Molecular Orbitals - Conservation of Orbital Symmetry in Concerted Processes

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.

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

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

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 = φ A  φ B

Bonding when: a) appreciable overlap of atomic orbitals b) energies of atomic orbitals are ~ equal c) same symmetry HydrogenH 2 H:H LCAO of two AO’s  two MO’s ψ 2 = φ A - φ B antibondingσ * one node ψ 1 = φ A + φ B bondingσ no nodes

π – molecular orbitals ethylene CH 2 =CH 2 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 = p z  p z

π*π* π π - molecular orbitals for ethylene

π – molecular orbitals for 1,3-butadiene? CH 2 =CH—CH=CH 2 How many AO’s in the π system? four How many MO’s result?four How many electrons in the π system? 4

1,3-butadiene

+ allyl cation CH 2 =CH—CH 2 3 AO’s  3 MO’s 2 π e - π*nππ*nπ

Electrocyclic reactions: Δ or hv conjugated polyenecyclic compound The mechanism is concerted!

Electrocyclic reactions are both stereoselective and stereospecific

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

In a photochemical electrocyclic reaction, the important orbital is HOMO * ( the first excited state ): HOMO * = ψ 3

Woodward – Hofmann Rules for Electrocyclic Reactions: conrotatory disrotatory conrotatory thermalphotochemical 4n 4n + 2

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

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

LUMO HOMO LUMO HOMO CH 2 =CH 2 CH 2 =CHCH=CH 2

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

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

thermal: LUMO + HOMO

Woodward – Hofmann Rules for Cycloadditions: supra-supra forbidden supra-supra allowed supra-supra allowed supra-supra forbidden 4n 4n + 2 ThermalPhotochemical [ i + j ]

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

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

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