN, ESEPER0<BR>> > > TETRA 0.000 (GAUSS,ROOT,TEMP,TETRA,ALL eval)<BR>> > > 0 0 4 0 4 4 6 0 6 4 6 2 6 6 8 0 8 4 8 8 10 0 10 2 10 4 10 6 10 8 1010<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 5 1<BR>> > > -5 1 5 3 -5 3 5 5 -5 5 6 0 6 2 -6 2 6 4 -6 4 6 6 -6 6 -7 7 -7 5 -7 3 -7 1<BR>> > > 7 1 7 3 7 5 7 7 -8 8 -8 6 -8 4 -8 2 8 0 8 2 8 4 8 6 8 8 -9 9 -9 7 -9 5<BR>> > > -9 3 -9 1 9 1 9 3 9 5 9 7 9 9-1010-10 8-10 6-10 4-10 2 10 0 10 2 10 4 10 6<BR>> > > 10 8 1010<BR>> > > 0 0 1 0 1 1 -1 1 2 0 2 1 -2 1 2 2 -2 2 3 0 3 1 -3 1 3 2 -3 2 3 3 -3 3<BR>> > > 4 0 4 1 -4 1 4 2 -4 2 4 3 -4 3 4 4 -4 4 5 0 5 1 -5 1 5 2 -5 2 5 3! -5 3<BR>> > > 5 4 -5 4 5 5 -5 5 6 0 6 1 -6 1 6 2 -6 2 6 3 -6 3 6 4 -6 4 6 5 -6 5 6 6<BR>> > > -6 6 -7 7 -7 6 -7 5 -7 4 -7 3 -7 2 -7 1 7 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7<BR>> > > -8 8 -8 7 -8 6 -8 5 -8 4 -8 3 -8 2 -8 1 8 0 8 1 8 2 8!
3 8 4 8
5 8 6 8 7<BR>> > > 8 8 -9 9 -9 8 -9 7 -9 6 -9 5 -9 4 -9 3 -9 2 -9 1 9 0 9 1 9 2 9 3 9 4 9 5<BR>> > > 9 6 9 7 9 8 9 9-1010-10 9-10 8-10 7-10 6-10 5-10 4-10 3-10 2-10 1 10 0 10 1<BR>> > > 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 1010<BR>> > > 0 0 1 0 1 1 -1 1 2 0 2 1 -2 1 2 2 -2 2 3 0 3 1 -3 1 3 2 -3 2 3 3 -3 3<BR>> > > 4 0 4 1 -4 1 4 2 -4 2 4 3 -4 3 4 4 -4 4 5 0 5 1 -5 1 5 2 -5 2 5 3 -5 3<BR>> > > 5 4 -5 4 5 5 -5 5 6 0 6 1 -6 1 6 2 -6 2 6 3 -6 3 6 4 -6 4 6 5 -6 5 6 6<BR>> > > -6 6 -7 7 -7 6 -7 5 -7 4 -7 3 -7 2 -7 1 7 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7<BR>> > > -8 8 -8 7 -8 6 -8 5 -8 4 -8 3 -8 2 -8 1 8 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7<BR>> > > 8 8 -9 9 -9 8 -9 7 -9 6 -9 5 -9 4 -9 3 -9 2 -9 1 9 0 9 1 9 2 9 3 9 4 9 5<BR>> > > 9 6 9 7 9 8 9 9-1010-10 9-10 8-10 7-10 6-10 5-10 4-10 3-10 2-10 1 10 0 10 1<BR>> > > 10 2 10 3 10 4 10 5 10 6 10 7 ! 10 8 10 9 1010<BR>> > > 20. GMAX<BR>>!
>
> FILE FILE/NOFILE write recprlist<BR>> > ><BR>> > > where the point symmetry of the four positions is the following (from <BR>> > case.outputsgroup) :<BR>> > > Sort number: 1<BR>> > > Names of point group: m-3 2/m-3 Th<BR>> > > Sort number: 2<BR>> > > Names of point group: m m Cs<BR>> > > Sort number: 3<BR>> > > Names of point group: 1 1 C1<BR>> > > Sort number: 3<BR>> > > Names of point group: 1 1 C1<BR>> > ><BR>> > > The exact number of spaces is important! In my example for KC60, lines end <BR>> > only with 1010 (other 'new lines' due to copy/paste, sorry).<BR>> > ><BR>> > > Hope this will do,<BR>> > ><BR>> > > Kevin Jorissen<BR>> > ><BR>> > > EMAT - Electron Microscopy for Materials Science <BR>> > (http://webhost.ua.ac.be/emat/)<BR>> > > Dept. of Physics<BR>> > ><BR>>!
>
> UA - Universiteit Antwerpen<BR>> > > Groenenborgerlaan 171<BR>> > > B-2020 Antwerpen<BR>> > > Belgium<BR>> > ><BR>> > > tel +32 3 2653249<BR>> > > fax + 32 3 2653257<BR>> > > e-mail kevin.jorissen@ua.ac.be<BR>> > ><BR>> > ><BR>> > > ________________________________<BR>> > ><BR>> > > Van: wien-admin@zeus.theochem.tuwien.ac.at namens stargmoon<BR>> > > Verzonden: wo 19-1-2005 18:27<BR>> > > Aan: Wien@zeus.theochem.tuwien.ac.at<BR>> > > Onderwerp: [Wien] LMMAX again<BR>> > ><BR>> > ><BR>> > > Dear WIEN community,<BR>> > ><BR>> > > A couple of days ago, I asked a question about LMMAX here and Kevin's answer <BR>> > helped me a lot. However, when I try to add LM list manually, I meet problems. <BR>> > For example, with a site symmetry "2/M", as listed in Table7.39 in usersguide, <BR>&g!
t; >
the LM combination should be (+-2l,2m). So I try to set l=0,1,2,3, (m=0,1,...l <BR>> > for each l) in order to reproduce the default lmmax up to 6, and I get 19 LM <BR>> > combinations manually. However, I only got 16 LM combinations after I run <BR>> > "SYMMETRY". Those three (-2,0) (-4,0) and (-6,0) do not show up in the LM list <BR>> > obtained from SYMMETRY. What's the problem here? Or I did something wrong? <BR>> > Your reply will be highly appreciated.<BR>> > ><BR>> > > Best,<BR>> > ><BR>> > > Stargmoon<BR>> > ><BR>> > > ________________________________<BR>> > ><BR>> > > Do you Yahoo!?<BR>> > > Yahoo! Mail - You care! about security. So do we.<BR>> > ><BR>> > ><BR>> > > > ATTACHMENT part 2 application/ms-tnef name=winmail.dat<BR>> > ><BR>> > ><BR>> > >________________________________<BR>> > ><B!
R>>
> >Do you Yahoo!?<BR>> > >The all-new My Yahoo! - What will yours do?<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>> > <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>> <BR>> <BR>>
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