  We introduce a general framework for many-body force field models, the
Completely Multipolar Model (CMM), that utilizes multipolar electrical moments
modulated by exponential decay of electron density as a common functional form
for all piecewise terms of an energy decomposition analysis of intermolecular
interactions. With this common functional form the CMM model establishes
well-formulated damped tensors that reach the correct asymptotes at both long-
and short-range while formally ensuring no short-range catastrophes. The CMM
describes the separable EDA terms of dispersion, exchange polarization, and
Pauli repulsion with short-ranged anisotropy, polarization as intramolecular
charge fluctuations and induced dipoles, while charge transfer describes
explicit movement of charge between molecules, and naturally describes
many-body charge transfer by coupling into the polarization equations. We also
utilize a new one-body potential that accounts for intramolecular polarization
by including an electric field-dependent correction to the Morse potential to
ensure that the CMM reproduces all physically relevant monomer properties
including the dipole moment, molecular polarizability, and dipole and
polarizability derivatives. The quality of the CMM is illustrated through
agreement of individual terms of the EDA and excellent extrapolation to
energies and geometries of an extensive validation set of water cluster data.
