The ABINIT Users Mailing List ( CLOSED )

[Nicola Marzari <marzari@mit.edu>]

Dear Alex,


well spotted. I think that the reason is that the solution of
the Kohn-Sham equations at any k-point is well-defined modulo
an arbitrary phase.

This means that if you take the wavefunction at any k-point
and you multiply it by exp (i alpha), where alpha is random,
you get an equally good solution. This is also the case for
the Schroedinger equation - it's a "gauge" freedom, and an
arbitrary phase does not change any of your physical expectation
values (there is interesting stuff buried in there of relevance
to the electronic-structure community - e.g. the Berry phase
theory of piezoelectricity).

Note that I am assuming that all the (significantly non-zero)
G-vectors coefficients change abruptly (as seemed from your
post) and not that only a few.

Bottom line - the phase that you get from any electronic structure
code for the wavefunction at a given k is random. The specific
subroutines somehow determine the result, and it seems that
the phase difference you got is close to -1 . The fact that is -1
rather than some absolutely random complex phase is probably
due on how abinit evolves wavefunctions (I would guess
as a diagonalization of the hamiltonian, rather than a
conjugate-gradient minimization, but I do not really know - I
actually read the mailing list only to understand what the community
finds easy or difficult, in electronic-structure modeling), and
so there is not a total randomness in initial choices. As a side note,
note that, unless explicity enforced, the often-cited
relation u_nk(r)=u_n(-k)^*(r) is also true only modulo a phase,
i.e. u_nk(r)=u_n(-k)^*(r) exp (i alpha).


                                nicola


Alex Kutana wrote:
> Dear abinit developers:
>
> I have made an observation that the Fourier coefficients of the 
> wavefunction sometimes change abruptly upon moving between two
> points that are very close in the Brillouine zone.
---------------------------------------------------------------------
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@mit.edu http://quasiamore.mit.edu