where all ∆ρ(r) belonging to fragment I are defined to integrate to zero. As electron densities of isolated molecules decay exponentially as a function of distance from their nuclei, we use Slater like densities for both ρ 0 and ∆ρ. While each may share the same center R i , there is no particular reason why they they have to have the same decay rate. As such, each density type has their own different exponential factors ζ frz and ζ pol ,