[Wien] Wavefunction above Fermi energy and normalization
tran at theochem.tuwien.ac.at
tran at theochem.tuwien.ac.at
Tue Dec 5 20:20:58 CET 2017
yes exactly
On Tuesday 2017-12-05 17:42, Leandro Salemi wrote:
>Date: Tue, 5 Dec 2017 17:42:36
>From: Leandro Salemi <leandro.salemi at physics.uu.se>
>Reply-To: A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
>To: A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
>Subject: Re: [Wien] Wavefunction above Fermi energy and normalization
>
>
>Dear FT,
>
>
>You mean that I take into account the the PW description is not valid in the sphere? Yes I take that into account by integrating over the whole cell and
>subtracting the atomic contributions.
>
>Here is what I do :
>
>https://drive.google.com/file/d/1zXKHoLpxdSF663E0hu1DIQ9RDAw5nJRp/view
>
>
>Best regards,
>
>
>Leandro Salemi
>
>________________________________________________________________________________________________________________________________________________________________
>From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> on behalf of tran at theochem.tuwien.ac.at <tran at theochem.tuwien.ac.at>
>Sent: Tuesday, December 5, 2017 3:42:26 PM
>To: A Mailing list for WIEN2k users
>Subject: Re: [Wien] Wavefunction above Fermi energy and normalization
>Hi,
>
>Are you multiplying the square of the orbitals with the step function
>(0 in spheres and 1 in interstitial) for the integral with the plane
>waves?
>
>FT
>
>On Tuesday 2017-12-05 15:31, Leandro Salemi wrote:
>
>>Date: Tue, 5 Dec 2017 15:31:47
>>From: Leandro Salemi <leandro.salemi at physics.uu.se>
>>Reply-To: A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
>>To: "wien at zeus.theochem.tuwien.ac.at" <wien at zeus.theochem.tuwien.ac.at>
>>Subject: Re: [Wien] Wavefunction above Fermi energy and normalization
>>
>>
>>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=fr
>>om:%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=da
>>te: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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>>
>>--
>>--------------------------------------------------------------------------
>>Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
>>Phone: +43-1-58801-165300 FAX: +43-1-58801-165982
>>Email: blaha at theochem.tuwien.ac.at WIEN2k: http://www.wien2k.at
>>WWW:
>>http://www.imc.tuwien.ac.at/tc_blaha---------------------------------------
>>----------------------------------
>>IMC : Prof. Dr. P. Blaha: Computational Materials Science - Home of
>>WIEN2k
>>www.imc.tuwien.ac.at
>>Homepage of Institute of Materials Chemistry
>>
>>
>>
>>_______________________________________________
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>>
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