Brodening in LCAO calculator

[Akash Ramasamy]

Dear all,
       I have a doubt regarding the default broadening value in the LCAO calculator which is 1000 K. What does it mean?

[Jahanzaib]

The default broadening value of 1000 K typically refers to the temperature used to define the width of the electronic states in energy calculations.

[filipr]

For general information on "broadening" in DFT: https://docs.quantumatk.com/manual/technicalnotes/occupation_methods/occupation_methods.html

When using a temperature such as 1000K as broadening it is automatically converted to an energy using E = kB T, so for T = 1000 K, E = 0.086 eV.

[Akash Ramasamy]

Thanks for your kind reply. If I change the broadening to 300K, how much change will occur in my results?  and it is correct.

[filipr]

As explained in the documentation it depends on whether your system is metallic or has a gap (semiconductor or insulator). For gapped systems the broadening should be smaller than the gap and you can in fact set it to something close to zero (like 1e-9). For metals there is no "magic number that suits every situation". For metals the broadening is correlated with the k-point sampling: the denser the k-points, the smaller the broadening you generally need. A broadening is an approximation and a tool to make calculations converge faster, but for accurate results you generally want to have it as small as possible - but that often means you have to increase the k-point sampling increasing the computational cost. What the "best" broadening and k-point sampling is is up to you. I recommend trying to do some convergence studies for a small system similar to what you are actually interested in. Try changing the k-point sampling and the broadening and see how it affects the results.

[Jahanzaib]

A follow up question on that:
I have a long stanene nanoribbon, and I am optimizing iron-tin cluster on it. My system is large in C direction so I need only few k-points, may be 1 k-point in C direction. So, I needs large broadening value?

This is what I understand from the discussion

[filipr]

If you look at the second formula in the documentation (how the density is calculated) you will see that it involves an integral over the Brillouin zone. This is turned into a numerical integral, a.k.a. sum weighted by the k-grid volume element dk = Δk_x Δk_y Δk_z. The broadening should be chosen proportional to this value. If your system is long along one dimension then the Δk will be small along that direction given a constant k-point density as the Brillouin zone is inversely proportional to the length along that direction: for a cell with perpendicular lattice vectors you have Δk = 2π/(LN), where L is the length of the cell along that direction and N is the number of k-points. If you keep only one k-point along the C direction then the broadening should be proportional to Δk_x Δk_y = (2π)²/(L_x N_x L_y N_y)

As a rule of thumb you can use a broadening of 1000K for metals and 100K for semiconductors and if the metal has a hard time converging you can either 1) increase the k-point sampling (expensive) or 2) increase the broadening (cheap, but reduces quality of results due to artificial smearing)