Now that we have discussed the bonding and molecular orbitals in individual molecules and other entities, it is time to examine how the molecular orbitals in the reacting species participate in a reaction to become those of the species produced.
Ultimately, all chemistry can be reduced to a question of the formation and cleavage of chemical bonds during chemical reactions. One of the major successes of the Lewis theory of bonding was the way in which it provided a clear qualitative picture of the bonding in chemical compounds, so that the bonding changes occurring during chemical reactions could be rationalized. In order for molecular orbital theory to be equally useful, it must be capable of doing at least what Lewis theory was able to accomplish, and we are probably justified in expecting more. Fortunately, molecular orbital theory does allow us to ratio- nalize reactions that cannot be explained at all using Lewis theory alone.
The heart and soul of organic chemistry is how molecular orbitals in different mole- cules (or different parts of the same molecule) interact and how electrons reorganize themselves during chemical reactions. This is the reason why we have spent as much time as we have reviewing molecular orbital theory. Let us begin by restating an extremely im- portant fundamental principle.
The Pauli Exclusion principle applies to molecules as well as to atoms and absolutely forbids placing an electron into any orbital already containing two electrons.
This means that any time electrons move from one molecule to another, they must move from an occupied orbital on the first molecule into an empty orbital of the second. If this electron reorganization is to result in the formation of a new covalent bond between atoms in two different molecules, electrons from one molecule must move into a position where they can be shared by the two nuclei between which the new bond is going to be formed. Because all the electrons of a molecule are in orbitals, one must overlap orbitals on both molecules for the reaction to occur. Thus, the Pauli Exclusion principle becomes the first principle of chemical reactions.
Chemical reactions can only be initiated by overlapping a filled or half-filled (occupied) orbital on one reactant with an empty (unoccupied) orbital on the other.
Having decided that the initiation of a chemical reaction involves the overlap of an empty orbital with a filled orbital, we must now answer the key question—which unoccu- pied orbital and which occupied orbital. Clearly, the reaction will proceed most readily if the two orbitals are closely matched in energy. The filled orbitals in most molecules are either bonding orbitals containing bonding electron pairs or nonbonding orbitals contain- ing lone pairs. The unoccupied orbitals are either antibonding orbitals or empty atomic orbitals. The Aufbau principle demands that the unoccupied orbitals of a molecule or ion
Chapter five
Frontier Orbitals and Chemical Reactions
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are always at higher energy than its occupied orbitals. Therefore, the two orbitals closest to each other in energy will be the highest energy occupied molecular orbital (HOMO), on one reactant, and the lowest energy unoccupied molecular orbital (LUMO), on the other.
These orbitals are called the frontier orbitals of the reacting molecules, and it is the frontier orbitals that actually govern much of the reactivity of organic compounds.
Since their emergence in the mid-1960s,1 the concepts of frontier orbitals and the conserva- tion of orbital symmetry2 have revolutionized the way in which organic chemists look at reac- tions, and we will cast many of our discussions of chemical reactivity in terms of the frontier orbital concepts. As with any theory, the conservation of orbital symmetry has limitations, especially when used to predict the outcomes of reactions of excited state reactions. Neverthe- less, the value of the theory has been shown by half a century of successful application.
By knowing the shapes and relative energies of the orbitals involved in most organic reactions, one can actually predict much of the reactivity of organic molecules. As implied in our earlier discussions, π bonds are usually weaker than σ bonds (i.e., the π orbital is usually higher in energy than the σ orbital, and the π* orbital is usually lower in energy than the σ* orbital). Therefore, the energies of frontier molecular orbitals (FMOs), which have important consequences for reactivity of organic compounds, generally increase in the order (worth the effort of committing to memory):
σ < π < n < π* < σ*
With the exception of the hydrogen cation, H+, which has no electrons at all and cannot therefore have a HOMO, all molecules and ions have both a HOMO and a LUMO.
In principle, therefore, there are always two possible HOMO-LUMO combinations for reactions in which H+ is not a participant. Fortunately, one of these combinations is usu- ally obviously right, and the other is usually obviously wrong. We can best illustrate the concept of HOMO and LUMO by looking at some examples. Let us begin with the three different reactive intermediate species with the molecular formula CH3: the methyl cation, CH3+, the methyl radical, CH3•, and the methyl anion, CH3−.
Before we begin, a caveat must be sounded; much of the discussion below is at a rather simplistic level, but this allows us to use it in the context of much more complicated examples without the need for recourse to a computer. Of course, if higher levels of rigor are needed, then one must go to the computer. However, provided that one understands the limitations of the theory one is using, one can usually obtain reliable results without doing so.
We will begin with the methyl cation. The Lewis structure of this cation, as well as its orbital energy level diagram and electron configuration, and its frontier orbitals are given in Figure 5.1. There are six valence electrons in this cation, which means that the valence electrons are all used in the formation of the three C–H σ bonds and that the central carbon atom carries a formal positive charge.
There are only three σ bonds about the central carbon atom, the central carbon atom is sp2 hybridized: the cation is trigonal planar in shape. The remaining orbital on the central carbon atom is the 2p orbital not used in the formation of the sp2 hybrid orbitals, and it is empty. We can think of the HOMO simplistically as a carbon-hydrogen σ orbital, but the HOMO is actu- ally a linear combination of all three C–H σ orbitals; the LUMO is fairly well approximated by
1. (a) Woodward, R.B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87, 395; The Conservation of Orbital Symmetry (Verlag Chemie/Academic Press: Weinheim, 1971)—this book is a stand-alone reprint of Angew. Chem.Int. Ed.
Engl. 1969, 8, 781. (b) Hoffmann, R.; Woodward, R.B. Acc. Chem. Res. 1968, 1, 17. (c) Fukui, K.; Fujimoto, H.
Bull. Chem. Soc. Jpn. 1967, 40, 2018; 1969, 42, 3399. (d) Fukui, K. Fortschr. Chem Forsch. 1970, 15, 1; Acc. Chem.
Res. 1971, 4, 57; Angew. Chem. Int. Ed. Engl. 1981, 21, 801. (e) Longuet-Higgins, H.C.; Abrahamson, E.W. J. Am.
Chem. Soc. 1965, 87, 2045.
2. (a) Fleming, I. Frontier Orbitals and Organic Chemical Reactions (Wiley-Interscience: New York, 1976).
(b) Gilchrist, T.L.; Storr, R.C. Organic Reactions and Orbital Symmetry, 2nd ed. (Cambridge University Press:
Cambridge, 1979). (c) Lehr, R.E.; Marchand, A.P. Orbital Symmetry (Academic Press: New York, 1970).
(e) Pearson, R.G. J. Chem. Educ. 1981, 58, 753.
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the 2p orbital on the carbon. This means that that the LUMO of the cation is an empty p orbital.
Although it is unoccupied, because this orbital is neither bonding nor antibonding, it must be a nonbonding orbital: not all nonbonding orbitals are occupied. Often in this book, we will use the symbol a to denote an unoccupied nonbonding molecular orbital.
The methyl free radical has the formula CH3•, and therefore it has just one electron more than the methyl cation for a total of seven valence electrons. Its Lewis structure, orbital energy level diagram and electron configuration, and its FMOs are given in Figure 5.2. These may be compared with those of the cation.
Figure 5.1 The orbital energy level diagram for the methyl cation. The highest energy occupied molecular orbital (HOMO) is one of the carbon-hydrogen σ orbitals, and the lowest energy unoc- cupied molecular orbital (LUMO) is the empty p orbital not used in forming the sp2 hybrid orbitals of the central carbon atom.
C H
H
H H H
H
σ σ σ
σ∗ σ∗ σ∗
n (LUMO)
(HOMO)
Energy
HOMO
LUMO
Figure 5.2 The orbital energy level diagram and the fron- tier molecular orbitals of the methyl free radical. HOMO, highest energy occupied mo- lecular orbital; LUMO, lowest energy unoccupied molecular orbital.
C H
H
H H H
H
σ σ σ
σ∗ σ∗ σ∗
n (HOMO) (LUMO)
Energy
HOMO LUMO
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In the free radical, the unpaired (nonbonding) electron is in the fourth valence orbital of the central carbon atom. However, whether this odd electron is in an unhybridized p orbital or an sp3 hybrid orbital depends on several factors, and examples of free radicals of both structural types are known. The methyl radical itself is planar. The HOMO of the methyl radical is the p orbital containing the unpaired electron, whereas the LUMO of the methyl radical is a C–H σ* antibonding orbital. Because the HOMO of every free radical is occupied by only one electron instead of two, it is called the singly occupied molecular orbital (SOMO).
The third case that we will examine here is the case of the methyl anion, CH3−, whose Lewis structure, orbital energy level diagram and electron configuration, and FMOs are given in Figure 5.3. This anion has one more electron than the free radical, and so it has eight valence electrons and a formal negative charge on the central carbon atom. The va- lence electrons are distributed as three C–H σ bonds and one lone pair. To accommodate this arrangement of valence electrons, the central carbon atom requires four hybrid orbit- als (one for each σ bond and one for the lone pair), and must therefore be sp3 hybridized.
The anion therefore, has a trigonal pyramidal shape, just like the ammonia molecule. The HOMO of the methyl anion is the (nonbonding) sp3 hybrid orbital containing the lone pair of electrons, whereas the LUMO is a C–H σ* antibonding orbital (or, more accurately, a linear combination of all three C–H σ* orbitals).
The presence of heteroatoms can complicate the picture somewhat because of the dif- ferent energies of the orbitals involved. There is, however, a general rule of thumb that one can use to decide what the relative energies of the orbitals will be. In general, the more polar the bond, the lower the energy of all the orbitals—bonding and antibonding—
associated with it.
Figure 5.3 The orbital energy level diagram and the fron- tier molecular orbitals of the methyl anion. HOMO, high- est energy occupied molecu- lar orbital; LUMO, lowest energy unoccupied molecu- lar orbital.
C H
H H
H H H
σ σ σ
σ∗ σ∗ σ∗
n (HOMO) (LUMO)
Energy
HOMO
LUMO
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Of course, the picture is not really this simple.
From the perspective of the discussion we have just had, the fortunate thing about methyl cations, anions, and free radicals is that they have only one carbon atom and three σ bonds. This makes the methyl system a very simple one to analyze, and what we have done up to now is usually more than sufficient. However, as the systems become more complex, the level of sophistication that we need to discuss them also rises (although not to prohibitive heights). Let us look at the corresponding ethyl species. In Table 5.1, the FMOs of the ethyl cation, the ethyl radical, and the ethyl anion are shown as obtained from computer calculations at the B3LYP/6-31+G* level. This level of sophistication in calculations is actually quite low, but it still provides a wealth of qualitative information that we can use in discussing chemical reactivity.
When we consider the chemistry of the ethyl cation, we know that the electron- deficient carbon atom dominates its reactivity: it usually behaves as the electrophile in reactions, which means that the LUMO is by far the more important of its two FMOs.
Likewise, the reactions of the ethyl free radical all involve the unpaired electron, which makes the SOMO (HOMO) the most important FMO in its reactions. The same analysis of the predicted reactivity of the ethyl anion, which we know is both a powerful nucleop- hile and a powerful base, leads to the conclusion that the orbital carrying the lone pair is going to dominate the reactivity of this species: its reactions involve the HOMO as the most important frontier orbital.
If we now examine these most important FMOs carefully, a remarkable consistency is revealed. In every one of these orbitals, not only is the orbital on carbon an important component of the orbital but also the carbon-hydrogen σ bonds on the adjacent carbon as well. In other words, hyperconjugation plays an extremely important role in each of these FMOs. We can generalize this observation to the molecular orbitals of most species with sp2-hybridized atoms. In almost every one of these species, the C–H σ orbitals on the carbon atom adjacent to the sp2-hybridized atom are involved in the HOMO or LUMO of the species. This accounts, for example, for why carbonyl compounds with α hydrogens
Table 5.1 Frontier Orbitals of Ethyl Species, CH3CH2*
Frontier Orbital (CH3CH2+)† (CH3CH2•) (CH3CH2−) LUMO
HOMO (SOMO)
†The actual structure of this ion is bridged, but computations at this low level return orbitals that can be compared directly with those of the radical and the anion. The highest energy occupied molecular orbital (HOMO) of this cation does not involve the p orbital on the cation carbon, so the orientation has been changed to show the σ orbitals that participate in the HOMO.
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can react with nucleophilic species to give either addition products (nucleophilic addition) or enolate anions (acid-base reactions), and why carbocations give products of both SN1 substitution and E1 elimination.
Let us now look at the LUMO of the ethyl cation again. Here we see that there are ac- tually two places for the HOMO, a nucleophile, to overlap effectively with the cation—the cation carbon and two of the β hydrogens. It is more than a coincidence that these two positions correspond to the two possible reactions of the ethyl cation with which we are already familiar (Figure 5.4). Overlap of the cation LUMO with the nucleophile HOMO at the carbon atom gives us the familiar second step of the SN1 substitution reaction, with the formation of a new carbon-nucleophile bond. If that overlap is moved to one of the β- hydrogen atoms, however, we get the second step of the E1 elimination reaction. You
Nu Nu
C C H H H
Nu
H H C
C H H H
H
C C H H H
H
H C
C H H
H H
H
Nu Nu
Figure 5.4 The reactions of the ethyl cation depend on the point at which the nucle- ophile attacks the cation lowest energy unoccupied molecular orbital.
Figure 5.5 The reactions of the ethyl anion depend on the point at which the electrophile attacks the anion highest energy occupied molecular orbital.
E E
C C H H H
E
H H C
C H H H
H
C C H H H
H
H C
C H H
H H
H
E E
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may recall that the SN1 and E1 reactions always compete—now you have a reason why (it simply depends on exactly where the HOMO-LUMO overlap occurs).
Likewise, when we examine the HOMO of the ethyl anion, we see that the electrophile may attack at the carbanion carbon or at the β hydrogen (Figure 5.5). In this case, the hy- drogen atom is transferred as a hydride ion, rather than as a proton. However, in all other ways this reaction is strictly analogous to the cation case. The transfer of a hydride anion from a carbanion nucleophile has become a very important synthetic method for the re- duction of carbonyl compounds.3
Conformational and Stereoelectronic Effects
The interaction of filled orbitals with empty orbitals is not restricted to reactions be- tween molecules but is also manifested in the overlap between a filled and an empty orbital on adjacent atoms in a molecule. Just as when atomic orbitals on adjacent atoms overlap, the product of the overlap of molecular orbitals on adjacent atoms leads to a change in the respective orbital energies, with the lower energy orbital becoming even lower in energy and the higher energy orbital becoming higher in energy. The extent to which the energy of the orbitals involved changes depends on the efficiency of the overlap.
One major form of this type of overlap is the overlap in carbocations that leads to stabilization of the cation by hyperconjugation. This type of overlap, and the effect on the energy of the system, is shown in Figure 5.6. The π-type overlap between the empty π orbital on carbon and the filled C—H σ orbital on the adjacent carbon has the effect of lowering the energy of the filled orbital and raising the energy of the empty orbital. However, because the energy of the carbocation depends only on the total energy of the electrons in the filled orbitals, this leads to a lowering of the energy of the cation.
Problem
5-1 A pair of ethyl radicals may react with each other in two different ways. Using the SOMO above as a working model, predict the products of these two possible reactions.
Another example of this type of overlap, between a filled orbital on one atom and an empty orbital on the adjacent atom, is provided by the ethane molecule. When one carries out high-level calculations on the conformers of ethane, one finds that not only does the
3. For reviews on the reduction of ketones by hydride transfer from trialkylboranes, for example: (a) Srebnik, M.; Ramachandran, P.V. Aldrichimica Acta 1987, 20, 9. (b) Dhar, R.K. Aldrichimica Acta 1994, 27, 43. (c) Cho, B.T. Aldrichimica Acta 2002, 35, 3. (d) Midland, M.M. Chem. Rev. 1989, 89, 1553. (e) Midland, M.M.; Greer, S.;
Tramontano, A.; Zderic, S.A. J. Am. Chem. Soc. 1979, 101, 2352. (f) Midland, M.M.; McDowell, D.C.; Hatch, R.L.; Tramontano, A. J. Am. Chem. Soc. 1980, 102, 867. (g) Midland, M.M.; Graham, R.S. Org. Syn. 1985, 63, 57.
H
Energy
σ
p
Figure 5.6 p-Overlap between the filled C—H σ orbital and the empty 2p orbital on the carbocation carbon leads to stabilization of the cation.
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dihedral angle change during the rotation about the carbon-carbon σ bond but that the bond distances also change. Thus, one finds that the carbon-carbon σ bond in the staggered conformation is slightly shorter than in the eclipsed conformation, whereas the carbon-hydrogen bonds are slightly longer. This may be viewed as reflecting an increased carbon-carbon bond order in the staggered conformation and a decreased carbon- hydrogen bond order relative to the values in the eclipsed conformation. This may be visualized in terms of a π-type delocalization of electron density from the filled σ orbital on one atom into the empty σ* orbital on the adjacent atom, as shown schematically in Figure 5.7.
The computed molecular orbitals show that even when a more sophisticated treatment us used, the overlap is more efficient in staggered ethane.
The antiperiplanar arrangement of the two C—H bonds results in the most efficient geometry for delocalizing electrons from the σ orbital to the adjacent σ* orbital, so we expect that this arrangement of bonds will be the lowest energy, leading to the staggered conformation being the most stable. By comparison, the overlap between the same or- bitals in the synperiplanar geometry is much less efficient, with a partial antibonding component.
A similar situation holds when we look at the conformations of alkenes and car- bonyl compounds. In this case, it is overlap between the σ orbitals of the C—H bonds and the π* orbital that influences conformational energy. This arrangement, where both C—H σ orbitals can overlap with the C—C π* orbital, is predicted to be the lowest energy, which leads to the conclusion that the eclipsed conformation is lowest energy (Figure 5.8).
Lone pairs can replace the σ orbitals in the forgoing discussion. This leads to two ef- fects that have been observed empirically. The first of these is the gauche effect,4 where the gauche conformer of a disubstituted ethane becomes more favored as the electronegativity of the two substituents increases.5 The second is the anomeric effect,6 which is the obser- vation that the conformational preference of substituents at the ring carbon adjacent to the heteroatom in a saturated six-membered heterocycle is generally lower than the con- formational preference of the same substituent in cyclohexane, leading to a higher per- centage of the axial conformer in the equilibrium mixture (Figure 5.9). The theoretical basis for the anomeric effect has been discussed at length, with most authors proposing the model just discussed, where the electron density from a lone pair is delocalized into the σ* orbital of the adjacent carbon-heteroatom bond.7 This rationalization is not, how- ever, universally accepted,8 and other rationalizations based on dipole-dipole interactions have also been proposed.9 The anomeric effect has been found to be particularly applicable in carbohydrates, where the β (equatorial) isomer of the six-membered hemiacetal is fre- quently found to be much less favored than the α (axial) isomer. These isomers are known as anomers.
4. (a) Huang, J.; Hedberg, K. J. Am. Chem. Soc. 1990, 112, 2070. (b) Dixon, D.A.; Matsuzawa, N.; Walker, S.C.
J. Phys. Chem. 1992, 96, 10740. (c) Wolfe, S. Acc. Chem. Res. 1972, 5, 102.
5. Phillips, L.; Wray, V. J. Chem. Soc. Chem. Commun. 1973, 90.
6. Monographs: (a) Kirby, A.J. The Anomeric Effect and Related Stereoelectronic Effects at Oxygen (Springer- Verlag: Berlin, 1983). (b) Szarek, W.A.; Horton, D. Anomeric Effect (American Chemical Society: Washington, D.C., 1979). (c) Deslongchamps, P. Stereoelectronic Effects in Organic Chemistry (Pergamon: Oxford, 1983).
Reviews: (d) Zefirov, N.S. Tetrahedron 1977, 33, 3193. (e) Lemieux, R.U. Pure Appl. Chem. 1971, 27, 527.
(f) Angyal, S.J. Angew. Chem. Int. Ed. Engl. 1969, 8, 157.
7. (a) Juarista, E.; Cuevas, G, Tetrahedron 1992, 48, 5019. (b) Salzner, U.; Schleyer, P.v.R. J. Am. Chem. Soc.
1993, 115, 10231. (c) Romers, C.; Altona, C.; Buys, H.R,; Havinga, E,. Top. Stereochem. 1969, 4, 39. (d) Wolfe, S.;
Whangbo, M.; Mitchell, D.J. Carbohydrate Res. 1979, 69, 1. (e) Fuchs, B.; Ellencweig, A.; Tartakovsky, E.; Aped, P. Angew. Chem. Int. Ed. Engl. 1986, 25, 287. (f) Praly, J.; Lemieux, R.U. Can. J. Chem. 1987, 65, 213. (g) Booth, H.; Khedair, K.A.; Readsha, S.A. Tetrahedron 1987, 43, 4699.
8. Box, V.G.S. Heterocycles 1990, 31, 1157.
9. (a) Pearson, R.G. J. Am. Chem. Soc. 1988, 110, 7684. (b) Hati, S.; Dhatta, D. J. Org. Chem. 1992, 57, 6056.
H
H H
H
H H
σ∗ σ
H
H H
H H
σ∗ σ
H
Figure 5.7 π-Overlap between adjacent filled and empty orbitals in ethane is most efficient when the bonds are antiperiplanar.
Synperiplanar overlap is much less efficient.
σ*
X Y
n
Figure 5.9 π-Overlap be- tween a filled nonbonding orbital on the heteroatom and the empty σ* orbital on the adjacent atom may ac- count for the extra stability of axial substituents in these six-membered rings.
R H H
σ π∗
σ
Figure 5.8 π-Overlap between adjacent filled σ and empty π* orbitals in propyl- ene is most efficient when the alkene conformation is eclipsed.
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