Skeletal bond orders

This is also supported by recent computations (22) on skeletal bond orders and net atomic charges (Chart I), using the MOPAC software package (23) and Gopinathan s procedure (24) based on the concept of molecular orbital valency. 

The values of 0(ASD) /2.3O3 R listed in Table 5 are the entropic components of log EM. These are the log EM- alues for ideal strainless cyclisation reactions, i.e. reactions where 0AH° = 0. It is of interest to note that, as far as the entropic component is concerned, symmetry corrected effective molarities on the order of 102 106M are found. This observation leads to the important conclusion that cyclisation reactions of chains up to about 7 skeletal bonds are entropically favoured over reactions between non-connected 1 M end-groups. The intercept of 33 e.u. corresponds to an effective molarity of exp(33/R) or 107 2M, which may be taken as a representative value for the maximum advantage due to proximity of end-groups in intramolecular equilibrium reactions. It compares well with the maximum EM of about 108M estimated by Page and Jencks (1971). 

Figure 3.119 Leading donor-acceptor interactions in AI2H6 (left) and Ga2H6 (right), showing overlap contours in the plane of three-center bridge-bonding (the pi plane, top row) and two-center skeletal bonding (the sigma plane, bottom two rows), with associated second-order stabilization energies in parentheses.

An even stronger case of intramolecular RAHB coupling is provided by the maleate ion (HOOCCH=CHCOO-), whose H-bonded and open conformers are shown in Fig. 5.22. Skeletal bond lengths and bond orders of these conformers are compared in Table 5.18. As shown in Fig. 5.22, the H-bonded conformer is favored in this case by more than 26 kcalmol-1, which is indicative of a powerful intramolecular no aoH interaction (estimated second-order stabilization 104 kcalmol-1) that is sufficient to overcome the severe steric repulsion of the extremely short H- -O nonbonded distance ( 1.3 A).56... 

These crude approximations allow the C—C skeletal geometry variations to be simply estimated from the bond-order variations in Figs. 5.61 and 5.62. 

The average edge bond order for a particular closo species can be calculated by dividing the total number of skeletal bond pairs ( 4- 1) by the number of edges, which, for exclusively triangular-faced poly-hedra with n vertices, is (3 — 6). This leads directly to the formal boron-boron bond order for those borane anions (ITU) and... 

Skeletal (Polyhedron-Edge) Bond Orders for Anions BnHn ... 

For deriving the aromaticity index AN proposed by Pozharskii (85KGS867) the sum of absolute values of all differences between the bond orders of n skeletal bonds including those with equal values of the orders is calculated and it is normalized with respect to the number of those differences equaling that of the dual combinations of n... 

The internal rotations around the skeletal bonds of PE are hindered due to interaction between the neighboring hydrogens. Since second and higher orders of interactions are not negligible, the internal rotations are interdependent. The statistics of such interdependent rotations is developed and applied to obtain the configurational partition function and the mean-square end-to-end... 

A method is developed for calculating even moments of the end-to-end distance r of polymeric chains, on the basis of the RIS approximation for rotations about skeletal bonds. Expressions are obtained in a form which is applicable in principle to arbitrary k, but practical applications are limited by a tremendous increase in the order of the matrices to be treated, with increasing k. An application is made to the PE chain by using the familiar three-state model. Approximate values of the distribution function Wn (r) of the end-to-end vector r, Wn (0), and , are calculated from these even moments. 

Figure 3.7. Skeletal two- and three-center bond arrangements possible for CH units of skeletal connectivity k = 3,4,5, or 6 (exo-hydrogens not shown). Bond orders h refer to the mean number of electron pairs per B-C hnk for the bond network in question.

The third row of bond networks in Figure 3.7, which are those possible for a tervalent atom with five neighbors, leads to a mean bond order of 13/30, that is, 0.433 , appropriate for all of the skeletal atoms in an icosahedron as in the borane dianion [B H JA For the carboranes 1,2-, 1,6-, and l,12-C2BioHi2, however, bonds to the carbon atoms can be expected to have orders greater than this, and bonds between boron atoms will be of lower order, as the more electronegative carbon atoms draw more of the skeletal electrons toward themselves, so increasing the orders of the bonds they form. 

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