[Pw_forum] Periodicity

[Yantao Wu]

Dear Axel,

Thank you very much for your reply. I understand that the energy wouldn't
exactly be doubled if you just put two identical systems together. But if
QE does treat the system as an infinite lattice, what is exactly the
meaning of the total energy in the output? How does QE obtain this output
energy from the calculated band energies in a manner that is proportional
to the size of the supercell. That is, I don't quite understand why you say

"the reason that you *do* get exactly twice the energy if you double
the system (and reduce the kpoint grid corresspondingly) is exactly
proof of that."

Thanks,
Yantao


On Wed, Jun 26, 2013 at 8:28 PM, Axel Kohlmeyer <akohlmey at gmail.com> wrote:

> there is no contradiction.
>
> QE *does* treat your system as if it was periodic and thus a _unit
> cell of an infinite crystal_.
> the reason that you *do* get exactly twice the energy if you double
> the system (and reduce the kpoint grid corresspondingly) is exactly
> proof of that. if it would treat just the input system, the energy of
> the double size system would be the energy of the two halves *plus*
> the interaction energy between them.
>
> does that make sense?
>      axel.
>
> On Thu, Jun 27, 2013 at 5:10 AM, Yantao Wu <ywu at g.hmc.edu> wrote:
> > Dear QE users,
> >
> > I have a general question on how QE treats periodicity of the system,
> e.g. a
> > bcc lattice. I originally thought QE only calculates the wave function
> for
> > the system you input into the program and enforce the Bloch periodic
> > boundary condition of Psi(r+R) = exp(ikR)Psi(r) on the wave-functions,
> where
> > R, the lattice constant, QE knows from the input of ibrav. In this case,
> QE
> > doesn't "know" anything about the infinite lattice that may be inferred
> from
> > the input system.
> >
> > But then I was told the other day that QE actually infers the infinite
> > lattice from the input system and calculates the wave-function for the
> > infinite system. Even though this sounds appealing to me, I'm still
> confused
> > by one seeming paradox. That is, if I double the size of the input system
> > but making sure that the infinite lattice inferred from this double-sized
> > system be the same as the original system, then the energy calculated for
> > the double-sized system will be almost precisely double of the energy of
> the
> > original system. This makes me feel like that QE treats the system of
> > interest to be just what the input system is.
> >
> > Can anyone clarify how exactly is periodicity treated in QE?
> >
> > Thank you much,
> > Yantao Wu,
> > Undergraduate Student,
> > Harvey Mudd College 15'
> >
> > _______________________________________________
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> > http://pwscf.org/mailman/listinfo/pw_forum
>
>
>
> --
> Dr. Axel Kohlmeyer  akohlmey at gmail.com  http://goo.gl/1wk0
> International Centre for Theoretical Physics, Trieste. Italy.
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