Average local ionization energy generalized to correlated wavefunctions

The average local ionization energy function introduced by Politzer and co-workers [Can. J. Chem. 68, 1440 (1990)] as a descriptor of chemical reactivity has a limited utility because it is defined only for one-determinantal self-consistent-field methods such as the Hartree-Fock theory and the Kohn-Sham density-functional scheme. We reinterpret the negative of the average local ionization energy as the average total energy of an electron at a given point and, by rewriting this quantity in terms of reduced density matrices, arrive at its natural generalization to correlated wavefunctions. The generalized average local electron energy turns out to be the diagonal part of the coordinate representation of the generalized Fock operator divided by the electron density; it reduces to the original definition in terms of canonical orbitals and their eigenvalues for one-determinantal wavefunctions. The discussion is illustrated with calculations on selected atoms and molecules at various levels of theory.