Numbering skeletal atoms

R for r-bond to another carbon P for p-bond to carbon and Z for bond (r- or p-) to electronegative heteroatom. The numbers of each kind of attachment are then h, r, p, z, respectively, and add up to four. This is summarized in Figure 3, which also indicates that, if its skeleton is known and numbered, any molecule can be described by a digital zp-list, generalizing its functionality, over the numbered skeletal atoms. This yields a specific, though abstracted, full description of any molecule in a linear bit list suited to computer manipulation. The skeleton itself is digitally... 

For main group elements the number of framework electrons contributed is equal to (t + a — 2) where v is the number of valence shell electrons of that element, and x is the number of electrons from ligands, eg, for Ff, x = and for Lewis bases, x = 2. Examples of 2n + 2 electron count boranes and heteroboranes, and the number of framework electrons contributed by their skeletal atoms, ate given in Table 1. 

Because atoms are neither created nor destroyed, chemists regard each elemental symbol as representing one atom of the element (with the subscripts giving the number of each type of atom in a formula) and then multiply formulas by factors to show the same numbers of atoms of each element on both sides of the arrow. The resulting expression is said to be balanced and is called a chemical equation. For example, there are two H atoms on the left of the preceding skeletal equation but three H atoms on the right. So, we rewrite the expression as... 

The octahedron is classified into the c/o o-structure by Wade [3,4]. Closo-structures with n skeletal atoms are stable when they have 4n-i- 2 valence electrons. Wade s rules predict that the 26 (= 4 x 6 + 2) valence electrons could stabilize the regular octahedrons since n is 6 for the octahedron. This prediction is contained in our 6N + 14 (N= 2) valence electron rule. Our rule also predicts the stability of octahedral metal clusters with the other numbers (14 and 20) of valence electrons. 

The most basic element in the molecular structure is the existence of a connection or a chemical bond between a pair of adjacent atoms. The whole set of connections can be represented in a matrix form called the connectivity matrix [249-253]. Once all the information is written in the matrix form, relevant information can be extracted. The number of connected atoms to a skeletal atom in a molecule, called the vertex degree or valence, is equal to the number of a bonds involving that atom, after hydrogen bonds have been suppressed. 

The problems outlined in the previous section can be avoided if, instead of allocating the skeletal bonding electron pairs to localized bonds, one simply compares their number with the number of skeletal bonding MO s (199). The closo, nido, and arachno structures of boranes and carboranes can then be seen to reflect the numbers of skeletal bond pairs that are available to hold their skeletal atoms together. 

The polyhedra in Fig. 1 thus represent suitable shapes for cluster species with n skeletal atoms (each of which can furnish three AO s for use in skeletal bonding) and with (n + 1) skeletal bond pairs. Since it is the cluster symmetry that determines the number of bonding MO s, the same polyhedra can serve as the basis for the structures of a whole range of isoelectronic species, including neutral carboranes of formula C2B 2Hn, bismuth clusters, such as the trigonal-bipyramidal Bis " ",... 

Tables II and III list the numbers of electrons provided by various potential cluster units, assuming that the skeletal atoms make available three AO s apiece for skeletal bonding, and use their remaining valence shell orbital(s) to bond ligands to the cluster. For example, a main group element E (Table II) such as boron can make three AO s available for cluster bonding if it uses its one remaining valence shell AO (an inert...

The C—C and C—B interatomic distances in carboranes can also be related to the coordination numbers of the skeletal atoms. Two factors tend to make these distances shorter than the B —B distances in comparable boranes the preference of the carbon atoms for sites of low coordination number and the greater electronegativity of carbon than boron, which increases the electron density in the region of the carbon atoms and so strengthens the bonds that they form. Table IX lists some C—C distances for closo- and wido-carboranes 13, 20, 21, 26, 98,121,168) and metal-acetylene 50, 58,112) complexes, relating them... 

General. Continuous-chain alkanes are the sole parent hydrides for all compounds, the skeleton of which is composed of chains. Cyclic parent hydrides are more diverse. In nomenclature, they are classified according to their structure as carbo-cycles (composed of carbon atoms only) and heterocycles (composed of carbon atoms and other atoms, such as N, O and Si). They are also classified as saturated and unsaturated. Saturated cycles have the maximum number of hydrogen atoms attached to every skeletal atom, as judged by a prespecified valence unsaturated cycles have fewer hydrogen atoms and multiple bonds between pairs of atoms. 

Figure ) r PFf-Pr1 top left, atom number identification top right, circular trace containing contacted and skeletal atoms ... 

There is an enormous number of compounds that possess metal-metal bonds. A metal cluster may be defined as a polynuclear compound in which there are substantial and directed bonds between the metal atoms. The metal atoms of a cluster are also referred to as skeletal atoms, and the remaining non-metal... 

Some isoelectronic species of C2B10H12, such as CBnH12-, NB11H12, and their derivatives, are known. Since they have the same number of skeletal atoms and the same bond valence, these compounds are isostructural. 

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