Frontier Molecular Orbitals and Pericyclic Reactions

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

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

3. Course Synopsis • Part Contents • 1 Pericyclic ReactionsThese lectureswill begin with a definition ofPericyclic 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. • 2iElectrocyclic 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). • 2iiCycloaddition Reactions These lectures will introduce cycloaddition reactions and the concepts of (i) phase relationships of the FMOs, (ii) geometry of approachof 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. • 3Photochemically 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 (i) Electrocyclic Reactions using FMO Theory (ii) Cycloaddition Reactions using FMO Theory

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

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

13. Revision: 1,3–Syndiaxial Interactions 1,3-syndiaxial interactions 1 3 2 axial equitorial

14. Thermodynamic and Kinetic Control Thermodynamic Product Not Formed in Cycloaddition Reaction Kinetic Product 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. Starting Material Product Revision: Transition States

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. Pericyclic Reactions Involve Cyclic Transition States Cyclic Transition State

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

27. – Learning Objectives Part 1 – Frontier Molecular Orbitals CHM2C3B – Introduction to FMOs – • 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 C2 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. 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 Negative Cd = -1/√2 Sc2= ca2 + cb2 = 1 p = caf1 + cbf2 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 Anti-bonding Non-bonding Bonding 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 Nodal Position Number of Nodes

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 Nodal Position Number of Nodes y4 3 5/4 = 1.25 y3 2 LUMO 5/3 = 1.66 y2 1 HOMO 5/2 = 2.5 y1 0 5/1 = 5 1 2 3 4 5

44. A Reminder: Sinusodal Wave Function

45. Coefficients, cn 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 Molecular Orbitals Nodal Position Number of Nodes

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 Nodal Position Number of Nodes y5 6/5 = 1.2 4 y4 3 6/4 = 1.5 y3 2 6/3 = 2 y2 1 6/2 = 3 y1 0 6/1 = 6 5 6 1 2 3 4

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