Abstract. Activation is a fundamental and well-known concept in chemistry. It may be qualitatively de®ned as an increase in the chemical reactivity pattern of a molecule at a given site k when the system is locally perturbed at a dierent site l, say. This external perturbation arise from a localized molecular rearrange- ment, a substitution, a selective solvation or simply by the approach of a reagent of variable hardness. This work presents a theoretical approach intending to quantify this activation concept in the density functional framework. This is done here by ®rst calculating the ¯uctuation of the electron density at a given site k for the ground state of the isolated substrate (static reactivity model) and then incorporating the substrate and model electrophile reagents in a spatial disposition related to a virtual transition structure for the parent system. This perturbation is assumed representable by local changes in the external potential. It is shown that a local approximation to the softness kernel s(r, r¢) yields a simple expression for the ¯uctuation of the electron density dq(r k ), which shows that this change becomes proportional to the variation of an eective potential du(r k ), containing the information on the variation in the chemical potential and the external perturbing potential at site k; the proportionality constant being the local softness s 0 (r k ) at that site. The strong local approxi- mation made to the kernel s(r, r¢) causes the second reactivity site (l) to implicitly appear in the formulation through the changes in the electronic chemical potential term. It is shown that the introduction of a less restrictive approach to the linear response function, obtained from a model Kohn-Sham one-electron density matrix, leads to the same result. Non-locality is therefore self-contained in the electronic chemical potential con- tribution to the modi®ed potential, and may be associ- ated with an intramolecular charge transfer between the active sites of the ambident nucleophilic/electrophilic substrate, promoted by the presence of the reagents. The resulting formulation of pair-site reactivity is illustrated for the electrophilic attack on the CN ) ion by dierent model electrophile agents of variable hardness. It is shown that correct reactivity indexes are obtained only when the topology of the transition structure is used as a vantage point to perturb the CN ) ion. The calculations were performed at both density functional theory and ab-initio Hartree-Fock levels. The results show that the proposed model is independent of the method used to obtain q(r). Key words: Chemical reactivity ± Density functional ± Non-local reactivity ± Response function ± CN ± Cyanide ion reactivity 1 Introduction Reactivity indexes have been introduced in chemistry since the early days of empirical molecular orbital approaches. Derivatives of the energy with respect to the a-parameter in the HuÈckel approach were extremely useful to study the reactivity of particular centers of polynuclear p-electron molecules. In a chemical reaction, be it in gas phase, liquid or solid state, there are two major factors determining the way atoms and molecules are interconverted into dierent species. The ®rst concerns the relative energies of reagents and products which determine the thermodynamic properties of the process. The second involves mechanistic and kinetic aspects. Modern quantum chemistry provides useful tools to rationalize and predict the thermodynamics involved in chemical reactions. For instance, in density functional theory (DFT), there are a number of global properties that have been used in connection with the energetic aspects that determine the relative stability of dierent reacting species, and energy barriers to inter- conversion between reagents and products [1±4]. One of the most useful global descriptors of chemical reactivity is the electronic chemical potential l [1±3], de®ned as the derivative of the electronic energy E with respect to the * On leave from Departamento de QuõÁmica, Facultad de Ciencias, Universidad de Chile, Casilla 653-Santiago, Chile Correspondence to: O. Tapia Regular article Theory of non-local (pair site) reactivity from model static-density response functions Renato Contreras 1,3 *, Juan AndreÂs 1 , Patricia PeÂrez 1,3 *, Arie Aizman 2 , Orlando Tapia 3 1 Departament de CieÂnces Experimentals, Universitat Jaume I, Box 242, E-12080, CastelloÂ, Spain 2 Facultad de Ciencia, Universidad F. Santa MarõÁa, Casilla 110-V, ValparaõÁso, Chile 3 Department of Physical Chemistry, Uppsala University, Box 532-75121, Uppsala, Sweden Received: 30 September 1997 / Accepted: 30 December 1997 Theor Chem Acc (1998) 99:183±191