According to the frontier orbital theory, the chemistry of conjugated π systems is largely determined by the HOMO and LUMO π orbitals in the reactant molecules. The outcome of reactions involving interaction of π orbitals can be rationalized using the concepts of orbital phase and symmetry. The figure on the right illustrates what is meant by the orbital phase using 1,3-butadiene as an example. In this molecule, four atomic p orbitals form four π molecular orbitals. The four molecular orbitals differ by the extent of favorable overlap, and thus in energy. The lowest energy MO forms from the in-phase overlap of all four p atomic orbitals; the next one forms when two pairs or in-phase atomic orbitals overlap; the third when one pair of in-phase atomic orbitals overlaps, and the highest energy molecular orbital forms when there are no in-phase overlaps. The MO’s are filled with electrons starting with the lowest-energy orbital such that two electrons occupy an MO. In case of 1,3-butadiene, there are 4 π electrons, thus the second lowest-energy orbital is the HOMO.

The Diels-Alder Reaction

The Diels-Alder reaction is a cycloaddition reaction between a conjugated diene and dienophile.

Diels-Alder reaction has high synthetic utility for making unsaturated six-membered rings. The reaction with unsubstituted dienophile (as shown above) is very slow but the Diels-Alder reactions occur readily when the alkene has a electron-withdrawing substituent. For example, acrolein is a good dienophile. Cycloalkenes, especially ones where the double bond is conjugated to a carbonyl, can be used as dienophiles. The diene is required to have an s-cis conformation and cyclic dienes work well in this reaction. For example, a reaction between 1,3-cyclohexadiene and chloroethene yields a bicyclic reaction product.

Note that chlorine is a relatively poor π-electron withdrawing group and the reaction above in not very fast. Interestingly, many Diels-Alder reactions occur much faster in water than in organic solvents. Scientists are still working on finding out why aqueous environment accelerates this reaction.

Molecular Orbitals in Diels-Alder Reaction

The Diels-Alder reaction is highly stereoselectivive: cis-substituted dienophiles yield cis-substituted cyclohexenes and trans-substituted dienophiles yield trans-substituted cyclohexenes. Stereoselectivity in Diels-Alder reaction can be rationalized considering the overlap of HOMO of one reactant with LUMO of the other. Table below shows π molecular orbitals for ethylene (dienophile) and 1,3-butadiene; clicking on the image will bring up Virtual Reality Modeling Language models for orbitals.

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Dienophile	LUMO (Lowest-Energy Unoccupied Pi Orbital). This orbital accepts electrons from the diene during the reaction. Electron-widtawing substituents conjugated to the double-bond reducing the Pi-electron density and allow for better “flow” of electrons to this orbital. In practice, alkenes with a conjugated carbonyl group are good dienophiles in the Diels-Alder reaction.
Dienophile	HOMO (Highest-energy Occupied Pi Orbital)

Diene	LUMO+1 High-energy unoccupied Pi molecular orbital in butadiene has three nodes and is asymmetric. This molecular orbial rearranges to become the asymmetric LUMO of the reaction product.
Diene	LUMO Lowest unoccupied Pi molecular orbital in butadiene has two nodes and is symmetric. This orbital allows for a favorable overlap with symmetric HOMO of the dienophile during the reaction.
Diene	HOMput DielsAlder.html O Highest occupied Pi molecular orbital in butadiene has one node and is asymmetric. Electrons from this Pi orbital could “flow” to the antisymmetric LUMO of dienophile during the reaction, allowing for formation of two new carbon-carbon bonds.
Diene	HOMO-1 Lowest-energy occupied Pi molecular orbital has no nodes and is symmetric. This molecular orbial rearranges to become the symmetric HOMO of the reaction product.

First, a little about definitions.
Orbital states can be described with several terms:

• Filled – An orbital that contains the maximum number of electrons it can hold.
• Empty – An orbital that contains no electrons.
• Occupied – An orbital that contains at least one electron.
• Unoccupied – An orbital that contains at least one open space for an electron.

	Filled/Occupied
	Occupied/Unoccupied
	Unoccupied/Empty

With these definitions in mind, we can see that a filled orbital is also occupied, but an occupied orbital is not necessarily filled. Also, an orbital can be both occupied and unoccupied. A good way to remember this is that occupied means that one space is occupied by an electron, and unoccupied measn at least one space is free to accept an electron. Thus, it is better to think of filled and empty in terms of the entire orbital, but of occupied and unoccupied in terms of the spaces for electrons.

So, the best way to remember the terms would be as follows:

• Filled – An orbital that is filled with the maximum number of electrons it can hold.
• Empty – An orbital that is empty of electrons.
• Occupied – An orbital that has at least one space occupied by one electron.
• Unoccupied – An orbital that has at least one unoccupied space for an electron.

So, turning now to Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO), we can understand what is meant by these terms better with our definitions form above. These orbitals are called the frontier orbitals, and determine the way the molecule interacts with other species. The HOMO is the orbital that could act as an electron donor, since it is the outermost(highest energy) orbital containing electrons. The LUMO is the orbital that could act as the electron acceptor, since it is the innermost(lowest energy) orbital that has room to accept electrons. In accordance with the above definitions, a single orbital may be both the LUMO and the HOMO.