[Wannier] center of MLWFs

[Xiaofeng Qian]

Dear Nafise,

The initial centers of MLWFs are just the initial guess to start with for 
the construction of MLWFs. It also happends to the initial guess of 
atomic, bonding or hybrid orbitals. In general, they are not necessary to 
be the same as the final centers and final orbitals you obtain from the 
Wannier90 package. However what Jonathan mentioned has already answered 
your question and he is talking about the FINAL center of MLWFs.

One key point is: if you include both valence and conduction states to 
calculate MLWFs, the final MLWFs are a linear combination of valence and 
conduction states. That means you can not tell which Wannier function is 
particularly for the valence states, or which Wannier function is 
particularly for the conduction states. Therefore, it is not very 
meaningful to compare the center of two sets of MLWFs constructed from 
valence states only and both valence+conduction states.

For example, usually the valence states correspond the bonding-like 
Wannier functions while the low-lying conduction states correponds to the 
anti-bonding-like Wannier functions. Then if you construct the MLWFs using 
valence states only, finally you will obtain bonding-like Wannier 
functions whose centers are the center of those bonds. If you include both 
valence and conduction states to construct MLWFs, finally you will obtain 
atomic-like Wannier functions whose centers are atomic positions. 
Obviously bond centers and atomic positions are very different. But the 
latter ones have contributions from both valence and conduction states, 
therefore we can not find any particular Wannier functions which is purely 
from the transformation of valence states only.

So the answer to your question is: the final centers of MLWFs do change 
when you use valence states only and valence+conduction states. But there 
is no specific MLWF which comes purely from valence states when you use 
valence+conduction states for the construction. So it is not valid to 
compare "the centers of MLWFs for the valence states".

Best,

Xiaofeng Qian


> ------------------------------
>
> Message: 4
> Date: Mon, 9 Jun 2008 18:21:00 +0430
> From: "nafise rezaei" <nafiserb at gmail.com>
> Subject: [Wannier] center of MLWFs
> To: wannier at quantum-espresso.org
> Message-ID:
>       <785b26a90806090651p4f921223wf51b2f8feba97ed7 at mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
>
> Dear Jonathan;
>
> I do not understand exactly your reply. My question was about final
> center of MLWFs for valence states.in the paper of  Maximally
> localized Wannier functions
> for entangled energy bands , any things about final center of MLWFs
> are not mentioned .
>
> You have spoken about initial center of MLWFs and the fact that
> initial center of MLWFs for valence states and for valence + low lying
> conduction states can be different.
> when I consider both of valence and conduction states ,will final
> center of MLWFs for valence states change respect with when only
> MLWFs for valence states be calculated?
>
> I appreciate your help.
>
> Best regards.