Modified Wolf electrostatic summation: Incorporating an empirical charge overlap

The original Wolf sum [D. Wolf et al., J. Chem. Phys. 110 (1999) 8254-8282] was modified to account for the effect of charge overlap in an empirical manner in order to correct the direct 1/r coulomb interaction in covalent systems. The resulting modified Wolf sum takes a form that is similar to the original one. More importantly, the inclusion of the charge overlap effect does not introduce any additional systematic error. Thus, the error analysis can be evaluated either analytically for 3D periodic systems or estimated numerically for general cases, which is the same as in the original Wolf sum. Application of this modified Wolf sum to covalent or partially covalent systems such as SiC and SiO₂ shows that it gives a more realistic description of the electrostatic interactions in those systems. Although the Wolf method does not conserve energy in principle, in practice the energy is conserved very well. Thus this method is particular suitable in molecular dynamics simulations.