Triatomics and Beyond
1) Complex, so we deal with simple symmetrical molecules
2) Same principles apply to orbital combinations as with Diatomics:
i)
ii)
Compatible symmetry
Compatible energy (within 1 Rydberg, 1 Ry)
3) The number of valence AO’s must equal the number of Mo’s
4) MO’s must conform to the symmetry of the molecule.
5) Orbitals of the same energy and the same number of nodes mix.
BeH2
Be
BeH2 is the simplest triatomic
molecule.
2pz
Linear the gas phase.
2pxy
2p
The relative energies for the AO’s
of Be and H are:
2s2s
1s
1s
Energy
1s (Be) = -9.38 Ry
1s (H) = -0.99 Ry
2s (Be) = -0.61 Ry
2p (Be) = +0.14 Ry
1s
1s
Be
Along bond axis
Which atomic orbitals will combine to make σ MOs?
Which will combine to make
H
p MOs?
Which will not combine remaining σ or
p nonbonding MOs?
BeH2
H (x2)
BeH2 MO Diagram
4s*
Along bond axis
HH*x 22
Be
Be
3s*
2pz
2pxy
2p
1p
1p
2s
Energy
1s
2s
Lewis Structure?
Electron Configuration?
BO?
HOMO?
LUMO?
Lewis Acid?
1s
CO2
Lewis Structure?
Shape Family?
Valence atomic orbitals on C and O: 2s and 3 x 2p
Consider s and p MO’s formed separately.
6 s and 6 p MO’s will be formed (12 possile for each)
C
9s
O*2
8s
2pz
Order of energies:
Energy
2s (O) + 2s(C) small
2s (O) + 2pz(C) smallest
2pz(O) + 2s(C) large
2pz(O) + 2pz(C) largest
3p
2p
2pxy
2pz
2p
2pxy
2p
2s
1p
7s
2s
6s
Along bond axis
Along bond axis
5s
4s
Valence MO Diagram for CO2
2s (O) + 2s(C) small
1s, 2s, 3s*, 2s
6s*
2s (O) + 2pz(C) smallest
3s, 2s, 3s, 4s*
5s*
2pz(O) + 2s(C) large
4s, 5s*, 4s, 3s
9s
8s
3p
2p
2pz(O) + 2pz(C) largest
6s*, 5s, 4s, 5s,
2px(O) + 2px(C) largest
1p , 2p, 3p*, 2p
2py(O) + 2py(C) largest
1p , 2p, 3p*, 2p
Energy
2p
2p
2s
4s
Free atom
3s*
2s
1s
C
1p
7s
6s
5s
4s
CO2
2s
Free atom
O (x2)
BH3
Lewis structure?
Shape Family?
B
HH x*3 3
B
2p
2pxy
2pz
2s
Along Bonding Plane
What orbital combinations are possible now?
1s
BH3 MO Diagram
4s*
HH x*3 3
B
B
3s*
2p
2pxy
2pz
3s*
1p
Energy
2s
1s
Along Bonding Plane
2s
2s
1s
CH4 - The third dimension…
Frontier MO Theory
BH3
Reactions take place during collisions.
4s*
Hx3
B
3s*
Bonds are formed and/or broken.
2p
That must mean that there is
Energy
some kind of orbital interaction.
Which orbitals are most likely
interact in forming the new bond?
H-
3s*
1p
2s
2s
Free atom
1s
2s
2s
1s
Free atom
1s
BH3 + H- —> BH4In general, reactions take place via the interaction of the HOMO of one component with the
LUMO of the other because these are the closest in energy.
These orbitals are known as the “frontier orbitals”.
Electron delocalization (Resonance)
In resonance structures, the only electrons that move are:
O
O
O
O
O
Delocalized electrons are always found in
O
p orbitals.
As p orbitals are usually found at higher energy than the s orbitals, the HOMO
and LUMO of molecules with multiple bonds are usually
As a result of this, we often look only at the
diagrams.
p orbitals.
p orbitals and construct p MO
Ethylene
H
H
C
2p*
C
H
H
C: 2*(2s + 3*(2p))
=> 8 AO’s
H: 4*(1s )
=> 4 AO’s
=> 12 AO’s
s*’s
1p
5s
4s
3s
2s
=> 12 MO’s
1s
p-MO diagram of Ethylene
H
Ozone
H
C
H
C
H
O
O
O
2p*
O
O
O
3p*
C2p
C2p
O2p
2pnb
O2p
1p
Nodes…
Pi-bond order…
Sigma bond order
Total bond order = p bond order + s bond order
When Ethylene reacts…
Ethyne?
1p
Nodes…
Sigma & Pi-bond order…
Total bond order
Lewis BO
Formal Charge:
Butadiene
Ethylene
H
H
C
C
H
H
H
H
LUMO
C
C
2p*
1.2
H
C
C
H
H
H
4p*
2
0.2
-7.3eV
C2p
12.2 ev
C2p
9.7ev
C2p
-11
3p*
LUMO
1p
HOMO
-9.5
HOMO
2p
-12
Nodes…
The importance of the HOMO/LUMO gap.
C2p
1p
Note: this is not two isolated
double bonds but a single p-system
spread out over four carbons.
Benzene
H
H
H
H
C
H
H
C
H
C
C
C
C
C
C
C
C
C
H
H
H
C
H
H
The polygon method for determining p-MOs of monocyclic unsaturated molecules:
4p*
3p*
3p*
2p
2p
1p
Works for any monocyclic molecule with contiguous atomic p orbitals.
The p-MOs of Benzene
How many pi-electrons?
Nodes…(Cuts?)
Aromatic Stabilization
(1,3,5-hexatriene)
3
4p*
3p*
3p*
2p
2p
2
1
1p
Benzene can’t be considered to have
“three double bonds and three single bonds”.
It has three p bonds with bond order _____.
Accordingly, all six C-C bonds in benzene are
140 pm
(whereas pure C-C bonds are 154 pm
and pure C=C bonds are 134 pm).
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