Skeletal atoms

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. 

Strychnine, the most celebrated member of the Strychnos alkaloids, possesses a complex polycyclic structure which is assembled from only twenty-four skeletal atoms. In addition to its obvious architectural complexity, strychnine s structure contains a contiguous array of six unsymmetrically substituted tetrahedral (asymmetric) carbon atoms of which five are included within one saturated six-membered ring. The intimidating structure of the strychnine molecule elicited the following remark by Sir Robert Robinson in 1952 For its molecular size it is the most complex substance known. 5... 

The (non-detachable) prefix carba- signifies replacement of a heteroatom by carbon in general natural product nomenclature [26], and may be applied to replacement of the hemiacetal ring oxygen in carbohydrates if there is a desire to stress homomorphic relationships. If the original heteroatom is unnumbered, the new carbon atom is assigned the locant of the non-anomeric adjacent skeletal atom, with suffix a . 

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. 

As reported in Table 1, inorganic polymers (e.g. polysiloxanes and polyphos-phazenes) usually posses wider angles and longer bonds among skeletal atoms... 

Let us consider a polymer chain with N->oo identical skeletal atoms, either in solution or in the melt, representing our polymer system. Our reference temperature is T0, i.e., the temperature above which no bundles may effectively contribute to crystallization. At T = T0 the chain is assumed to be unperturbed and its configurational partition function is ZN(T0) = kN (N -> oo) [107] for simplicity we use a reduced form Zn = Z /kN (henceforth simply the partition function) so that Zn(T0) = 1. Only at T < To effective bundles may form, see Fig. 1, and we have ZN(T) = 1 + AZN(T - T0) note that the unit term corresponds to the bundle-free infinite-chain configuration. Each bundle with n chain atoms in -c N) will contribute to AZn... 

Nomenclature based on a parent term with an appended suffix accounts for most natural product names. However, as related compounds are identified, or even when a suffix has to denote multiple functional groups, a variety of modifying terms can be employed. For example, the common prefix nor- denotes the removal of a skeletal atom from the parent structure the loss of two or more skeletal atoms is indicated by combining an appropriate numerical prefix with nor- , e.g., dinor- , trinor- (Giles 1999). Table 1.2 lists additional examples of commonly encountered modifying terms. 

Aza (C -> N) Oxa (C —> 0) Abeo (general rearrangement) Cyclo (cyclic rearrangement) Iso (isomeric form) Seco (bond removal) Apo (side chain loss) De (functional group loss) Homo (add skeletal atom) Nor (skeletal atom loss)... 

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 " ",... 

Compounds with a skeletal atoms and b skeletal bond pairs adopt closo structures if 6 = (o + 1), nido structures if 6 = (a + 2), and arachno structures if 6 = (o + 3). 

The relationship between boranes and metal-carbonyl clusters can be extended by considering the compound Fe5(CO)i5C, which has the square-based pyramidal structure shown in Fig. 13, with the carbide carbon atom just below the center of the Fe square, clearly contributing all its valence shell electrons to the cluster 24). The metal-carbonyl residue FeB(CO)i4 formally left by removal of this carbon as has the nido structure appropriate for a cluster with 5 skeletal atoms and seven skeletal bond pairs. 

In addition to the close- and nido-metal-carbonyl clusters already mentioned, with structures based on the octahedron, another interesting category of structure that is found among metal-carbonyl clusters is one in which n skeletal atoms are held together formally by n skeletal bond pairs. These adopt structures based on polyhedra with ( — 1) vertices, as might be expected. The extra metal atom caps one of the triangular faces of the closo residue, where the three vacant orbitals that it can formally furnish for cluster bonding enable it to bond to the 3 metal... 

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...

By no means do all metallocarboranes have the metal atoms occupying vertices of the basic polyhedra. Apart from many derivatives in which o-bonded metal residues occupy exo sites attached to particular skeletal atoms, several metalloboranes and -carboranes are known in which the metal occupies an edge-bridging site, effectively replacing a bridging hydrogen atom of the parent borane. Many are nido species related to BeHio, for example, the /x-silyl and /i-germyl carboranes. 

The mixed cluster Co4(CO)io(C2Et2) (50) has already been quoted (Fig. 15) as an example of a closo cluster with 6 skeletal atoms and 7 skeletal bond pairs. Nido clusters also formally based on an octahed-... 

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