The Quantum Theory of Atoms in Molecules: bond paths, chemical bonds and chemical binding

Defining and characterizing a chemical bond through the existence of, and the properties at the associated bond critical point (BCP), is at the core of the Quantum Theory of Atoms in Molecules (QTAIM) study of chemical bond in molecules and crystals. However, this association is also a continuous source of controversies, misinterpretations and misuses. One of the recurrent criticisms that are encountered in the literature is related to the physical meaning of bond paths and BCPs. In this lecture, after introducing a number of recently discussed cases, it will be shown how much of the existing controversies have their origin in the main drawback of current QTAIM energetic analyses: a lack of interaction energy terms between quantum atoms. By introducing the interacting quantum approach (IQA) into the QTAIM formalism, the total energy of a system may be written as a sum of atomic self-energies, which contain all the intra-atomic terms, plus a sum of pair-wise additive interaction energies, which may be further decomposed into a classical electrostatic component and a stabilizing quantum-mechanical correction, the exchange-correlation potential energy. Using IQA, it emerges that bond paths between an atom A and the atoms B in its environment are determined by a competition among the A–B exchange–correlation energies, which always contribute to stabilize the A–B interactions.