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Frost developed this mnemonic patterning as an extension of the Huckel (4n+2) rule. A Frost diagram is usually applied to all-carbon, monocyclic, pi systems. It allows one to find the number of molecular orbitals in the molecule's pi system and their energetic positions. To construct a Frost diagram, proceed as follows:

• Draw a circle and inscribe a regular polygon with a vertex located at the bottom of the circle. If you are interested in benzene draw a hexagon, for tropylium ion draw a heptagon.
• Energy-wise, the top and bottom of the circle are defined as $\ce{+2\beta}$ and $\ce{-2\beta}$ respectively (so the circle has radius $\ce{2\beta}$); the center of the circle is located at $\ce{0\beta}$; other points can be interpolated accordingly; the bottom of the circle is at lower energy than the top of the circle.
• Wherever a vertex of the polygon touches the circle, that is the energetic location of a molecular orbital.
• Include an $\ce{\alpha}$ in front of the $\ce{\beta}$ term in order to properly state the energy of the molecular orbital (MO)

Using benzene as an example, the lowest MO has energy $\ce{\alpha-2\beta}$; the HOMO is degenerate (2 MO's) and located at $\ce{\alpha{-}\beta}$; the LUMO is also degenerate and located at $\ce{\alpha{+}\beta}$. Any orbital below the center of the circle is bonding, any orbital at the center is non-bonding and any orbital in the top-half of the circle is antibonding.

Frost developed this mnemonic patterning as an extension of the Hückel ($4n+2$) rule. A Frost diagram is usually applied to all-carbon, monocyclic, π systems. It allows one to find the number of molecular orbitals in the molecule's π system and their energetic positions. To construct a Frost diagram, proceed as follows:

• Draw a circle and inscribe a regular polygon with a vertex located at the bottom of the circle. The polygon has the same shape as the ring you are interested in. For example, if you are interested in benzene, draw a hexagon; for the tropylium ion, draw a heptagon.
• Energy-wise, the top and bottom of the circle are defined as $\alpha+2\beta$ and $\alpha-2\beta$ respectively (so the circle has radius $2\beta$); the center of the circle is located at $\alpha$; other points can be interpolated accordingly; the bottom of the circle is at lower energy than the top of the circle.
• Wherever a vertex of the polygon touches the circle, that is the energetic location of a molecular orbital.

Using benzene as an example, the lowest MO has energy $\alpha-2\beta$; the HOMO is degenerate (2 MO's) and located at $\alpha-\beta$; the LUMO is also degenerate and located at $\alpha+\beta$. Any orbital below the center of the circle is bonding, any orbital at the center is non-bonding and any orbital in the top-half of the circle is antibonding.

Frost developed this mnemonic patterning as an extension of the Huckel (4n+2) rule. A Frost diagram is usually applied to all-carbon, monocyclic, pi systems. It allows one to find the number of molecular orbitals in the molecule's pi system and their energetic positions. To construct a Frost diagram, proceed as follows:

• Draw a circle and inscribe a regular polygon with a vertex located at the bottom of the circle. If you are interested in benzene draw a hexagon, for tropylium ion draw a heptagon.
• Energy-wise, the top and bottom of the circle are defined as $\ce{+2\beta}$ and $\ce{-2\beta}$ respectively (so the circle has radius $\ce{2\beta}$); the center of the circle is located at $\ce{0\beta}$; other points can be interpolated accordingly; the bottom of the circle is at lower energy than the top of the circle.
• Wherever a vertex of the polygon touches the circle, that is the energetic location of a molecular orbital.
• Include an $\ce{\alpha}$ in front of the $\ce{\beta}$ term in order to properly state the energy of the molecular orbital (MO)

Using benzene as an example, the lowest MO has energy $\ce{\alpha-2\beta}$; the HOMO is degenerate (2 MO's) and located at $\ce{\alpha-\beta}$; the LUMO is also degenerate and located at $\ce{\alpha+\beta}$. Any orbital below the center of the circle is bonding, any orbital at the center is non-bonding and any orbital in the top-half of the circle is antibonding.

Frost developed this mnemonic patterning as an extension of the Huckel (4n+2) rule. A Frost diagram is usually applied to all-carbon, monocyclic, pi systems. It allows one to find the number of molecular orbitals in the molecule's pi system and their energetic positions. To construct a Frost diagram, proceed as follows:

• Draw a circle and inscribe a regular polygon with a vertex located at the bottom of the circle. If you are interested in benzene draw a hexagon, for tropylium ion draw a heptagon.
• Energy-wise, the top and bottom of the circle are defined as $\ce{+2\beta}$ and $\ce{-2\beta}$ respectively (so the circle has radius $\ce{2\beta}$); the center of the circle is located at $\ce{0\beta}$; other points can be interpolated accordingly; the bottom of the circle is at lower energy than the top of the circle.
• Wherever a vertex of the polygon touches the circle, that is the energetic location of a molecular orbital.
• Include an $\ce{\alpha}$ in front of the $\ce{\beta}$ term in order to properly state the energy of the molecular orbital (MO)

Using benzene as an example, the lowest MO has energy $\ce{\alpha-2\beta}$; the HOMO is degenerate (2 MO's) and located at $\ce{\alpha{-}\beta}$; the LUMO is also degenerate and located at $\ce{\alpha{+}\beta}$. Any orbital below the center of the circle is bonding, any orbital at the center is non-bonding and any orbital in the top-half of the circle is antibonding.

A Frost diagram is usually applied to all-carbon, monocyclic, pi systems. It allows one to find the number of molecular orbitals in the molecule's pi system and their energetic locations. To construct a Frost diagram, proceed as follows:

• Draw a circle and inscribe the polygon with a vertex located at the bottom of the circle.
• Energy-wise, the top and bottom of the circle are defined as $\ce{+2\beta}$ and $\ce{-2\beta}$ respectively; the center of the circle is at $\ce{0\beta}$; other points can be interpolated accordingly; the bottom is lower energy than the top of the circle.
• Wherever a vertex of the polygon touches the circle, that is the location of a molecular orbital.
• Include an $\ce{\alpha}$ in front of the $\ce{\beta}$ term in order to state the energy of the molecular orbital (MO)

Benzene has one MO energetically located at $\ce{\alpha-2\beta}$. It also has two degenerate MO's located at $\ce{\alpha-\beta}$.

Frost developed this mnemonic patterning as an extension of the Huckel (4n+2) rule. A Frost diagram is usually applied to all-carbon, monocyclic, pi systems. It allows one to find the number of molecular orbitals in the molecule's pi system and their energetic positions. To construct a Frost diagram, proceed as follows:

• Draw a circle and inscribe a regular polygon with a vertex located at the bottom of the circle. If you are interested in benzene draw a hexagon, for tropylium ion draw a heptagon.
• Energy-wise, the top and bottom of the circle are defined as $\ce{+2\beta}$ and $\ce{-2\beta}$ respectively (so the circle has radius $\ce{2\beta}$); the center of the circle is located at $\ce{0\beta}$; other points can be interpolated accordingly; the bottom of the circle is at lower energy than the top of the circle.
• Wherever a vertex of the polygon touches the circle, that is the energetic location of a molecular orbital.
• Include an $\ce{\alpha}$ in front of the $\ce{\beta}$ term in order to properly state the energy of the molecular orbital (MO)

Using benzene as an example, the lowest MO has energy $\ce{\alpha-2\beta}$; the HOMO is degenerate (2 MO's) and located at $\ce{\alpha-\beta}$; the LUMO is also degenerate and located at $\ce{\alpha+\beta}$. Any orbital below the center of the circle is bonding, any orbital at the center is non-bonding and any orbital in the top-half of the circle is antibonding.