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K-point
Posted: Tue Mar 22, 2011 7:59 am
by Amal Giri
Dear All,
I am new learner of abinit.
Please tell me what is k-point and by,for example, 12X12X12 k- point what does it mean.
Thanks
Re: K-point
Posted: Tue Mar 22, 2011 12:53 pm
by jzwanzig
Hi, your question relates to basic solid state physics more than to abinit. You should read carefully the review paper by Payne et al., Rev. Mod. Phys. 64, 1045 (1992), and also study the book Electronic Structure. Basic Theory and Practical Methods. R. M. Martin. Cambridge University Press (2004).
best wishes,
Re: K-point
Posted: Tue Mar 22, 2011 1:28 pm
by Alain_Jacques
Dear Amal,
To make long stories short (I'm taking the risk of starting a serious flamewar) ... k-points and the Brillouin zone (BZ) are related concepts. The (first) Brillouin zone is a primitive cell in the reciprocal space. In a periodic system, the wavefunction of a particle is fully characterized in a single BZ. So when calculating the total energy of a structure, the electronic wavefunctions are integrated over the occupied states and over the BZ. In practice, the integral is approximated by a sum over selected points in the BZ i.e over a regular mesh of equally spaced k-points or a (reduced, probably more efficient) mesh like the Monkhorst & Pack grid.
Kind regards,
Alain