Interacting Quantum Atoms—A Review

Abstract

The aim of this review is threefold. On the one hand, we intend it to serve as a gentle introduction to the Interacting Quantum Atoms (IQA) methodology for those unfamiliar with it. Second, we expect it to act as an up-to-date reference of recent developments related to IQA. Finally, we want it to highlight a non-exhaustive, yet representative set of showcase examples about how to use IQA to shed light in different chemical problems. To accomplish this, we start by providing a brief context to justify the development of IQA as a real space alternative to other existent energy partition schemes of the non-relativistic energy of molecules. We then introduce a self-contained algebraic derivation of the methodological IQA ecosystem as well as an overview of how these formulations vary with the level of theory employed to obtain the molecular wavefunction upon which the IQA procedure relies. Finally, we review the several applications of IQA as examined by different research groups worldwide to investigate a wide variety of chemical problems.

A Critical Overview of Current Theoretical Methods of Estimating the Energy of Intramolecular Interactions

“…The first of these methods was proposed by Espinosa et al [ 115 ] and it is based on a quantity computed at the bond critial point of the interaction, the energy of which is to be determined. The another method is based on the partition of the total energy of a system into individual monoatomic and diatomic contributions and functions under the name of Interacting Quantum Atoms (IQA) [ 116 , 117 ]. These two methods will now be discussed in the next two subsections.…”

“…As already mentioned, the Interacting Quantum Atoms (IQA) approach [ 116 , 117 ], which is based on QTAIM, allows for the total energy of a system to be divided into mono- and polyatomic components. Among many energy terms available by means of IQA, the most important one in the context of this article is the interatomic interaction energy defined as follows where is the repulsion energy between nuclei of atoms E 1 and E 2 , is the attraction energy between electrons of the atom E and the nucleus of the atom E 2 , is the attraction energy between the nucleus of the atom E and the electrons of the atom E 2 , and is the interatomic two-electron repulsion energy.…”

“…As already mentioned, the Interacting Quantum Atoms (IQA) approach [116,117], which is based on QTAIM, allows for the total energy of a system to be divided into mono-and polyatomic components. Among many energy terms available by means of IQA, the most important one in the context of this article is the interatomic interaction energy defined as follows…”

Energetics of Electron Pairs in Electrophilic Aromatic Substitutions

“…Electron-nuclear attractions are density dependent quantities that are not expected to respond clearly to X effects, so they will be skipped in this first contribution. As repeatedly shown [ 25 ], V xc is a measure of the covalent energy associated to the interaction between the electrons contained in domains A and B. For the sake of clarity and given its direct connection with the delocalization index, we represent V xc for the pairs of basins under study with respect to benzene (Δ V xc ) basins in Figure 6 (see Supplementary Table S4 for the numeric values of the complete set of molecules).…”

“…To do that we exploited the topology induced by the Electron Localization Function (ELF) proposed by Becke [ 17 ], given its ability to define electron pair regions in real space [ 18 ], and its good performance in the understanding of chemical properties and structure [ 19 , 20 ], as well as in reactivity [ 21 , 22 ]. We coupled the ELF with the interacting quantum atoms (IQA) approach [ 23 , 24 ], a powerful real-space quantum-chemical topology tool that allows partitioning the total energy of a system into chemically meaningful contributions, and has also been successfully applied in the analysis of a number of chemical phenomena from an intuitive chemical bond perspective [ 25 , 26 , 27 ]. With this methodology, it was shown that all kinetic, electrostatic, and exchange-correlation terms for the electron pairs follow straightforward scaling laws that were proven to be valid in widely different bonding regimes, ranging from homopolar to highly polar.…”