Since ABINIT is based on periodic boundary conditions, every wavefunction is characterized by a wavevector, usually denoted k-point.
Any list of k-point can be specified, thanks to the keywords nkpt and kpt.
Still, k-points are used in two different contexts in the vast majority of cases:
In the first case, the Brillouin zone must be sampled adequately, with grids that, in general will be homogeneous distributions of k-points throughout the Brillouin Zone (e.g. Monkhorst-Pack grids, or their generalisations).. For such grids, see ngkpt, nshiftk, shiftk or even the more general kptrlatt. A list of interesting k point sets can be generated automatically, including a measure of their accuracy in term of integration within the Brillouin Zone, see prtkpt, kptrlen. For metals, a joint convergenc study on tsmear AND the k-point grid is important.
For the definition of a path of k-points, see topic_ElecBandStructure.
More detailed explanation concerning the convergence with respect to the k-point sampling.
The number of k-points to be used
for this sampling, in the full Brillouin zone, is inversely
proportional to the unit cell volume, but may also
vary a lot from system to system. As a rule of thumb, a system
with a large band gap will need few k-points, while metals will need
lot of k-points to produce converged results.
For large systems, the inverse scale with respect to the unit cell volume
is unfortunately stopped because at least one k-point must be
used. The effective number of k-points to be used will be strongly
influenced by the symmetries of the system, since only the
irreducible part of the Brillouin zone must be sampled. Moreover
the time-reversal symmetry (k equivalent to -k) can be used for
ground-state calculations,
to reduce sometimes even further the portion of the brillouin zone
to be sampled. The number of k points to be used in a calculation
is named nkpt. There is another way to take advantage of the
time-reversal symmetry, in the specific case of k-points that are
invariant under k => -k , or are sent to another vector distant
of the original one by some vector of the reciprocal lattice.
See below for more explanation about the advantages of using
these k-points.
As a rule of thumb, for homogeneous systems, a reasonable accuracy may be
reached when the product of the number of atoms by the number of k-points
in the full Brillouin zone is on the order of 50 or larger, for wide gap
insulators, on the order of 250 for small gap semiconductors like Si,
and beyond 500 for metals, depending on the value of the input variable
tsmear. As soon as there is some vacuum in the system, the product
natom * nkpt can be much smaller than this (for an isolated molecule
in a sufficiently large supercell, one k-point is enough).
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Basic input variables:
... chksymbreak [CHecK SYMmetry BREAKing]
... kptopt [KPoinTs OPTion]
... ngkpt [Number of Grid points for K PoinTs generation]
Useful input variables:
... istwfk [Integer for choice of STorage of WaveFunction at each k point]
... kpt [K - PoinTs]
... kptbounds [K PoinT BOUNDarieS]
... kptnrm [K - PoinTs NoRMalization]
... kptrlatt [K - PoinTs grid : Real space LATTice]
... kptrlen [K - PoinTs grid : Real space LENgth]
... ndivk [Number of DIVisions of K lines]
... ndivsm [Number of DIVisions for the SMallest segment]
... nkpath [Number of K-points defining the PATH]
... nkpt [Number of K - Points]
... nshiftk [Number of SHIFTs for K point grids]
... prtkpt [PRinT the K-PoinTs sets]
... shiftk [SHIFT for K points]
... wtk [WeighTs for K points]
Relevant internal variables:
... %kptns [K-PoinTs re-Normalized and Shifted]
Input variables for experts:
... vacuum [VACUUM identification]
... vacwidth [VACuum WIDTH]
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tests/v2/Input: t43.in
t44.in
t61.in
t62.in
t63.in
t64.in
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