An efficient grid-based scheme to compute QTAIM atomic properties without explicit calculation of zero-flux surfaces

We introduce a method to compute atomic properties according to the "quantum theory of atoms in molecules." An integration grid in real space is partitioned into subsets, ω_i. The subset, ω_i, is composed of all grid points contained in the atomic basin, Ω_i, so that integration over Ω_i is reduced to simple quadrature over the points in ω_i. The partition is constructed from deMon2k's atomic center grids by following the steepest ascent path of the density starting from each point in the grid. We also introduce a technique that exploits the cellular nature of the grid to make the algorithm faster. The performance of the method is tested by computing properties of atoms and nonnuclear attractors (energies, charges, dipole, and quadrupole moments) for a set of representative molecules.