[Wannier] Nonorthogonal wannier function

David Vanderbilt dhv at physics.rutgers.edu
Sat Feb 3 17:37:50 CET 2007

Claudio, Nicola,

If you have in mind that the WFs are going to end up being roughly
atom-centered, so that each WF is identified with a given atom, then
I think it would not be very difficult to set up a framework in which
you ask for maxloc WFs that are orthonormal on-site but not between
sites.  If you have in mind a more general framework (e.g., where
some WFs may be bond-centered), then I'm not so sure such an approach
would make sense.

I'm not sure what the Williamson-Reboredo/Alfe schemes are, but I
think a projection scheme should work pretty well.  Note, however,
that simple projection is probably not good; one should do an extra
step to construct dual functions.  See the discussion in the top
paragraph, second column, p. 5343, of He and Vanderbilt,
http://prola.aps.org/abstract/PRL/v86/i23/p5341_1 .  Do the
Williamson-Reboredo/Alfe schemes include a step like this?


On Fri, 2 Feb 2007, Nicola Marzari wrote:

> Dear Claudio,
> the current Wannier90 code deals only with orthogonal wavefunctions.
> Non-orthogonal WFs have been recently used in linear-scaling
> quantum Monte Carlo approaches - both Andrew Williamson (Williamson
> and Reboredo) and Dario Alfe' have developed some heuristic approaches
> based on projections (a maximal localization strategy on non-orthogonal
> WFs is somehow ill-conditioned: if you take a rare gas atom, the orthogonal 
> MLWFs are 4 sp3 hybrids, but the non-orthogonal MLWFs would
> probably be 4 identical s orbitals, each with an infinitesimal amount
> of sp3 thrown in, to preserve linear independence).
> Paolo Umari has coded the Williamson (or Alfe') algorithm as part of his
> GW work, in a Gamma sampling implementation only - so I'm CC'ing him.
> The plan on our side is to insert by the summer the orthogonal
> Gamma-specific routines of localization and disentanglement into the
> Wannier code (these have been written by Manu Sharma and Young-Su Lee).
> Having a non-orthogonal option would also be great - and if you were 
> interested or involved, it would also be great to coordinate.
> 				nicola
> Claudio Attaccalite wrote:
>> Hi
>> a simple question:
>> 1) it is possible to obtain nonorthogonal wannier functions (ok if want 
>> call them very localized orbitals) with the wannier code?
>> 2) if not, does someone know another code that does it? or you think it is 
>> easy to modify the wannier code in such a way to relax the orthogonality 
>> condition?
>> Thanks
>> Claudio
>> -- 
>> ==========================================================
>> Claudio Attaccalite
>> Institute for Electronics, Microelectronics, and Nanotechnology
>> Dept. ISEN
>> B.P . 60069
>> 59652 Villeneuve d'Ascq Cedex France
>> Skype: claudioattaccalite
>> web site: www.attaccalite.altervista.org 
>> <http://www.attaccalite.altervista.org>
>> ===========================================================
>> Freely download scientific books from: www.freescience.info 
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> -- 
> ---------------------------------------------------------------------
> 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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