In a recent paper [J. Am. Chem. Sec. 2000, 122, 2010], the authors explored variational principles that help one understand chemical reactivity on the basis of the changes in electron density associated with a chemical reaction. Here, similar methods are used to explore the effect changing the external potential has on chemical reactivity. Four new indices are defined: (1) a potential energy surface that results from the second-order truncation of the Taylor series in the external potential about some reference, Y(R-1,R-2,...,R-M); (2) the stabilization energy for the equilibrium nuclear geometry (relative to some reference), Xi; (3) the flexibility, or "lability", of the molecule at equilibrium, Lambda; and (4) the proton hardness, Pi, which performs a role in the theory of Bronsted-Lowry acids and bases that is similar to the role of the chemical hardness in the theory of Lewis acids and bases. Applications considered include the orientation of a molecule in an external electric field, molecular association reactions, and reactions between Bronsted-Lowry acids and bases.