Hi,
I would like to know the significance of k-points in optimization steps of a crystal in qunatum espresso. iam doing optimization of gc3n4 and TiO2. Can we set same k-points for both crystals while converging k points? I can't find the significance of k-point convergence in and is there any relation between dimensionality of the crystal and k-point.If there is any books please suggest me
Please help me. thanks in advance
Crystal systems are generally considered infinite. Conditions
at periodic boundaries and lattice symmetries are usually taken into account for the choice of wave functions used to project the electron density.
Instead of working in real space, work is usually done in
Fourier space (reciprocal space) this space generally has the same symmetries as real space. so we can
characterize a crystal by vectors of a region called the first Brillouin zone (primitive Wigner-Seitz cell
in the reciprocal network). It is therefore in this volume that the periodic functions of Blochl are calculated.
To numerically compute the bloch functions u in a volume, it is necessary to
cut this volume (the first Brillouin zone) into small volumes. This can be achieved by
uniformly dividing the considered volume. If we take into account the punctual symmetries
of the system, the volume of the first Brillouin zone can be reduced and at the same time
the number of elementary volumes necessary for the final calculation of the wave functions. Grates
of the “Monkhorst-Pack” type are generally used. In the latter, we only consider the points 𝑘 lying in the reduced Brillouin zone. They constitute the points
specials from Monkhorst. Their number and their choice depends on the symmetry of the system, and therefore
of the specific group of the system studied.
the higher the number of kpoints, the more the convergence is ensured and the finer the precision.
on quantum Espresso, the place to do is to optimize the number of points k.
https://www.materialssquare.com/blog/2-convergence-test-k-points-optimization-for-silicon-bulk-2
Number of k-points is usually determined by size of unit cell. Bigger cell size, less k-points required.
In general rule of thumb, (lattice constant) x (k-points number) > 30 , as introduced in link above, is good starting point and works well for most case.
You may use less number of k-points if you want just brief crystal relaxation, and may increase the number if higher accuracy required.
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