Conceptual Density Functional Theory in the Grand Canonical Ensemble

Conceptual density functional theory is nowadays an important tool for the analysis of chemical reactivity. In this chapter, the theoretical framework provided by the grand canonical ensemble is used to present a general perspective of this approach through the analysis of the total differentials of the average electronic energy, density and chemical potential in terms of the average number of electrons, the external potential and the temperature. Then, by making use of the three ground states ensemble, the finite temperature expressions for the electronic chemical potential, hardness, Fukui function, dual descriptor, thermodynamic hardness and thermodynamic dual descriptor, together with the local counterparts of the global indexes and the non‐local counterpart of the local indexes are discussed. Their zero temperature limits provide the numerical values that should be used for these reactivity parameters at temperatures of chemical interest. Thus, through this procedure one can examine all the fundamental features of the original development of conceptual density functional theory, but complemented with the consequences of temperature in the formal aspects and in the study of the reactivity principles.