ABSTRACT
The advent of density functional theory (DFT) [1,2] has had a profound impact on quantum and computational chemistry. The ingenious proof, given in 1964 by Hohenberg and Kohn [1], that the wave function of a many-electron system
(atom, molecule, etc.), a function of the three spatial and a single spin coordinate of all N electrons of that system, could be replaced as basic carrier of information by the electron density function r(r), a function of only three spatial coordinates, offered a perspective for dramatic computational simplification of electronic structure calculations. The price to be paid was (and still is) the unknown exchange correlation potential vXC(r) also appearing in the working equations of DFT, the celebrated Kohn Sham equations [3], being the counterpart of the Hartree-Fock equations in wave function theory. Due to the efforts of many leading quantum chemists, exchange correlation potentials of ever increasing performance were presented in the past two decades (although sometimes suffering from heavy parameterization) [4] so that at this moment DFT is undoubtedly the main workhorse for computational studies on geometrical and electronic characteristics of molecular ground states and their evolution upon a chemical reaction, for molecules involving not too heavy main or transition group elements, representable by a single configuration [5]. On the other hand, since the pioneering work by Parr in the late 1960s [6], DFT turned out to be a highly valuable instrument for describing and interpreting chemical reactivity starting from sharper definitions of various traditional chemical concepts such as electronegativity, hardness, and softness. This branch of DFT, termed conceptual density functional theory [7], plays a fundamental role in understanding reactions on the basis of the properties of the individual reactions following Parr’s dictum ‘‘to calculate a molecule is not to understand it’’ [7] (for reviews see Refs. [8-12]). The basic ingredient is the perturbation expansion [13] of the energy of a system in terms of the two variables characterizing the Hamiltonian: the number of electrons N and the external potential v(r), i.e., the potential felt by the electrons due to the nuclei (the influence of external electromagnetic fields will be left out of consideration) [13-15]. The final aim is to describe the interaction between two systems A and B in terms of the coefficients @nE=@Nmdv(r)m
0 (n¼mþm0) of the isolated reactants
A and Bwhen expanding the E¼E[N, v(r)] functional. The latter quantities can easily be looked upon as response functions and can be global in nature (i.e., r-independent, e.g., the electronegativity x ¼ (@E=@N)v), local (i.e., r-dependent, e.g., the density itself r(r) ¼ dE=dv(r)Nð Þ, or nonlocal (i.e., dependent on two or more positions in space, e.g., the linear response function x(r, r0) ¼ d2E=dv(r)dv(r0) N (vide infra)).
