As noted in Ref. for uniform grids, topographical properties (such as Bader charges) can be affected by a grid bias, whereby a systematic error arises due to geometrical properties of the arrangement of grid points. This error is due to steepest-ascent paths on the graph diverging from the true gradient path of the function, and, remarkably, persists even in the infinite-grid-density limit. In particular, gradient paths which are nearly, but not quite, aligned with move directions on the graph will lead to gradually-diverging steepest-ascent paths, as can FIG. . The divergence of steepest on-graph paths from the true gradient ∇f for different grids. At each step of the steepest-ascent path the gradient is followed as closely as possible on the graph, but small errors at each step accumulate and the paths eventually diverge. Note that the diagonal moves introduced into a uniform grid via triangulation help (more so in 3D), but do not remove the problem. The easiest way to see that this problem is scale independent is by considering the upper-left uniform grid case -the steepest ascent path will always be "upward" (the horizontal moves will never be taken), regardless of the grid spacing.