March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

Chapter 2. Delocalized Chemical Bonding

2.D. Cross-Conjugation⁵¹

In a cross-conjugated compound, three groups are present, two of which are not conjugated with each other, although each is conjugated with the third. Some examples are benzophenone (21), triene (22),⁵² and divinyl ether (23). The MO method shows that the overlap of six p orbitals in 22 (a member of a family of compounds known as dendralenes)⁵² gives six molecular orbitals, and the three bonding orbitals are shown in Fig. 2.6, along with their energies. Note that two of the carbon atoms do not participate in the α + β orbital.

Fig. 2.6 The three bonding orbitals of the dendralene, 3-methylene-1,4-pentadiene (22).

The total energy of the three occupied orbitals is 6α + 6.900β, so the resonance energy is 0.900β. Molecular orbital bond orders are 1.930 for the C-1–C-2 bond, 1.859 for the C-3–C-6 bond, and 1.363 for the C-2–C-3 bond.⁵¹Comparing these values with those for butadiene (Sec. 2.C), the C-1–C-2 bond contains more and the C-3–C-6 bond less double-bond character than the double bonds in butadiene. The resonance picture supports this conclusion, since each C-1–C-2 bond is double in three of the five canonical forms, while the C-3–C-6 bond is double in only one. In most cases, it is easier to treat cross-conjugated molecules by the MO method than by the valence bond method.

One consequence of this phenomenon is that the bond length of a cross-conjugated C=C unit is slightly longer than that of a non-cross-conjugated bond. In 24, for example, the cross–conjugated bond is ~ 0.01 Å longer.⁵³ The conjugative effect of a C=C or CC unit can be measured for a conjugated enone: 4.2 kcal mol⁻¹ (17.6 kj mol⁻¹) for an ethenyl substituent, but ~ 2.3 kcal mol⁻¹ (9.6 kj mol−1) for an ethynyl substituent, which is more variable.⁵⁴

The phenomenon of homoconjugation is related to cross-conjugation in that there are C=C units in close proximity, but not conjugated one to the other. Homoconjugation arises when the termini of two orthogonal π-systems are held in close proximity, as in compounds with a spiro-tetrahedral carbon atom.⁵⁵ Spiro[4.4]nonatetraene (25)⁵⁶ is an example and it is known that the HOMO (see Sec. 15.60) of 25 is raised relative to cyclopentadiene, whereas the LUMO is unaffected.⁵⁷ Another example is 26, where there are bond length distortions caused by electronic interactions between the unsaturated bicyclic moiety and the cyclopropyl moiety.⁵⁸ It is assumed that cyclopropyl homoconjugation is responsible for this effect.