[Wien] Wavefunction above Fermi energy and normalization
Peter Blaha
pblaha at theochem.tuwien.ac.at
Mon Dec 4 18:31:50 CET 2017
Your approach seems right.
Use x lapw2 -qtl to get the partial charges inside the spheres for
each eigenvalue.
You can compare this with your normalization program for the parts
inside the sphere.
Am 04.12.2017 um 18:01 schrieb Leandro Salemi:
> Dear Pr. Blaha,
>
> Thank you for your quick answer. You are totally right with the case.in2
> file …
>
>
> For the wavefunction, that’s how I do :
>
>
> For the interstitial, I integrate the product of PW over the whole space
> and subtract the part from the spheres using a Rayleigh-expansion of a
> PW in terms of spherical harmonics.
>
>
> In the spheres, I compute terms like Alm* Blm \int u_l(r) dot(u)_l(r)
> r*r dr for the spheres. These coefficients are found in case.almblm and
> are actually Alm(k) = SUM_G C_G Alm(k+G) (this I got from a previous
> mailing thread). I have also terms like Alm* Clm \int u_l(r) u_lo__l(r)
> r*r dr to take into account the APW+lo and LO ! I guess that the Clm’s
> in case.almclm are also the ones multiplied by their coefficient C_G(LO)
> (which are not really part of the PW expansion), just like for Alm and
> Blm. I sum those terms over the different indexes l,m and over the spheres.
>
>
> Actually, I follow more less what is presented in the paper of C.
> Ambrosch-Draxl and J. O. Sofo (Computer Physics Communications 175
> (2006) 1–14). They computed <Psi_mk| p |Psi_nk> so I of course adapted
> the formalism to my need.
>
>
> Since you said that wavefunctions where all normalized, even above E_F,
> I must have missed something somewhere … If you see any mistake in what
> I have written there or have any references, works or source code I
> should look at, I would be pleased to hear that ! My aim is to extract
> exactly the wavefunctions. I will then manipulate them.
>
>
> Thank you very much,
>
>
> Best regards,
>
>
> Leandro Salemi
>
>
> P.S. : I might have answered in a not-proper way since I had not
> received the mail (I did not pay attention that my account was disabled
> for the reception of the mail ...). Sorry for the inconvenience (now it
> is enabled).
>
>
>
>
>
> Peter Blaha
> <https://www.mail-archive.com/search?l=wien@zeus.theochem.tuwien.ac.at&q=from:%22Peter+Blaha%22>
> Mon, 04 Dec 2017 06:13:01 -0800
> <https://www.mail-archive.com/search?l=wien@zeus.theochem.tuwien.ac.at&q=date:20171204>
>
>
> Of course all the wave functions are normalized. It comes automatically
> after solving the generalized eigenvalue problem in lapw1. Without
> properly normalized wave functions, how should we calculate an electron
> density which yields the desired number of electrons ??
>
> Why did you modify the code ?
> It would be much simpler to set NE in case.in2 to a larger number ....
>
> I don't know how you actually calculated the norm of a wave function,
> but due to the dual representation, it is not so straightforward.
>
> On 12/04/2017 02:55 PM, Leandro Salemi wrote:
>
> Dear WIEN2K users and developers,
>
>
> I am currently playing with the wavefunctions in WIEN2K in order to
> compute material-dependent properties. I must then extract them !
>
>
> I managed to extract the relevant quantities (C_nk(G), the coefficents
> A_lm, B_lm, C_lm and the radial functions) in order to build the
> wavefunction. When I try to compute the norm of the wavefunction, I find
> that it is quite well normalized BUT only for states which are below the
> Fermi energy … For states above, discrepancies arise and I find numbers
> like 0.8 or 1.3 …
>
>
> To output the A_lm, B_lm of unoccupied states with "x lapw2 -alm", I
> modified slightly the l2main.F routine. The following has been done :
>
> IF(MODUS.EQ.'ALM ') then
>
> !LEANDRO INCLUDE EMPTY BANDS (START)
>
> NEMAX_SAVE=NEMAX
>
> NEMAX=NE
>
> !LEANDRO INCLUDE EMPTY BANDS (END)
>
> WRITE(24,2055) s_kvec,t_kvec,z_kvec,n,ne,bname
>
> write(24,*) jatom,nemin,nemax,' jatom,nemin,nemax'
>
> endif
>
>
> where my modification is in between the “!LEANDRO …”. What I did it just
> saying that the NEMAX (which normally refers to the number of occupied
> bands) should go up to the highest computed state and thus, can go above
> the Fermi level.
>
>
> I was wondering that may be, the states are automatically normalized but
> only for those below the Fermi level. If this is the case, then I can
> compute the norm and divide by the sqrt. Am I right or am I missing
> something ? Since the wavefunction is the basic mathematical description
> of the material, extracting wrong quantities would be quite problematic ...
>
> I am of course taking into account the local orbitals in the process !
>
> Are the wavefunctions only normalized below E_F ? If yes, do you know in
> which part the normalization is done ?
>
>
> If anyone has experience with this topic or any suggestion, I would be
> please to hear ! I have already checked throughout the mailing list and
> the user guide ...
>
>
> Thank you,
>
>
> Leandro Salemi
>
>
>
>
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