In strained molecules

Another kind of imperfect sideways-on overlap, this time in n bonds, is found in strained molecules like cyclopropane and cyclobutane. 

Whereas strained ring systems are usually reactive and often unstable, molecules which satisfy the criteria for aromaticity exhibit enhanced stability. As is evident from the structural formula of 1, the cycloproparenes set these features in juxtaposition as they are strained molecules in which a single carbon atom is fused across adjacent centres of an aromatic system. The interest of the experimentalist in strained molecules has been matched by the theoretician in the search for suitable models for developing the concepts of chemical bonding and aromaticity. The cycloproparenes have been particularly important in this regard as they meet the criterion for partial aromatic bond localization and consequent bond length alternation in the aromatic ring as proposed by Mills and Nixon in 1930, viz. la vs lb. The cation 5, anion 6 and radical 7 derived from 1, and also the ketone 8 and exocyclic methylene derivative 9, are of interest in this respect. 

Bond strain in small-ring molecules generally shows itself in a displacement of deformation density peaks outside of the ring. As a consequence of the curvature of the C-C bond paths in strained molecules, the charge density is not distributed so as to maximize the force of attraction between the nuclei. As a result of this effect, the bonds are weakened in spite of the fact that in general they exhibit intranuclear distances shorter than normal bonds. 

A general equation can be derived that describes the variation in direction of the valence electron density about the nucleus. The distortion from sphericity caused by valence electrons and lone-pair electrons is approximated by this equation, which includes a population parameter, a radial size function, and a spherical harmonic function, equivalent to various lobes (multipoles). In the analysis the core electron density of each atom is assigned a fixed quantity. For example, carbon has 2 core electrons and 4 valence electrons. Hydrogen has no core electrons but 1 valence electron. Experimental X-ray diffraction data are used to deri e the parameters that correspond to this function. The model is now more complicated, but gives a better representation of the true electron density (or so we would like to think). This method is useful for showing lone pair directionalities, and bent bonds in strained molecules. Since a larger number of diffraction data are included, the geometry of the molecular structure is probably better determined. 

Hybridization of the carbon to which a proton is attached also influences electron density. As the proportion of s character increases from sp to sp to sp orbitals, bonding electrons move closer to carbon and away from the protons, which then become deshielded. For this reason, methane and ethane resonate at 8 0.23 and 0.86, respectively, but ethene resonates at 8 5.28. Ethyne (acetylene) is an exception in this regard, as we shall see. Hybridization contributes to shifts in strained molecules, such as cyclobutane (8 1.98) and cubane (8 4.00), for which hybridization is intermediate between sp and sp. ... 

The lack of alkane C-C activation also arises from the fact that two relatively weak M-C bonds are formed in the process [Eq. (6.105)]. However, in strained molecules such as small-ring cycloalkanes (cyclopropanes, cyclobutanes), relief of strain is an additional favorable factor. Furthermore, C-C activation can be rendered thermodynamically more favorable when an extra driving force is available, such as formation of an aromatic structure or by utilizing an activating functionality. 

A well-established approach for studying the bonds in strained molecules is by means of the bond path concept. A bond path corresponds to the ridge of highest electron density that links two nuclei. For many bonds, such as those between the carbons in propane, the bond path is essentially identical with the internuclear axis. In molecules with strained bonds, however, there can be a... 

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