where ρ k 0 (r) is the transition density coupling the kth state to the ground state. From a link between conceptual DFT and statistical thermodynamics, it has been shown that the perturbation energy due to intermolecular electrostatic interactions can be understood in terms of effective work and heat exchange, 484 the first-order correction ρ (r) δ v (r) dr being the effective work and the second-order correction in eqn (60) being the heat exchange. A polarization entropy and a polarization temperature can also been defined by this analogy. Therefore, using the external electrostatic potential as a probe and the polarization energy, entropy, and density as electronic responses, one can get qualitative and quantitative insight into the reactivity and the selectivity of molecular fragments. 483 (3.9.5) Fuentealba : One should not forget that, along with density functionals, one has density functions as a special case. Ramon Carbó-Dorca Carre has studied the mathematical structure of such functions. (3.9.6) Ayers : One advantage of the popularity of DFT is that it gave publicity to methods based on the direct analysis of the the electron density (and higher-order electron distribution functions), some of which developed concurrently with, or even predated, the emergence of modern DFT. Simply stated, DFT is a useful method not only for predicting reactivity as discussed in contribution (3.9.1) but also for describing and characterizing molecular electronic structure. Indeed, the framework of the quantum theory of atoms in molecules (QTAIM) and more generally quantum chemical topology (QCT) 487 were largely developed alongside DFT, and use the same quantities (notably the density and its derivatives, various energy densities, and various strategies for characterizing, representing, and approximating the exchange-correlation hole) to obtain insight into molecular structure and chemical bonding. Importantly, DFT can resolve a bottleneck problem of wave-function theory and DMFT regarding the reliable description of dynamical electron correlation. Indeed, nondynamical correlation can be efficiently accounted for with the small CAS CI and DMRG ab initio approaches or with DMFT functionals of the extended Löwdin-Shull (ELS) type, all in relatively small basis sets. It is the description of the residual dynamical correlation, which requires the inclusion of prohibitively many CI excitations in a sufficiently large basis, or many very weakly occupied natural orbitals, which is difficult to describe with approximate DMFT functionals.