Chem 331 Fall 2014
Molecular Orbital Theory
Part 1
Prof. Donald Watson
"
"
"
Molecular Orbitals
1.  Molecular Orbitals (MO’s) are created by combining Atomic Orbitals
(AO’s)
2.  Symmetry of AOs must match and there must be overlap to combine.
3.  Cardinal Rule:
number of MOs = number of AOs used to make them
4.  Population of MO’s with electrons leads to the formation OR BREAKING
of bonds.
5.  MO exist REGARDLESS if they have electrons in them or not.
Dihydrogen
H
H
H
H
What does this really mean?
Adding Waves
constructive
in phase
waves
bigger wave
destructive
out phase
waves
no wave
Dihydrogen
H 1s
H 1s
σ∗
destructive
H
+
H
H
H
anti-bonding
out of phase
σ
H 1s
H 1s
H
+
in phase
constructive
H
H
H
bonding
σ orbital (major lobe) lies mainly between atoms (i.e. "the bond")
σ∗ orbital (major lobes) lies mainly behind atoms but in-line with the bond
“Molecular Orbital Diagram”
H
H
σ∗ (anti-bonding)
Energy
H 1s
H 1s
H
H
σ (bonding)
•  Shows AO energies relative to MO energies in both constructive
(stabilization) and destructive (destabilization) addition.
•  Almost always qualitative.
Add Electrons
H
H
σ∗ (anti-bonding)
H 1s
H 1s
H
Bond order for H2 is 1.
H
σ (bonding)
H
H
σ∗ (anti-bonding)
H 1s
ΔE = Stablization Energy
(Bond Strenght, 104 kcal/mol for H 2)
H 1s
H
H
σ (bonding)
Molecular Orbital Theory – Organic Molecules
H
H
H
C
H
H
H
H-C-H
Angle = 109 °
H
C
H
H
H
C
H
H
tetrahedral carbon
AO’s
4 X H1S
1 X 22S
3 X C2P
8 AO’s
8 MO’s
Orient Molecule
z
z
z
y
y
y
z
x
x
x
2px
2S
y
x
2py
2pz
z
y
H
H
H
H
x
C
H
H
H
H
SALCS
"1/4" of a 1S orbital at all sites
combine to
make salcs
4 H1S
"1/4" of a 1S orbital at all sites
4 AO's
4 symmetry adapted linear combination of atomic orbitals (SALCS)
MO’s with Carbon 2S
1X SALC 1
22S
out of phase with 1st SALC (anti-bonding)
1x 2s
c2S
in phase with 1st SALC (bonding)
MO’s with Carbon 2P
C2P
out of phase with SALCS (anti-bonding)
3X SALC 2
2x 2p
C2P
in phase with SALCS (bonding)
Complete Picture
3X SALC 2
1X SALC 1
2x 2p
1x 2s
Electronic Configuration
3X SALC 2
1X SALC 1
2x 2p
photoionization spectrum methane
(valance)
1x 2s
NOTE: 2 BANDS!
C AO's
(4 valance e –)
H SALCS
(4 X 1 valance e –, 4 total)
MO’s “Complex” Organic Molecule
Taxol – anticancer – C47H51NO14
51 H1S + 47 C2S + 162 C2P + 1 N2S + 3 N2P + 14 O2S + 42 O2P
= 320 AO’s! = 320 MO’s!!!!
Palytoxin – marine toxin from coral – C129H223N3O54
= 967 MO’s!!!!!!
Much Simpler Picture – Hybrid Orbitals
•  Take linear combination of s and p orbitals to make “hybrid” orbitals.
•  Allows you to easily consider molecular orbitals of individual or small
groups of bonds in isolation.
•  Gives a close approximation of full MO picture, but allows for rapid
analysis of complex, low symmetry molecules (most organic
molecules).
•  WE WILL CALL THIS FRONTIER MOLECULAR ORBITAL THEORY
(FMO)
sp3 Hybrid Orbitals
2px
2py
4 sp3 hybrid orbitals
y
x
x
x
z
y
y
y
2S
z
z
z
x
2pz
sp3 Hybrid Orbitals
two phases of unequal size
atom at node
Each sp3 orbital is comprised of ¼ S orbital and ¾ P orbitals.
sp3 Hybrid Orbitals
H
C
H
Angle = 109 °
Angle = 109 °
H
H
All H-C-H angles 109 °
All sp3 orbitals oriented at angles 109 °
Bonding with sp3 hybrid orbitals
H
Look at a single C-H bond
C
H
H
H
C sp3
σ∗
H 1s
destructive
+
C
H
out of phase
C sp3
H
C
anti-bonding
σ
H 1s
constructive
C
+ H
C
H
in phase
bonding
MO Diagram
H
C
σ∗ (anti-bonding)
C sp3
H 1s
C
H
σ (bonding)
Geometry Is Critical to Understand
H
H
C
H
H
H
σ orbital (major lobe) lies
mainly between atoms
(i.e. "the bond")
C
H
H
H
σ∗ orbital (major lobes) lies mainly behind
atoms but in-line with the bond
The Small Problem
4 degenerate
σ∗ (anti-bonding)
4 degenerate
C sp3
4 degenerate
H 1s
4 degenerate
σ (bonding)
Hybrid model suggests 4 degenerate bonding and 4 degenerate antibonding orbitals… not correct, but okay to ignore!