Banana bond

There is little experience with the von Niessen method, but for most molecules the remaining three schemes tend to give very similar LMOs. The main exception is systems containing both a- and vr-bonds, such as ethylene. The Pipek-Mezey procedure preserves the cr/yr-separation, while the Edmiston-Ruedenberg and Boys schemes produce bent banana bonds. Similarly, for planar molecules which contain lone pairs (like water), the Pipek-Mezey method produces one in-plane cr-type lone pair and one out-of-plane yr-type lone pair, while the Edmiston-Ruedenberg and Boys schemes produce two equivalent rabbit ear lone pairs. 

The double bond can also be pictured as consisting of two equivalent orbitals, where the centers of electron density point away from the C—C axis. This is the bent-bond or banana-bond picture. Support for this view is found in Pauling, L. Theoretical Organic Chemistry, The Kekule Symposium Butterworth London, 1959, p. 2 Palke, W.E. J, Am. Chem. Soc., 1986,108, 6543. However, most of the literature of organic chemistry is written in terms of the a-7t picture, and in this book we will use it. 

Bachrach has argued against the surface delocalization by comparing the electron density at the centers of the banana bonds to that of the centers of cyclopropane 1 and phosphirane 10 (Scheme 3) [22]. Density is spread over the ring in 1, but not... 

This alternative description follows from classical ideas and from a VB description utilizing hybrid orbitals. According to this description, a double bond is described as consisting of two bent bonds, sometimes called r bonds or banana bonds, formed by the overlap of... 

FIGURE 17. On the left is shown the pair of localized banana bond orbitals Ab>Up and Ab.down obtained according to step 2 of Section II.E.2. Their out-of-phase linear combination n = (Ab,Up - Ab.downl/v defined in equation 5 yields the n basis orbital shown on the right... 

A fascinating feature of the G 2 species occurs in the excited singlet state. The 1G 2 species is bound by 29.0 kcalmol-1 at Re = 2.7444 A and has ordinarylooking bond order b = 1. However, the bonding character is remarkably different in the ot and (3 spin sets, corresponding to bent banana bonds of opposite curvature with respect to the internuclear axis. Figure 3.32 displays the form of one of these spin-NBOs, showing the off-axis curvature with respect to the Ga—Ga line of... 

Figure 3.50 Carbon-carbon NBOs of CH2=CHNH2 at

Still another way to picture the conformational preferences is to visualize the C=C double bond in terms of two equivalent banana bonds (Fig. 3.50). In this picture the preferred conformations are those with C—F in staggered orientation with respect to the three bonds (two banana bonds and one C—H bond) of the vinyl moiety, analogous to the preferred conformations of ethane. However, in using this ethane-like mnemonic one should recall that its essential origin lies in the hyperconjugative interactions of E(SL> rather than the steric and electrostatic interactions of (L). 

Figure 3.102 The residual ate NBO in H3BC2H4, showing the strong banana-bond shape of the NBO and the effective preparation for forming a second three-center bond (or agostic interaction) with an empty orbital approaching from the opposite face of the original ethylene moiety.

The strongly bent nature of the NBOs of W(CH2)3 is depicted in Fig. 4.19, confirming the inadequacy of a simple a/7t-bonding picture for this species. Both contour plots are plotted in a plane perpendicular to the CH2 plane, showing the expected bending of the nominal a- and 7t-bond-forming hybrids centered both on M and on C in directions above and below the internuclear M—C axis. While the NBOs can still be crudely described with nominal a and 7t labels, incipient banana-bond character is clearly significant. 

Figure 4.20 A schematic illustration comparing parent hydride and symmetry (above cf. Figs. 4.2(b), 4.3(c), and 4.5(b)) with the derivative alkylidene (below) in the idealized banana-bonded limit for Ir(CFl2)F[ (left), Os(CH2)2 (center), and W(CH2)3 (right).

To view W(CH2)3 in the corresponding limit of six sd5 hybrid banana bonds, begin with the distorted trigonal prismatic C3v isomer. Place the three methylidene carbons midway along the three vertical edges of the prism with the methylidene... 

As described in Section 3.4.2, hyperconjugative donor-acceptor stabilizations favor conformers in which one of the rotor C—H bonds eclipses an adjacent double bond. (This is equivalent to an ethane-like staggered preference if the double bond is pictured in terms of two bent banana bonds. ) Hence, in the case of a perfectly localized Lewis structure I, the methyl group would be expected to adopt the preferred pseudo-cA conformation la (with in-plane C—H syn to A=C),... 

The noteworthy point is a shortening of C-C bond distance as compared to the aliphatic C-C bond distance which is 1.54 A. This shortening manifests itself in the development of special character of the bonds. Since the sp orbitals of carbon now cannot overlap as effectively as they do in alkanes where perfect end-on overlap occurs the bonds in cyclopropane becomes bent and weak and also lead to an angle strain and so the molecule has greater potential energy. So this bent or banana bond accounts for the most of the ring strain. 

This leads to modifications of the localized it orbitals. In benzene, for example, a Kekule localization which mixes the a and ir orbitals to form double banana bonds is preferred over the other equivalent ir localizations discussed. 60) In naphthalene a Kekule type structure is found similar to the one presently discussed, but different in that the (jtE2) are hybridized with corresponding o-CC bonding orbitals to form banana bonds, whereas the (ttC2 ) remains a pure jt orbital. 61 > While this is of interest in the discussion of the whole molecule, it is clear that certain intrinsic properties of the ir-electrons are more readily recognized by the localization which has been discussed here. We hope to discuss elsewhere localized orbitals involving a bonds in organic molecules. 

Figure D.l The usual a and tt orbitals of a doubly bonded system (left) and the banana bonds formed by their linear combination (right)...

Figure D.l to create so-called banana-bond orbitals. We define these as...

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