The most striking and counterintuitive consequences of quantum mechanics play out in the strong correlations of many-particle systems. The physics of these phenomena are exponentially complicated and often non-local. In chemistry, these strong correlations are vital to even qualitative pictures of chemical bonding, but they grow intractably more numerous with the number of particles and remain a significant challenge for models of chemical behavior. Luckily, the strong correlations relevant to most chemical situations can be significantly simplified and compressed using the heuristics which have been developed by chemists up to present day: ideas like bonding electron pairs, and resonance. In this thesis we present a convergent and systematically improvable series of approximations to the many-electron Schro ̈dinger equation which exploit these patterns. Two themes dominate the work: the use of bonding electron pairs as local units for developing efficient models, and an exponential parameterization of the many-electron wave-function.