[Wien] LMMAX again

Peter Blaha pblaha at zeus.theochem.tuwien.ac.at
Fri Jan 21 22:06:29 CET 2005 

Te charge density is expanded in "real spherical harmonics". These 
functions can be constructed from the (more common) "complex spherical 
harmonics" by various linear combinations. As you all know, a complex 
spherical harmonics is Y_lm = P_lm(cos theta) . exp(i m phi)

The LM list defines linear combinations, which produce the required "real 
harmonics".

Obviously, when m=0, the imaginary part (exp(im.phi) is always zero, thus 
there is only ONE (l 0) pair, but never a negative l.

Of course also in the general case, negative l's do not exists, but the 
notation of the 4 possible combinations to produce real harmonics are 
indicated by (l m),(-l m),(l -m) and (-l -m). The possible linear 
combinations are

Y_lm + Y_l-m
Y_lm - Y_l-m
(Y_lm - Y_l-m)*i
(Y-lm - Y_lm-m)*i


> I think the lm list looks okay, for (+-l,l-2m) the sets should be (1,1),(-1,1) 
> for m=0 and for m=1 gives (1,-1) and (-1,-1)... I'm not an expert but I've 
> negative m values are not valid and (-1,0), (-2,0),...(-n,0) never seem to be 
> included in the lm-list, though I have no idea why.  Maybe someone can 
> explain?
> 
> Javier
> 
> >===== Original Message From "Jorissen Kevin" <Kevin.Jorissen at ua.ac.be> =====
> >Hello,
> >the lm-list is usually read and used explicitly, which sounds like the order 
> doesn't matter, but I'm not sure (perhaps the last value is used as 'maximum' 
> somehow)?  Better play safe and put them in the right order, unless someone 
> else tells us it's okay not to.
> >How I got them : 1/ I remember finding something about it in the old archives 
> which gave some examples; 2/ for pointgroup "1" it's not very difficult, 
> obviously ;-).
> >As for the second atom, it would surprise me to find a mistake in the l=1 
> group, since I definitely took that from wien and only added l=7 tot 10 
> myself.  But who knows, it's a file I haven't used in a while.
> >
> >
> >
> >Kevin Jorissen
> >
> >EMAT - Electron Microscopy for Materials Science   
> (http://webhost.ua.ac.be/emat/)
> >Dept. of Physics
> >
> >UA - Universiteit Antwerpen
> >Groenenborgerlaan 171
> >B-2020 Antwerpen
> >Belgium
> >
> >tel  +32 3 2653249
> >fax + 32 3 2653257
> >e-mail kevin.jorissen at ua.ac.be
> >
> >
> >________________________________
> >
> >Van: wien-admin at zeus.theochem.tuwien.ac.at namens stargmoon
> >Verzonden: do 20-1-2005 3:17
> >Aan: wien at zeus.theochem.tuwien.ac.at
> >Onderwerp: RE: [Wien] LMMAX again
> >
> >
> >Dear Kevin,
> >
> >First of all, thanks a lot for your reply.  But I still have questions.
> >
> >In your example, the second sort has point group "m", so its LM combination 
> should take (+-l,l-2m). As "l" takes value 1, there are supposed to have four 
> sets of LM, that is, (1,0),(1,1),(-1,0) and (-1,1), I think. However I can't 
> find (-1,0) in the corresponding line (second line) in your .in2 file. Am I 
> right?
> >
> >By the way, how do you get the LM combinations up to L=10? Do you just change 
> the default value 6 to 10 in the source code directly? If I add it by hand, 
> does the order of the LM list matter?
> >
> >Looking forward to your reply!
> >
> >Best,
> >
> >Stargmoon
> >
> >
> >
> >
> >
> >Jorissen Kevin <Kevin.Jorissen at ua.ac.be> wrote:
> >
> >	Did you enter them in 'fixed format'?
> >	Here's an example for TiO:
> >	0 0 4 0 4 4 6 0 6 4 8 0 8 4 8 8
> >	0 0 4 0 4 4 6 0 6 4 8 0 8 4 8 8
> >
> >	And this is a (working) example for KC60 :
> >	tsm2.cmi.ua.ac.be> more vijf.in2
> >	TOT (TOT,FOR,QTL,EFG,FERMI)
> >	-9.0 249.0 0.50 0.05 EMIN, NE, ESEPERMIN, ESEPER0
> >	TETRA 0.000 (GAUSS,ROOT,TEMP,TETRA,ALL eval)
> >	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
> >	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
> >	-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
> >	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
> >	-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
> >	10 8 1010
> >	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
> >	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
> >	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
> >	-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
> >	-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
> >	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
> >	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
> >	10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 1010
> >	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
> >	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
> >	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
> >	-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
> >	-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
> >	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
> >	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
> >	10 2 10 3 10 4 10 5 10 6 10 7 ! 10 8 10 9 1010
> >	20. GMAX
> >	FILE FILE/NOFILE write recprlist
> >
> >	where the point symmetry of the four positions is the following (from 
> case.outputsgroup) :
> >	Sort number: 1
> >	Names of point group: m-3 2/m-3 Th
> >	Sort number: 2
> >	Names of point group: m m Cs
> >	Sort number: 3
> >	Names of point group: 1 1 C1
> >	Sort number: 3
> >	Names of point group: 1 1 C1
> >
> >	The exact number of spaces is important! In my example for KC60, lines end 
> only with 1010 (other 'new lines' due to copy/paste, sorry).
> >
> >	Hope this will do,
> >
> >	Kevin Jorissen
> >
> >	EMAT - Electron Microscopy for Materials Science 
> (http://webhost.ua.ac.be/emat/)
> >	Dept. of Physics
> >
> >	UA - Universiteit Antwerpen
> >	Groenenborgerlaan 171
> >	B-2020 Antwerpen
> >	Belgium
> >
> >	tel +32 3 2653249
> >	fax + 32 3 2653257
> >	e-mail kevin.jorissen at ua.ac.be
> >
> >
> >	________________________________
> >
> >	Van: wien-admin at zeus.theochem.tuwien.ac.at namens stargmoon
> >	Verzonden: wo 19-1-2005 18:27
> >	Aan: Wien at zeus.theochem.tuwien.ac.at
> >	Onderwerp: [Wien] LMMAX again
> >
> >
> >	Dear WIEN community,
> >
> >	A couple of days ago, I asked a question about LMMAX here and Kevin's answer 
> helped me a lot. However, when I try to add LM list manually, I meet problems. 
> For example, with a site symmetry "2/M", as listed in Table7.39 in usersguide, 
> the LM combination should be (+-2l,2m). So I try to set l=0,1,2,3, (m=0,1,...l 
> for each l) in order to reproduce the default lmmax up to 6, and I get 19 LM 
> combinations manually. However, I only got 16 LM combinations after I run 
> "SYMMETRY". Those three (-2,0) (-4,0) and (-6,0) do not show up in the LM list 
> obtained from SYMMETRY. What's the problem here? Or I did something wrong? 
> Your reply will be highly appreciated.
> >
> >	Best,
> >
> >	Stargmoon
> >
> >	________________________________
> >
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                                      P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
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Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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