the change in population of the C atom in CO is the same when the same changes are made in either the V$_{atom}$ or the V$_{sys}$ grid; *i.e.* the change in the population (in absolute value) of the C atom is comparable when going from the black to the red curve and when going from a point at $10$ grid points per Å to a point at $20$ grid points per Å on the same curve in Fig. \[fig:HIR\_GridConv\]. Figure \[fig:HIR\_GridConv\] and Table \[table:gridConv\] also show that quite a dense mesh is needed to obtain very accurate results. Though this is not a big problem for periodic systems with small unit cells, it could become problematic for molecules which require big unit cells to accommodate the vacuum required to prevent interaction between the periodic copies. The same is true for high accuracy V$_{atom}$ grids, which are required for high accuracy atomic radial densities. Fortunately, these must only be generated once, and the high resolution radial densities can then be stored in a library.\

![(a) Convergence behavior of the population/charge as function of the number of grid points per spherical integration shell. For the C(black line) and O(red line) atom of 