Improved grid-based algorithm for Bader charge allocation

An improvement to the grid-based algorithm of Henkelman et al. for the calculation of Bader volumes is suggested, which more accurately calculates atomic properties as predicted by the theory of Atoms in Molecules. The CPU time required by the improved algorithm to perform the Bader analysis scales linearly with the number of interatomic surfaces in the system. The new algorithm corrects systematic deviations from the true Bader surface, calculated by the original method and also does not require explicit representation of the interatomic surfaces, resulting in a more robust method of partitioning charge density among atoms in the system. Applications of the method to some small systems are given and it is further demonstrated how the method can be used to define an energy per atom in ab initio calculations.