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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Quantum mechanics Concerted Processes: 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.


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vibrating strings or waves Concerted Processes

wave function: Eψ = h2d2ψ/2mdx2 + v(x)ψ

 

n = 3 nodes = 2

n = 2 nodes = 1

n = 1 nodes = 0

PHASE!


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Electrons and Concerted Processesatomic 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


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Molecular Concerted Processes 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


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Bonding when: Concerted Processes

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


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π – molecular orbitals Concerted Processes

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


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π Concerted Processes - molecular orbitals for ethylene

π*

π


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π – molecular orbitals for 1,3-butadiene? Concerted Processes

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


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1,3-butadiene Concerted Processes


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+ Concerted Processes

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

π*

n

π


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Electrocyclic reactions: Concerted Processes

Δ or hv

conjugated polyene cyclic compound

The mechanism is concerted!


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Electrocyclic reactions are both Concerted Processesstereoselectiveand stereospecific


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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


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In a conserved for bonding to take place.photochemical electrocyclic reaction, the important orbital is HOMO* ( the first excited state ):

HOMO* = ψ3


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Woodward – Hofmann Rules for Electrocyclic Reactions: conserved for bonding to take place.

thermal photochemical

4n

4n + 2


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Cycloadditions conserved for bonding to take place.

Diels-Alder

diene + dienophile  cyclohexene

[ 4 + 2 ] cycloaddition

1. diene must be sigma-cis

2. syn- addition


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The Diels-Alder cycloaddition is a concerted reaction: conserved for bonding to take place.

Molecular orbital symmetry must be conserved.


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CH conserved for bonding to take place.2=CH2

LUMO

HOMO

CH2=CHCH=CH2

LUMO

HOMO


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Which orbitals? conserved for bonding to take place.thermal = HOMO + LUMO

HOMO = highest occupied molecular orbital

LUMO = lowest unoccupied molecular orbital


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


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thermal: LUMO + HOMO conditions, but occur easily photochemically.


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Woodward – Hofmann Rules for Cycloadditions: conditions, but occur easily photochemically.

Thermal Photochemical

[ i + j ]

4n

4n + 2


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Sigmatropic rearrangements conditions, but occur easily photochemically.

“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


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


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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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