[Wien] QTL quantization axis for Y_lm orbitals

[pluto]

Dear Sylwia, dear Prof. Blaha, dear All,

Having these A_lm, B_lm etc is of course a problem if one wants to 
estimate interferences in dipole optical matrix element due to phases at 
which different Y_lm orbitals enter the wave function. It would be good 
to have a single complex number per Y_lm.

For this it would be good to have the LAPW wavefunction projected onto 
hydrogenic orbitals that just have a single radial component. Then there 
would be just one complex coefficient. For a particular l (i.e. s, p, or 
d) one would have a common radial part of the wave function, since the 
radial part does not depend on m. Then one would need to assume the 
final state expansion in Y_lm (can always be done even for free-electron 
final state) and do some estimation of the XMCD process within the 
simplified LCAO way of thinking.

Is there any tool already existing to project WIEN2k wave function onto 
hydrogenic orbitals?
I was thinking something like this might be a part of the WIEN2Wannier, 
but I wanted to ask here before investing further time into this.

Best,
Lukasz


-- 
PD Dr. Lukasz Plucinski
Group Leader, FZJ PGI-6
Phone: +49 2461 61 6684
https://electronic-structure.fz-juelich.de/



-------- Original Message --------
Subject: Re: [Wien] QTL quantization axis for Y_lm orbitals
Date: 2023-01-17 20:02
 From: gutowska at agh.edu.pl
To: A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
Reply-To: A Mailing list for WIEN2k users 
<wien at zeus.theochem.tuwien.ac.at>

Dear Lukasz,

the reason is that the (radial part) of the wave function is actually 
the sum of 5 terms.
As mentioned at http://www.wien2k.at/lapw/index.html in sector 
"LAPW+LO", the wave function is the sum of the atomic radial wave 
function and its energy derivative multiplied by the factors A_lm(k) and 
B_lm(k) respectively.
There is also an additional radial wave function called the local 
orbital with the coefficient C_lm(k).
Then comes the APW+lo method, where the local orbital is the sum of the 
new radial wave function and its energy derivative multiplied by the new 
coefficients A'_lm(k) and B'_lm(k), respectively.
This gives 5 coefficients: A_lm(k), B_lm(k), C_lm(k), A'_lm(k), B'_lm(k) 
in the case.almblm file. Each of them has a real and an imaginary part.
This is explained in Chapter 2 of the User's Guide.

what's best
Sylwia