Analytical representations of atomic partial charges and charge fluxes in dissociating systems

Atomic partial charges and their changes along dissociating coordinates are investigated in the model systems HF, [HF⋯H]⁺, H₂O, H₃O⁺, H₂O⋯HOH and [H₂O⋯H⋯OH₂]⁺. Ab initio calculations of dipole moment derivatives as computational observables representing the partial charges are presented. The results are fitted with an analytic distribution function of atomic partial charges that can capture the opposing limiting behaviors of dissociating X-H bonds in both protonated and unprotonated cases. Specifically, it is found that a Fermi-Dirac type distribution function provides a reasonable economical representation for charge transfer across bonds. Atom types in dissociating systems are necessarily variables and an appropriate atom type function is introduced as a parameter of the analytic charge distribution function.