  Fluctuating-charge models are computationally efficient methods of treating
polarization and charge-transfer phenomena in molecular mechanics and classical
molecular dynamics simulations. They are also theoretically appealing as they
are minimally parameterized, with parameters corresponding to the chemically
important concepts of electronegativities and chemical hardness. However, they
are known to overestimate charge transfer for widely separated atoms, leading
to qualitative errors in the predicted charge distribution and exaggerated
electrostatic properties. We present the charge transfer with polarization
current equilibration (QTPIE) model, which solves this problem by introducing
distance-dependent electronegativities. A graph-theoretic analysis of the
topology of charge transfer allows us to relate the fundamental quantities of
charge transfer back to the more familiar variables that represent atomic
partial charges. This allows us to formulate a unified theoretical framework
for fluctuating-charge models and topological charge descriptors. We also
demonstrate the important role of charge screening effects in obtaining correct
size extensivity in electrostatic properties. Analyzing the spatial symmetries
of these properties allows us to shed light on the role of charge conservation
in the electronegativity equalization process. Finally, we develop a water
model for use in classical molecular dynamics simulations that is capable of
treating both polarization and charge transfer phenomena.
