A new local property, the local electron attachment energy [E(r)], is introduced and is demonstrated to be a useful guide to predict intermolecular interactions and chemical reactivity. The E(r) is analogous to the average local ionization energy but indicates susceptibility toward interactions with nucleophiles rather than electrophiles. The functional form E(r) is motivated based on Janak's theorem and the piecewise linear energy dependence of electron addition to atomic and molecular systems. Within the generalized Kohn-Sham method (GKS-DFT), only the virtual orbitals with negative eigenvalues contribute to E(r). In the present study, E(r) has been computed from orbitals obtained from GKS-DFT computations with a hybrid exchange-correlation functional. It is shown that E(r) computed on a molecular isodensity surface, ES(r), reflects the regioselectivity and relative reactivity for nucleophilic aromatic substitution, nucleophilic addition to activated double bonds, and formation of halogen bonds. Good to excellent correlations between experimental or theoretical measures of interaction strengths and minima in ES(r) (ES,min) are demonstrated.