Limonene is a ten-carbon hydrocarbon. Limonene’s skeleton can be viewed as an adduct of two isoprene molecules (see below). Compounds of this type are called terpenes. Other familiar, naturally occurring terpenes include menthol, camphor, and citronellal.
The following figure shows how the carbon skeletons of limonene and camphor can be divided into two isoprenes linked by two or three additional CC bonds. The OChemPal at Utah Valley University provides some basic information about terpenes and how to identify them.
Selectivity in Diels-Alder Cycloadditions
Limonene is manufactured commercially by the Diels-Alderdimerization of isoprene. One isoprene acts as the diene and the other acts as the dienophile. Isoprene is an electron-rich compound, so it is a relatively unreactive dienophile and high temperatures must be used. The racemic product obtained from this reaction is often referred to as dipentene.
Our experiment also uses a Diels-Alder reaction, but we combine isoprene with methyl vinyl ketone (MVK). MVK is an electron-poor dienophile and is more reactive. This allows lower reaction temperatures.Even so, the thermal reaction of isoprene and MVK must be carried out at 120 oC. Since this temperature is well above the boiling temperatures of both starting materials, the reaction must be carried out in a sealed vessel. Worse, the product is a 71:29 mixture of para and meta regioisomers (only the para regioisomer is useful for making limonene).
Fortunately, chemists have discovered that adding a Lewis acid like AlCl3 to the starting materials simultaneously accelerates the Diels-Alder reaction and makes it more regioselective (Lutz and Bailey). This discovery allows an easy and selective two-step synthesis of limonene: Lewis acid-catalyzed Diels-Alder reaction followed by a simple Wittig reaction.
How Do Chemists Rationalize the Characteristics of Diels-Alder Reactions?
The previous section described three Diels-Alder reactions that exhibit very different characteristics:
- dimerization of isoprene is very slow
- cycloaddition of isoprene and methyl vinyl ketone (MVK) is faster than isoprene dimerization, but is not very regioselective
- Lewis acid-catalyzed cycloaddition of isoprene and MVK is noticeably faster and more regioselective than the uncatalyzed reaction
These observations encompass such large variations in reaction rate and selectivity that it might seem like three different cycloaddition mechanisms must be at work. All of the experimental evidence, however, points to a common reaction mechanism for all three systems. In addition, the evidence suggests that the cycloaddition occurs in a single step, i.e., without intermediates. Therefore, if we want to make sense of these observations, we must think carefully about the transition state for this reaction.
Unfortunately, transition states are hard to draw, much less think about. For example, the following drawing shows how we might compare reaction #1 (X = CH2) with reaction #2 (X = O). Laboratory experiments tell us that #2 is much faster, but the transition state drawings look virtually the same. How are we supposed to “think carefully” about the different transition states? What differences are there?
When conventional drawings (Lewis structures, etc.) fail to shed light on a situation, the solution is too look more deeply into our bag of electronic structure models and see if another theory can help. Frontier molecular orbital (FMO) theory is relatively easy-to-use theory that can rationalize these observations. Briefly, FMO theory says that key transition state properties (energy, geometry) can be estimated by looking at the properties of just one or two molecular orbitals in the reactant molecules. These orbitals are easily calculated using a molecular modeling program like Spartan so FMO theory is a fairly convenient tool.
The following sections sketch the main ideas behind FMO theory. The first section uses a familiar reaction, the SN2 reaction between Br– and CH3Cl, to show how key bond changes in the transition state can be related to just one or two reactant orbitals. This is followed by a section that shows how to predict rates using reactant orbitals, and then a final section that describe an FMO analysis of the Diels-Alder reaction.
FMO Theory I: Bonding Changes Are Mainly Due to Interactions Between Reactant Frontier Orbitals
Molecular orbitals (MOs) come in a variety of shapes and energies, but only certain MOs will interest us. The following chart shows the energies and occupancies of a typical set of molecular orbitals.
Notice that two electrons have been assigned to each of the lowest energy orbitals. These orbitals are “occupied”. The highest energy occupied MO is called the HOMO, and other occupied MOs can be identified by their position in the energy chart relative to the HOMO.
Because electrons are not assigned to the orbitals that have energies above the HOMO, these MOs are “unoccupied”. The lowest energy unoccupied MO is called the LUMO, and other unoccupied MOs can be identified by their position in the chart relative to the LUMO.
You may have noticed that a fairly large energy gap separates the HOMO and LUMO. This can be explained by the fact that occupied MOs are mainly bonding orbitals, while unoccupied MOs are mainly antibonding orbitals. (Note: a “free” or isolated electron is arbitrarily assigned an energy of zero. Occupied MOs invariably have negative energies, but, even though this chart does not show any unoccupied MOs with negative energies, this is not at all unusual.)
Frontier MO theory focuses on the energy and shape of the HOMO and LUMO (and sometimes nearby orbitals like HOMO-1 or LUMO+1). These orbitals are called “frontier” orbitals because they are positioned right next to the “No Man’s Land” that separates the occupied and unoccupied orbitals.
If a molecule gives up an electron during a chemical reaction, it will usually be removed from the molecule’s HOMO because these electrons are the closest (energetically) to being “free”. Likewise, if a molecule gains an electron, it will usually enter the LUMO. Therefore, the frontier MOs are expected to play a major role in defining the electronic shifts that occur during a reaction.
If you reflect on the reactions that you have studied, you will probably agree that most organic reactions shift electrons between different atoms. For example, the following scheme shows how a nucleophile’s lone pair electrons will turn into a bond pair that gets shared by the nucleophile and electrophile. In this case, the “reacting” electrons are described initially by the nucleophile’s HOMO, but they end up in a bonding orbital that looks a little like the nucleophile’s HOMO and also a little like the electrophile’s LUMO.
The contributions of the HOMO and LUMO are particularly evident at the transition state. At this point, the nucleophile (Nu) and electrophile (El) molecules are positioned so that HOMO(Nu) and LUMO(El) overlap. This overlap creates two new orbitals that are superpositions(mathematical mixtures) of the reactant orbitals. One of the new orbitals is a bonding combination of HOMO(Nu) and LUMO(El), and the other is an antibonding combination.Since the bonding orbital is occupied and the antibonding orbital is empty,we ignore the latter.
A good example of a bonding HOMO(Nu)-LUMO(El) interaction can be found in the orbitals of the SN2 transition state. To make things simple, we will use Br– as the nucleophile and CH3Cl as the electrophile. According to FMO theory, the new bonding orbital in the transition state should be a superposition of HOMO(Br–) and LUMO(CH3Cl).
The Br– HOMO is a p-type atomic orbital:
The CH3Cl LUMO looks complicated because it is delocalized over all five atoms, but its interpretation is actually straightforward.
The LUMO’s largest lobes (and the only lobes that face outward towards an approaching nucleophile) are the red lobe near C (left end) and the blue lobe near Cl (right end). If we imagine a nucleophile (Br–)attacking C from the “backside”, it will approach from the left end and the nucleophile HOMO and CH3Cl LUMO will overlap.
Another interesting feature of the LUMO is the node that falls between the small blue and red lobes. This node crosses the region between C and Cl. In other words, the LUMO is C-Cl antibonding or σ* orbital.
The transition state for the SN2 reaction brings Br– and CH3Cl into close proximity (see below). Despite this close approach, most of the transition state orbitals look like reactant orbitals, that is, they preserve their original shapes and energies.
An exception to this rule is provided by the following occupied MO:
This orbital is special because it is delocalized over both reactants and it is occupied. It must, therefore, say something about how the nucleophile and electrophile interact.The energy of this orbital must somehow relate to the energy of the transition state.
The shape of this orbital is also informative. Notice that the left side of the orbital looks like HOMO(Br–), and the right side has the same nodal pattern seen in LUMO(CH3Cl). This orbital is essentially a superposition of the reactant frontier MOs. Also, notice that a single red lobe spans most of the region between Br and C. This orbital is not only a superposition of reactant frontier MOs, it is essentially a bonding combination of HOMO(Br–) and LUMO(CH3Cl), just as FMO theory predicted.
Now that we have identified and described this orbital, we can use it to tell an “MO story” of the SN2 reaction. As the reactants approach, HOMO(Br–) evolves into this new MO. This has two important effects. First, the electron pair that was entirely associated with the nucleophile is delocalized to the electrophile and leaving group; this transfers negative charge from the nucleophile to the leaving group. Second, as HOMO(Br–) evolves, it develops Br-C bonding character and C-Cl antibonding character; this forms a Br-C bond in the transition state and simultaneously breaks the C-Cl bond.
This SN2 reaction is unusual in that the evolution of a single pair of frontier MOs is enough to paint a complete picture of the reaction. There are other reactions in which additional orbitals contribute to the “story” of the reaction, but even when other reactant orbitals are involved, the frontier orbitals are still likely to be important.
FMO Theory II: Rules for Predicting Reactivity and Selectivity
To see how we use the HOMO(Nu)-LUMO(El) interaction to make predictions, we must add one more hypothesis: anything that strengthens the incipient bond between the reactants will stabilize the transition state. Since FMO theory says this bond is created by the HOMO(Nu)-LUMO(El)interaction, we can recast this principle as follows: any modification of the reactants, or transition state geometry, that strengthens the HOMO(Nu)-LUMO(El)interaction will stabilize the transition state and lead to a faster reaction.[Note: both principles could have been stated in the opposite direction as well;weakening the HOMO-LUMO interaction should destabilize the transition state.]
As you may recall from our discussion of bonding last fall, there are two ways to improve a bonding interaction between two orbitals:
- reduce the energy gap – Shrinking the energy gap between HOMO(Nu) and LUMO(El) will strengthen the bonding interaction between these orbitals. Since the gap is defined by two orbital energies,there are two ways to shrink the gap: raise HOMO(Nu) or lower LUMO(El).
- enhance orbital overlap – Improving overlap between HOMO(Nu) and LUMO(El) will strengthen the bonding interaction between these orbitals.
These ideas lead to the following FMO rules for predicting reactivity and selectivity:
- Nucleophiles that have “high energy” (less negative) HOMOs tend to be more reactive.
- Electrophiles that “low energy” (more negative) LUMOs tend to be more reactive.
- The preferred transition state for any reaction is the one that creates the best HOMO(Nu)-LUMO(El) overlap.
FMO Theory III: Diels-Alder Reactivity
The previous section cast FMO theory in terms of nucleophiles and electrophiles, but the reactants in a Diels-Alder reaction do not seem to warrant these labels. How can a neutral diene or alkene correspond to a “nucleophile” or “electrophile”? As it happens, we can use MO energies to assign each Diels-Alder reactant the role of nucleophile or electrophile.
MO calculations show that most Diels-Alder dienes have higher energy HOMOs than Diels-Alder dienophiles. According to FMO rule #1, this observation suggests that dienes are better “nucleophiles” than are dienophiles.
The same MO calculations show that most dienophiles have lower energy LUMOs than their diene partners. According to FMO rule #2, we can regard dienophiles as “electrophiles”.
These assignments, diene = Nu and dienophile = El, are also consistent with experimental observations. Efficient Diels-Alder reactions usually require an electron-rich diene and an electron-poor dienophile.
Now that these electronic roles have been established, we can employ FMO theory to make a simple claim about Diels-Alder reactivity: Diels-Alder reaction rates should correlate with the HOMO(diene/Nu)-LUMO(dienophile/El) energy gap. When this gap is small, a stronger diene-dienophile bond should form in the transition state. This will stabilize the transition state and lead to a faster reaction.
The three Diels-Alder reactions we are considering here combine a common diene/Nu (isoprene) with three different dienophiles/El. Since the dienophile plays the role of electrophile, FMO rule #2 tells us that reaction rate should correlate with LUMO(dienophile) energy. You will test this prediction by using Spartan’18 to calculate the LUMO energies of the following dienophiles:
The previous discussion has focused on reaction rates. However, it is also possible to rationalize the regioselectivity of Diels-Alder cycloadditions using FMO theory. This topic is covered in Chemistry 324, Adv. Physical Organic Chemistry, but students who would like to explore this question now are encouraged to contact Alan Shusterman for more information.