Bond-path

The second-order kappa index is determined by the count of two-bond paths, written P. The maximum value is expressed by a star shape = (A — 1) (A — 2) fl) and the mini-... 

Fig. 1.32. (a) Molecular graphs and electron density contours for pentane and hexane. Dots on bond paths represent critical points, (b) Comparison of molecular graphs for bicycloalkanes and corresponding propellanes. (Reproduced from Chem. Rev. 91 893 (1991) with permission of the American Chemical Society.)... 

The existence of alternative bond paths through a molecular skeleton as a consequence of the presence of cyclic subunits gives rise to a topological complexity which is proportional to the degree of internal connectivity. Topological strategies are those aimed at the retrosynthetic reduction of connectivity. 

The present interpretation of water structure is that water molecules are connected by uninterrupted H bond paths running in every direction, spanning the whole sample. The participation of each water molecule in an average state of H bonding to its neighbors means that each molecule is connected to every other in a fluid network of H bonds. The average lifetime of an H-bonded connection between two HgO molecules in water is 9.5 psec (picoseconds, where 1 psec =10 sec). Thus, about every 10 psec, the average HgO molecule... 

A richer fingerprint description is provided by the Daylight [45, 46] or UNITY (Tripos Inc., St. Louis) fingerprints. These incorporate a much broader range of features, notably including connected bond path fragments up to seven bonds long. 

The network of bond paths for a molecule is called its molecular graph. It is identical with the network of lines generated by linking together all pairs of atoms that are believed to be bonded to one another according to conventional bonding ideas such as Lewis structures. A bond path can therefore be taken as the AIM definition of a bond. 

Bond paths are usually but not always straight lines. For example, in a hydrocarbon containing a small ring (e.g., cyclopropane), the bond paths are curved outward from the inter-... 

We have discussed the properties of atoms in molecules. What can we find out about the bonds in a molecule We have seen that the bond path shows us where bonds are located in a molecule, that is, which atoms are bonded together because of the accumulation of elec-... 

The many higher boranes such as B5H9 and BgH 2 are similarly electron deficient and cannot be described by a single Lewis structure. They can often be described in terms of a combination of two- and three-center bonds. Alternatively, their structures can be rationalized by electron-counting schemes such as those proposed by Wade. Analysis of the electron density of these molecules by the AIM method shows that there are bond paths between all adjacent pairs of atoms. So from the point of view of the AIM theory there are bonds between each adjacent pair of atoms, but these cannot all be regarded as Lewis two-center, two-electron bonds as is the case in B2H6. 

We have seen in Chapter 6 (Figure 6.16) that there is only one bond path between carbon and oxygen in H2CO and this is the case for any CO bond, although this bond may be due to one, two, or three or any intermediate number of electron pairs. In this respect a CO bond is just like a CC bond. 

Figure 2. Contour maps of the electron density of (a) SCI2 and (b) H2O. The density increases from the outermost 0.001 au isodensily contour in steps of 2 x 10", 4 x 10", and 8 x 10" au with n starting at 3 and increasing in steps of unity. The lines connecting the nuclei are the bond paths, and the lines delimiting each atom are the intersection of the respective interatomic surface with the plane of the drawing. The same values for the contours apply to subsequent contour plots in this paper.

Figure 14. Contour plot of the electron density of B2H6 in the plane of the bridging hydrogen. Each hydrogen is connected to the two boron atoms by a bond path to each. In contrast, the boron atoms do not share a bond path linking them to one another. (See legend to Fig. 2 for contour values.)...

Bond paths are observed between bonded atoms in a molecule and only between these atoms. They are usually consistent with the bonds as defined by the Lewis structure and by experiment. There are, however, differences. There is only a single bond path between atoms that are multiply bonded in a Lewis structure because the electron density is always a maximum along the internuclear axis even in a Lewis multiple bond. The value of pb does, however, increase with increasing Lewis bond order, as is shown by the values for ethane (0.249 au), ethene (0.356 au), and ethyne (0.427 au), which indicate, as expected, an increasing amount of electron density in the bonding region. 

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. 

Bond paths are normally found in cases in which there is a bond as defined by Lewis. There is only one bond path for a multiple bond irrespective of the bond order. The bond order is, however, reflected in the value of pbcp. Bond paths are also found in molecules for which a single Lewis structure cannot be written. 

Silylation of AN is chemoselective (path (a)) that is, in no case does the silicon atom form the Si-C bond (path (b)). Moreover, if the initial AN contains a functional group at the a-C atom, the trialkylsilyl fragment in the resulting SENA is bonded, as a rule, to the oxygen atom of the nitro group. 

Fig. 7.2 A display of the trajectories of Vp for the same plane as in Fig. 7.1 d, complemented with arrows denoting the two unique trajectories that originate at the BCP, marked by an open circle, and terminate at each of the neighboring nuclei. They define the bond path.

The density is a maximum in all directions perpendicular to the bond path at the position of a bond CP, and it thus serves as the terminus for an infinite set of trajectories, as illustrated by arrows for the pair of such trajectories that lie in the symmetry plane shown in Fig. 7.2. The set of trajectories that terminate at a bond-critical point define the interatomic surface that separates the basins of the neighboring atoms. Because the surface is defined by trajectories of Vp that terminate at a point, and because trajectories never cross, an interatomic surface is endowed with the property of zero-flux - a surface that is not crossed by any trajectories of Vp, a property made clear in Fig. 7.2. The final set of diagrams in Fig. 7.1 depict contour maps of the electron density overlaid with trajectories that define the interatomic surfaces and the bond paths to obtain a display of the atomic boundaries and the molecular structure. 

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