Double-Bond Orbitals

We would like to suggest the following explanation. A 5-substituent favors 1-6 bond formation (cf. p. 218). Now, when AVE takes the reactive chair conformation, the 1,2-double bond orbitals are raised by conjugation with the oxygen lone pairs, as confirmed by 6-31G calculations ... 

Hence we have two molecular orbitals, one along the line of centres, the other as two sausage-like clouds, called the n orbital or n bond (and the two electrons in it, the n electrons). The double bond is shorter than a single C—C bond because of the double overlap but the n electron cloud is easily attacked by other atoms, hence the reactivity of ethene compared with methane or ethane. 

These absorptions are ascribed to n-n transitions, that is, transitions of an electron from the highest occupied n molecular orbital (HOMO) to the lowest unoccupied n molecular orbital (LUMO). One can decide which orbitals are the HOMO and LUMO by filling electrons into the molecular energy level diagram from the bottom up, two electrons to each molecular orbital. The number of electrons is the number of sp carbon atoms contributing to the n system of a neuhal polyalkene, two for each double bond. In ethylene, there is only one occupied MO and one unoccupied MO. The occupied orbital in ethylene is p below the energy level represented by ot, and the unoccupied orbital is p above it. The separation between the only possibilities for the HOMO and LUMO is 2.00p. 

FIGURE 2 17 The carbon-carbon double bond in ethylene has a cr component and a tt compo nent The cr component arises from overlap of sp hybridized orbitals along the internuclear axis The tt component results from a side by side overlap of 2p orbitals... 

Section 2 20 Carbon is sp hybridized in ethylene and the double bond has a ct com ponent and a rr component The sp hybridization state is derived by mix mg the 2s and two of the three 2p orbitals Three equivalent sp orbitals result and their axes are coplanar Overlap of an sp orbital of one car bon with an sp orbital of another produces a ct bond between them Each carbon still has one unhybridized p orbital available for bonding and side by side overlap of the p orbitals of adjacent carbons gives a rr bond between them... 

The structure of ethylene and the orbital hybridization model for its double bond were presented m Section 2 20 and are briefly reviewed m Figure 5 1 Ethylene is planar each carbon is sp hybridized and the double bond is considered to have a a component and a TT component The ct component arises from overlap of sp hybrid orbitals along a line connecting the two carbons the tt component via a side by side overlap of two p orbitals Regions of high electron density attributed to the tt electrons appear above and below the plane of the molecule and are clearly evident m the electrostatic potential map Most of the reactions of ethylene and other alkenes involve these electrons... 

In principle cis 2 butene and trans 2 butene may be mterconverted by rotation about the C 2=C 3 double bond However unlike rotation about the C 2—C 3 single bond in butane which is quite fast mterconversion of the stereoisomeric 2 butenes does not occur under normal circumstances It is sometimes said that rotation about a carbon-carbon double bond is restricted but this is an understatement Conventional lab oratory sources of heat do not provide enough energy for rotation about the double bond m alkenes As shown m Figure 5 2 rotation about a double bond requires the p orbitals of C 2 and C 3 to be twisted from their stable parallel alignment—m effect the tt com ponent of the double bond must be broken at the transition state... 

Bonding m alkenes is described according to an sp orbital hybridization model The double bond unites two sp hybridized carbon atoms and is made of a ct component and a rr component The ct bond arises by over lap of an sp hybrid orbital on each carbon The rr bond is weaker than the CT bond and results from a side by side overlap of p orbitals... 

Figure 6 6 focuses on the orbitals involved and shows how the rr electrons of the double bond flow in the direction that generates the more stable of the two possible carbocations... 

We can consider the hydroboration step as though it involved borane (BH3) It sim phfies our mechanistic analysis and is at variance with reality only m matters of detail Borane is electrophilic it has a vacant 2p orbital and can accept a pair of electrons into that orbital The source of this electron pair is the rr bond of an alkene It is believed as shown m Figure 6 10 for the example of the hydroboration of 1 methylcyclopentene that the first step produces an unstable intermediate called a tt complex In this rr com plex boron and the two carbon atoms of the double bond are joined by a three center two electron bond by which we mean that three atoms share two electrons Three center two electron bonds are frequently encountered m boron chemistry The tt complex is formed by a transfer of electron density from the tt orbital of the alkene to the 2p orbital... 

FIGURE 10 2 Electron delo calization in an allylic carbo cation (a) The tt orbital of the double bond and the vacant 2p orbital of the posi tively charged carbon (b) Overlap of the tt orbital and the 2p orbital gives an ex tended tt orbital that encom passes all three carbons The two electrons in the tt bond are delocalized over two car bons in part (a) and over three carbons in part (b)... 

FIGURE 10 5 (a) Isolated double bonds are separated from one another by one or more sp hybridized carbons and cannot overlap to give an extended it orbital (b) In a conjugated di ene overlap of two it orbitals gives an extended it system encompassing four carbon atoms... 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

The pattern of orbital energies is different for benzene than it would be if the six tt electrons were confined to three noninteracting double bonds The delocalization provided by cyclic conjugation in benzene causes its tt electrons to be held more strongly than they would be in the absence of cyclic conjugation Stronger binding of its tt electrons is the factor most responsible for the special stability—the aromaticity—of benzene... 

In pyrrole on the other hand the unshared pair belonging to nitrogen must be added to the four tt electrons of the two double bonds m order to meet the six tt elec tron requirement As shown m Figure 11 166 the nitrogen of pyrrole is sp hybridized and the pair of electrons occupies a p orbital where both electrons can participate m the aromatic tt system... 

TT bond (Section 2 20) In alkenes a bond formed by overlap of p orbitals in a side by side manner A tt bond is weaker than a u bond The carbon-carbon double bond in alkenes con sists of two sp hybridized carbons joined by a a bond and a TT bond... 

Geometrical Isomerism. Rotation about a carbon-carbon double bond is restricted because of interaction between the p orbitals which make up the pi bond. Isomerism due to such restricted rotation about a bond is known as geometric isomerism. Parallel overlap of the p orbitals of each carbon atom of the double bond forms the molecular orbital of the pi bond. The relatively large barrier to rotation about the pi bond is estimated to be nearly 63 kcal mol (263 kJ mol-i). 

A common example of the Peieds distortion is the linear polyene, polyacetylene. A simple molecular orbital approach would predict S hybddization at each carbon and metallic behavior as a result of a half-filled delocalized TT-orbital along the chain. Uniform bond lengths would be expected (as in benzene) as a result of the delocalization. However, a Peieds distortion leads to alternating single and double bonds (Fig. 3) and the opening up of a band gap. As a result, undoped polyacetylene is a semiconductor. 

The propylene double bond consists of a (7-bond formed by two ovedapping orbitals, and a 7t-bond formed above and below the plane by the side overlap of two p orbitals. The 7t-bond is responsible for many of the reactions that ate characteristic of alkenes. It serves as a source of electrons for electrophilic reactions such as addition reactions. Simple examples are the addition of hydrogen or a halogen, eg, chlorine ... 

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