[Pw_forum] About maximally localized wannier function

[Nicola Marzari]

Silviu, I had already written this out, so I still post it
for clarification. Apologies for the bandwidth.

Suppose in PWSCF you use infinite k-points. This allows you to calculate
the perfectly converged charge density with respect to k-point sampling.
This perfect charge density is then read by CP, and it allows it
to construct the perfect Hamiltonian, and perfectly diagonalize it
at Gamma (but nowhere else !). If your unit cell is (very) small, these
Gamma eigenstates will be different than those that would have
been calculated self-consistently by CP (you are using the
perfect charge density). (Of course, you shouldn't use CP to do
small calculations where you need BZ sampling finer than Gamma).

But now the issue is that, with the perfect Gamma-orbitals, CP will
allow you to construct localized wavefunctions using only Gamma, while
in principle you should use all states at all k-points. So your CP MLWFs
will not be equivalent to the PWSCF MLWFs, even if the Hamiltonian is
the same. In particular, the CP MLWFs, since they use only the
Bloch orbitals at Gamma, will have the same periodicity of your unit 
cell, while the PSCF MLWFs, calculated from a nk X nk X nk
Monkhorst-Pack mesh, while be periodic with the periodicity of a
nk X nk X nk supercell.

Best,

			nicola

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Prof Nicola Marzari   Department of Materials Science and Engineering
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