Organizing chemical reactions and compounds into classes is a long-standing hallmark of organic chemistry. Recall how compounds are grouped into classes based on their func- tional groups and how reactions are classified according to their outcomes (e.g., addition, elimination, substitution, oxidation, reduction) and mechanisms. In this chapter, we will examine the common classes of organic reactions and categorize them in terms of the frontier orbitals involved. Later in this book, we will expand our discussion of synthetic reactions to retrosynthetic analysis, and the design of syntheses. For now, however, let us focus on the frontier orbitals of the reacting species and on how the combination of fron- tier orbitals involved directs the outcome of the reaction.
Bond-forming reactions can be broadly characterized as being unimolecular or bimo- lecular. Because of the Pauli Exclusion principle, bimolecular reactions must always in- volve the overlap of an empty orbital on one reactant with a filled orbital on the other: the HOMO in one reactant (which may contain either one or two electrons) must overlap with the LUMO of the other unless two free radicals are involved. Unimolecular reactions, on the other hand, involve the HOMO only. Bimolecular reactions leading to bond formation are much more common than unimolecular bond-forming reactions and include some of the most widely used synthetic reactions known.
In simple organic compounds, there are only three types of orbitals that can function as a HOMO—an occupied σ orbital, an occupied π orbital, or an occupied nonbonding (n or nπ) orbital (carrying either a lone pair or single electron). Similarly, there are only three possible types of orbitals that can function as a LUMO—an empty nonbonding molecular or atomic (a or aπ) orbital (e.g., the 2p orbital on CH3+), an empty π* orbital, or an empty σ* orbital. Some typical examples of these orbitals are given in Table 5.2.
The n and nπ orbitals in Table 5.1 are actually subsets of the same type of frontier orbital—as are the a and aπ orbitals. Those orbitals designated with the subscript π are nonbonding orbitals in conjugated systems. There are nine and only nine possible com- binations of the three types of HOMO and the three types of LUMO; they are tabulated in Table 5.3.10
10. (a) Lewis, D.E. J. Chem. Educ. 1999, 76, 1718. (b) Jensen, W.B. J. Chem. Educ. 2001, 78, 727.
Table 5.2 Representative Frontier Orbitals Frontier
Orbital Examples
a Empty p orbital on B, C Al, and so on; empty d orbitals on Si, Sb, and so on Electrophilic
aπ ψ2 of allyl cation, and so on; ψ4 of benzyl cation, and so on Electrophilic n Lone pairs in hybrid atomic orbitals Nucleophilic
nπ ψ2 of allyl anion, and so on; ψ4 of benzyl anion, anisole, aniline, and so on Nucleophilic π π orbital of alkene, carbonyl group, cyano group, and so on; ψ2 of diene, conjugated
carbonyl compound or nitrile, and so on; ψ3 of benzene, and so on Nucleophilic π* π* orbital of alkene, carbonyl group, cyano group, and so on; ψ3 of diene, conjugated
carbonyl compound or nitrile, and so on; ψ4 of benzene, and so on Electrophilic σ σ orbital (usually C—H σ orbital) Nucleophilic
σ* σ* orbital (usually C—X σ* orbital of bond to a leaving group) Electrophilic
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Every organic reaction known in which a new bond is formed by transfer of an elec- tron pair from one reactant to another fits one of these HOMO-LUMO (FMO) combina- tions. In general, we look at organic reactions in terms of the bonds being formed.
However, on occasion we will need to look at reactions in which a bond is broken and those in which no bond is formed. Although such reactions can (with some difficulty) be fitted into the classifications above, the relationships are less clear-cut than in reactions in which a bond is formed; we will address such bond rupture reactions at the time we encounter them.
The transfer of a pair of electrons from the HOMO of one molecule to the LUMO of the other corresponds to the reaction between a Lewis acid and a Lewis base.11 The com- pound that reacts via a filled HOMO is functioning as an electron pair donor (i.e., a Lewis base or a nucleophile). A nucleophile, or Lewis base, participates in reactions via its HOMO.
In such reactions, the pair of electrons from the HOMO is placed into the LUMO, so that the compound that reacts via its LUMO is functioning as an electron pair acceptor (i.e., a Lewis acid or an electrophile). An electrophile, or Lewis acid, participates in reactions via the LUMO. What this means, of course, is that much of organic chemistry can actually be reduced to the reaction of a Lewis acid with a Lewis base—or the reaction of an electro- phile with a nucleophile.
The process of examining a reaction from the perspective of what orbitals are over- lapping and what new orbitals are formed can be thought of as a type of “orbital inven- tory.” In generating an orbital inventory for a reaction, one need only adhere to the rules for orbital combination that we have already discussed for atomic orbitals:
1. Orbitals may be combined in a variety of different ways but neither created nor destroyed.
2. For every bonding molecular orbital there is a corresponding antibonding orbital.
One may take this orbital inventory to its logical conclusion and map the correspon- dence between the orbitals of the reactants and the orbitals of the product. Such a mapping is called an orbital correlation diagram. As the occasion arises, we will make use of both
11. (a) Jensen, W.B. Lewis Acid-Base Concepts: An Overview (Krieger Publishing Co.: Melbourne, FL, 1979).
(b) Jensen, W.B. Chem. Rev. 1978, 78, 1. (c) Jensen, W.B. Chemtech 1982, 12, 755.
Table 5.3 Possible Frontier Molecular Orbital Combinations in Organic Chemistry HOMO LUMO Examples of Typical Outcome
n a Bond formation in step 2 of SN1 substitution
n π* Bond formation + bond rupture in nucleophilic or free radical addition n σ* Bond formation + bond rupture in SN2 substitution; anomeric effects in
cyclic systems
π a Bond formation + bond rupture in electrophilic addition π π* Bond formation + bond rupture in cycladdition
π σ* Bond formation + bond rupture in electrophilic addition σ a Bond formation + bond rupture in cation rearrrangements σ π* Stabilization of conformations of unsaturated compounds σ σ* Stabilization of conformations of saturated compounds
*HOMO, highest energy occupied molecular orbital; LUMO, lowest energy unoccupied molecular orbital.
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the pictorial orbital diagrams and the simplified energy level diagrams when discussing organic reactions as well as using orbital inventories and correlation diagrams. First, you should become familiar with the basic concepts so that you can use them later.
Perturbation Approximations for Orbital Coefficients
The use of FMOs for studying organic reactions can be enhanced, especially in reactions involving π-bonded systems, by approximating second-order effects on the coefficients of the contributing basis orbitals in those π bonding systems. This method, which is really a combination of simple Hückel theory and resonance concepts, gives the chemist a way to approximate the FMOs in a more “exact” way, and this allows them to be used with greater confidence in predicting reaction regiochemistry. The basic concepts of this approach and its applications have been discussed in much greater detail than is possible in this single chapter in the book by Fleming.12
O O O
H H H
major minor minor
(5.1) (5.2) (5.3)
At its heart, the perturbation method for approximating the FMOs of a reacting spe- cies leads to a prediction of the relative sizes (larger or smaller) of the lobes of the orbital at a particular position in the orbital. Let us take acrolein (Example 5.1) as an example. The aldehyde molecule can be represented using traditional resonance models as shown at left.
In this case, there is one major (Example 5.1; neutral), and two minor (Examples 5.2 and 5.3; dipolar) canonical forms.
When discussing the chemistry of compounds containing π bonds between unlike atoms (e.g., a carbonyl group), one must be careful when talking about the HOMO, be- cause the HOMO of a carbonyl group, for example, is actually a lone pair (or linear com- bination of lone pairs), and not the C=O π orbital. For this reason, when talking about reactions of π-bonded systems, we will use the term HOMO (π) when referring to the highest energy occupied π molecular orbital.
When we look at the π orbital system of acrolein, we note that it is composed of four atoms (the three sp2-hybridized carbon atoms and the sp2-hybridized oxygen atom) and four electrons. The system will have two occupied and two unoccupied molecular orbitals. To pre- dict its reactivity, we now need to approximate its FMOs. This can be done by separating the orbitals into (1) a base system, which is the hydrocarbon that most closely approximates the neutral canonical form; and (2) the perturbing influence, which is the hydrocarbon ion that most closely resembles the bipolar canonical form.
If we apply this approach to approximating the π molecular orbitals of the acrolein mol- ecule, we infer that the base π molecular orbitals of the acrolein molecule should be modeled on those of 1,3-butadiene (Example 5.4) and that the perturbing influence should be the π orbitals of the allyl cation (Example 5.5). The HOMO (π) should be ψ2 of 1,3-butadiene mod- ified by ψ1 of the allyl cation, and the LUMO should be ψ3 of 1,3-butadiene modified by ψ2 of the allyl cation. In similar fashion, one can approximate the π molecular orbitals of 1- methoxy-1,3-butadiene (Example 5.6) by perturbing the molecular orbitals of 1,3- butadiene (Example 5.4) with those of the 2,4-pentadienyl anion (Example 5.7). In this case, the HOMO (π) should be ψ2 of 1,3-butadiene modified by ψ3 of the pentadienyl anion, and the LUMO should be ψ3 of 1,3-butadiene modified by ψ4 of the pentadienyl anion (Figure 5.10).
12. Fleming, I. Frontier Orbitals and Organic Chemical Reactions (Wiley-Interscience: New York, 1976).
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This removes the symmetry of the orbital coefficients and leads to the situation where there are now preferred sites of attack. It is clear that the superimposition of ψ1 of the allyl cation on ψ2 of 1,3-butadiene gives an orbital where the largest orbital coefficient is at the β carbon (Figure 5.11).
The characteristic reaction of acrolein and other conjugated carbonyl compounds is nucleophilic addition. The LUMO that we have just approx- imated strongly suggests that the preferred regiochemistry of this reac- tion will be either 1,2- or 1,4-. We expect that nucleophiles attacking the alkene π bond will do so preferentially at the β position. Again, because FMO interactions become more important as the reacting species become softer, we expect that soft nucleophiles will tend to give more attack at the β carbon of acrolein.
Perturbation methods can also permit us to estimate the relative ener- gies of the FMOs of a molecule. Based on the same model that we have just used, we can calculate that the energy of the HOMO (π) of acrolein will lie between those of the allyl cation [α + 2βcos(π/4)] and 1,3-butadiene [α + 2βcos(2π/5)]. Likewise, we can predict that the LUMO energy of acrolein will lie between those of the allyl cation [α + 2βcos(π/2)] and 1,3-butadi- ene [α + 2βcos(3π/5)]. This allows us to obtain the following energies for the two frontier orbitals of acrolein:
EHOMO = α + 2βcos(2π/5) + c[α + 2βcos(π/4)] (5.1) ELUMO = α + 2βcos(3π/5) + c[α + 2βcos(π/2)] (5.2)
where c is a coefficient that determines the contribution of the allyl cation wave function to the complete wave function (in other terms, here we see the importance of the minor contributor to the resonance hybrid). This analysis, simplified as it is, allows us to predict that the conjugation of an alkene π bond with a carbonyl group will lead to a lowering of both the HOMO (π) and LUMO energies. We can carry out a similar analysis with ethyl vinyl ether, which can now be approxi- mated by an ethylene molecule perturbed by an allyl anion. This leads to the conclusion that both π molecular orbitals have their energy raised by an electron-donating group, and that the β carbon has the larger or- bital coefficient in the HOMO (π).
When a π bond is formed between a pair of like atoms, the magni- tudes of the orbital coeficients are equal at the same location relative to the center of the orbital. This is not the case, however, when the two atoms participating in the π bond are different. One example of this is provided
larger lobe smaller lobe
Figure 5.11 The asymmetry in the basis orbital contribu- tions to the lowest energy unoccupied molecular or- bital of acrolein leads to dif- ferent outcomes with different nucleophilic additions
OR O
systemBase Perturbing influence
LUMO
HOMO (π)
systemBase Perturbing influence
LUMO
HOMO (π) OR
(5.1) (5.4) (5.5)
(5.6) (5.4) (5.7)
base perturbation
base perturbation result result
Figure 5.10 Construction of the approximate frontier molecular orbitals of acrolein (left) and 1-alkoxy-1,3-butadiene (right). HOMO, highest energy occupied molecular orbital; LUMO, lowest energy unoccupied molecular orbital.
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by the carbonyl group (Figure 5.12). Here, the overlap is between the carbon 2p orbital and the oxygen 2p orbital. Because the carbon 2p orbital is higher in energy, we find that the π orbital is closer in energy to the oxygen atomic orbital and the π* orbital closer in energy to the carbon atomic orbital. This extends to the orbital coefficients as well. The π orbital has a larger coefficient on the oxygen, and the π* orbital has a larger coefficient on carbon. This is illustrated for the LUMOs of C—C and C—O π bonds in Figure 5.12. As we see, the LUMO of an alkene π bond is symmetric, as expected. The LUMO of the car- bonyl group, on the other hand, is quite asymmetric, with large lobes on carbon and small lobes on oxygen, consistent with attack of a nucleophile on a carbonyl group occur- ring at carbon.
Worked Problem
5-1 The Diels-Alder reaction is a cycloaddition reaction where the participating orbit- als are ψ2 of the diene and π* of the dienophile. Using perturbation molecular orbital theory, deduce the qualitative coefficients of the FMOs in Diels-Alder re- action below. What is the regiochemistry of the reaction?
CN +
OMe
§Answer below
§Answer to Worked Problem:
The diene orbital may be viewed as ψ2 of 1,3-butadiene perturbed by ψ2 of the allyl cation. This means that the largest lobe of the diene is at the end of the conjugated system opposite to the methoxy group.
OMe OMe
OMe OMe OMe
The dienophile orbital may be viewed as the π* orbital of ethylene perturbed by ψ2 of the allyl cation, so a similar analysis gives the result that the larger lobe of the dienophile is at the end of the conjugated system opposite to the cyano group.
C N C
N CN
N CN
Figure 5.12 Orbital overlap to generate the π orbitals of the C=O group, and a compari- son of the lowest energy un- occupied molecular orbitals of C=C and C=O bonds.
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Problem
5-2 Using perturbation molecular orbital theory, deduce the qualitative orbital coefficients in the diene ψ2 orbital and the dienophile π* orbital in each of the Diels-Alder reactions below. Use the results of this analysis to predict the re- giochemistry of the reactions:
CN
(a) +
Ph
CN
(b) + NMe2
CHO
(c) +
CN
CO2H
(d) + MeO
CO2
(e) +
Ph
CN
(f) + CO2
Me3SiO MeO
Let us now look at the nine possible FMO combinations of Table 5.2, which are all represented by real reactions in organic chemistry, although the first six entries represent much more common reaction types.