# [Wannier] center of trial wannier function

Nicola Marzari marzari at MIT.EDU
Tue Aug 18 15:45:15 CEST 2009

```Mohammad R. Rasoulian wrote:
> Dear Arash
>    in our interface code between Wien2k and Wannier90 in calculation
> of Amn matrix we have a problem.
> the center of trial wannier function is important in swift of
> calculation and final result.
> we don't know how can we exert the position of trial wannier functions
> centers role in Amn matrix calculation ?
> we read "Maximally Localized Wannier Functions within the FLAPW
> formalism" paper but it is only for atom center trial function type .
> How we can change the centers to position except the centers of atom.
> we think it's possible for compute the other type with  linear
> combination of  atom center trial functions . but it's hard to
> definite the center every where on the bond.
> and we want know how exert  your code the position of the trial
> wannier function for calculate the Amn matrix?
>
> Thank you very much in advance.
> With kind regards.
> Mohammad.

Dear Mohammed,

not sure I understood better your question. I suppose the issue is that
in FLAPW it
is easy for you to calculate scalar products between Bloch orbitals and atom
centered trial functions, to construct Amn, and you want to know how to deal
with the case of trial functions that shoudl sit on bonds. Is this the
case ?

If it is, then you need to think at how a linear combination of atom
centered
functions would give you the right shape and center. In silicon, e.g.,
you would want 4 trial wave function centered on the bonds. How to
achive that ?
Well, there are 4 linear combination of the s and p_x/p_y/p_z orbitals
that give you
sp3 hybrids - so you have an alphabet of 4 sp3 hybrids on each silicon atom.

Call sp3_1 the one that sits on the atom at the origin, and points along
111, and
sp3_2 the one that stis on the atom in 1/4 1/4 1/4, and points along -1
-1 -1 ; then
the sum of those two (normalized by sqrt(2)) gives you a trial wfc
centered in the middle
of the bonds.

Hope this helps,

nicola

--
---------------------------------------------------------------------
Prof Nicola Marzari   Department of Materials Science and Engineering
13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu

```

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