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 = h2d2ψ/2mdx2 + 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 = φA φB

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 antibonding σ* • •

one node

ψ1 = φA + φB bonding σ • •

no nodes

•

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

C C

C C

LCAOs MOs

E

1

2 π*

π

π - molecular orbitals for ethylene

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

C C C C

C C C C

C C C C

C C C C

LCAOs MOs

E

3

1

2

4

1,3-butadiene

C C C

C C C

C C C

LCAOs MOs

E

3

1

2

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

π*

n

π

Electrocyclic reactions: Δ or hv

conjugated polyene cyclic compound

The mechanism is concerted!

trans- cis-

trans- cis-

geometric isomers

CH3

CH3 CH3CH3

cis -3,4-dimethyl-cyclobutene

heat

cis,trans -2,4-hexadiene

trans -3,4-dimethyl-cyclobutene

heat

trans,trans -2,4-hexadiene

Electrocyclic reactions are both stereoselective and stereospecific

H

CH3

H

CH3

CH3

H

H

CH3

conrotatory

conrotatory

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

C C C C

C C C C

C C C C

C C C C

LCAOs MOs

E

3

1

2

4

HOMO

heat

HOMO = 2

motion must be conrotatory for bonding

HOMO = 2

disrotatory motion wouldresult in antibonding

cis -3,4-dimethyl-cyclobutene

heat

cis,trans -2,4-hexadiene

trans -3,4-dimethyl-cyclobutene

heat

trans,trans -2,4-hexadiene

CH3

H

CH3

H

CH3

H

H

CH3

heat

trans,cis,trans -2,4,6-octatriene

cis -5,6-dimethyl-1,3-cyclohexadiene

disrotatory!CH3

HH

CH3heat

heat

HOMO = 3

disrotatory CH3

HH

CH3

HOMO (polyene) = ? 6 AO 6 MO 6 e-

heat

heat

hv

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

C C C C

C C C C

C C C C

C C C C

LCAOs MOs

E

3

1

2

4

HOMO* = ψ3

HOMO* =3

motion must be disrotatory for bonding

hv

hv

CH3H3C

disrotatoryCH3

H

CH3

H

Woodward – Hofmann Rules for Electrocyclic Reactions:

conrotatory disrotatory

disrotatory conrotatory

thermal photochemical

4n

4n + 2

heat

polyene 6 AOs - 6 MO's 6 e-

thermal HOMO

HOMO = 3

two nodes -

Disrotatory

hv

polyene 6 AOs - 6 MO's 6 e-

photochemical HOMO*

HOMO* = 4

three nodes -

conrotatory

Cycloadditions

Diels-Alderdiene + dienophile cyclohexene

[ 4 + 2 ] cycloaddition

1. diene must be sigma-cis

2. syn- addition

+[ 4 + 2 ]

The Diels-Alder cycloaddition is a concerted reaction:

Molecular orbital symmetry must be conserved.

C C C C

C C C C

C C C C

C C C C

LCAOs MOs

E

3

1

2

4

C C

C C

LCAOs MOs

E

1

2 LUMO

HOMO

LUMO

HOMO

CH2=CH2

CH2=CHCH=CH2

Which orbitals? thermal = HOMO + LUMO

HOMO = highest occupied molecular orbital

LUMO = lowest unoccupied molecular orbital

HOMO

LUMO

symmetryallowedsupra-supra

LUMO

HOMO

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

+hv

+heat

NR

C C

C C

LCAOs MOs

E

1

2 LUMO

HOMO

LUMO

HOMOsymmetryforbidden forsupra-supra

thermal: LUMO + HOMO

C C

C C

LCAOs MOs

E

1

2 HOMO*

LUMO

HOMO*symmetryallowed forsupra-supra

photochemical = HOMO* & LUMO

Woodward – Hofmann Rules for Cycloadditions:

supra-supra

forbidden

supra-supra

allowed

supra-supra

allowed

supra-supra

forbidden

4n

4n + 2

Thermal Photochemical[ i + j ]

+

[ 4 + 4 ]

HOMO = 2

LUMO =

3

forbidden!

+

[ 4 + 4 ]

[ 4 + 2 ]

+

[ 4 + 4 ]

HOMO* = 3

LUMO =

3

hv

allowed

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

G

C C C C C C

G[ 1,3 ]

G

C C C C C C[ 1,5 ]

C C C C

G

G = H, R

Cope rearrangement

[ 3,3 ]

migration of allyl across allyl

HOMO [

HOMO [

[ 1,3 ]

[ 1,5 ]

[ 1,7 ]

[ 1,3 ]

[ 1,5 ]

[ 1,7 ]

Suprafacial migration of H

forbidden

allowed

forbidden

CH3

CD2 CHD2

CH2[1,5]-H

[ 1,3 ]

[ 1,5 ]

[ 1,7 ]

Suprafacial migration of R

allowed with inversionof configuration

allowed with retentionof configuration

allowed with inversionof configuration

H

D

OAc

H* H

H

OAc

D*

[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

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