[Wannier] center of MLWFs
Xiaofeng Qian
qianxf at MIT.EDU
Tue Jun 10 16:38:11 CEST 2008
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.
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