Introduction to FMO Theory
MO*
AO
AO.
MO
Introduction to FMO Theory
• No net stabilization
Net Stabilization
LUMO
E
HOMO
*s-s
+
 s-s
* p-p
+
 p-p
* sp 3-sp 3
+
sp 3-sp 3
* s-sp 3
+
s-sp 3
* p-p
+
p-p
Electrocyclic Reactions
Example
Me
Me
Me
Me
Me
HOMO
LUMO
Me
LUMO
E
HOMO
LUMO
E
HOMO
LUMO
E
HOMO
Me
Me
HOMO
Me
Me
HOMO
Me
Me
HOMO
Orbital
match
Me
Me
HOMO
Orbital
match
Me
Me
HOMO
Orbital
match
LUMO
Me
Me
HOMO
Orbital
match
Me
Me
Me
LUMO
Me
HOMO
Orbital
match
LUMO
Me
Me
Me
Me

Me
Me
Me
Me
h
Me
Me


HOMO
HOMO

Me
LUMO
LUMO

Me
HOMO
Me
Me
h
LUMO
Me
Me
Cycloaddition Reactions
Cycloaddition Reactions
LUMOR
HOMOR
I'
m'
I
m
k'
k
HOMOS
n'
n
LUMOS
The Mathematical Basis of
Cycloaddition Predictions
2(l k + l' k') 
.
SE =
. 2. 2
2(m n + m' n') 
.
+
. 2. 2
(HOMO)S - (LUMO)R (HOMO)R - (LUMO)S
[2+2] cycloaddition
• Can you react two ethylene molecules by
thermal conditions?
+
Heat
Orbital Analysis of
[2+2]Cycloaddition Reaction
LUMO
LUMO
No
Match
HOMO
HOMO
Molecule 1 Molecule 2
Match
Regiochemical Predictions
O-Me
+
O-Me
h
Me-O
O-Me Me-O
and / or
O-Me
CH 2-
O-Me
as a model for
LUMO
  SOMO*
HOMO

•

h

•

