Bond path network

A full description is beyond the scope of this review, but it is noted that the topological method identifies other chemical features in the electron density. The union of all bond paths gives a bond path network that is normally in a 1 1 correspondence with the chemical bond network drawn by chemists. The bond paths for bonds in strained rings are curved, reflecting their bent nature. In Figure 6, we show the gradient paths in the molecular plane of cyclopropane. The C—C bond paths are distinctly bent outward. The value of the Laplacian at the bond critical point discriminates between ionic and covalent bonding." Maps of the Laplacian field reveal atomic shell structure, lone pairs, and sites of electrophilic and nucleophilic attack. The ellipticity of a bond measures the buildup of density in one direction perpendicular to the... 

Another situation that deserves caution is the general 1 1 correspondence between chemical bonding networks and bond path networks. The union of all bond paths in a molecule, called the bond path network, is usually coincident with the chemical structures normally written. However, a number of ground state structures possess additional bond paths. > For example, in meth-... 

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... 

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. 

Malta and co-workers [41] conclude that stability of the molecules investigated is explained partially in terms of the energy that is necessary to disrupt the encasing network of these H-H bond paths. These interactions must be ubiquitous, and their stabilization energies contribute to the sublimation energies of hydrocarbon molecular crystals. 

The mathematical theory of topology is the basis of other approaches to understanding inorganic structure. As mentioned in Section 1.4 above, a topological analysis of the electron density in a crystal allows one to define both atoms and the paths that link them, and any description of structure that links pairs of atoms by bonds or bond paths gives rise to a network which can profitably be studied using graph theory. 

Molecular geometry Molecular graph Network of bond paths plus bond critical points... 

It has been demonstrated that the network of bond paths defined by the unique axis of the [3, —1] critical points coincides with the network formed by linking together those pairs of atoms which are presumed to be bonded chemically. 

Networked multiple bond paths (in-plane carrier mobility)... 

The topology of p for fee transition metals (y5-Co, Ni, Cu, Rh, Pd, Ag, Ir, Pt, and Au) was studied and all BCPs in the unit cell systematically calculated. The network of bond paths describing the atomic connectivity confirms that the crystal graph of these metals is the result of packing octahedra and tetrahedra. A good correlation between the experimental cohesive energy and p at the BCP corroborates that this parameter provides a measine of the bond strength in transition metals. 

Matter is a distribution of charge in real space-of pointUke nuclei embedded in the diffuse density of electronic charge, p(r), defined as the expectation value of the density operator... A molecular graph, the linked network of bond paths, defines a system s molecular structure. 

Formation of the hydrogen-bonded water networks may affect conductivity of a system in a drastic way, as these networks provide the paths for the conduction of protons, ions, or other charges in the system. So, the qualitative changes in the conductivity may be expected at hydrations, close to the percolation transition of water. Surface conductivity of quartz increases relatively slowly with increasing hydration level until the completion of the adsorbed water monolayer, but much faster at higher hydrations [582]. The hydration dependence of the dielectric losses of hydrated collagen... 

The crucial reaction intermediate PCHA in the HDN network of quinohne-type compounds has been clearly observed. Formation of cis-PCHA was faster than that of trans-PCHA, but isomerization was relatively rapid. The presence of H2S in the reaction stream favours the cleavage of the first C-N bond in DHQ, but slows down the C-N bond cleavage in PCHA. The presence of H2S decreases the adsorption constants of DHQ and NH.i. It is concluded that 40% of the HDN reaction of DHQ takes place through the reaction path of DHQ- THQl->OPA —>HC at 593 K and 3.0 MPa in the absence of H2S, while less than 10% takes place in the presence of H2S. 

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