Frontier Molecular Orbital Theory Explained

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Frontier molecular orbital theory is an application of the MO theory that describes the interactions of HOMO and LUMO interactions. First published in the Journal of Chemical Physics by Kenichi Fukui in 1952, it is a theory of reactivity that would eventually help Fukui share a Nobel Prize in Chemistry for reaction mechanisms.

He would become the first Asian scientist to win a chemistry-based Nobel Prize.

The foundation of the theory is found by looking at the frontier orbitals, which are the HOMO and LUMO interactions. Fukui made three primary observations for his theory as he watched two molecules interact with one another.

  • When there are occupied orbitals of different molecules, they will repel one another.
  • The positive charges of one molecule with attract the negative charges of the other molecule.
  • The occupied orbitals of one molecule and the unoccupied orbitals of the other molecule, with specificity to the HOMO and LUMO interactions, cause an attraction between the two molecules.

Because of these observations, the frontier molecular orbital theory can explain how the interactions of HUMO in one species are naturally attracted the LUMO of another species.

Why Is It Called the “Frontier” Molecular Orbital Theory?

Frontier molecular theory looks at the orbitals which are at the outer edges of a molecule instead of all the orbitals that may exist. These outer-edge orbitals, on the “frontier” of the molecule, are the ones that tend to be the most spatially delocalized. This means they tend to have the highest and lowest energies, whether they are occupied or unoccupied.

This is where the HOMO and LUMO interactions come into play.

HOMO stands for “highest occupied molecular orbital.” LUMO stands for “lowest unoccupied molecular orbital.” The “high” and “low” components of the description refer to the energies that are present.

Different degrees of energy are present within these components. The next highest occupied molecular orbital, for example, would be designated HOMO +1. It would be followed by HOMO +2 and so forth. The same applies to the LUMO.

Why We Need the Frontier Molecular Orbital Theory

Molecules can begin to form bonds when they are able to share an electron. When two atoms can share two electrons, then you’ve constituted a chemical bond. Atoms can share up to three electrons, forming singular, double, and triple bonds in the process.

Electrons orbit the nucleus, but not in the way that the Earth orbits the sun. They exist as standing waves. That means the lowest possible energy that an electron can take is analogous to the fundamental frequencies of a wave on a string. Using classical mechanics, electrons would eventually have their orbits decay and spiral into the nucleus of the atom. This would cause it to collapse, which means a different orbital process must take place.

This is where FMO comes to help the reaction process of the positive and negative energies which exist in the orbits of every atom. The positive potential energy of an electron will become more negative as it moves toward the attractive field of the atom’s nucleus. The total energy remains constant, however, so the loss of potential energy is compensated by an increase in kinetic energy.

Then, by examining the particles that are in the furthest orbits, the amount of attraction that one has for the other can become a predictor of a chemical reaction. The highest orbitals have energy to give and the lowest orbitals want to take that energy away. In doing so, a balance can be created within an atom.

It also provides the potential of bonding when two atoms are brought together.

Why Is HOMO and LUMO So Important to FMO?

In frontier molecular orbital theory, the HOMO and LUMO are the orbitals which are the most likely to be involved in a chemical reaction. This reaction involves the redistribution of electrons in some way, including the creation or destruction of bonds, through reduction, oxidation, and other allowed methods.

HOMO is the orbital that is still occupied with the highest energy level. That makes it the easiest orbital to have the electrons removed from it.

LUMO is the lowest lying orbital that is not occupied. That makes it the easiest orbital to have electrons added to it.

Frontier molecular orbital theory may focus on HOMO and LUMO, but they are not always involved during chemical reactivity. Symmetry has a role to play within this theory. If the correct symmetry is not present in the reaction, it may shift to the next highest HOMO and next lowest LUMO to complete the process.

By recognizing this process, it becomes possible to predict what can happen during a chemical reaction.

The Three Applications of Frontier Molecular Orbital Theory

There are three specific reactions that occur within frontier molecular orbital theory that are worth noting.

1. Cycloadditions.

This is the reaction that simultaneously forms when a minimum of two new bonds converts into 2+ open-chain molecules into rings. It becomes a pericyclic reaction because these reactions typically involve the electrons within the molecules moving in a continuous ring. The theory also finds that the stereoselectivity of the reaction can be predicted through the consideration and example of how ethane and butadiene react with one another.

Through this process, only the reaction of cyclopentadiene HOMO and maleic anhydride LUMO would be allowed. This is due to the endo-product being favored in frontier molecular orbital theory. Each orbital interaction offers secondary non-bonding interactions which lower the overall energy of the reaction.

2. Sigmatropic Rearrangement

This is a reaction that occurs when a sigma bond moves across a conjugated pi system. A concomitant shift in the pi bonds must be present for this reaction to occur. Antarafacial and suprafacial shifts in the sigma bond are possible. This creates a predictable result through the frontier molecular orbital theory by observing the HOMO and LUMO of the two species.

  • In this application, two separate idea should be considered.
  • Is the reaction allowed or is not allowed?
    Which mechanism of the reaction proceeds through?

3. Electrocyclic Reactions

This is a pericyclic reaction that involves the creation of a sigma bond with the formation of a ring while involving the net loss of a pi bond. It is a reaction which proceeds with wither a disrotatory or conrotatory mechanism. Depending on how the pi system moves from LUMO to HOMO, the reaction will be allowed.

The frontier molecular orbital theory is foundational model of organic chemistry. By observing the HOMO and LUMO and how they react, it becomes possible to predict the results of a chemical reaction.

To understand the benefits of FMO, however, it is necessary to have a solid introduction to molecular orbital theory. FMO is based on the key principles of MO theory, which in itself is based on Lewis Theory, which helps to understand the mechamisms of many reactions.