Dear Prof. Blaha,
I looked the case.radwf file. For my test case of bulk-fcc-Al it
consists to following header:
1 781 0.0001000000 0.0129828604 2.5000000000
Here "1" seems to indicate the atom number from the case.struct (there
is only one inequivalent for fcc Al) and "781" indicates the number of
mesh points between the center of the atom and the radius of the sphere
(starting at the radius and ending at the center). Radius in this case
is 2.5 Bohr, as also indicated.
After this there are sections, each with 781 rows. These sections are
marked by 0, 1, 2, 3...8 which for me seems to be s, p, d, f, ...
Now each of these sections contains up to 10 columns. Can you explain
the meaning of these columns?
To me it looks as if 2 columns are assigned to each of u, u-dot, u_lo,
... But I would expect a single column of real numbers, in the spirit of
R_nl for the hydrogen.
I plotted some of these columns for check, and the first columns of the
first section looks like 3s, but the second column looks a bit strange.
Best,
Lukasz
On 2023-02-13 10:21, Peter Blaha wrote:
It was mentioned several times on the mailing list that
x lapw2 -alm
prints the radial functions into a file (just once) as well as all
Alm,Blm,... for each k-point and band-index.
For further details search the mailing list.
For the interstitial matrix elements you can get them by the integral
between two plane wave expansions (times the dipole operator ?)
multiplied with the "step-function". Such detaisl are well explained
in D. Singh's book...
Am 12.02.2023 um 20:10 schrieb pluto via Wien:
Dear Prof. Blaha,
Thank you for your comments.
Are the functions u and u-dot provided in some output file? Manual
mentions different types of u and u-dot for the cases of Psi^LO and
Psi^lo. Manual also mentions that u and u-dot are obtained by
numerical integration of radial Schrodinger equation on the mesh. Are
they all tabulated somewhere?
Having all the A_lm, B_lm, C_lm and all the u and u-dot would allow to
have the full wave function Psi(r) inside the spheres as a function of
wave-vector and energy. That would allow to numerically calculate the
matrix elements which I need, with the assumption of my favorite final
state, and without any further assumptions. The only remaining problem
would be the interstitial region, but it would also be under control
by knowing how much charge leaks out of the spheres.
Best,
Lukasz
On 2023-02-09 18:06, Peter Blaha wrote:
Well, I'm not sure I do understand all your problems, but a few
comments:
a) XMCD is implemented in optics !
b) I do not see the problem with A_lm, B_lm C_lm,..., because in any
case A_lm (or for semicore a C_lm) will dominate and you can
probably
neglect the B_lm and the corresponding u-dot radial function.
When you chose a good expansion energy for your radial wf., you more
or less have this "hydrogenic orbital" with one fixed radial
function.
Of course, this argument holds only when your states are "localized",
otherwise you will have a large interstital (PW) contribution.
c) I'm not the real expert of Wannier functions, but I guess the WF
might be complicated linear combinations of different l,m ....
Am 09.02.2023 um 15:46 schrieb pluto via Wien:
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
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