Bond path concept

A well-established approach for studying the bonds in strained molecules is by means of the bond path concept. A bond path corresponds to the ridge of highest electron density that links two nuclei. For many bonds, such as those between the carbons in propane, the bond path is essentially identical with the internuclear axis. In molecules with strained bonds, however, there can be a... 

The concept of a bond has precise meaning only in terms of a given model or theory. In the Lewis model a bond is defined as a shared electron pair. In the valence bond model it is defined as a bonding orbital formed by the overlap of two atomic orbitals. In the AIM theory a bonding interaction is one in which the atoms are connected by a bond path and share an interatomic surface. 

The theory of AIM allows one to study the concept of chemical bond and the bond strength in terms of electron density distribution function [6, 193]. It exploits the topological features of electron density and thereby a definition of chemical bonding through bond path and bond critical point (BCP). A BCP (it is a point at which gradient vector vanishes, Vp(r) = 0) is found between the... 

Before proceeding with the development of relating the pressure to the surface virial, it is useful to introduce a related concept, the interatomic surface virial. An atomic surface S( 2 r) consists in general, of a number of interatomic surfaces S( 2 2 r), one with each of its bonded neighbours, that is, atoms linked to it by bond paths. Correspondingly, the surface virial for the atom will consist of a sum of contributions, one for each bonded atom, and each bonded interaction will contribute to the pressure exerted on the atom. One has... 

In addition to the electron density contour lines in Figures 4.65 and 4.66, there are also essentially straight lines cormecting the nuclei. Each of these lines indicates a bond path, which follows the path of maximum electron density from one nucleus to another. The concept of a bond path is thus quite... 

Although AILs (bond paths) in AIM theory often coincide with our basic understanding of what a chemical bond is, this is not always the case. There has been a lot of debate on this topic in the literature, with the main source of disagreement arising from insufficient distinction between the AIM concept and our... 

Calculated electron density topologies for adamantane encapsulating a helium atom show four bond paths between the carbon cage and the noble gas, and 60 for the system He C6o- Use these data to discuss the difference in the concepts of chemical bonding in the conventional sense, and within the framework of AIM theory. 

Thus, in the case of the structures with small cycles (Fig. 1.6b and c) the bond paths are bent, which is an evidence in favor of the concept of bent (banana) bonds in these compounds. For pyramidal pentaborane B5H9 the molecular graph does not contain any bond paths between the basal boron atoms, which means that there is no concentration of the electron density in the basal plane (Fig. 1.6g). 

The bond path is always found to be accompanied by a shadow graph, the virial path, first discovered by Keith, Bader, and Aray [17]. The virial path is a line of maximally-negative potential energy density in three-dimensional space that links the same pair of atoms that share a bond path and an interatomic surface of zero-flux. No theoretical basis has ever been provided that requires the presence of a virial path as a doppelganger of every bond path that links two chemically bonded atoms, however, there is no known computational violation of this observation to date known to the authors. The presence of the virial path links the concept of chemical bonding directly with the concept of energetic stability as amply discussed in literature on QTAIM. 

Keywords Bond path Bond critical point Laplacian of the electron density Hydrogen bond Halogen bond Pnicogen bond Lewis acid-Lewis base interaction Quantum Theory of Atoms in Molecules (QTAIM) Natural Bond Orbitals (NBO) method o-hole concept Electrostatic potential... 

The aim of this chapter is to show, on the basis of several examples, how the location of the bond path may be useful to characterize, define and/or verify the specific, considered interaction. Mainly the QTAIM approach [4-7] is considered here however sometimes there are also references to other methods and concepts as for example the Namral Bond Orbitals (NBO) method [21, 22] or the o-hole concept [25-27]. This is worth to note that the results presented hereafter are mainly based on the MP2/aug-cc-pVTZ level of calculations those results are taken from earlier studies or the calculations were carried out especially for the purposes of this chapter. Consequently the QTAIM calculations were performed on the MP2/aug-cc-pVTZ wave functions. The binding energies (Ebin s) were calculated as differences between the energy of the complex and the sum of energies of monomers optimized separately and they were corrected for the basis set superposition error (BSSE) by the counterpoise method [28]. Since the NBO method is based on the Hartree-Fock method thus the corresponding NBO results, i.e. orbital-orbital interactions or atomic charges, if presented, are based on the HF/aug-cc-pVTZ//MP2/aug-cc-pVTZ level. Hence there is rather not indicated the level of calculations for the next systems discussed hereafter unless the results presented were obtained within other levels of calculations. 

The topological analysis of p(r) as formulated in the quantum theory of atoms in molecules (QTAIM) theory of Bader and co-workers [8] led to the concepts of bond path (BP) and bond critical point (BCP). The electron density along BP(r) descends steeply from each nucleus toward the unique intermediate stationary point BCP [9]. Because p r = tbcp) = Pbcp th 4S well as its Laplacian V pgcp are directly observable quantities from both experimental diffraction studies and ab initio calculations, pgcp Be the natural starting point when aiming to establish links of the bond valence approach to the physical world. 

As in molecular chemistry, an alternative path to compensate for electron deficiency is the formation of multiple bonds, through 7r-interactions, as in unsaturated and aromatic molecular systems. Our work in Houston focuses on probing the efficacy of the ZintI concept in rationaUzing stoichiometries, crystal structures and chemical bonding of complex electron-poof ZintI phases that exhibit novel i-systems. Their chemical bonding is reflected by their unusual crystal structures related to unsaturated hydrocarbons [53]. 

Enthalpies are often used to describe the energetics of bond formations. For example, when an amide forms through the condensation reaction between an ester and an amine, the new C-N bond, has an enthalpy of formation of -293 kj/mole. The higher the negative value for the bond enthalpy of formation, the stronger the bond. An even more useful concept is the enthalpy of a reaction. For any reaction, we can use the fact that enthalpy is a state function. A state function is one whose value is independent of the path traveled. So, no matter how we approach a chemical reaction, the enthalpy of the reaction is always the same. The enthalpy of... 

---