Dear Martin,

yes usually considering the RIM for the first Brillouin zone is enough, but it depends on the geometry of the BZ itself.

Beside the divergence, it happens that for non-3D sampling the \int_Vi 1/q^2 d^3q in each small portion you divide the BZ

is different from 1/q^2_i x V_i (V_i volume of the fraction of the Bz, where q_i is contained), in particular for the q_i close to the origin.

Out of the first BZ, if it is large enough then the two expressions are very similar, so no RIM is needed for the integral beyond the first Bz. Note that in the report when calculating the RIM you can look at:

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`Summary of Coulomb integrals for non-metallic bands`

Here there is indeed the ratio between these two expressions for each q point, which will be very different from 1 for the smallest q, while becomes to be close to 1 for large q at the border to the Bz. If you see that also the q at the border differs from 1 (let's more than 10^-3) then you can add shells of G vectors where the RIM is considered (RandGvec). Of course, you can do a check of you final results by changing the number of the variables (e.g the Sigma_x which is fast and very sensible to the RIM).

Hope it is clear enough,

Best,

Daniele