Expectation Value Averages of Size Consistent Hermitian Operators and the Definition of Fukui Functions

摘要

The Ayers expectation value of size consistent operator averages is analyzed, leading to a general description of Fukui functions in terms of a possibly multidimensional gradient. The expectation value involves the density of an arbitrary collective of chosen ions or excited states. Molecular Orbital (MO) densities and Fukui functions are proved to be connected through the gradient of the first order state density functions with respect to the MO occupation numbers. The mathematical development taken as a whole opens the way to a general framework, where Fukui functions arise as a general theoretical tool to study molecular reactivity. Finally, shape functions appear as a plausible link between Ayers framework and the general ideas presented in this study.