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Molecular Orbitals - Conservation of Orbital Symmetry in Concerted Processes

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Molecular Orbitals - Conservation of Orbital Symmetry in Concerted Processes. Quantum mechanics : application of mathematics and physics to describe phenomena that exhibit quantized functions.

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slide2

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.

slide3

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!

slide4

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

slide5

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

slide6

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

slide7

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

slide9

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

slide11

+

allyl cation CH2=CH—CH2 3 AO’s  3 MO’s 2 π e-

π*

n

π

slide12

Electrocyclic reactions:

Δ or hv

conjugated polyene cyclic compound

The mechanism is concerted!

slide16

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

slide24

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

HOMO* = ψ3

slide30

Cycloadditions

Diels-Alder

diene + dienophile  cyclohexene

[ 4 + 2 ] cycloaddition

1. diene must be sigma-cis

2. syn- addition

slide31

The Diels-Alder cycloaddition is a concerted reaction:

Molecular orbital symmetry must be conserved.

slide32

CH2=CH2

LUMO

HOMO

CH2=CHCH=CH2

LUMO

HOMO

slide33

Which orbitals? thermal = HOMO + LUMO

HOMO = highest occupied molecular orbital

LUMO = lowest unoccupied molecular orbital

slide34

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

slide37

Woodward – Hofmann Rules for Cycloadditions:

Thermal Photochemical

[ i + j ]

4n

4n + 2

slide41

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

slide48

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

slide49

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

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