Bonding banana bond” description

Again, just as in the phosphine oxides2, there is disagreement about the exact electron distribution in the P=C bond with one view corresponding to the a/n description of multiple bonds and the other a bent (banana) bond description. 

Each Be atom is connected to four H atoms, and each H atom is connected to two Be atoms. Since Be has two valence electrons, and H only one, obviously there are insufficient electrons to fulfill the traditional organic two-center, two-electron bonding description. Alternatively, three-center interactions persist, whereby banana-shaped molecular orbitals (a three-center, two-electron bond, see Three-center Bond) connect the Be-H-Be atoms, each containing two electrons (see Figure 2 for the molecular orbital scheme see Molecular Orbitals) for this type of Delocalized... 

Figure 2.8 Equivalent bent (or banana) bond description of the double bond...

This is true only for the MO approximation. Ab initio VB calculations by Palke (1986) on ethylene show the equivalent banana bond description of the double bond in terms of equivalent nonorthogonal hybrids to be more stable than the a-n description. 

Hi) Three Q bonds (banana bonds). There are neither a nor n bonds, bnt the P-0 bond is a formal triple bond with the three curved regions of electron density between P and O in a symmetrical fashion. The remaining lone pair on the oxygen atom points away from phosphoras along the P-0 axis. The banana bond description originates from a Boys localization scheme [1,29-31] and from generalized valence bond calculations [6,32-34] for the phosphine oxide derivatives. 

FIGURE 15.12 Banana-bond description of the ethylene double bond. The cross sections are the same as in Hg. 15.11. 

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... 

Bi2B22 Bent (or Banana) Description of the Double Bond... 

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... 

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-... 

There has been considerable controversy as to whether the ethylene double bond is best described as two equivalent bent banana bonds or as a <7 and a rr bond. Kaldor calculated the energy-localized MOs of ethylene from the minimal-basis-set SCF MOs [U. Kaldor, J. Chem. Phys., 46,1981 (1%7)]. Since there is no a priori necessity that the energy-localized MOs be equivalent orbitals, this calculation provides evidence as to which is the better description of the carbon-carbon double bond. Kaldor found the energy-localized carbon-carbon bond orbitals in ethylene to be the two equivalent banana bonds. For acetylene he found the energy-localized carbon-carbon bond orbitals to be three equivalent banana bonds and not one a- and two ir bonds. Of course, although the electron densities in the individual MOs differ for the banana-bond versus o--7r descriptions, the total probability density for the four or six electrons in the double or triple bond is the same in either picture. 

For C2H4 a GVB calculation gave a description of the double bond as composed of one cr and one tt bond, in contrast to the energy-localized MOs (Section 15.10), which are two equivalent bent banana bonds. 

This conclusion was reinforced by a number of investigations. The title of one publication was Double Bonds Are Bent Equivalent Hybrid (Banana) Bonds. Another study concluded that the GVB description of the double bond in (C2F4) is not the traditional picture of o and n bonds but rather a representation in terms of two bent bonds. Still another paper comparing... 

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