-1-
PERICYCLIC REACTIONS NOTES
Pericyclic reactions cannot be treated adequately by “curly-arrow” formalisms and a
knowledge of molecular orbital theory is crucial to their understanding.
They are reactions in which “all first order changes in bonding relationships takes
place in concert on a closed curve” (Woodward & Hoffmann).
More simply, the term “pericyclic” covers all concerted reactions involving a cyclic
flow of electrons through a single transition state.
Pericyclic reactions can be predicted and controlled to a great degree, which makes
them very useful in synthesis.
There are broadly four classes of pericyclic reaction:
Sigmatropic –
These are unimolecular isomerisations, and involve the movement of a σ-bond from
one position to another. An illustration would be the first step of the Claisen
Rearrangement:
Note the nomenclature of this reaction, being described as a [i,j] shift. For example,
this following is a [1,7] shift:
Electrocyclic –
These are unimolecular. They are characterised by ring opening or closing with a σ-
bond forming at one end. Ring closing is more common, since this is formation of a
σ-bond at the expense of a π-bond, but ring strain can lead to opening. Two
examples are:
Cycloaddition –
This is the largest class of pericyclic reaction. It is characterised by two fragments
coming together to form two new σ-bonds in a ring. Some examples are Diels-Alder
and Ozonolysis reactions, which are described below.
Chelotropic reactions are a specific type of cycloaddition, where the two bonds are
made or broken at the same atom. The classic example of this is carbene addition to
a double bond.
Group Transfer –
There are only a few of these reactions, the most common of which is the ene
reaction (see further down). They resemble [1,5] sigmatropic shifts, since a σ-bond
moves, and they also resemble Diels-Alder, but replacing a π-bond with a σ-bond.
These Notes are copyright Alex Moss 2003. They may be reproduced without need for permission.
www.alchemyst.f2o.org
, -2-
Huckel Molecular Orbitals for Linear π-Systems
1) Count the contributing p-orbitals. Total = n.
2) Count the electrons held in these orbitals; two for each double bond, two for a
carbanion or lone pair, one for an unpaired electron, zero for a carbocation.
Total = m.
3) For n contributing p-orbitals there will be n molecular orbitals.
4) Draw n horizontal lines stacked on top of each other to represent the
molecular orbitals and feed in the m electrons two at a time from the bottom
(lowest energy) up (highest energy).
5) Identify the HOMO, the LUMO, and, for radicals, the SOMO. These are the
Frontier Molecular Orbitals (FMOs).
6) Each molecular orbital ψk is considered to be a linear combination of atomic
orbitals φi [ where i designates the atom position with the π-system (an integer
in the range 1-n) ].
Each atomic orbital is “scaled” by a factor cki which is the coefficient at a
particular atom position i within a particular molecular orbital ψk.
n
ψ k = ∑ c kiφi
i =1
For a particular ψk, Σci2 = 1; for a particular atom position i, Σck2 = 1. Evaluated
in radians the value of the orbital coefficient is given by the formula:
2 ⎛ πki ⎞
c ki = . sin ⎜ ⎟
n +1 ⎝ n +1⎠
Aromatic Transition State
All thermally induced pericyclic reactions have transition structures involving a total of
4n+2 electrons. This explanation in terms of an aromatic transition state can be
extended to cover all situations (including those involving antarafacial thermal
reactions) using Frontier Orbitals.
Frontier Molecular Orbitals
These are the HOMO of one component and LUMO of the other.
Compare the following:
The diagram on the left shows a [2+2] addition – not allowed due to the repulsion
(antibonding effects of opposite sign of wavefunction). The other two show a [4+2]
addition (the difference is the LUMO and HOMO are reversed – still both allowed).
Note that barrier to [2+2] addition is only present when both bonds are trying to form
at the same time – stepwise is allowed, but not pericyclic.
An alternative would be for the upper lobe of the C1 in the [2+2] addition to interact.
This would represent an antarafacial reaction, which is allowed. However, this
requires a long flexible conjugated chain.
From a photochemical viewpoint, one molecule has an electron promoted from
HOMO to LUMO, and this excited state molecule reacts with a molecule in the
ground state. The excited LUMO may react with the LUMO of the ground state
molecule, or the excited HOMO with the ground state HOMO. Both of these are the
These Notes are copyright Alex Moss 2003. They may be reproduced without need for permission.
www.alchemyst.f2o.org
, -3-
lowest energy transition states, and can be depicted as ends of the [2+2] addition
and it is thus allowed photochemically.
This can be shown in the following diagram, where the pair on the left represent a
[2+2] addition and the pair on the right a [4+2]:
Frontier Orbital Theory is however only of any use for selectivity and small
differences in reactivity. It is also inherently bimolecular. Thus, for unimolecular
sigmatropic and electrocyclic reactions it is no use, nor does it explain why the barrier
to forbidden reactions is so high.
π-MOs for Ethene
- calculate cki at each position within ψ1 and ψ2 (c11, c12 and c21, c22)
- represent this as a picture showing p-orbitals with the upper lobe shaded
where the coefficients are positive and with the lower lobe shaded at positions
with negative coefficients. This gives a representation of the relative phase
properties of the atomic orbitals contributing to a particular MO.
- the HOMO of ethene (π) has no sign inversions (no nodes), the LUMO (π*)
has one node.
π-MOs for 1,3-Butadiene (n=4, m=4)
The number of nodes increases by one on going to the next higher MO and, in
general, the number of nodes within a particular MO (ψk) is k-1. In a linear π-system if
the number of nodes is Even then the terminal orbital coefficients will be of Equal
sign (i.e. both positive or both negative); if the number of nodes is Odd the terminal
coefficients will be of Opposite sign.
These Notes are copyright Alex Moss 2003. They may be reproduced without need for permission.
www.alchemyst.f2o.org
PERICYCLIC REACTIONS NOTES
Pericyclic reactions cannot be treated adequately by “curly-arrow” formalisms and a
knowledge of molecular orbital theory is crucial to their understanding.
They are reactions in which “all first order changes in bonding relationships takes
place in concert on a closed curve” (Woodward & Hoffmann).
More simply, the term “pericyclic” covers all concerted reactions involving a cyclic
flow of electrons through a single transition state.
Pericyclic reactions can be predicted and controlled to a great degree, which makes
them very useful in synthesis.
There are broadly four classes of pericyclic reaction:
Sigmatropic –
These are unimolecular isomerisations, and involve the movement of a σ-bond from
one position to another. An illustration would be the first step of the Claisen
Rearrangement:
Note the nomenclature of this reaction, being described as a [i,j] shift. For example,
this following is a [1,7] shift:
Electrocyclic –
These are unimolecular. They are characterised by ring opening or closing with a σ-
bond forming at one end. Ring closing is more common, since this is formation of a
σ-bond at the expense of a π-bond, but ring strain can lead to opening. Two
examples are:
Cycloaddition –
This is the largest class of pericyclic reaction. It is characterised by two fragments
coming together to form two new σ-bonds in a ring. Some examples are Diels-Alder
and Ozonolysis reactions, which are described below.
Chelotropic reactions are a specific type of cycloaddition, where the two bonds are
made or broken at the same atom. The classic example of this is carbene addition to
a double bond.
Group Transfer –
There are only a few of these reactions, the most common of which is the ene
reaction (see further down). They resemble [1,5] sigmatropic shifts, since a σ-bond
moves, and they also resemble Diels-Alder, but replacing a π-bond with a σ-bond.
These Notes are copyright Alex Moss 2003. They may be reproduced without need for permission.
www.alchemyst.f2o.org
, -2-
Huckel Molecular Orbitals for Linear π-Systems
1) Count the contributing p-orbitals. Total = n.
2) Count the electrons held in these orbitals; two for each double bond, two for a
carbanion or lone pair, one for an unpaired electron, zero for a carbocation.
Total = m.
3) For n contributing p-orbitals there will be n molecular orbitals.
4) Draw n horizontal lines stacked on top of each other to represent the
molecular orbitals and feed in the m electrons two at a time from the bottom
(lowest energy) up (highest energy).
5) Identify the HOMO, the LUMO, and, for radicals, the SOMO. These are the
Frontier Molecular Orbitals (FMOs).
6) Each molecular orbital ψk is considered to be a linear combination of atomic
orbitals φi [ where i designates the atom position with the π-system (an integer
in the range 1-n) ].
Each atomic orbital is “scaled” by a factor cki which is the coefficient at a
particular atom position i within a particular molecular orbital ψk.
n
ψ k = ∑ c kiφi
i =1
For a particular ψk, Σci2 = 1; for a particular atom position i, Σck2 = 1. Evaluated
in radians the value of the orbital coefficient is given by the formula:
2 ⎛ πki ⎞
c ki = . sin ⎜ ⎟
n +1 ⎝ n +1⎠
Aromatic Transition State
All thermally induced pericyclic reactions have transition structures involving a total of
4n+2 electrons. This explanation in terms of an aromatic transition state can be
extended to cover all situations (including those involving antarafacial thermal
reactions) using Frontier Orbitals.
Frontier Molecular Orbitals
These are the HOMO of one component and LUMO of the other.
Compare the following:
The diagram on the left shows a [2+2] addition – not allowed due to the repulsion
(antibonding effects of opposite sign of wavefunction). The other two show a [4+2]
addition (the difference is the LUMO and HOMO are reversed – still both allowed).
Note that barrier to [2+2] addition is only present when both bonds are trying to form
at the same time – stepwise is allowed, but not pericyclic.
An alternative would be for the upper lobe of the C1 in the [2+2] addition to interact.
This would represent an antarafacial reaction, which is allowed. However, this
requires a long flexible conjugated chain.
From a photochemical viewpoint, one molecule has an electron promoted from
HOMO to LUMO, and this excited state molecule reacts with a molecule in the
ground state. The excited LUMO may react with the LUMO of the ground state
molecule, or the excited HOMO with the ground state HOMO. Both of these are the
These Notes are copyright Alex Moss 2003. They may be reproduced without need for permission.
www.alchemyst.f2o.org
, -3-
lowest energy transition states, and can be depicted as ends of the [2+2] addition
and it is thus allowed photochemically.
This can be shown in the following diagram, where the pair on the left represent a
[2+2] addition and the pair on the right a [4+2]:
Frontier Orbital Theory is however only of any use for selectivity and small
differences in reactivity. It is also inherently bimolecular. Thus, for unimolecular
sigmatropic and electrocyclic reactions it is no use, nor does it explain why the barrier
to forbidden reactions is so high.
π-MOs for Ethene
- calculate cki at each position within ψ1 and ψ2 (c11, c12 and c21, c22)
- represent this as a picture showing p-orbitals with the upper lobe shaded
where the coefficients are positive and with the lower lobe shaded at positions
with negative coefficients. This gives a representation of the relative phase
properties of the atomic orbitals contributing to a particular MO.
- the HOMO of ethene (π) has no sign inversions (no nodes), the LUMO (π*)
has one node.
π-MOs for 1,3-Butadiene (n=4, m=4)
The number of nodes increases by one on going to the next higher MO and, in
general, the number of nodes within a particular MO (ψk) is k-1. In a linear π-system if
the number of nodes is Even then the terminal orbital coefficients will be of Equal
sign (i.e. both positive or both negative); if the number of nodes is Odd the terminal
coefficients will be of Opposite sign.
These Notes are copyright Alex Moss 2003. They may be reproduced without need for permission.
www.alchemyst.f2o.org
