# Quastion about K-points and energy cutoff

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1. May 2, 2014

### omaralrawi

Dear All,

I have three questions about the relation between the K-points and energy cutoff. The first one is : how many k points should I use in my theoretical calculation to get a good result in lattice constant and the converge of Emin especially for using DFT? The second one is : What is the relation in K-point and energy cutoff and is there any equation that can I use to describe this relation? How can I calculate this relation for graphene?

I have used in my calculation GaAs to gain an accurate result.

Regards.

2. May 6, 2014

### bsmile

Which software are you using? Seems like planewave based DFT calculation, I guess.

(1) if using pseodupotential, then less K points can be used as compared with all-electron calculations. For VASP and insulator calculation, 4*4*4 might be good enough. Of course you can always use more K points to test K point convergence. You can refer to the vasp manual to find more information

(2) Energy cutoff has nothing to do with K point. Energy cutoff is related to so-called G points, plane wave basis, and their relationship is simply E_cutoff=h_bar^2 G_cutoff^2/2m_e.

(3) Energy cutoff is different from the dispersion relation relating K to E. Energy cutoff in a DFT software is more a technical trick than a physically meaningful quantity.

3. May 20, 2014

### Douasing

Here is a question making me feel puzzled.
Actually,I don't know very clear why 4*4*4 might be good enough for insulator,especially for atomic or molecular system,generally, 1*1*1 is enough.
For k points (lowercase,k),it should perform the periodic boundary condition. In my opinion,the number of k points is just equal to N1*N2*N3. Whatever the system is insulator or molecular,they need to be calculated through periodic boundary condition (for molecular,say,supercell).
Because the calculation is always made in a primitive cell (or,supercell),in other words, the number of k points stands for the number of primitive cells. But ,Why should the number of k-points for metals be more than insulator or semicoductor ? And why 1*1*1 for molecular (just one k point)?

4. May 20, 2014

### bsmile

The VASP software manual might address your question better. For insulator, there is no band around Fermi surface, thus K space sampling can be sparse.

For atom and molecule calculation, you do only need 1*1*1 with a very big unit cell, which means two nearby atoms/molecules are separated faraway such that their interaction is tiny. Why 1*1*1 is enough is because the K dependence of density/wavefunction/potential has very weak dependence on K (imagine the dispersion for a single atom in K space, which is basically flat).

I think lowercase k in your language is similar to G in my language (VASP). We might use the same uppercase K to denote crystal momentum within the 1st Broullin zone.