Beginning from two theories, classical and quantum mechanical, as realized in terms of Newton’s second law and the time-independent Schrödinger equation, we put forth a framework for understanding the development of atomistic potentials that include chemistry. Our analysis introduces, explains, and exploits the Fragment Hamiltonian approach to the electronic structure of molecular and condensed matter systems. Illustrations of the Fragment Hamiltionian display the roles of various physical concepts in the formation of these atomistic potentials. Electron density fluctuations are clearly seen as essential to the realistic description of interatomic interactions over a large range of nuclear (ionic) configurations. Finally, we present a novel approach to the parameterization of interatomic potentials that explicitly include the effect of charge fluctuations, the environment-dependent dynamic charge potential.