Lecture 5
Homonuclear Diatomic Molecules
- Making MO Energy Level
Diagrams Easy
- Making MO Theory Easy
Dr. Sylvia Draper
SNIAMS 2.5
[email protected]
74
Objectives – a fundamental understanding
•
Wave mechanics / Atomic orbitals
– The flaws in classical quantum mechanics (the Bohr Model) in the
treatment of electrons
– Wave mechanics and the Schrödinger equation
– Representations of atomic orbitals including wave functions
– Electron densities and radial distribution functions
– Understanding shielding and penetration in terms of the energies of
atomic orbitals
•
Bonding
– Revision of VSEPR and Hybridisation
– Linear combination of molecular orbitals (LCAO), bonding /
antibonding
– Labelling of molecular orbitals (s, p and g, u)
– Homonuclear diatomic MO diagrams
– MO diagrams for Inorganic Complexes
75
2nd row Homonuclear Diatomics
•
Li2, Be2, B2, C2, N2, O2, F2, Ne2
Bonding and antibonding interactions are possible between 1s, 2s and 2p on
one atom with the other
σ bonding s – s
π bonding
px – px
pz – pz
py - py
Energy level diagram for O2
•
•
2s and 2p energies sufficiently spaced no mixing
Simple picture of the MO
Unpaired electrons
∗
∗
6σ
σu
4σ u
Paramagnetic
2π∗g
2p
2p
1πu
2s
1πu
5σg
3σg
4σ
σ∗u
2σ∗u
2s
3σ
σg
Energy
1s
1s
1σ
σg
Label MOs starting from the
bottom usually discount core
electrons - only valence
orbitals important for
bonding
1σg
2σ
σ∗u
O
2π∗g
O
1s AO’s very small very
small overlap in lower levels
(small ∆E)
Other possible interactions
σ interactions between s and pz can be important
– Depend on the energy difference between 2s and 2pz
– The larger the energy difference (like in O2) the less likely the interaction
•
How does the energy of the 2s and 2p vary with Z (shielding / penetration)
2p
NO s and p mixing
2s
YES s and p mixing
Energy
Li
Be
B
C
N
O
F
Ne
• Gap increases – 2p more effectively shielded as 2s is pulled toward an ever
increasing nuclear charge - critical point between O and N
MO diagram for N2
•
2s and 2p energies sufficiently close for interaction
– 1σ and 2σ shift to lower energy
– 3σ and 4σ shifted to high energy
– 3σ now above 1π
– π levels unaffected
more complex
4σ
σ∗u
2π∗g
2p
2p
3σg
1πu
2s
2s
2σ
σ∗u
1σ
σg
σ interactions in N2
• Take basic model for oxygen – no s and p interaction - and
apply changes to examine how the MO’s can interact
– π and σ cannot interact – zero overlap
π level remain the same
– Examine σ −σ interactions
4σ∗u
2π∗u
Bonding interactions can interact
with each other 1σg and 3σg
3σg
2p
1πg
3σg
2σ∗u
2s
1σg
1σg
Thus 1σg goes down in energy and 3σg
goes up in energy
σ* interactions in N2
•
Now examine the anti-bonding
interaction (2σ∗ and 4σ∗)
4σ*
4σ∗u
2π∗u
2p
1πg
3σg
2σ∗u
2s
1σg
2σ*
Thus 2σ∗u goes down in energy and 4σ∗u
goes up in energy
For bonding with anti-bonding (1σ – 4σ∗
or 2σ∗ – 3σ) the sign changes on one wave
function zero overlap.
MO diagrams for 2nd row diatomics
•
The effect of the overlap between 2s and 2p is greatest for the Li. The MO
diagram changes systematically as you go across the periodic table
•
s – p mixing
B2 – paramagnetic and C2 diamagnetic
MO diagram for CO
•
Same orbitals as homonuclear diatomics isoelectronic with N2
– different energies give rise to significant 2s - 2p mixing
– As heteronuclear diatomic the orbitals have either C or O character
2p
2p
2s
C
4σ
σ
C-O anti - bonding (more C)
2π∗
π∗ (uneven – more carbon)
3σ
Primarily carbon (pz)
1π
π bond (uneven – more oxygen)
2σ
σ
Primarily oxygen (pz)
1σ
σ
C-O bonding interaction (more O)
2s
O
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Homonuclear Diatomic MO energy diagrams
No mixing
Li2 to O2
Mixing
N2 to Ne2
4σ
σ∗u
2p
4σ
σ∗u
2π∗g
2π∗g
1πu
3σg
2p
3σg
2p
1πu
2σ
σ∗u
2s
1σ
σg
2s
2σ
σ∗u
1σ
σg
2s
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MO treatment of BeH2
•
VSEPR linear molecule,
H – Be – H
– Be – 1s2 2s2 2p0 H – 1s1
– Examine interaction of 6 AO with each other
– 2 H 1s, Be 2s and Be 2px, Be 2py Be 2pz 6 MO’s
Interaction between H 1s and Be 2s
Interaction between H 1s and Be 2pz
Be
bonding
Be
Z
Be
anti-bonding
bonding
Be
Be
anti-bonding
Be
Each of these is delocalised over three atoms and can hold up to two electrons
px and py have zero overlap
non bonding
Energy level diagram for BeH2
4σ*u
3σ*g
2p
Non bonding px and py
2s
2σu
Be
BeH2
2H
1σg
Compare these two MO’s with no mixing of s and p orbitals with the localised
model generated from two equivalent bonds formed via sp hybridization
Alternative approach
• Stepwise approach (ligands first)
Mix hydrogen 1s orbitals first
two Molecular orbitals
H – Be – H
Z
Then mix with Be s (zero overlap with pz) Then mix with Be pz (zero overlap with s)
Alternative Route to energy level diagram for BeH2
4σ*u
3σ*g
Non bonding px and py
2p
2s
2σu
1σg
Be
BeH2
2H
MO treatment of H2O
z
H
O
H
•
H2O is not linear – but why ?
x
– We will examine the MOs for a non-linear tri-atomic and find out.
– What orbitals are involved – 2 H 1s + O 2s, O 2px O 2py, and O 2pz
•
Start by creating MO’s from the hydrogen 1s orbitals.
•
Taking the in-phase pair first – the result will interact with the O 2s and O
2pz (zero overlap with O 2px and O 2py)
•
Problem - this is mixing three orbitals
orbitals
must produce three molecular
MO’s of H2O
•
Three orbitals
three MO’s
anti - bonding
H
H
x
approx. 2pz - 2s + H
Approximately
non-bonding
+
Bonding
O
O
approx. -2pz + H
2pz
2s
z
approx. 2s + 2pz (a little) + H
2H
MO’s of H2O
•
Out of phase H 1s orbitals
– Only interact with px 2 MO’s
– Zero overlap with py
z
O
H
anti - bonding
2px
O
Bonding
2H
H
x
Energy level diagram for H2O z
O
H
H
x
There are not two lone pairs !
H
2py, n.b.
σ n.b.
2p
Slightly bonding Pz
Non bonding Py
2σ
non bonding py
2s
H2O
Very different to the VB
concept of two identical sp3
filled orbital
H
1σ
O
H
2H
H
H
H
MO theory correct.
Comparison of H2O and BeH2
•
Both cases of XA2 same MO – different No of electrons
– Bonding MO’s as a function of A-X-A bond angle
BeH2
linear
BH2
131o
CH2 (t) 134o
CH2 (s) 102o
NH2
103o
OH2
105o
90º
H2O
CH2(T)
180º
π MO’s of Benzene
•
π bonding is more important for reactivity –independent of σ (zero overlap)
– six px orbitals combine to form six MO’s
–
–
–
–
Lowest energy – all in phase
Degenerate levels (1 nodal plane
Degenerate levels (2 nodal planes
Highest energy – all out of phase
2 nodes)
4 nodes)
– 2 electron per MO spread over 6 atoms
– Compare with Lewis structure
– has to resort to resonance structures to explain benzene