A fast algorithm to compute atomic charges based on the topology of the electron density

This work proposes a novel algorithm to compute atomic charges as defined b y the theory of "atoms in molecules" (AIM). Using the divergence theorem it is possible to express the 3D volume integral over an atomic basin purely in terms of 2D surface integrals. Hence, it can be proven that an atomic ch arge is equal to the flux of the electric field of the whole molecule throu gh the atom's complete boundary. This boundary consists of the interatomic surfaces and the so-called outeratomic surface, which is the open side of t he atom. When fine-tuned the algorithm can generate atomic charges in the o rder of minutes without introducing any approximations. Moreover. the probl em of the geometrical cusp occurring in atomic basins and that of multiple intersections is also eliminated. The computational overhead of computing t he electric field (which is analytical) is compensated by the gain in compu ting time by eliminating one dimension of quadrature. The proposed algorith m opens an avenue to invalidate the oft-quoted drawback that AIM charges ar e computationally expensive. We explain the details of the implementation i n MORPHY01 and illustrate the novel algorithm with a few examples.