We present an overview of the energy functions used in two Anisotropic Polarizable Molecular Mechanics (APMM) procedures namely SIBFA (Sum of Interactions Between Fragments Ab initio computed) and GEM (Gaussian Electrostatic Model). As SIBFA is a second generation APMM scheme based on distributed multipoles, GEM is the first third generation APMM as it uses distributed hermite densities obtained from density fitting. The two approaches are formulated and calibrated on the basis of quantum

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... try. They embody nonclassical effects such as electrostatic penetration, exchange-polarization, and charge transfer. We address here the technical issues of anisotropy, nonadditivity, transferability and computational speedup of methods. In addition, we review the several ab initio intermolecular energy decomposition techniques that can be used to refine polarisable force fields. As we summarize their differences and similarities, we present our own scheme based on Fragment Localized Kohn-Sham orbitals through a Singles-Configuration Interaction (CI) procedure. We also present a chemically intuitive method based on the Electron Localization Function (ELF) which allows to unravel the local electrostatic properties beyond atomic centers: i.e., on bonds, lone pairs and π system, an useful asset to understand bonding in molecules in order to build models