Pauling bond orders

Correlation of the SiSi bond lengths in disilane derivatives X3Si-SiX3 with X = CH3, C(CH3)3 and Si(CH3)3 together with those of sterically overcrowded cyclic [7a] and linear [7b] trisilane derivatives versus their Pauling bond orders [5a,6b,7], expectedly, produces a linear regression (Fig. 4). 

Figure 4. Correlation of SiSi bond lengths in di- and trisilanes versus Pauling bond orders, lg(PBO) = [d(l) - d(x)]/60 (framed PBO values).

The distance-dependent Pauling bond orders range from 1.00 in hexamethyldisilane with a SiSi bond of 235 pm in length (Fig. 4 standard d(l)) to 0.26 for hexakis(rert.butyl)disilane with an extremely elongated spacer distance of 270 pm between its bulky Si(C(CH3)3)3 half-shells [6b]. To rationalize the sometimes considerably weakened SiSi bonds - hexakis(rm.butyl)disilane does not dissociate into two radicals -, it has been proposed [6b,7] that additional attractive van der Waals interactions within the hydrocarbon wrapping contribute to the bonding within the respective organosilicon molecules. This assumption is further supported by the structure of hexakis(trimethylsilyl)disilane (Fig. 2), in which (presumably due to the considerable polarization Si -C5e-H5 calculated [5b]) extremely short non-bonded C(H3)-- (H3)C distances of only 352 pm are found. 

The Pauling bond order (PBO) concept was introduced by L. Pauling, L. O. Brockway, and J. Y. Beach [1] (1935). The determination of the PBOs requires counting Kekule structures in GBSs. N. S. Ham [16] (1958) proved that, for a KBS, Pauling s bond order pu for neighbouring carbon atoms i, j equals the bond order defined by K. Ruedenberg [17] (1954) which results from LCAO-MO considerations further, he showed that ptJ is equal to the entry in position (i, j) of the inverse A 1 of the adjacency matrix A of the system (note that, by Eq. (2), det A = K2 > 0). 

Figure 4 - Pauling bond orders and free valences for benzene, naphthalene, and trimethylene-methyl.

We first mention an interesting result by Heilbronner [26] relating the inverse of the adjacency matrix with the Pauling bond order ... 

A = Alkali metal AE = Alkaline-earth metal a-P = Amorphous phosphorus CN = Mean coordination number (i(M-P) = Distance between M and P atom Distances between P atoms E = Element = Band gap M = Metal PBO = Pauling bond order (P) = Formal charge of a P atom (M) = Formal charge of a M atom R = Zr, Ftf, rare earth metal or actinoid metal RE = Rare earth element / cov = Covalent radius ... 

A definition of resonance energy which relates jr-energies to the Pauling - bond order 7t by the following expression ... 

Bartell, L.S. (1963). Resonance Energies from Pauling Bond Orders. J.Phys.Chem., 67, 1865-1868. 

Bartell, L.S. (1964). Semiquantitative Theory of Resonance Using Pauling Bond Orders. Tetrahedron, 20,139-153. 

Sedlar, J., Andelic, 1., Gutman, 1. and Vukicevic, D. (2006) Vindicating the Pauling-bond-order concept. Chem. Phys. Lett., 427, 418-420. 

Another rather interesting relation between the resonance theory and elementary MO theory was established by Ham and Ruedenberg 107>. Let Pp be the Pauling bond-order matrix known from resonance theory 179>. If the adjacency matrix of the -th Kekute graph is Aj, then... 

The Pauling bond order between atoms i and7, is riij = where is the bond length... 

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