[Wien] Wavefunction above Fermi energy and normalization
Peter Blaha
pblaha at theochem.tuwien.ac.at
Tue Dec 5 16:17:41 CET 2017
For instance in SRC_mixer, there is a routine integrn.f
which integrates the charge density in the interstitial (with the help
of the cfft array (stepfunction), which has been setup previously in setn.f
In fact, you can even direct lapw2 to calculate the charge density of
just ONE eigenvalue ((x lapw2 -all emin emax; such that only the desired
state is in).
The resulting clmval file can go as input to mixer.
Remove any clmsum_old and clmcor files and run mixer.
Mixer will complain (:NCE01) that the input charge is not equal sum(Z),
but it will print you the charge inside spheres and the interstitial.
On 12/05/2017 03:31 PM, Leandro Salemi wrote:
> Dear Pr. Blaha,
>
>
> Thank you very much for your help ! I compared with the result given by
> x lapw2 -qtl and my integration inside the spheres gives the same
> results (which is already a good point).
>
> However, the integration in the interstitial part is still puzzling me
> as it seems to give the good answer for occupied states (the sum of the
> interstitial and spheres ~ 1) but does not for the unoccupied states ...
>
>
> I will go through the maths and the routines once again ! If you have
> any suggestion or know some similar routine which are worth looking at,
> I would be please to hear from you !
>
>
> Thank you again for your help and suggestions,
>
>
> Best regards,
>
>
> Leandro
>
> ------------------------------------------------------------------------
> *From:* Wien <wien-bounces at zeus.theochem.tuwien.ac.at> on behalf of
> Peter Blaha <pblaha at theochem.tuwien.ac.at>
> *Sent:* Monday, December 4, 2017 6:31:50 PM
> *To:* wien at zeus.theochem.tuwien.ac.at
> *Subject:* Re: [Wien] Wavefunction above Fermi energy and normalization
>
> 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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>>
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>
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> Phone: +43-1-58801-165300 FAX: +43-1-58801-165982
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Phone: +43-1-58801-165300 FAX: +43-1-58801-165982
Email: blaha at theochem.tuwien.ac.at WIEN2k: http://www.wien2k.at
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