Ethylene bond order

Defining ethane, ethylene and acetylene to have bond orders of 1, 2 and 3, the constant a-is found to have a value of approximately 0.3 A. For bond orders less than 1 (i.e. breaking and fonning single bonds) it appears that 0.6 A is a more appropriate proportionality constant. A Mulliken style measure of the bond strength between atoms A and B can be defined from the density matrix as (note that this involves the elements of the product of the D and S matrices). 

In contrast, polar and resonance effects must be separated in order to analyze the data for a-substituted arylolefins [ArC(R)=CHR with R H]. Their bromination involves open carbocation intermediates only. Resonance effects cannot be fully developed at the transition states, since the aromatic ring is not in the same plane as that of the developing carbocation, because of steric constraints. Accordingly, application of (33) gives pT < pn. Attenuation of resonance arises mainly from stereochemical factors, at least in the monosubstituted 1,1-diphenylethylene [20] and a-methylstilbene [21] series the pr/pn ratios can be related to the dihedral angle between the substituted phenyl ring and the plane of the ethylenic bond. 

As a result, the CO bond orders in 4 (2.027) are nearly equivalent to those of ethylene, showing that glyoxal is more localized than 1-3 or other molecules to be considered below. 

To illustrate the importance of vicinal connectivity of conjugating units, we consider two dienes in non-vicinal relationships 1,5-hexadiene, 9, and allene, 10. As shown in Table 3.19, the direct diene conjugations are negligible in both species, on account of spatial separation in 9 and symmetry-imposed orthogonality of the two pi planes in 10. Consistently with the essential absence of conjugation, the unsaturated C—C bonds of 9 and 10 have calculated bond orders characteristic of ethylene or other unconjugated systems and the ficc NLMOs have essentially localized character ... 

In addition to being bent, in contrast lo ethylene, the Gc—Ge and Sn—Sn bonds are not as short us expected for true double bonds.11 Calculations indicate that p.,-p bonding is less important and other interactions may become increasingly important Calculated bond orders are Ge—Ge = I 61 and Sn—Sn = 1.46.w... 

The cfleet of bond order is exemplified by the familiar shortening of Ihe carbon-carbon bond in ethane (1.543 A), graphite (1.4210 A), benzene 11.397 A), ethylene (1.353 A), and acetylene (1.207 A) as the bond order goes from I to 1 i to I j to 2 to 3. Bond orders affect the covalent radii of other elements similarly. 

Calculate the bond orders for ethylene in (a) the ground state and (b) the first excited state (n -> n ). What are the chemical consequences of these results ... 

The same simple scheme gives the correct description of the dimeric hydrocarbons. Acetylene has 10 valence electrons and three bonds, H-C-C-H, leaving two odd couples, predicting a bond order of 3. Ethylene with 12 electrons, 5 bonds and 1 odd couple has bond order 2. Ethane is saturated. 

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