Pauling bond

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. 

Figure 5.35 displays a schematic energy-level diagram for each stationary species along the proton-transfer reaction coordinate. Although Pauling bond strengths... 

All oxygen-based polyhedra with the same Pauling bond strength (cationic charge/coordination number see section 1.10.3) have the same mean polyhedral linear expansion. 

Donnay G. (1969). Further use for the Pauling-bond concept. Carnegie Inst. Wash. Yb., 68 292-295. 

C = anion charge, z = cation charge, v = cation coordination number, 5 = (Pauling) bond strength.]... 

FIGURE 2. A plot of the average bond lengths, , of the XOn coordination polyhedra observed for silicate and oxide crystals vs the Pauling bond strength, s, of the X—O bond. The Roman numeral superscript denotes the coordination number of the X-cation... 

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). 

Calculations for MeMMMe, M = Ge, Sn led to the conclusion that the M—M bond in these molecules is a double bond rather than a triple bond. Thus, the Pauling bond... 

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 ... 

The population of charged surface sites is determined by the first and second surface protonation constants of the oxide (AG°ads e+4 and AG°ads H+ 2). These terms depend, in turn, on the crystal-chemical parameter, s/r, which is the Pauling bond strength34 per metal-OH bond length, and on l/ek.35 37... 

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