Orbital banana-bond

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. 

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... 

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 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...

The conceptual interrelations of species with three-membered rings and those with double bonds are among the oldest and best-established in the study of strained species18,21. These interrelations have ramifications in the understanding of reactivity and stability patterns, spectra, geometry and electronic delocalization and have been expressed in terms of the Walsh (Walsh Sugden), a and n orbitals, bent and banana bonds, and cyclopropane and cycloethane 22. For this chapter we will but consider some of the thermochemical aspects. 

D. G. Gilheany, Chem. Rev., 94,1339 (1994). Nod Orbitals but Walsh Diagrams and Maybe Banana Bonds Chemical Bonding in Phosphines, Phosphine Oxides, and Phosphonium Ylides. 

There are two classical approaches to bonding in cyclopropane namely the Walsh molecular orbital approach and the bent bonds or banana bonds of the Coulson-Mofiit model. 

The interaction of the bent banana bonds of the classical Coulson-Mofiit valence bond model of cyclopropane which uses methane-like sp hybrids and joins three units to form the alicyclic ring imply a resonance energy in cyclopropane of 69 kcalmol" Modern molecular orbital calculations (STO-3G) support an electron rich n system and an electron deficient cr-system for cyclopropane. 

FIGURE 17. On the left is shown the pair of localized banana bond orbitals Ab,up and Ab,down obtained... 

This leads to two equivalent molecular orbitals of mixed a, tt character, which are sometimes called banana bonds ... 

It should be noted that, because of the invariance properties of the density function with respect to a unitary transformation among its orbitals, the a-n description of double or triple bonds in terms of nonequivalent orbitals is not the only possible one a description in terms of two or three equivalent bent banana bonds is possible as well. It is... 

Small angle strain The strain that results from the angles being much less than those resulting from normal orbital overlap. In three- and four-membered rings, the bonds that form the ring are called bent or banana bonds. 

The lifetime (t) of 3-nortricyclanylidene (46) has never been measured. It is clear, however, that carbene 46 should be more stable than typical dialkylcarbenes. That is because the vacant p-orbital on the divalent carbon of 46 likely receives electron density from the bent banana bonds of its embedded cyclopropane ring, especially from C2.148 The resulting electron delocalization should lower the energy of carbene... 

Interestingly, and probably due to a very exciting connection between the Fermi-hole and the localized orbitals [28], various localization methods result in rather similar localized orbitals, except for the description of double bonds by a o- and 7r-orbital-pair or two equivalent r (banana) bonds. Boys localization gives r orbitals, while the Edmiston-Ruedenberg and the popula-... 

It is thus apparent that 01 is made up of two canted p orbitals (NA 2 px and Nb 2 px) as indicated in Fig. 8 (e), i.e., it is a bent bond in the region toward which the sp2 GO pointed. Since the sp2 GO s are trigonally disposed, the other two sp2 hybrid GO s generate localized bent bonds which can be obtained from the one just discussed by a rotation of 120° around the bond axis. Thus one sigma and two pi bonds can be recast into three banana bonds. 

From the foregoing it is apparent that the 3 banana bonds are induced by the directionality of the sp2 GO s. By the same token the directionality of the sp2 GO s can be considered to induce the contributions to any of the three banana bonds on each of the N atoms. These contributions are, however, linear combinations of N valence p AO s and hence themselves are p AO s rotated in new directions. Thus the directionality of the sp2 GO s can be imagined to induce a set of three p orbitals 2px,... 

Because the s GO generates the BMO j/1 from the N 2s AO s and also the BMO i//2 from the N 2 px AO s, some mixing of 2s and 2px character occurs in the actual delocalized MO s, as mentioned earlier. The same is true for the ABMO s and i//2 and also for the localized MO s. In the latter, this mixing leads to an sp hybridization which places some p character in the lone pairs and some s character in the banana bonds as depicted below. Even so the lone pair orbitals have substantially more s character than the bonding orbitals, and this leads to the VSEPR idea that the lone pair orbitals occupy more space around atoms then do bond pairs. Consequently the... 

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