Finite difference representation of information-theoretic approach in density functional theory

Using density-based quantities to establish a qualitative or even quantitative framework to predict molecular reactivity in density functional theory is of considerable interest in the current literature. Recent developments in information-theoretic approach (ITA) represent such a trend. Traditionally, we represent ITA quantities in terms of the electron density, shape function, and atoms in molecules. In this contribution, we expand the theoretical framework of ITA by introducing a new representation. To that end, we make use of the first-order partial derivative of ITA quantities with respect to the number of total electrons and then approximate them in the finite difference approximation. The new representation has both local (three-dimensional) and global (condensed to atoms) versions. Its close relationship with Fukui function from conceptual density functional theory was derived analytically and confirmed numerically. Extensions of our present approach to include other types of derivatives are discussed. This work not only enriches the theoretical framework of ITA with a new representation, but also provides opportunities to expand its territory as well as the scope of its applicability in dealing with molecular processes and chemical reactivity from a new perspective.