Input constraints while comparing different DFT calculated properties for the same material but different atomic arrangement

Question

Let's consider a fictitious AB type binary alloy. AB is known to exist in a B2 type ordered structure. We want to compare the DoS (density of states) between this structure for AB and a completely disordered structure. On disordering, AB would become a BCC type random solid solution.

Now, what are the inputs for a DFT code that we must consider carefully? Should the k-mesh spacing, plane wave energy cut-off, and smearing width ($\sigma$) be the same for both to be able to compare them or should we converge these for each of them individually?

Answer 1

The best strategy when performing convergence tests is to directly converge the quantity you are interested in. This "quantity" can be a straight-forward physical property, like the band gap of a material, or a composite (for lack of a better word) property. In your case, you are interested in comparing the electronic density of states (DOS) between two compounds, so my suggestion would be to build a relevant composite property.

Here is a naïve proposal for your case. Let $g_A(E)$ and $g_B(E)$ be the densities of states of the two compounds you are comparing, and let $(E_1,E_2)$ be the energy range over which you want to compare the densities of states. Then I can define a quantity $\Delta$ that measures the difference between the two densities of states, for example as:

$$ \Delta=\frac{1}{E_2-E_1}\int_{E_1}^{E_2} \sqrt{\left[g_A(E)-g_B(E)\right]^2} dE. $$

My suggestion would be to converge $\Delta$ with respect to the relevant parameters. If you individually converge $g_A$ and $g_B$, then their difference should also be converged, but converging $\Delta$ instead may provide important computational gains because there may be some "cancellation of errors" in the convergence of the difference between $g_A$ and $g_B$, which is what you are really interested in.

As to the parameters you should converge, I agree that $\mathbf{k}$-points (both for the self-consistent and non-self-consistent parts of the calculation), energy cut-off, and smearing width are important. Depending on what you want to achieve with the comparison, it may also be important to play around with the limits $(E_1,E_2)$ in an expression like the one for $\Delta$ above.

Answer 2

To compare calculations, it’s best to have all the calculation parameters possible the same, including the k-mesh spacing, plane wave energy cut-off, and the Brillouin zone integration method (with the same smearing width, if applicable). The settings must also be sufficiently converged for each case.

In your example, if the B2 case a tighter k-point spacing while the disordered case required a higher energy cutoff to be converged, then the calculations to be compared should use both the tighter k-point spacing and the higher energy cutoff.

It’s also key to highlight that the calculations should have the same k-point spacing, i.e. no matter the crystal size, the density of points in the volume is the same. This pattern should be applied to any setting related to an extrinsic property, such as the k-point sampling, since cell volume is an extrinsic property.

Some settings like smearing width are complicated, because there’s not necessarily a converged value in terms of correctness. Too small or too large can cause issues, as discussed in this answer.