Molecular Orbitals - Conservation of Orbital Symmetry in Concerted Processes

1. Molecular Orbitals - Conservation of Orbital Symmetry in Concerted Processes

2. Quantum mechanics: application of mathematics and physics to describe phenomena that exhibit quantized functions. eg. Electrons in atoms behave like waves. Wave mechanics can be used to solve for energies and orbitals. The math is very complicated and time consuming. By making assumptions and approximations, it is possible to get solutions that are useful, if not exact. In fact, we do not need to do any math if we understand the results on a qualitative level.

3. vibrating strings or waves wave function: Eψ = h2d2ψ/2mdx2 + v(x)ψ   n = 3 nodes = 2 n = 2 nodes = 1 n = 1 nodes = 0 PHASE!

4. Electrons and atomic wave functions. Three dimensional in a spherical potential  energies and probabilities of finding an electron with given energy, orbitals. s, p, d, f Atomic Orbitals (AOs) phase is important! n = 1, no nodes, lowest energy, s orbital n = 2, one node, higher energy, p orbital

5. Molecular Orbitals (MOs) Covalent bonds result from the overlap (combinations) of atomic orbitals to produce molecular orbitals. Molecular orbitals result from Linear Combinations of Atomic Orbitals. LCAO wave mechanics of MO’s φ = atomic wave function ψ = molecular wave function For molecule A—B ψ = φA φB

6. Bonding when: a) appreciable overlap of atomic orbitals b) energies of atomic orbitals are ~ equal c) same symmetry Hydrogen H2 H:H LCAO of two AO’s  two MO’s ψ2 = φA- φB antibondingσ* • • one node ψ1 = φA+ φB bondingσ • • no nodes •

7. π – molecular orbitals ethylene CH2=CH2 look only at π orbitals How many AO’s in the π system? p + p two How many MO’s result? also two How many electrons in the π system? 2 ψ = pz pz

8. π - molecular orbitals for ethylene π* π

9. π – molecular orbitals for 1,3-butadiene? CH2=CH—CH=CH2 How many AO’s in the π system? four How many MO’s result? four How many electrons in the π system? 4

10. 1,3-butadiene

11. + allyl cation CH2=CH—CH2 3 AO’s  3 MO’s 2 π e- π* n π

12. Electrocyclic reactions: Δ or hv conjugated polyene cyclic compound The mechanism is concerted!

14. Electrocyclic reactions are both stereoselectiveand stereospecific

16. In the concerted electrocyclic reactions, symmetry must be conserved for bonding to take place. The molecular orbital involved = highest occupied molecular orbital in thepolyene. HOMO HOMO

24. In a photochemical electrocyclic reaction, the important orbital is HOMO* ( the first excited state ): HOMO* = ψ3

27. Woodward – Hofmann Rules for Electrocyclic Reactions: thermal photochemical 4n 4n + 2

30. Cycloadditions Diels-Alder diene + dienophile  cyclohexene [ 4 + 2 ] cycloaddition 1. diene must be sigma-cis 2. syn- addition

31. The Diels-Alder cycloaddition is a concerted reaction: Molecular orbital symmetry must be conserved.

32. CH2=CH2 LUMO HOMO CH2=CHCH=CH2 LUMO HOMO

33. Which orbitals? thermal = HOMO + LUMO HOMO = highest occupied molecular orbital LUMO = lowest unoccupied molecular orbital

34. [ 2 + 2 ] cycloadditions do not occur readily under thermal conditions, but occur easily photochemically.

35. thermal: LUMO + HOMO

37. Woodward – Hofmann Rules for Cycloadditions: Thermal Photochemical [ i + j ] 4n 4n + 2

41. Sigmatropic rearrangements “no mechanism, no reaction – reaction.” Migration of an atom or group with its sigma bond within a conjugated π framework. G G | | C—(C=C)n (C=C)n—C

48. [1,3] sigmatropic rearrangement of carbon requires inversion of configuration about a chiral center:

49. Conservation of molecular orbital symmetry is useful in concerted reactions. Electrocyclic reactions: stereochemistry, conrotatory or disrotatory thermal HOMO (polyene) photochemical HOMO* (polyene) Cycloadditions: supra-supra allowed or forbidden thermal LUMO & HOMO photochemical LUMO & HOMO* Sigmatropic rearrangements suprafacial allowed or forbidden HOMO (π + 1) retention or inversion of configuration