Dispersion correction and band structure

Question

Let's say I optimized geometry with PBE+D3. I want to carry out band structure calculation with HSE06, should I add the dispersion correction to the band structure calculation or not?

I tried both and in two cases I got the equivalent band structures. So;

$$\tag{1} \textrm{Graphene}_{GO}^{\textrm{PBE-D3}} + \textrm{Graphene}_{BS}^{\textrm{HSE06-D3}} = \textrm{Graphene}_{GO}^{\textrm{PBE-D3}} + \textrm{Graphene}_{BS}^{\textrm{HSE06}} $$

I assume that dispersion correction affects bandstructure due to optimized geometry. So it really does not have any effect on a single point band structure calculation. If it's like that why in some papers, it shows for example as: PBE+D3 or HSE06+D3. If I just use dispersion correction at the geometry optimization level, still can I put HSE06+D3 on the figure, or should I add the dispersion correction to the band structure calculation even it does not have any effect.

Answer 1

@Xivi76 is correct. Dispersion corrections have no direct influence on the band structure. As such, there is no need to add the D3 correction on your HSE06 static calculation if you're only interested in the band structure. Nonetheless, some people include the D3 correction because the dispersion correction is basically free, and it's consistent with the use of dispersion corrections during the geometry optimization. It won't make a difference though unless you're interested in other properties (e.g. absolute energy, force).

As for your question "If I just use dispersion correction at the geometry optimization level, still can I put HSE06+D3 on the figure," the answer is you should report exactly what you used. If you didn't use D3 with HSE06, don't mention it. Your level of theory here is HSE06//PBE-D3(BJ).