[Wannier] parameter to control convergence

[Nicola Marzari]

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.
> 

-- 
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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