[Wannier] parameter to control convergence

Tadashi Ogitsu ogitsu at llnl.gov
Thu Aug 24 07:31:04 CEST 2006

Dear Nicola and Jonathan,

Thank you very much for your responses. Those are very useful for me.


I will definitely look into the papers you suggested. Here, I'd like  
to explore a bit further possibility how much information we can  
extract from MLWFs.

If I understand correctly, those problematic cases are all related to  
multiple (double) bond. Am I right? Do you know any case where even  
MLWFs in single bond system could give misleading picture?

I feel that the word, banana bond is a bit incomplete expression, I  
should have used the alternative word, the three-centre bond (in  
contrast to two-centre bond). It is a little bit more than a mere  
terminology; it conveys the essence of the bonding nature, i.e., the  
bonding electron has to be localized in  the middle of triangle (bent  
is not the essence).

I guess, I'm trying to say that if the system does not form multiple  
bond, the location of MLWFs (and spreads) could be used to  
distinguish between three-centre bond and two-centre bond (not as a  
definite proof but as a qualitative explanation). Do you still find a  
critical pitfall in my argument? Thanks.

#Now I understand why Francois once implemented the MLWF function  
with localization in energy space as well. With this way, you can  
distinguish the sigma bond and pi bond since those are located in  
different positions in energy space. The example, you have pointed  
out are the typical cases that if you minimize only spread, it will  
mix the sigma bond and the pi bond equally, which produces a bit  
confusing picture (in contras to sigma/pi picture).

On Aug 23, 2006, at 1:52 PM, Nicola Marzari wrote:

> Dear Tadashi,
> a couple of comments following Jonathan reply:
> 1) if chemical intuition is what you are after, you might want to
> consider also the electronic localization function of Savin
> and others (Nature ca. 1994). That covers insulators and metals.
> 2) banana bonds were one of the things chemists didn't like about
> the Boys-Foster criterion of the '60s (to which our max-loc criterion
> is equivalent, in molecules). One example I think I remember is
> ethylene C2H4, where the double bond between the two carbons is
> represented with an up-banana, and a down-banana, mixing sigma and  
> pi. Very unpalatable.
> 3) Boys-Foster localization can give un-chemical results: CO2
> (linear molecule, O=C=O) has 3 MLWFs between C and each of the Os,
> and one on the outside of each O. Something like .O...C...O. ,
> where ... looks like a triple bond (so C would have two triple
> bonds...).
> Anyhow there is a vast chemical literature in the '60 and '70s
> describing all of this.
> 4) even if the disentangled DMLWFs are not "chemical", or "physical",
> they still tell you who is hybridizing with who, and so offer some
> intuituion.
> Best luck,
> 			nicola
> Tadashi Ogitsu wrote:
>> Dear Nicola,
>> Thanks for your quick reply. I'd like to develop chemical  
>> intuition of boron crystal from Wannier functions.
>> As you might know, boron chemistry is very unique; as it is  
>> described in many chemistry textbook, it does not follow  
>> conventional electron counting rule such as Lewis dot diagram  
>> (which works very well for carbon based systems). Typical example  
>> is B2H6 molecule, in which two hydrogen atoms are shared by two  
>> boron atoms forming two banana like bond (the other four hydrogen  
>> atoms seem to form the conventional bonds with boron atoms). I  
>> noticed that the Wannier function can be used to identify the  
>> banana bonds in boron system, e.g., the Wannier centre of the  
>> banana bond in B2H6 molecule indeed is located in the middle of  
>> triangle formed by two boron atoms and one hydrogen atom, contrary  
>> to a conventional covalent picture where the Wannier centre will  
>> be in the middle of two atoms (which could correspond to Lewis dot  
>> diagram). I'm trying to analyze the bonding nature of beta-boron  
>> crystal with this way and to compare with known empirical rule for  
>> boron chemistry such as mno rule.
> -- 
> ---------------------------------------------------------------------
> 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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