Empirical Versus Nonempirical Parameter Fitting

For a collection of N particles, we can express the total potential energy of the system V as a sum over contributions arising from interacting pairs, triplets, etc. 

A level of approximation intermediate between a completely nonempiri-cal and an empirical potential can be constructed by explicitly incorporating 

The effective potential in this formulation V ff, is not the same as Vgff iii Eq. [45]. Whereas an effective polarization was treated in Eq. [45] by assigning fitted charges commensurate with an enhanced dipole moment, the charges in Eq. [46] should correspond to the gas phase moments. Although the self-consistent dipole polarization does select all N-body interactions arising from dipole polarization, the corrections to higher order electrostatic moments— especially the quadrupole moments— are not properly accounted for. Three-body corrections to dispersion and repulsive components of the potential still remain in the effective two-body V ff term. 

---