1. Frontier Molecular Orbitals and Pericyclic Reactions
Third Year
Organic Chemistry Course
CHM3A2
Frontier Molecular Orbitals
and
Pericyclic Reactions
- Prof Jon A Preece -
School of Chemistry
University of Birmingham

2. Prof Preece’s Powerpoint Lecture Presentations
and answers to questions can be found at…
Username: Undergradchem
Password: Preece57nano
Teaching Resources
Queries on course after reading around the subject to
Be Specific with the problem(s) in your .
Give me three times when you are free to see me.
I will you back with a time to see me.

3. Course Synopsis Part Contents
1 Pericyclic Reactions These lectures will begin with a definition of Pericyclic reactions, and will be exemplified by considering examples of cycloaddation, sigmatropic, and electrocyclic reactions. It will be highlighted how it is possible to use FMO theory (and other theories) to predict the constitution and stereochemical outcome of the products. Attention will be drawn to the cyclic transition state and the number of electrons involved (Huckel or Mobius), highlighting that when 4n+2 electrons are involved the reaction proceeds readily under thermal conditions, and the reversibility of such reactions. The concept of Linear Combination of Atomic Orbitals to form a bond(s) (and antibond(s)) will be revised, and extended to the linear combination of frontier molecular orbitals. The p-molecular orbitals of ethene, butadiene and 1,3,5-hexatriene will be considered and the identities of the HOMO and LUMO will be established, as well as the FMOs of a C–H bond.
2i Electrocyclic Reactions This lecture will extend the predicative nature of FMO theory regarding the stereochemical outcomes to electrocyclic reactions for 4 and 6 -electron transition states (by defining the disrotatory or conrotatory movement of the termini of the HOMO in the Transition State).
2ii Cycloaddition Reactions These lectures will introduce cycloaddition reactions and the concepts of (i) phase relationships of the FMOs, (ii) geometry of approach of the FMOs (suprafacial and antarafacial will be defined), and (iii) minimum energy differences between the HOMO and LUMO. These concepts will be exemplified by several Diels-Alder and related reactions. Attention will be drawn to the nature (chemical and stereochemistry) of substituents and their stereochemistry in the product.
3 Photochemically Induced Pericyclic reactions These lecture will extend the predicative nature of FMO theory regarding the outcomes of electrocyclic reactions and cycloaddition reactions by considering how they can be induced photochemically, to give alternative stereochemical outcomes and allow reactions that did not go thermally.

4. Part 1. Frontier Molecular Orbitals
Constructing molecular orbitals and identifying the frontier molecular orbitals
Part 2. Thermal Pericyclic Reactions
(i) Electrocyclic Reactions using FMO Theory
(ii) Cycloaddition Reactions using FMO Theory
Part 3. Photochemical Pericyclic Reactions

5. Second Year Organic Chemistry Course
CHM3A2
Recommended Reading
I Fleming
Frontier Orbitals and Organic Chemical Reactions, John Wiley and Sons, 1996.
Part 1: Ch 1 and Ch 2
Part 2 and 3: Ch 4

7. Part 1(i): The Questions FMO Analysis Can Answer
Second Year Organic Chemistry Course
CHM3A2
Frontier Molecular Orbitals and
Pericyclic Reactions
Part 1(i):
The Questions FMO Analysis Can Answer
100% 0%

8. Ionic And Radical Reactions
To date you have seen two broad categories of reaction:
(i) Ionic reactions
Here pairs of electrons move in one direction
e.g. SN2, SN1, E2 and E1 mechnisms
(ii) Radical reactions
Here single electrons move in a correlated manner
e.g. chlorination of alkanes

9. Pericyclic Reactions
Pericyclic reactions are the third distinct class.
They involve cyclic transition states
In which all bond breaking and bond making steps take place in commensurate manner
And there is no sense of the flow of electrons.

10. Pericyclic Reactions: Electrocyclic Reactions
Stereospecific Reaction
100% 0%
Clockwise
There is no real senses of flow for the electrons in pericyclic reactions
Anti-Clockwise

11. Thermodynamic Product
Pericyclic Reactions: Cycloaddition Reactions
Kinetic Product
Thermodynamic Product
Stereospecific Reaction
100% 0%
Regiospecific Reaction 0%
100%

13. Revision: 1,3–Syndiaxial Interactions2
axial
equitorial

14. Formed in Cycloaddition Reaction Not Formed in Cycloaddition Reaction
Thermodynamic and Kinetic Control
Kinetic
Product
Formed in Cycloaddition Reaction
Thermodynamic
Product
Not Formed in Cycloaddition Reaction

15. Pericyclic Reactions: Sigmatropic Reactions
Stereospecific
Reaction
Regiospecific
Reaction
100% 0%

16. Pericyclic Reactions: Why are they so specific?
Pericyclic reactions show high degrees of
(i) Stereoselectivity
(ii) Regioselectivity, and
(iii) Diastereoselectivity
Thus, an obvious question to ask ourselves at this point is why are pericyclic reactions so selective?
To help begin to answer this question we shall briefly need to revise the SN2 reaction mechanism where YOU WILL remember that this reaction type was highly stereoselective leading to inversion of chiral centres.

18. Revision: SN2 Reaction Mechanism
Nucleophile attacks from behind the C-Cl s-bond.
This is where the s*-antibonding orbital of the C-Cl bond is situated.

19. The concerted flow of both pairs of electrons in the SN2 reaction mechanism leads to the transition state which allows the stereochemical information to be retained,
i.e. a stereoselective reaction.
This SN2 reaction mechanism should be contrasted to the SN1 reaction mechanism where the arrow-pushing is the same but the two pairs electrons do not flow in a concerted fashion. Instead, the haloalkane C-Cl bond heterolytically cleaves to give the planar sp2 hybridised carbocation reactive intermediate. Now the nucleophile can attack from either side of the carbocation leading to racemisation,
i.e. a non-stereoselective reaction.

20. Revision: Transition States
Discussion of reaction mechanisms frequently include discussions of the nature of the transition state for each step in a reaction sequence – or at least for the slowest or rate limiting step.
A transition state is the point of highest energy in a reaction or in each step of a reaction involving more than one step.
The nature of the transition state will determine whether the reaction is a difficult one, requiring a high activation enthalpy (DG‡), or an easy one.
Transition states are always energy maxima, I.e. at the top of the energy hill, and therefore, can never be isolated: there are no barriers to prevent them from immediately “rolling” downhill to form the reaction products or intermediates (or even reform the starting materials).
A transition states structure is difficult to identify accurately. It involves partial bond cleavage and partial bond formation. However, it is nigh on impossible to estimate whether the transition state is an early one (looks more like the starting materials) or a late one (looks more like the products)

21. Revision: Transition States
Product
Starting
Material

22. Pericyclic Reactions: Transition States
Thus, now we can start to understand why pericyclic reactions are so highly stereo-, regio-, and diasteroselective.
Pericyclic reactions involve concerted flow of pairs of electrons going through transition states which retains stereochemical information that was present in the starting material.

23. Cyclic Transition State
Pericyclic Reactions Involve Cyclic Transition States
Cyclic Transition State

24. How do the orbitals overlap?
Pericyclic reactions involve ene and polyene units.
Thus, the transition states involve the overlap of p-molecular orbitals in the case of electrocyclic and cycloaddition reactions, and a p-molecular orbital and s-molecular orbital in the case of sigmatropic reactions.
How do the orbitals overlap?

25. Frontier Molecular Orbitals
In order to understand the selectivity of pericyclic reactions, we need to understand these molecular orbitals and how they overlap.
In particular, we need to know how the Frontier Molecular Orbitals (FMOs) interact in the starting material(s) which lead to the cyclic transition states.
We will first revise some simple molecular orbitals of a C-H s-bond and a C=C p-bond and then extend this analysis to highly conjugated linear polyenes and related structures/

26. Part 1(ii): Frontier Molecular Orbitals
Second Year Organic Chemistry Course
CHM2C3B
Frontier Molecular Orbitals and
Pericyclic Reactions
Part 1(ii):
Frontier Molecular Orbitals

27. Frontier Molecular Orbitals
CHM2C3B
– Introduction to FMOs –
– Learning Objectives Part 1 –
Frontier Molecular Orbitals
After completing PART 1 of this course you should have an understanding of, and be able to demonstrate, the following terms, ideas and methods.
Given a set of n p-orbitals you should be able to construct a molecular orbital energy level diagram which results from their combination.
(ii) In this diagram you should be able to identify for each MO
nodes
the symmetric (S) or antisymmetric (A) nature of the MO towards a C axis or mirror plane
the bonding, nonbonding or antibonding nature of it
(iii) For a set of n molecular orbitals you should be able to identify the frontier molecular orbitals.
the highest occupied molecular orbital (HOMO )
the lowest unoccupied molecular orbital (LUMO)
(iv) The HOMO (thermal reaction) interactions are important when evaluating the probability of an unimolecular reaction occurring and the stereochemical outcome – see electrocyclic reactions.
The HOMO/LUMO (thermal reaction) interactions of the reacting species are important when evaluating the probability of (i) a bimolecular reaction occurring and the stereochemical outcome– see cycloaddition reactions, and (ii) a unimolecular reaction occurring and the stereochemical outcome – see sigmatropic reactions.
The geometry, phase relationship and energy of interacting HOMOs and LUMOS is important for evaluating the probability of a reaction occurring and the stereochemical outcome.

28. s-Bond
Two s Atomic Orbitals
Molecular Orbitals

29. s-Bond
One s Atomic Orbital and One sp3 Atomic Orbital
Molecular Orbitals

30. p-Bond:
Two p Atomic Orbitals
Molecular Orbitals

31. The linear combination of
n atomic orbitals
leads to the formation of
n molecular orbitals

32. A SIMPLE Mathematical Description of a MO
The combination of two (or more) p-atomic orbitals (or any orbitals) to afford 2 p-molecular orbitals can be described by the following simple mathematical relationship
p* = ccf1 + cdf2
p = caf1 + cbf2
fm = Electronic distribution in the atomic orbitals
Cn = Coeffecient: a measure of the contribution which the atomic orbital is making to the molecular orbital

33. p* = ccf1 + cdf2 Sc2 = cc2 + cd2 = 1 p = caf1 + cbf2
The probability of finding an electron in an occupied molecular orbital is 1.
The probability of finding an electron in an occupied molecular orbital is the Sc2
Thus, for the ethene p-molecular orbitals…
p* = ccf1 + cdf2
Sc2 = cc2 + cd2 = 1 1 2
Cc = 1/√2
Cd = -1/√2
Negative
p = caf1 + cbf2
Sc2 = ca2 + cb2 = 1 1 2
Ca = 1/√2
Cb = 1/√2

34. So what about the combination of 3 or 4 or 5 or 6 p-atomic orbitals.
That is to consider conjugated systems…

35. The Allyl Cation, Radical and Anion – 3p AOs to give 3p MOs

36. Allyl Cation
Allyl Radical
Allyl Anion

37. Thus, allyl systems result from the combination of 3 conjugated p-orbitals.
Therefore, this will result in 3 p-molecular orbitals.
When we constructed the p-molecular orbitals of ethene, each contributing AO was the same size, i.e. the coeffecient c were 1/√2 or -1/√2.
When there are three or more p-atomic orbitals combining the size of each contributing p-atomic orbital will not be equal (but they will be symmetrical about the centre).
Finally, we refer to the p-MOs and p*-MOs as y1, y2, y3 (…yn)

38. The Allyl p-Molecular Orbitals
We can consider the molecular orbital (the electron density) being described by a SINE WAVE starting and finishing one bond length beyond the molecule…
y3 = 2 Nodes y3
Nodal
position
4/3 = 1.33
1.33
Nodes
y2 = 1 Nodes
Nodal
position
4/2 = 2 y2 2
y1 = 0 Nodes
Nodal
position
4/1 = 4 y1 1 2 3 4 4

39. For our analysis of molecular orbitals we do not have to concern ourselves with the coefficients.
We can draw the p-AOs that make up the p-MOs all the same size.
However, we have to always remember they are not the same size.
But it is of the utmost importance that we know how to calculate where the nodes are placed

40. Bonding, Non-Bonding, and Anti-bonding Levels
We can consider the molecular orbital (the electron density) being described by a sine wave starting and finishing one bond length beyond the molecule…

41. LUMOs and HOMOs LUMO = Lowest Unoccupied Molecular Orbital
HOMO = Highest Occupied Molecular Orbital
Allyl
Cation
(2e)
Allyl
Radical
(3e)
Allyl
Anion
(4e)
LUMO
LUMO
LUMO
HOMO
HOMO
HOMO

42. Question 1: 4 p-Molecular Orbital System – Butadiene
Construct the p-molecular orbitals of butadiene.
Identify the number of nodes, nodal positions, HOMO and LUMO. yn
Number of
Nodes
Nodal
Position

43. Answer 1: 4 p-Molecular Orbital System – Butadiene
Construct the p-molecular orbitals of butadiene.
Identify the number of nodes, nodal positions, HOMO and LUMO. yn
Number of
Nodes
Nodal
Position y4 3
5/4 = 1.25 y3 2
LUMO
5/3 = 1.66 y2 1
HOMO
5/2 = 2.5 y1
5/1 = 5 1 2 3 4 5

44. A Reminder: Sinusodal Wave Function

45. Coefficients, cn n= caf1 + cbf2 + ccf3 + cnfn Sc2 = 1
Each molecular orbital is described by an equation…
n= caf1 + cbf2 + ccf3 + cnfn
Where c is referred to as the coefficient
Such that the…
Sc2 = 1
That is to say the probability of finding an electron in a molecular orbital is 1

46. 3= caf1 + cbf2 + ccf3 + cdf4

47. We Keep FMO Analysis Simple!!
For the purpose of this course and the third year course (Applied Frontier Molecular Orbitals and Stereoelectronic Effects) you are expected
(i) to be able to place the nodal planes in the correct place
(ii) but not to be able to assign the coefficients to the molecular
orbitals.
That is to say you can draw the p-orbitals that make up each
molecular orbital as the same size, whilst remembering that in reality they are not and for high level FMO analysis this
needs to be taken into account.

48. Question 2: 5 p-Molecular Orbital System – Pentadienyl
Construct the p-molecular orbitals of the cyclopentenyl system.
Identify the number of nodes and nodal positions. yn
Number of
Nodes
Nodal
Position
Molecular
Orbitals

49. Answer 2: 5 p-Molecular Orbital System – Pentadienyl
Construct the p-molecular orbitals of the cyclopentenyl system.
Identify the number of nodes and nodal positions.
Molecular
Orbitals yn
Number of
Nodes
Nodal
Position y5 4
6/5 = 1.2 y4 3
6/4 = 1.5 y3 2
6/3 = 2 y2 1
6/2 = 3 y1
6/1 = 6 1 2 3 4 5 6

50. Question 3: Pentadienyl Cation, Radical & Anion
Introduce the electrons and identify the HOMOs and LUMOs

51. Answer 3: Pentadienyl Cation, Radical & Anion
Introduce the electrons and identify the HOMOs and LUMOs

52. Question 4: Pentadienyl Cation & Anion
Generate the cation and anion and draw the resonance structures of the above species

53. Answer 4: Pentadienyl Cation, Radical & Anion
Generate the cation and anion and draw the resonance structures of the above species

54. 6 p-Molecular Orbital System – 1, 3, 5-Hexatriene

55. 7 p-Molecular Orbital System

56. Question 5: 6p MO System
By shading the p atomic orbitals, generate the molecular orbitals for hexa-1,3,5-triene .
Identify the number of nodes characterising each molecular orbital.
With reference to both a mirror plane (m) and a two-fold axis, designate the orbitals as symmetric (S) or antisymmetric (A).
Using arrows to represent electrons, associate the six p-electrons with the appropriate molecular orbitals of hexa-1,3,5-triene in its ground state.
Finally, identify the HOMO and LUMO.

57. Answer 5: 6p MO System
By shading the p atomic orbitals, generate the molecular orbitals for hexa-1,3,5-triene .
Identify the number of nodes characterising each molecular orbital.
With reference to both a mirror plane (m) and a two-fold axis, designate the orbitals as symmetric (S) or antisymmetric (A).
Using arrows to represent electrons, associate the six p-electrons with the appropriate molecular orbitals of hexa-1,3,5-triene in its ground state.
Finally, identify the HOMO and LUMO.

58. Question 6: MO System
Protonation of A affords B. Draw the three resonance structures of B in which the positive charge has formally been shifted from the oxygen atom onto three of the five carbon atoms .
Considering only these three resonance structures, how many
(i) carbon atoms are involved in the hybrid structure,
(ii) carbon p-orbitals are there,
(iii) p-electrons are associated with the carbon atoms, and
(iv) molecular orbitals are associated with the combination of these carbon p-orbitals
In an analogous fashion to how question 1 was set out, draw out the molecular orbitals resulting from the p-orbital combination on this carbon framework, making sure you identify all of the items listed in question 1.

59. Answer 6: 5p MO System
Protonation of A affords B. Draw the three resonance structures of B in which the positive charge has formally been shifted from the oxygen atom onto three of the five carbon atoms .
Considering only these three resonance structures, how many
(i) carbon atoms are involved in the hybrid structure,
(ii) carbon p-orbitals are there,
(iii) p-electrons are associated with the carbon atoms, and
(iv) molecular orbitals are associated with the combination of these carbon p-orbitals
In an anologous fashion to how question 5 was set out, draw out the molecular orbitals resulting from the p-orbital combination on this carbon framework, making sure you identify all of the items listed in question 5.

62. Part 1(iii): HOMO and LUMO Combination
Second Year Organic Chemistry Course
CHM2C3B
Frontier Molecular Orbitals and
Pericyclic Reactions
Part 1(iii):
HOMO and LUMO Combination

63. What is the Driving Force for Controlling Pericyclic Reactions?
The driving force which controls the product outcome in pericyclic reactions is the in phase combination of the FMOs (the HOMO and LUMO) of the reacting species in the transition state.
FMO Theory is Extremely Powerful.

64. Pericyclic Reactions Involve Conjugated Polyene Systems
Enes and Polyenes are made by the linear combination of p-AOs.
Thus, we first need to construct the molecular orbitals of polyenes.
Then we need to identify the Frontier Molecular Orbitals.
Finally, we will need to construct the correct geometry for orbital overlap of the FMOs in the transition states of the reactions.

65. Highest Occupied Molecular Orbitals
HOMOs and LUMOs
Highest Occupied Molecular Orbitals
Lowest Unoccupied Molecular Orbitals
In bimolecular reactions (like the SN2 and the Diels-Alder reaction), interaction between the two molecular components is represented by interaction between suitable molecular orbitals of each.
The extent of the interaction depends upon the geometry of approach of the components since the relative geometry affects the amount of possible overlap.
It also depends on the phase relationship of the orbitals – and also upon their energy of separation, a small energy favouring a greater interaction.
Generally, the two reactants will interact, via the highest occupied molecular orbital (HOMO) of one component and the lowest unoccupied molecular orbital (LUMO) of the other component, the so-called frontier molecular orbitals (FMOs). Consider the next five frames to appreciate this paragraph of text. Consider an SN2 Reaction…

66. Revision: Transition State Geometries of Nucleophiles Attacking sp3 Tetrahedral Centres
Inversion of Configuration Supports this Attack Angle
LUMO
Nucleophile
HOMO
LUMO

67. The orbital containing the lone pair of electrons on the Nu is the…
HOMO (Highest Occupied Molecular Orbital)
The s* orbital of the C-X bond is the…
LUMO (Lowest Unoccupied Molecular Orbital)
Any bimolecular reaction can be analysed in this fashion

68. Frontier Molecular Orbital Theory (FMOs)
This analysis of FMOs (HOMOs and LUMOs) for such a simple reactions may seem pointless for a simple SN2 reaction.
It is not!
Understand it.
Appreciate that for a bimolecular reaction the HOMO of one component interacts with the LUMO of the second component. (Additionally, for unimolecular reaction the HOMO of the molecular component dictates the reaction course).
In this course we will examine the use of FMOs to explain and predict the outcomes of a class of reactions referred to as pericyclic.
The use of FMOs is an extremely powerful tool to the synthetic organic chemist when analysing and predicting the outcome of pericyclic reactions.

69. – Introduction to FMOs – Frontier Molecular Orbitals
CHM3A2
– Introduction to FMOs –
– Summary Sheet Part 1 –
Frontier Molecular Orbitals
Molecular orbital theory is a powerful and versatile asset to the practice of organic chemistry. As a theory of bonding it has almost superseded the valence bond theory.
Molecular orbital theory has
proven amenable to pictorial non-mathematical expression,
given the right answers to some decisive questions in organic chemistry,
proven the theory of most theoretical chemists,
given insight into not only to the theory of bonding, but also to the theory of making and breaking chemical bonds, and
proven a theory which has been able to explain the pattern of reactivity in a class of reactions, known as pericyclic reactions.
In this course we will concentrate solely on the use of MO theory in predicting the outcome of pericyclic reactions. But it should not be forgotten that MO theory is applicable to other types of chemical reraction
To understand the importance of MO theory, we shall consider three types of pericyclic reactions and show how frontier molecular orbitals of the reactants can be used in a predicative nature to work out whether the reaction will proceed and what the stereo/regiochemical outcome will be.
The three types of pericyclic reactions we will consider are
electrcyclic reactions
cycloaddition reactions
sigmatropic reactions
We will see how it is possible to predict the stereoselectivity, diastereoselectivity, and regioselectivity of pericyclic reactions by the analysis of the FMOs of the transition states

70. The precise construction of the p-molecular orbitals by the linear combination of p-atomic orbitals is extremely important if FMO theory is to yield the correct stereochemical product outcomes,
Key points to note when constructing p-molecular orbitals from the combination of p-AOs are
(i) the combination of n Aos always affords n MOs
(ii) The lowest p-MOs (1) has no nodal planes
(iii) The next highest (2) has one nodal plane, and so on
(iv) The nodal planes need to be placed exactly in the Mos as described in the lecture notes
(v) Electrons fill from the lowest MO first with no more than two electrons in each MO.