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In a recent paper J. Am. Chem. Soc. 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, Upsilon(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 Brönsted-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 Brönsted-Lowry acids and bases.
Ayers et al. (Sat,) studied this question.