The ABINIT Users Mailing List ( CLOSED )

[Takeshi Nishimatsu <takeshi@physics.rutgers.edu>]

Dear Marc Torrent,

Thank you for your advice.

So, real spherical harmonics are equivalent to cubic harmonics (basis
of irreducible representation of O_h group) for l<=2 and hexagonal
harmonics (that of D_{6h} group) for l<=3.

Changing the plane-wave part may useful for many purposes of many users.
But changing the PAW part (only partial_dos_fractions_paw.F90) may be
easier than changing the plane-wave part as you wrote.

Thank you again! I will try it. -- Takeshi


Marc Torrent a ecrit :
> Dear Takeshi Nishimatsu,
> 
> The solution of your problem is subtle.
> 
> In the partial_dos_fractions routine (where the "plane-wave" part of the
> PAW DOS is computed), COMPLEX spherical harmonics are used !
> In the partial_dos_fractions_paw routine (where the "on-site" part of
> the PAW DOS is computed), REAL spherical harmonics are used !
> 
> REAL spherical harmonics are sum of two COMPLEX spherical harmonics with
> the same l and with opposite m.
> You can find the definition of the REAL SH used in Abinit at
> http://www1.elsevier.com/homepage/saa/eccc3/paper48/eccc3.html or in the
> initylmr.F90 Abinit file.
> 
> When you sum over m (this is done in the official version of the code),
> you obtain the same result either with REAL or COMPLEX spherical harmonics.
> 
> But, if you discretize each m, the results are differents, except for m=0.
> For m=1, results are wrong but you get the same value for m=1 and m=-1.
> For m>=2, results are differents...
> 
> So, the solution is to "convert" your dos_fractions_m in
> partial_dos_fractions_paw.F90 from REAL to COMPLEX spherical harmonics
> (apply some "rotation" matrix)...
> 
> 
> Marc Torrent
> CEA-Bruyeres-le-Chatel - France
> 
> 
> Takeshi Nishimatsu a e'crit :
>> Dear all,
>>
>> The attached path 14-27.diff is a quick hack for abinit-5.4.4.tar.gz
>> to get m-decomposed LDOS. You can apply this patch as follows:
>>
>>  $ tar zxf abinit-5.4.4.tar.gz
>>  $ cd abinit-5.4.4/
>>  $ ./config/scripts/makemake
>>  $ patch -p0 < SOME/WHERE/14-27.diff
>>  $ mkdir g95-O3
>>  $ cd g95-O3
>>  $ FC=gfortran FCFLAGS=-O3 ../configure
>>  $ make
>>
>> Note that it is the SPHERICAL harmonics decomposition, *not* the
>> CUBIC harmonics one, i.e. NOT dyz, dzx, dxy, d3z2-r2, and dx2-y2.
>> Attached scTi-05-Fermi-Teter.tar.gz and scTiPAW-05-Fermi.tar.gz
>> are test cases (Simple cubic Ti. Still need spgroup=1.).
>>
>>  $ tar zxf SOME/WHERE/scTi-05-Fermi-Teter.tar.gz
>>  $ cd scTi-05-Fermi-Teter
>>  $ cp POTENTIAL_FILE/22ti.psp.mod .
>>  $ ../src/main/abinis < files > abinis.log
>>  $ ./dos.gp
>>  $ cd ..
>>  $ tar zxf SOME/WHERE/scTiPAW-05-Fermi.tar.gz
>>  $ cd scTiPAW-05-Fermi
>>  $ cp POTENTIAL_FILE/ti_ps.abinit.paw .
>>  $ ../src/main/abinis < files > abinis.log
>>  $ ./dos.gp
>>
>> I guess m=+2 and m=-2 (magenta and orange lines in both plots)
>> orbitals of Ti 3d electrons must have the same LDOS. In the
>> Teter-potential calculation, they are same. But in the PAW
>> calculation, they are NOT same. (Plots in PDF are attached.)
>>
>> Did I make something wrong? Please check my patch and give
>> me your advice!
>>
>>
>> Happy Thanksgiving and Hacking,
>>   
>