[Wien] missing electrons

[Rossitza Pentcheva]

Hello Peter,

I realise I had similar problems recently. In order to simulate 
photoemission spectra,  the density of states along the Gamma-X 
direction was needed. Since Wien integrates over the whole Brillouin 
zone, I decided to take three points along the Gamma -X direction 
(Gamma, X/2,X) separately and then add the DOS taking into account  the 
weight of each k-point. Unfortunately due to the problem with 
Delta-functions you discuss below, tetra produced no output for the 
single k-points. Is there an alternative way of getting the DOS along a 
particular direction in BZ?

Best regards,
Rossitza

Peter Blaha wrote:

>Hi,
>I could verify your "problem" and got the same results, i.e. the integrated
>DOS (case.dos1) does not yield the proper number of electrons.
>
>First I was a little shocked, but now it appears that everything is in
>principle correct, only your k-mesh is too crude to give a good DOS.
>
>Let me explain what the problem is:
>
>The DOS is an integral over k; done numerically by the tetrahedron
>method. Thus the BZ is divided into tetrahedra and the DOS is a sum of
>all those tetrahedra integrals (which can be done analytically).
>For small k-meshes it may now occur that a single tetrahedron has 4
>identical vertices !, i.e. that all 4 k-points for this tetrahedron are
>the same. If this happens, it means that the DOS contribution due to this
>tetrahedron is a delta-function at e=e_k (with a normalization equal to
>the volume of this tetrahedron). Of course with any finite E-mesh
>(the mesh where you calculate the DOS (eg. -1, 0.001, 1.)), even a very fine
>one you will "never" catch these spikes of the delta-functions in your
>DOS nor will you be able to integrate the DOS numerically over energy, when
>it has such singularities.
>
>It will always occur when in case.kgen you find tetrahedra with identical
>vertices like:
>
>         4        19  0.185185185185E-01       101         1
>         <6         1         1         1         1>         <4
>         1         1         1         2>         ...
>
>The first line means that there are 4 k-points with 19 tetrahedra.
>In the 2nd and 3rd line I've added < > to indicate their meaning:
>The first tetrahedron has "weight" 6 and four identical vertices (1,1,1,1)
>(first k-point), while the second tetrahedron has weight 4, but vertices
>1,1,1,2 (thus one k-point is different),....
>
>Thus the first tetrahedron is such an example. All eigenvalues of band i
>will be identical leading to a delta-function at this eigenvalue and give
>zero contribution to DOS(E) on your energy-mesh E.
>
>Hope this explains the problem.
>
>Without shift the probablility of tetrahedra with identical vertices
>decreases. With a shift it seems that even for very dense meshes such
>critical tetrahedra occur (always the first one ?), but their weight get
>drastically reduced so that you don't see the problem anymore.
>However, from some tests on tio2 this does not necessarely mean that
>the DOS of an unshifted mesh is "better". The DOS with a crude unshifted
>mesh "integrates" properly, but has nothing in common with the final DOS
>with a converged (shifted or unshifted) k-mesh.
>
>It also explains, why you do not "see" any problems with bulk Rh or other
>(smaller) cells, because there you probably have very dense k-meshes
>(or no shift).
>
>>However, when we integrate  the Density of States (case.dos1ev)  by
>>"xmgrace" over the energy interval : -0.1 Ry to the Fermi Level, we get
>>150 electrons (i.e., we lose 50 electrons). However, when we do the same
>>for the DOS calculated by another DFT code (with pseudopotential
>>approximation), we get almost the right number of electrons. Now, if  we
>>plot these DOS's together on the same graph, it becomes obvious that the
>>DOS calculated by WIEN2k has a lot of electrons or states missing
>>(because the DOS-curves corresponding to the pseudopotential code lie
>>far above that of the WIEN2k code).
>>
>>When I add up the partial DOS's and that of the interstitial, I get the
>>total DOS. This part is alright. Therefore, I would guess that tetra
>>commits some error in projecting the partial DOS's, which leads to
>>partial loss of electrons per muffin-tin sphere and these losses add up
>>to 50 electrons for the whole supercell.
>>
>>However, I do not encounter this problem when I integrate the DOS over
>>the same energy interval for Ru bulk, RuO2 bulk and the Ru(0001) surface
>>by the same software, "xmgrace". These 3 systems are perfectly ok.
>>
>
>
>                                      P.Blaha
>--------------------------------------------------------------------------
>Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
>Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
>Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
>--------------------------------------------------------------------------
>
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-- 

Dr. Rossitza Pentcheva
Department fuer Geo- und Umweltwissenschaften	phone: +49 89 2180 4352	
Sektion Oberflaechenkristallographie 		fax: +49 89 2180 4334	
Ludwig-Maximilians-Universitaet Muenchen	e-mail: pentcheva at lrz.uni-muenchen.de
Theresienstr. 41         
80333 Muenchen             www: http://www.krist.geo.uni-muenchen.de/ober/pentche.htm

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