Handling G = [0.0, 0.0, 0.0]

[jackbaker1001]

Hi @hema-ted

From what I can tell from the code, the contribution to the accumulation over G-vectors just ignores the contribution at G =[0.0, 0.0, 0.0].

I know that this done to avoid the singularity in the expression (dividing by zero), but I am not sure this just warrants ignoring the term.

Do we have any justification for this?

[jackbaker1001]

Just adding to this:

1. We should consider what is done for other G-space computations at this limit. The Hartree potential, for example, leads to a similar equation in G-space to the spin-spin interaction. Sometimes we set n(G = 0) to zero (for both ions and electrons) and add a neutralizing background charge to compensate. Perhaps we could add this?

2. I was taking a look at $lim_{\mathbf{G} \rightarrow 0} \frac{G_aG_b}{G^2}$. Unfortunately, the limit doesn't exist as the limit has a different values depending on the path to the origin.