[Wien] about Harmonic expansion

[Peter Blaha]

Hi,
These multipole moments are used to calculate the Coulomb potential. 

First, the Multipole moments from the charge density inside the spheres 
are calculated.
Second, the multipolemoments from a charge density represented by the 
plane wave charge density inside these spheres are also calculated and 
finally these two MP-moments are subtracted ("Pseudo-MPM") and later on 
used to construct a "pseudo charge", which is represented by a Fourier 
series having exactly these multipole moments, but is zero in the 
interstital and can thus be added to the PW charge density of the 
interstital. 
One has then a Fourier expansion, which gives the correct density in the 
interstital AND has correct multipole moments inside the spheres, thus you 
can simply solve Poissons equation and obtain a Fourier series of the 
potential (valid in the interstital).

This is described in the paper by M.Weinert 1981 ?, yo may find the exact 
reference in the UG (References).


         I want to know the detail of harmonic expansion used in wien2k.
> This is part of case.output0, I dont know its meaning, could you give me an explan?
>      ------------------------------
>                               M U L T I P O L M O M E N T S
>                               ------------------------------
> 
> 
>    ATOM=  1   Si1          Z=14.00   LM=  6     POSITION=  0.875  0.375  0.375
> 
>    L=  0   M= 0   SPHERE MM =   0.629969486  0.000000000
>    L=  4   M= 0   SPHERE MM =   0.137908491  0.000000000
>    L=  4   M= 4   SPHERE MM =   0.082416087  0.000000000
>    L=  6   M= 0   SPHERE MM =  -0.038451045  0.000000000
>    L=  6   M= 4   SPHERE MM =   0.071935319  0.000000000
>    L= -3   M= 2   SPHERE MM =   0.000000000  0.281234883
> 
> 
>    ATOM=  1   Si1          Z=14.00   LM=  6     POSITION=  0.875  0.375  0.375
> 
>    L=  0   M= 0   PLANE WAVE MULTIPOLMOMENT =   0.552128554  0.000000000
>    L=  4   M= 0   PLANE WAVE MULTIPOLMOMENT =  -0.136937612  0.000000000
>    L=  4   M= 4   PLANE WAVE MULTIPOLMOMENT =  -0.081835876  0.000000000
>    L=  6   M= 0   PLANE WAVE MULTIPOLMOMENT =   0.038123303  0.000000000
>    L=  6   M= 4   PLANE WAVE MULTIPOLMOMENT =  -0.071322169  0.000000000
>    L= -3   M= 2   PLANE WAVE MULTIPOLMOMENT =   0.000000000 -0.279651825
> 
>    ATOM=  1   Si1          Z=14.00   LM=  6     POSITION=  0.875  0.375  0.375
> 
>    L=  0   M= 0   PSEUDO MULTIPOLMOMENT     =   1.182098040  0.000000000
>    L=  4   M= 0   PSEUDO MULTIPOLMOMENT     =   0.000970878  0.000000000
>    L=  4   M= 4   PSEUDO MULTIPOLMOMENT     =   0.000580211  0.000000000
>    L=  6   M= 0   PSEUDO MULTIPOLMOMENT     =  -0.000327742  0.000000000
>    L=  6   M= 4   PSEUDO MULTIPOLMOMENT     =   0.000613150  0.000000000
>    L= -3   M= 2   PSEUDO MULTIPOLMOMENT     =   0.000000000  0.001583058
>    L=  4   M=-4   PSEUDO MULTIPOLMOMENT     =   0.000580211  0.000000000
>    L=  6   M=-4   PSEUDO MULTIPOLMOMENT     =   0.000613150  0.000000000
>    L= -3   M=-2   PSEUDO MULTIPOLMOMENT     =   0.000000000 -0.001583058
> 
> Best wish to you!
>  Yonghua
> 
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> 


                                      P.Blaha
--------------------------------------------------------------------------
Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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