QTAIM molecules

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 ... 

The atomic properties satisfy the necessary physical requirement of paralleling the transferability of their charge distributions - atoms that look the same in two molecules contribute identical amounts to all properties in both molecules, including field-induced properties. Thus the atoms of theory recover the experimentally measurable contributions to the volume, heats of formation, electric polarizability, and magnetic susceptibility in those cases where the group contributions are found to be transferable, as well as additive additive [4], The additivity of the atomic properties coupled with the observation that their transferability parallels the transferability of the atom s physical form are unique to QTAIM and are essential for a theory of atoms in molecules that purports to explain the observations of experimental chemistry. 

Atomic volumes play an important role in relating physicochemical properties to biological effects. Most atoms in molecules are not entirely bounded by interatomic surfaces and an atomic volume is defined as a measure of the space enclosed by the intersection of the atom s zero-flux surfaces with some outer envelope of the density. The envelope with a value of 0.001 au is generally chosen as this has been shown to yield molecular sizes in good agreement with experimentally assigned van der Waals radii [16, 17]. A related property is the van der Waals surface area, which QTAIM determines by integrating an atom s exposed contribution to a molecule s isovalued surface. 

Two objects are similar and have similar properties to the extent that they have similar distributions of charge in real space. Thus chemical similarity should be defined and determined using the atoms of QTAIM whose properties are directly determined by their spatial charge distributions [32]. Current measures of molecular similarity are couched in terms of Carbo s molecular quantum similarity measure (MQSM) [33-35], a procedure that requires maximization of the spatial integration of the overlap of the density distributions of two molecules the similarity of which is to be determined, and where the product of the density distributions can be weighted by some operator [36]. The MQSM method has several difficulties associated with its implementation [31] ... 

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

That molecules do have definite bonds, and that these tend to correspond in direction and number to the conventional bonds of simple valence theory, is indicated by the quantum theory of atoms-in-molecules (AIM, or QTAIM) [2], This is based on an analysis of the variation of electron density in molecules. 

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 ... 

The QTAIM parameters may also be useful to analyze the other interactions, for example, the intramolecular DHBs. Similarly, as it is in the case of HBs where the proton donor and the proton acceptor may belong to the same species, malonalde-hyde is an example for the existence of intramolecular HB. Figure 12.6 presents the relief map of the species where intramolecular O-H—H-B interaction exists [30]. 7 This relief map is displayed in the plane of the molecule. Interestingly, the intramolecular DHBs often occur in the crystal structures. The first studies on DHBs in crystals of metal-organic compounds have also examined this type of interactions [11],... 

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. 

Bader has shown that the topological partitioning of the molecules into atomic basins coincides with the requirements of formulating quantum mechanics for open systems [93], and in this way all the so-called theorems of quantum mechanics can be derived for an open system [94], Furthermore, the zero-flux condition, Eq. 1, turns out to be the necessary constraint for the application of Schwinger s principle of stationary action [95] to a part of a quantum system [93], The successful application of QTAIM to numerous chemical problems has thus deep physical roots since it is a theory which expands and generalises quantum mechanics themselves to include open and total systems, both treated on equal formal footing. 

Abstract In this chapter we discuss the influence of ir-electron delocalization on the properties of H-bonds. Hence the so-called resonance-assisted hydrogen bonds (RAHBs) are characterized since such systems are mainly classified in the literature as those where TT-electron delocalization plays a very important role. Both the intramolecular and intermolecular RAHBs are described. RAHBs are often indicated as very strong interactions thus, their possible covalent nature is also discussed. Examples of the representative crystal structures as well as the results of the ab initio and DFT calculations are presented. Additionally the RAHB systems, and the other complexes where rr-electron delocalization effects are detectable, are characterized with the use of the QTAIM (Quantum Theory Atoms in Molecules ) method. The decomposition scheme of the interaction energy is applied to expand the knowledge of the nature of the RAHBs. 

To provide more insight into the nature of heteronuclear intermolecular RAHBs, ab initio calculations at the MP2/6-311++G(Quantum Theory Atoms in Molecules ) calculations were performed for the formamide dimer (Fig. 13) and its simple fluoro derivatives... 

Since the appearance of the paper by Pendas [50], QTAIM has progressed and the atomic statement of the virial theorem can now be applied to define the energy of an atom in a molecule in non-equilibrium situations [51]. 

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 quahtative bonding model for stmcture B is supported by a topographical analysis of the calculated electronic structure which rests on the QTAIM (Quantum Theory of Atoms in Molecules) method. Figure 2.7 shows the Laplacian of... 

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