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<p><span style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;">Dear Pr. Blaha,</span><br>
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<p>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).</p>
<p>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 ...</p>
<p><br>
</p>
<p>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 !</p>
<p><br>
</p>
<p>Thank you again for your help and suggestions,</p>
<p><br>
</p>
<p>Best regards,</p>
<p><br>
</p>
<p>Leandro</p>
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<div id="x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Wien <wien-bounces@zeus.theochem.tuwien.ac.at> on behalf of Peter Blaha <pblaha@theochem.tuwien.ac.at><br>
<b>Sent:</b> Monday, December 4, 2017 6:31:50 PM<br>
<b>To:</b> wien@zeus.theochem.tuwien.ac.at<br>
<b>Subject:</b> Re: [Wien] Wavefunction above Fermi energy and normalization</font>
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<div class="PlainText">Your approach seems right.<br>
<br>
Use x lapw2 -qtl to get the partial charges inside the spheres for <br>
each eigenvalue.<br>
<br>
You can compare this with your normalization program for the parts <br>
inside the sphere.<br>
<br>
Am 04.12.2017 um 18:01 schrieb Leandro Salemi:<br>
> Dear Pr. Blaha,<br>
> <br>
> Thank you for your quick answer. You are totally right with the case.in2 <br>
> file
<br>
> <br>
> <br>
> For the wavefunction, thats how I do :<br>
> <br>
> <br>
> For the interstitial, I integrate the product of PW over the whole space <br>
> and subtract the part from the spheres using a Rayleigh-expansion of a <br>
> PW in terms of spherical harmonics.<br>
> <br>
> <br>
> In the spheres, I compute terms like Alm* Blm \int u_l(r) dot(u)_l(r) <br>
> r*r dr for the spheres. These coefficients are found in case.almblm and <br>
> are actually Alm(k) = SUM_G C_G Alm(k+G) (this I got from a previous <br>
> mailing thread). I have also terms like Alm* Clm \int u_l(r) u_lo__l(r) <br>
> r*r dr to take into account the APW+lo and LO ! I guess that the Clms <br>
> in case.almclm are also the ones multiplied by their coefficient C_G(LO) <br>
> (which are not really part of the PW expansion), just like for Alm and <br>
> Blm. I sum those terms over the different indexes l,m and over the spheres.<br>
> <br>
> <br>
> Actually, I follow more less what is presented in the paper of C. <br>
> Ambrosch-Draxl and J. O. Sofo (Computer Physics Communications 175 <br>
> (2006) 114). They computed <Psi_mk| p |Psi_nk> so I of course adapted <br>
> the formalism to my need.<br>
> <br>
> <br>
> Since you said that wavefunctions where all normalized, even above E_F, <br>
> I must have missed something somewhere
If you see any mistake in what <br>
> I have written there or have any references, works or source code I <br>
> should look at, I would be pleased to hear that ! My aim is to extract <br>
> exactly the wavefunctions. I will then manipulate them.<br>
> <br>
> <br>
> Thank you very much,<br>
> <br>
> <br>
> Best regards,<br>
> <br>
> <br>
> Leandro Salemi<br>
> <br>
> <br>
> P.S. : I might have answered in a not-proper way since I had not <br>
> received the mail (I did not pay attention that my account was disabled <br>
> for the reception of the mail ...). Sorry for the inconvenience (now it <br>
> is enabled).<br>
> <br>
> <br>
> <br>
> <br>
> <br>
> Peter Blaha <br>
> <<a href="https://www.mail-archive.com/search?l=wien@zeus.theochem.tuwien.ac.at&q=from:%22Peter+Blaha%22" id="LPlnk263512" previewremoved="true">https://www.mail-archive.com/search?l=wien@zeus.theochem.tuwien.ac.at&q=from:%22Peter+Blaha%22</a>>
<br>
> Mon, 04 Dec 2017 06:13:01 -0800 <br>
> <<a href="https://www.mail-archive.com/search?l=wien@zeus.theochem.tuwien.ac.at&q=date:20171204" id="LPlnk138552" previewremoved="true">https://www.mail-archive.com/search?l=wien@zeus.theochem.tuwien.ac.at&q=date:20171204</a>><br>
> <br>
> <br>
> Of course all the wave functions are normalized. It comes automatically <br>
> after solving the generalized eigenvalue problem in lapw1. Without <br>
> properly normalized wave functions, how should we calculate an electron <br>
> density which yields the desired number of electrons ??<br>
> <br>
> Why did you modify the code ?<br>
> It would be much simpler to set NE in case.in2 to a larger number ....<br>
> <br>
> I don't know how you actually calculated the norm of a wave function, <br>
> but due to the dual representation, it is not so straightforward.<br>
> <br>
> On 12/04/2017 02:55 PM, Leandro Salemi wrote:<br>
> <br>
> Dear WIEN2K users and developers,<br>
> <br>
> <br>
> I am currently playing with the wavefunctions in WIEN2K in order to<br>
> compute material-dependent properties. I must then extract them !<br>
> <br>
> <br>
> I managed to extract the relevant quantities (C_nk(G), the coefficents<br>
> A_lm, B_lm, C_lm and the radial functions) in order to build the<br>
> wavefunction. When I try to compute the norm of the wavefunction, I find<br>
> that it is quite well normalized BUT only for states which are below the<br>
> Fermi energy
For states above, discrepancies arise and I find numbers<br>
> like 0.8 or 1.3
<br>
> <br>
> <br>
> To output the A_lm, B_lm of unoccupied states with "x lapw2 -alm", I<br>
> modified slightly the l2main.F routine. The following has been done :<br>
> <br>
> IF(MODUS.EQ.'ALM ') then<br>
> <br>
> !LEANDRO INCLUDE EMPTY BANDS (START)<br>
> <br>
> NEMAX_SAVE=NEMAX<br>
> <br>
> NEMAX=NE<br>
> <br>
> !LEANDRO INCLUDE EMPTY BANDS (END)<br>
> <br>
> WRITE(24,2055) s_kvec,t_kvec,z_kvec,n,ne,bname<br>
> <br>
> write(24,*) jatom,nemin,nemax,' jatom,nemin,nemax'<br>
> <br>
> endif<br>
> <br>
> <br>
> where my modification is in between the !LEANDRO
. What I did it just<br>
> saying that the NEMAX (which normally refers to the number of occupied<br>
> bands) should go up to the highest computed state and thus, can go above<br>
> the Fermi level.<br>
> <br>
> <br>
> I was wondering that may be, the states are automatically normalized but<br>
> only for those below the Fermi level. If this is the case, then I can<br>
> compute the norm and divide by the sqrt. Am I right or am I missing<br>
> something ? Since the wavefunction is the basic mathematical description<br>
> of the material, extracting wrong quantities would be quite problematic ...<br>
> <br>
> I am of course taking into account the local orbitals in the process !<br>
> <br>
> Are the wavefunctions only normalized below E_F ? If yes, do you know in<br>
> which part the normalization is done ?<br>
> <br>
> <br>
> If anyone has experience with this topic or any suggestion, I would be<br>
> please to hear ! I have already checked throughout the mailing list and<br>
> the user guide ...<br>
> <br>
> <br>
> Thank you,<br>
> <br>
> <br>
> Leandro Salemi<br>
> <br>
> <br>
> <br>
> <br>
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna<br>
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