Molecular skeleton, bond valence

Consider a molecular skeleton composed of n main-group atoms, M , which takes the form of a chain, ring, cage, or framework. Let g be the total number of valence electrons of the molecular skeleton. When a covalent bond is formed between two M atoms, each of them effectively gains one electron in its valence shell. In order to satisfy the octet rule for the whole skeleton, 5 (Sn—g) electron pairs must be involved in bonding between the M atoms. The number of these bonding electron pairs is defined as the bond valence b of the molecular skeleton ... 

When the total number of valence electrons in a molecular skeleton is less than the number of valence orbitals, the formation of normal 2c-2e covalent bonds is insufficient to compensate for the lack of electrons. In this type of electron-deficient compound there are usually found 3c-2e bonds, in which three atoms share an electron pair. Thus one 3c-2e bond serves to compensate for the lack of four electrons and corresponds to a bond valence value of 2, as discussed in 13.2. 

For a molecular skeleton consists of m transition-metal atoms and 2 main-group atoms, such as transition-metal carboranes, its bond valence is... 

The bond valence b of a molecular skeleton can be calculated from expressions (13.4.1) to (13.4.3), in which g represents the total number of valence electrons in the system. The g value is the sum of ... 

Similar to SMILES, InChI does not store atom coordinates. In contrast to SMILES, which by default omits hydrogen atoms that are then added implicitly to match the most common valency of an atom, InChI stores hydrogen atoms but does not store bond orders. These two techniques are just different approaches to the same problem for a given molecular skeleton, the bond orders and number of hydrogen atoms... 

The identifying characteristics of atoms include atomic number and number of electrons partitioned between valence electrons and core electrons. The immediate bonding environment of atoms in the molecular skeleton depends on the number and arrangement of the valence electrons and the number and type of bonds. In most graph theoretical methods, a hydrogen-suppressed skeleton is used to facilitate the counting and enumeration of skeletal features. 

This pair of delta values is seen as a characterization of the atom in its valence state. The simple delta, 5, describes the role of the atom in the skeleton in terms of its connectedness and count of sigma electrons it could be called the sigma electron descriptor. The valence delta, 8, encodes the electronic identity of the atom in terms of both valence electron count and core electron count. It could be called the valence electron descriptor. The isolated, unbonded atom may be thought of as characterized by its atomic number, Z, and the number of valence electrons, Z. In its valence state, the bonded atom is characterized by 8 and 8. Embedded in the molecular skeleton, the full characterization of the atom in the environment of the whole molecule is given by the topological equivalence value, described in a later section, and the electrotopological state value, presented separately.A representation of the whole molecule is accomplished by the combination of chi, kappa, and topological state indexes. 

The structure of an alkane consists of the carbon atoms connected to each other by the network of bonds and connected to an appropriate number of hydrogen atoms. This network of connections, called the molecular skeleton, consists of chemical bonds. From the valence bond viewpoint, the bond may be considered to be made up of the overlap of (7 type orbitals, although such a bonding interpretation is not necessary to our approach. It is this network of connections which determines the structure features of the molecule. It is this network which distinguishes among the structures of six-carbon alkanes such as hexane, 3-methylpentane, cyclohexane and methylcyclopentane. Having specified the molecular skeleton, one can deduce much of the structure information for a given molecule. 

Sheng" outlined an economical two-vertex elimination method for deciding whether a polycyclic ben-zenoid hydrocarbon has Kekule valence structure, and brothers He Wenjie (mathematician) and He Wenchen (chemist) discuss enumeration of Kekule structures using a matrix corresponding to peak and valley carbon atoms." ° We should also mention the quick and robust method of Kearsley" for assigning CC double bonds in a Kekule valence structure on the basis of an ordered fragmentation of the molecular skeleton. 

At the top left in Figure 101 we illustrate one of the four Kekule valence structures for one of the isomers of pyracylene. We decomposed this valence structure into its conjugated circuits R2, Rz, and Q3, outlined in the center of the top row over the molecular skeleton as the peripheries of azulene (twice) and the periphery of the molecule as a whole. We assume in this qualitative representation that the two Rz conjugated circuits will contribute a current of strength +1 in the positive (anti-clockwise) sense to each bond of the azulene periphery. On the other hand, the bonds that belong to the molecular periph-... 

In principle, a homodinuclear transition-metal species can form up to six bonds using the ns and five (n-l)d valence orbitals. In a simplified bonding description of Ar CrCrAr, the planar C-Cr-Cr-C skeleton has idealized molecular symmetry C2h with reference to a conventional z axis lying perpendicular to it. For each chromium atom, a local z axis is chosen to be directed toward... 

The mathematical chemist will recognize a as one of the Kekule valence-bond structures of the hydrocarbon, while is the corres nd-ing molecular graph Model is called an inner dual or dualist [2], is a caterpillar tree [3], and is called a Clar graph [4]. The latter two models are apparently quite different from the original skeleton, however, as it will turn out later, the topological properties of this benzenoid system are best modeled by either d or e-... 

When one (or more) hydrogen atom(s) of the polyethylene monomeric unit is (are) replaced by a heteroatom, an aliphatic or an aromatic group, modifications are induced in the valence band spectrum new peaks, band shift and/or splitting, redistribution of the electronic population among the molecular orbitals will denote the new bonds created in the molecule. Similar effects will be observed for the insertion of heteroatom(s) between two carbon elements of the polymer skeleton. 

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