HOMO and LUMO In the Diels Alder Reaction

The HOMO and LUMO In The Diels Alder Reaction

• The Diels-Alder reaction is a concerted reaction between a diene (with 4 pi-electrons) and a dienophile (2 pi-electrons) that forms a new 6-membered ring
• The new C-C sigma bonds are formed from the overlap of the pi molecular orbitals at C1 and C4 of the diene and C1 and C2 of the dienophile.
• In order for the new bonds to form, there has to be constructive overlap between these orbitals – that is, they have to have the same phase.
• By analyzing the molecular orbitals of the diene and dienophile in the Diels-Alder reaction, it becomes clear that constructive overlap is possible between the highest-occupied molecular orbital (HOMO) of the diene with the lowest-unoccupied molecular orbital (LUMO) of the dienophile.
• This type of overlap is not possible in a reaction between two alkenes.

Table of Contents

1. A Quick Recap Of The Diels-Alder Reaction
2. Bond Formation Requires Overlap Between The HOMO Of One Molecule (The Nucleophile) With The LUMO Of Another Molecule (The Electrophile)
3. Concerted Reactions: When Two Bonds Form At The Same Time, Multiple Orbitals Must Overlap
4. Molecular Orbitals In The [2+2] Cycloaddition Between Ethene And Ethene Show Why The Reaction Is Unfavorable Under “Thermal” Conditions
5. Molecular Orbitals In The Diels-Alder Reaction: Interaction of the Diene HOMO with the Dienophile LUMO Is Favorable At Both Bond-Forming Sites
6. Under “Photochemical” Conditions, The [2+2] Actually Works Pretty Well
7. Summary – The Key Role Of Orbital Symmetry In Concerted Reactions Of Pi-Systems
8. Notes

1. A Quick Recap Of The Diels-Alder Reaction

Today we’re going to go into the mechanism of the Diels-Alder reaction from a molecular orbital perspective. Using our previous posts on how to build up molecular orbitals, we’ll show how the Diels-Alder results from the constructive orbital overlap between the highest-occupied molecular orbital (HOMO) of the diene with the lowest-unoccupied molecular orbital (LUMO) of the dienophile.

But first, let’s recap where we are with the Diels-Alder so far:

• The Diels-Alder reaction combines a diene with a dienophile to form a new six-membered ring [see: Introduction to the Diels-Alder reaction] 
• three bonds form (two sigma bonds and a pi bond) and three bonds break (three pi bonds)
• the stereochemistry of the product can be reliably predicted from analyzing the stereochemistry of the diene and dienophile [see: Stereochemistry of the Diels-Alder Reaction]
• in certain cases, mixtures of diastereomers (exo– and endo- ) are obtained.  Generally the endo– is favored over the exo. [see this post on exo and endo] 

What we haven’t really covered is why the Diels-Alder actually works. After all, we’ve seen plenty of examples of things that don’t work; two alkenes, for example, don’t combine to form four membered rings upon heating in the way that a diene and a dienophile combine to form a six-membered ring. Nor do two dienes combine easily upon heating to give eight-membered rings.

Why is the Diels-Alder so easy, and many seemingly related reactions so hard?

The answer to this question lies in the arrangement of pi molecular orbitals in the two components of this reaction.

In the 1960’s a theory of orbital symmetry was developed to understand these reactions, which provided a very useful set of predictive rules – the Woodward-Hoffmann rules.

We will scratch the surface of the orbital symmetry rules here and use them to show why the reaction of dienes with alkenes (the Diels-Alder) occurs readily upon heating,  but the reaction of alkenes with alkenes (a.k.a. [2+2] cycloadditions) does not.

2. Bond Formation Requires Overlap Between The HOMO Of One Molecule (The Nucleophile) With The LUMO Of Another Molecule (The Electrophile)

Most reactions we’ve seen involve a nucleophile (an electron-pair donor) reacting with an electrophile (an electron-pair acceptor) to form ONE new bond.

In order for that bond to form, the filled orbital on the nucleophile containing the electron pair has to come into contact (overlap) with the empty orbital on the electrophile which can accept the electron pair.

[Perfect orbital overlap between nucleophile and electrophile.]

• The pair of electrons on the nucleophile almost always comes from the highest-energy occupied molecular orbital (HOMO) of the nucleophile. Why? Because these are the electrons that are the least tightly held.
•  The orbital on the electrophile that accepts the pair of electrons is almost always the lowest-energy unoccupied molecular orbital (LUMO), because this will result in the lowest-energy transition state (and the fastest reaction). 

In most reactions (such as the S_N2) only one bond is forming at a given center at any one time:

One little note.  In the S_N2 we make the assumption that the HOMO and LUMO have the same phase. This is perfectly valid – so long as we’re only dealing with one bond being formed at a time. 

3. Concerted Reactions: When Two Bonds Form At The Same Time, Multiple Orbitals Must Overlap

Things get more complex when we have a reaction where two or more bonds are formed at the exact same time. This is known as a concerted reaction (as opposed to “stepwise”).

Take the combination of two alkenes to give a cyclobutane ring.  (This is often called a [2+2] cycloaddition.)

Since we have two bonds forming at the same time, we have two orbital interactions to consider.

What’s the nucleophile and the electrophile here?

Ethene and ethene.  : – )

More specifically, the nucleophile is the HOMO of one ethene molecule, and the electrophile is the LUMO of another ethene.

The HOMO of one ethene molecule must combine with the LUMO of another ethene molecule. [We can’t combine two occupied orbitals – Nature has a strict 2-electron occupancy limit per orbital. And since we can’t form a bond without electrons, combining two LUMOs would be silly]

4. Molecular Orbitals In The [2+2] Cycloaddition Between Ethene And Ethene Show Why The Reaction Is Unfavorable Under “Thermal” Conditions

Let’s look at the π molecular orbitals of ethene. The HOMO has zero nodes, and the LUMO has a single node. [We learned how to build up molecular orbitals of ethene in this post]. 

In order for the reaction to occur in a concerted fashion, we must have constructive overlap between each of the lobes where the bonds are being formed. [If the phases are opposite, there is destructive interference between the orbitals and therefore zero electron density between the atoms]

Now let’s bring the two molecules of ethene together:

Note that only one of the interactions between the lobes has lobes of like phase interacting (bonding). The other interaction has lobes of opposite phase interacting, which will not result in a bond. [Note 1]

This helps us understand why [2+2] cycloadditions don’t generally occur under “thermal” conditions (i.e.  heating). The orbitals don’t both overlap! [Note 2]

[2+2] cycloadditions do occur under photochemical conditions, however. More on that in a moment.

5. Molecular Orbitals In The Diels-Alder Reaction: Interaction of the Diene HOMO with the Dienophile LUMO Is Favorable At Both Bond-Forming Sites

Now let’s perform the same kind of analysis on the Diels-Alder reaction.

Since we’ve already seen the molecular orbitals of ethene, let’s look at butadiene. [Relevant post: The Pi Molecular Orbitals of Butadiene].

Now let’s see what happens when we try to line up the HOMO of butadiene with the LUMO of ethene.

[Why not the other way around, with the LUMO of butadiene and the HOMO of ethene? See Note 3 ] 

Here we have the  diene (in the green plane) approaching the dienophile (orange plane) from the top, as a helicopter might approach a landing pad.  New bonds form between C₁ –C₆ and C₄–C₅ . Note that the phases of the lobes for each pair of interactions match and thus have constructive orbital overlap.

[Also note that although the diene is depicted as being on “top” here,  it works equally well if it’s on the bottom  hover here for a pop-up image  or click this link. The symmetry works out in both cases – just like it does for two Lego blocks, even though the phases of the “lobes” on each face are opposite ]

This helps us understand why the Diels-Alder reaction works – the orbital interactions are favorable.

We’ll stop with the Diels-Alder, but  [Note 4] continues the discussion [nerds only].

6. Under “Photochemical” Conditions, The [2+2] Actually Works Pretty Well 

Above, I said the [2+2] cycloaddition doesn’t work under “normal” conditions, by which I meant “heating”. [Organic chemists  usually use the term “thermal” conditions]

However, it’s been observed that if one exposes the reaction to ultraviolet (UV) light, the reaction can proceed quite well. [These are called, “photochemical conditions”].

Why?

Ultraviolet light promotes an electron from the HOMO to the LUMO, resulting in a “new” HOMO. [sometimes called HOMO-prime, or SOMO (for “singly occupied molecular orbital”)]. [Here is a previous post on UV spectroscopy].

Now there are two bonding interactions between the lobes. And the reaction actually works!

Not that one would want to mess with perfection, but it’s at least worth a brief note that promotion of the Diels-Alder reaction is done through heating, not via photochemical means. An attempt to run a Diels-Alder under “photochemical conditions” would be met with the same failure as a [2+2] cycloaddition under thermal conditions, and for the same reasons – because the orbital symmetry is wrong.

7. Summary – The Key Role Of Orbital Symmetry In Concerted Reactions Of Pi-Systems

Under “thermal conditions” (heating, no UV light) the [2+2] is “forbidden” and the Diels-Alder is “allowed”. [Note 4]

The situation reverses in the presence of ultraviolet light, where an electron can be promoted to give a new HOMO with different orbital symmetry.

Under photochemical conditions, the [2+2] cycloaddition between two alkenes is “allowed” and the Diels-Alder is “forbidden”.

We can boil this all down to a simple table:

As we continue to explore this topic, we’ll revisit this table and make updates, because there’s a whole family of reactions where orbital symmetry plays a crucial role.

Notes

Note 1. We’re making the assumption here that one molecule of ethene approaches the other molecule of ethene in the same way we’d bring together two pieces of Lego. The bottom face of one component joins with the top face of another.

Each pair of lobes involved in bonding is on the same face of the molecule. This arrangement is called suprafacial . It’s analogous to “syn“.

There’s another possibility. What if, instead of the “shaded” lobe of the ethene HOMO combining with the “white” lobe of the LUMO, it instead got together with the “shaded” lobe on the other face of the LUMO. Since both lobes have the same phase, this would be a bonding interaction!

There’s a name for the situation where lobes on opposite faces of a reactant participate in a reaction: it’s called, “antarafacial” (similar to “anti“).

You might ask why this doesn’t happen in the [2+2] cycloaddition between alkenes. If you build a model however, you’ll quickly see that the answer is that it ain’t so frickin’ easy! The transition state for a [2+2] between two alkenes with a single antarafacial component is highly strained.

[There are examples of [2+2] cycloadditions that work under thermal conditions, such as those involving ketenes, that do have an antarafacial component. That’s not a topic for today. ]

Note 2. The success of this analysis implies is that during these types of reactions, the symmetry of the molecular orbitals is conserved – in other words, we can treat the relative phases of the lobes on the orbitals as constant on the timescale of the transition state. This is why these rules are titled, “The Conservation of Orbital Symmetry”.

Note 3.  Interactions between the HOMO of the dienophile and the LUMO of the diene are just as favorable from an “orbital symmetry” perspective. The reaction rate, however, will be fastest in situations where the energies of the HOMO/LUMO pair are close together. Most Diels-Alder reactions you’ll see will be of electron-rich dienes (high-energy HOMO) with electron-poor dienophiles (low-energy LUMO).

There are also favorable Diels-Alder reactions between electron-poor dienes (low-energy LUMO) with electron-rich dienophiles (high-energy HOMO). These are known as inverse electron-demand Diels-Alder reactions.

Note 4 – The pattern continues to alternate as additional pi bonds are added; the [4+4] is “thermally forbidden” and the [6+4] is “thermally allowed”. The [6+6] is “thermally forbidden” again, and so on. The cycloaddition with the largest number of pi electrons I am aware of is a [14+2] cycloaddition. This is thermally allowed only because one of the reaction components (heptafulvalene) reacts in an antarafacial fashion.