Quantum Theory of Atoms in Molecules QTAIM

As the given example Illustrates, the concept of a chemical bond, which is so fundamental to our understanding of chemistry, is in fact a nebulous one. How, then, should we define a chemical bond One modern approach derives from the quantum theory of atoms in molecules (QTAIM or simply AIM), which was developed by Bader and his colleagues in the 1970s and paralleled the increasingly sophisticated development of computational quantum mechanical methods. The AIM approach is 

Electron contour diagram of diborane in the piane of the terminal H atoms. [Reproduced from J Amer Chem Soc 1979,707, 1389-1395. Used with permission of the American Chemical Society.] 

Another indicator of the percent ionic character in a chemical bond has to do with the atomic charge in a molecule. We have already shown how the different 

The atomic charge q(Q) can then be calculated by subtracting N(Q) from the atomic number Z, according to Equation (13.2)  

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The atoms defined in the quantum theory of atoms in molecules (QTAIM) satisfy these requirements [1], The atoms of theory are regions of real space bounded by a particular surface defined by the topology of the electron density and they have all the properties essential to their role as building blocks ... 

Recently, quantum calculations and topological analysis using the Quantum Theory of Atoms in Molecules (QTAIM) provide an explanation... 

The quantum theory of atoms in molecules (QTAIM) [25, 26] is based on analyses of the electron density distribution. The electron density of such systems such as simple molecules or ions, and also complexes, complex molecular and ionic aggregates, as well as crystals may be analyzed using this approach. QTAIM is a powerful tool that allows characterizing of various interactions covalent bonds, ionic bonds, van der Waals interactions and, what is the most important for this review, also HBs. The analysis of critical points of the electron density is very useful. For the critical points (CPs), the gradient of electron density, p(r), vanishes ... 

In the spirit of the opening quote of this chapter, the quantum theory of atoms in molecules (QTAIM) [63] has been extensively applied to classify and understand bonding interactions in terms of a quantum mechanical observable the electron density p(r). In this chapter we will take advantage of this theory to... 

SOME BASIC CONCEPTS OF THE QUANTUM THEORY OF ATOMS IN MOLECULES (QTAIM)... 

Parallel to the exciting reports about new types of hydrogen-hydrogen interactions, a paradigm shift was (and is) taking place in interpretative theoretical chemistry. Since the publication of Bader s classic monograph in 1990 [63], the quantum theory of atoms in molecules (QTAIM) has become a standard tool for the interpretation of theoretical and experimental [65-69] electron density distribution maps. The theory and its applications have been reviewed on a number of occasions by its principal author [63, 70-78] and by others [65-67, 69, 79-84]. A brief reminder of some of the basic concepts of QTAIM will be presented here with the sole purpose of keeping this chapter self-contained, but the interested reader is referred to the previously cited literature for in-depth treatments. 

Another interesting theory was proposed by Vila and Mosquera within the framework of the Quantum Theory of Atoms in Molecules (QTAIM) procedure. In particular, computational studies on 2-methoxyoxane and 2,2-dimethox5q>ropane as model systems, led to the conclusion that the... 

The Quantum Theory of Atoms in Molecules (QTAIM) [41, 42] is useful to characterize and classify inter- and intramolecular interactions [31] since it is possible to analyze the electron density of any system considered molecule, ion, complex, more or less complicated cluster, even the analysis of the electron density of crystals is possible [42, 43]. Figure 17.5 presents the molecular graph of... 

Shghtly earher than the appearance of NICS, attempts to construct numerical characteristics of the electron delocalization based on Bader s quantum theory of atoms in molecules (QTAIM) (1990MI) or electron localization function (ELF) (1990JCP5397) had begun. The most important for aromaticity description are electron sharing indices. For example, the delocalization index (DI) provides a value 6(A,B) which is the number of electrons delocalized or shared between atoms A and B. The next useful aromaticity... 

Historically, multiple theoretical descriptor-based approaches to H-bond strength ranking were proposed. That includes approaches based on group contribution method [46], electrostatic potentials [47], electrophilic superdelocalizability and self-atom polarizability [48], Quantum Theory of Atoms In Molecules (QTAIM) descriptors [49-51], the two-center shared electron number a and the product of ionization potential [45, 52], and local quantum mechanical molecular parameters, which quantify electrostatic, polarizability, and charge transfer contributions to H-bonding [53, 54],... 

The issue was investigated in detail by the whole cornucopia of contemporary theoretical methods, among them are the density functional theory (DFT), the electron localization function (ELF), the electron localization indicator (ELI), the quantum theory of atoms in molecules (QTAIM, vide infra Chap. 2) and the valence electron equivalent (/). DFT calculations and QTAIM topological analyses... 

The large maxima of the electron density are expected and are found at the nuclear positions Ra. These points are m-limits for the trajectories of Vp(r), in this sense they are attractors of the gradient field although they are not critical points for the exact density because the nuclear cusp condition makes Vp(Ra) not defined. The stable manifold of the nuclear attractors are the atomic basins. The non-nuclear attractors occur in metal clusters [59-62], bulk metals [63] and between homonu-clear groups at intemuclear distances far away from the equilibrium geometry [64]. In the Quantum Theory of Atoms in Molecules (QTAIM) an atom is defined as the union of a nucleus and of the electron density of its atomic basin. It is an open quantum system for which a Lagrangian formulation of quantum mechanics [65-70] enables the derivation of many theorems such as the virial and hypervirial theorems [71]. As the QTAIM atoms are not overlapping, they cannot share electron pairs and therefore the Lewis s model is not consistent with the description of the matter provided by QTAIM. 

Recently a chapter on the Quantum Theory of Atoms in Molecules (QTAIM) [1] was commissioned by editors Frenking and Shaik for their book on fundamental aspects of chemical bonding. This detailed and lengthy chapter has meanwhile been published [2], and features alongside authoritative chapters on alternative approaches such as EDA, NBO, Valence Bond, conceptual DFT, Block-localised... 

Nasertayoob P, Shahbazian S (2008) Revisiting the foundations of quantum theory of atoms in molecules (QTAIM) the variational procedure and the zero-flux conditions. Int J Quant Chem 108 1477-1484... 

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