Conceptual Density Functional Theory

Abstract

Within the context of Density Functional Theory (DFT), Conceptual DFT (CDFT) has proven its merit for the analysis and interpretation of both experimental and theoretical studies of chemical phenomena, especially the thermodynamics and kinetics of chemical reactions. In the first part of this chapter, CDFT is introduced from a perturbative perspective. This approach exposes the machinery necessary to approximate reactivity indicators, computationally. Starting from an (approximate) energy model, E=E[v(r);N], a reference state is chosen which is usually the reactant molecule of interest. Its change in energy upon interaction with a second reactant, caused by changes in the number of electrons, N, and external potential, v(r), can then be written as a Taylor series where the expansion coefficients are partial derivatives with respect to N and/or functional derivatives with respect to v(r). These coefficients are only dependent on the (first) reactant, whereas the characteristics of the second reactant are reflected in the changes in N and v(r). The coefficients or response functions therefore characterize the intrinsic reactivity of the reactant molecule and can be considered reactivity indicators. These indicators are introduced up to third order in the expansion, and identified with chemical concepts, both in the canonical ensemble, characterized by the E=E[v(r);N] state function and in other Legendre-transformed ensembles. The Grand Canonical Ensemble with its associated Grand Potential Ω=Ω[v(r);µ] turns out to be more suitable for systems where the number of electrons is not easily controlled, paving the way to the description of open systems.