Atomic orbitals alkenes

The simple carbocation intermediate of Equation 10-1 does not account for formation of the antarafacial-addition product. The results with SN1 reactions (Section 8-6) and the atomic-orbital representation (see Section 6-4E) predict that the bonds to the positively charged carbon atom of a carbocation should lie in a plane. Therefore, in the second step of addition of bromine to cyclo-alkenes, bromide ion could attack either side of the planar positive carbon to give a mixture of cis- and trans-1,2-dibromocyclohexanes. Nonetheless, antarafacial addition occurs exclusively ... 

Figure 5.50 shows three related molecules, the 7-methyl substituted (the visual orbital progression explained here is not quite as smooth for the unsubstituted molecules) derivatives of the 7-norbomyl cation (a), the neutral alkene norbomene (b), and the 7-norbomenyl cation (c). For each species an orbital is shown as a 3D region of space, rather than mapping it onto a surface as was done in Fig. 5.49. In (a) we see the LUMO, which is as expected essentially an empty p atomic orbital on C7, and in (b) the HOMO, which is, as expected, largely the n molecular orbital of the double bond. The interesting conclusion from (c) is that in this ion the HOMO of the double bond has donated electron density into the vacant orbital on C7 forming a three-center, two-electron bond. Two n electrons may be cyclically delocalized, making the cation a bishomo (meaning expansion by two carbons) analogue of the aromatic cyclopropenyl cation [326], This delocalized bishomocyclopropenyl structure for 7-norbomenyl cations has been controversial, but is supported by NMR studies [327].

Alkenes contain a C=C double bond. The C=C double bond can be described with two different models. According to the most commonly used model, a C=C double bond consists of a <7- and a tr-bond. The bond energy of the a-bond is 83 kcal/mol, about 20 kcal/mol higher than the tr-bond (63 kcal/mol). The higher stability of <7 bonds in comparison to n bonds is due to the difference in the overlap between the atomic orbitals (AOs) that form these bonds. Sigma bonds are produced by the overlap of two spn atomic orbitals (n 1,2,3), which is quite effective because it is frontal. Pi bonds are based on the overlap of 2,pz atomic orbitals, which is not as good because it is lateral or parallel. 

There are a variety of methods for the computation of the MOs that interact in the transition states of [4+2]-cycloadditions. The LCAO method (linear combination of atomic orbitals) is often employed, and the basic idea is as follows. The MOs of the -systems of alkenes, conjugated polyenes, or conjugated polyenyl cations, radicals, or anions all are built by so-called linear combinations of 2p AOs. In a somewhat casual formulation, one might say that the MOs of these -systems are constructed with the help of the 2pz AOs. These AOs are centered at the positions of the n C atoms that are part of the -system. LCAO computations describe a conjugated -electron system that extends over n s/ 2-hybridized C atoms by way of n Ji-type MOs. 

The only electrons that might be useful in the kind of attraction we have discussed so far are the lone pair electrons on bromine. But we know from many experiments that electrons flow out of the alkene towards the bromine atom in this reaction—the reverse of what we should expect from electron distribution. The attraction between these molecules is not electrostatic. In fact, we know that reaction occurs because the bromine molecule has an empty orbital available to accept electrons. This is not a localized atomic orbital like that in the BF3 molecule. It is the antibonding orbital belonging to the Br-Br G bond the c orbital. There is therefore in this case an attractive interaction between a full orbital (the Jt bond) and an empty orbital (the o orbital of the Br-Br bond). The molecules are attracted to each other because this one interaction is between an empty and a full orbital and leads to bonding, unlike all the other repulsive interactions between filled orbitals. We shall develop this less obvious attraction as the chapter proceeds. 

The n orbital results from combining the two 2p orbitals of the separate carbon atoms. Remember that when we combine two atomic orbitals we get two molecular orbitals. These result from combining the p orbitals either in-phase or out-of-phase. The in-phase combination accounts for the bonding molecular orbital (ji), whilst the out-of-phase combination accounts for the antibonding molecular orbital (jc ). As we progress to compounds with more than one alkene, so the number of Jt orbitals will increase but will remain the same as the number of Tt orbitals. 

But this ignores the alkene. The interaction between 7t (C=C) and the adjacent G (C-Br) will as usual produce two new orbitals, one higher and one lower in energy. The lower-energy orbital, it + a, will now be the LUMO. To construct this orbital we must put all the atomic orbitals parallel and make the contact between 71 + G a bonding contact. 

Unsaturated hydrocarbons have double or triple bonds between carbon atoms. The alkenes have C —C double bonds, described by sp hybridization of the carbon atoms. The alkynes have C —C triple bonds, described by sp hybridization of the carbon atoms. Because bond rotation does not occur readily about a carbon-carbon double bond, many alkenes exist in contrasting isomeric forms, depending on whether bonding groups are on the same (cis) or opposite sides (trans) of the double bond. When two or more double or triple bonds are separated by one single bond, the p orbitals form a conjugated system, in which the de-localized tr orbitals are best described by MO theory. 

Unsaturated hydrocarbons have double or triple bonds between carbon atoms. The alkenes have C —C double bonds, described by sp hybridization of the carbon atoms. A a bond forms by overlap of sp orbitals on adjacent carbon atoms. The parallel nonhybridized 2p orbitals on adjacent carbon atoms overlap to form a C—C 77 bond. 

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