# Which properties of a material calculated using density functional theory are affected by smearing?

Smearing (smearing width $$\sigma$$, to be precise) has always been confusing. I understand what it is but can't pin it down when it comes to DFT calculations. Should it be converged like k-points and energy cut-off? If yes, then when - before we converge k-points and energy cut-off or after?

Also, which properties does it affect in the calculation, and how?

In brief, it will influence the electronic energy and thereby all properties derived from that. Too small a smearing width and you might have trouble converging the self-consistent field. Too large and the extrapolation back to 0 K from the fictitious finite temperature will be less accurate. Depending on the smearing method (e.g. Gaussian smearing), you can treat it as a property you can decrease until the energy extrapolation is minimal. This is not necessarily the case for all smearing methods though. The order in which you carry out convergence tests is somewhat a matter of opinion, and you should always validate your assumptions. However, I would probably do it after determining a plane-wave kinetic energy cutoff and $$k$$-point grid. I should also mention that the smearing width may influence the band edges and thereby the computed band gap depending on its value, so this is another property to take into consideration.

• Thanks for the answer. I went through the VASP wiki's entry for ISMEAR and realised it's been updated. For convergence, they suggest using a value of smearing width that results in $-T*S\: = 1$ meV/atom or less. [vasp.at/wiki/index.php/ISMEAR] Aug 18, 2020 at 19:38
• Not only the energy, also the electron density! Aug 20, 2020 at 10:44
• Absolutely true! So, in short, pretty much everything! Aug 20, 2020 at 13:18
• Note that the smearing width is usually used to smooth the Brillouin zone integration, rather than actually simulating a finite-temperature system, and so it couples to the k-point sampling. As you increase the k-point sampling density you are able to decrease the smearing width, improving the accuracy without compromising the stability of the SCF algorithm. Nov 15, 2020 at 0:19

You can make a convergence test to obtain reasonable results. Usually, for k-sampling and energy cutoff, you can take some values from experiences (of course, you can also make convergence tests).

• (a) ENCUT=largest ENMAX on the POTCAR file $$\times$$ 1.5
• (b) KPOINTS: you can using VASPKIT to generate KPOINTS when you prepare a POSCAR.

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Why we need the smearing method?

The original idea of the smearing method can refer this paper, this method is devoted to dealing with the numerical integration in the Brillouin zone for metals.

• One useful definition of a metal is that in metal the Brillouin zone can be divided into regions that are occupied and unoccupied by electrons. The surface in k space that separates these two regions is called the Fermi surface.

• From the point of view of calculating integrals in k space, this is a significant complication because the functions that are integrated change discontinuously from nonzero values to zero at the Fermi surface. If no special efforts are made in calculating these integrals, very large numbers of k points are needed to get well-converged results.

• After that, the smearing method has been developed to dealing with semiconductors and insulators.

How to choose a suitable smearing method for your system? (I assume you are using the VASP package and provide a recipe to perform the calculation.)

• If you don't have enough information (metal/semiconductor/insulator), you can always use the Gaussian smearing method. The setting [ISMEAR=0, SIGMA=0.05] in VASP will give you a reasonable result.
• When you know the system is metal, you can use the MP smearing method to relax your system. [ISMEAR=1, SIGMA=0.2] (Keep the entropy term less than 1 meV per atom. )
• For semiconductors or insulators, use the tetrahedron method [ISMEAR=-5], if the cell is too large (or if you use only a single or two k-points) use ISMEAR=0 in combination with a small SIGMA=0.03-0.05.
• For the calculations of the density of states and very accurate total energy calculations (no relaxation in metals) use the tetrahedron method [ISMEAR=-5].

Should it be converged like k-points and energy cut-off?

• For simple system, you can take the previous recipe to obtain resonable results.
• For some complex systems, you should take ISMEAR=0 and testing the value of SIGMA.

If yes, then when - before we converge k-points and energy cut-off or after?

You can take a higher energy cut-off and a fine k-mesh to test the convergence of SIGMA. ($$\dfrac{3}{2} \times$$ the maximum cut-off in POTCAR and using VASPKIT to generate KPOINTS with high accuracy.)

Also, which properties does it affect in the calculation, and how?

As Andrew Rosen said, it will affect the integral of total energy and thereby all properties derived from it. Because the pickup of SIMGA decides the convergence of numeric integral.

May it helps.

• This is rather unrelated to the question about smearing width. Aug 17, 2020 at 17:03
• I upvoted you, and one other did too, but you got 4 downvotes. Please: take our advice and make this answer more clear about how it is related to the question. I don't want you getting anymore downvotes! Aug 17, 2020 at 17:58
• I updated my answers and may it helps.
– Jack
Aug 19, 2020 at 12:39