Introduction to FMO Theory

AO. AO

MO*

MO

LUMOHOMO

LUMO

HOMO

Introduction to FMO Theory

• No net stabilization

Net Stabilization

ΔE

HOMO

LUMO

hν

LUMO

HOMO

hν

LUMO

HOMO

SOMO

σ*s-s

σ s-s

+σ*p-p

σ p-p

+σ*sp3-sp3

σsp3-sp3

+σ*s-sp 3

σs-sp 3

+

+

π*p-p

πp-p

Electrocyclic Reactions

Example

Me

Me

Me

Me

Me

Me LUMO

HOMO

LUMO

HOMO

E

LUMO

HOMO

E

LUMO

HOMO

E

Me

Me

Me

Me

HOMO

Me

Me

HOMO

Me

Me

HOMO

Orbitalmatch

Me

Me

HOMO

Orbitalmatch

Me

Me LUMO

HOMO

Orbitalmatch

Me

Me

Me

Me

LUMO

HOMO

Orbitalmatch

Me

Me LUMO

HOMO

Orbitalmatch

Me

MeMe

Me

Δ

Me

Me

Me

Me

hν

ψ4

ψ3

ψ2

ψ1

Me

MeLUMO

HOMOHOMO

LUMO

Me

Me Me

Me

HOMO

LUMO

hν

Cycloaddition Reactions

Cycloaddition Reactions

LUMOSHOMOS

HOMORLUMOR

I

n

n'k'

k

m

m'I'

The Mathematical Basis of Cycloaddition Predictions

SE = 2(l.k + l' .k') 2 . β2

α( )HOMO S - α( )LUMO R α( )HOMO R - α( )LUMO S

2(m. + n m'. )n' 2 .β2

+

[2+2] cycloaddition

• Can you react two ethylene molecules by thermal conditions?

Heat +

Orbital Analysis of [2+2]Cycloaddition Reaction

NoMatch

Match

Molecule 1 Molecule 2

LUMO

HOMO

LUMO

HOMO

SOMO*

hν

LUMO

HOMO

SOMO*

hν

LUMO

HOMO

LUMO

HOMO

1 2Molecule Molecule

SOMO*

hν

LUMO

HOMO

LUMO

HOMO

1 2Molecule Molecule

Match

Regiochemical Predictions

O-Me O-Me O-MeMe-O Me-O

O-Me

and / orhν

+

CH 2- O-Me

• •

ψ1 ψ1

hνHOMO ψ2 ψ2

SOMO* ψ3ψ3LUMO

as a model for