Molecular Orbital Theory and
Charge Transfer Excitations
Chemistry 123
Spring 2008
Dr. Woodward
Molecular Orbital Diagram H2
H 1s
Orbital
Bonding
Molecular Orbital
(Orbitals interfere
constructively)
H 1s
Orbital
Energy
Antibonding
Molecular Orbital
(Orbitals interfere
destructively)
Orbital overlap – Constructive Interference
B o n d in g O v e rla p
1 s A to m 1
Constructive
Interference
W a v e fu n c tio n (  )
1 s A to m 2
Between the nuclei the
wavefunctions add together.
Electron density maximized
in the internuclear region.
A to m (2 )
A to m (1 )
This type of overlap leads
to formation of a covalent
bond.
-4
-3
-2
-1
0
1
2
3
z (A n g s tro m s )
+
=
4
Orbital overlap – Destructive Interference
A n tib o n d in g O v e rla p
Destructive
Interference
1 s A to m 1
1 s A to m 2
W a v e fu n c tio n (  )
Between the nuclei the
wavefunctions cancel each
other out.
Electron density pushed
away from internuclear
region.
A to m (2 )
A to m (1 )
This type of overlap
works against formation
of a covalent bond.
-4
-3
-2
-1
0
1
2
3
z (A n g s tro m s )
+
=
4
Pi (π) Bonding
Sigma (σ) Bonding
side on overlap
head on overlap
+
Atom 1
pz orbital
=
Atom 2
pz orbital
+
Bonding pi
molecular
orbital
Constructive Interference
+
Atom 1
pz orbital
Atom 1
py orbital
Atom 2
py orbital
+
Antibonding
pi molecular
orbital
Destructive Interference
Bonding sigma
molecular
orbital
Constructive Interference
=
Atom 2
pz orbital
=
Atom 1
py orbital
=
Atom 2
py orbital
Bonding sigma
molecular
orbital
Destructive Interference
Principles of MO Theory
1. Conservation of Orbitals: The number of Molecular Orbitals is equal to
the number of Atomic Orbitals.
2. Conservation of Electrons: The number of electrons occupying the
molecular orbitals is equal to the sum of the valence electrons on the
constituent atoms.
3. Pauli Exclusion Principle: Each MO can hold two electrons of opposite
spin.
4. Hunds Rule: When orbitals are degenerate (at the same energy) all
electron spins are the same direction (up) until we have to start
putting two electrons in the same orbital.
5. Principle of Orbital Mixing: The splitting between bonding and
antibonding MO’s decreases as:
a. The spatial overlap decreases (due to orientation of the orbitals,
interatomic distance, or size of orbitals)
b. The orbital electronegativities become different
Cr3+
5 d-orbitals on Cr
(Cr3+ = d3 ion)
3 electrons in the
d-orbitals
[Cr(NH3)6]3+
Octahedron
:NH3
: N
H
H
H
6 Ligand Orbitals
Nitrogen lone pairs
(all containing 2 e-)
Only sigma interactions
are allowed
[Cr(NH3)6]3+
Antibonding (s*)
Metal-Ligand MO’s
eg orbitals (dz2, dx2-y2)
D = Crystal Field Splitting Energy
t2g orbitals (dxz, dyz, dxy)
Energy
Metal (Cr) d-orbitals
Nonbonding
Metal d MO’s
Nonbonding
Ligand MO’s
Bonding (s)
Metal-Ligand MO’s
Ligand (N) lone-pair
orbitals
Absorption Spectra Cr3+ Solutions
Antibonding (s*)
Metal-Ligand MO’s
1 .4
[C r(H 2 O )6 ]3 +
1 .2
[C r(O H )4 (H 2 O )2 ]1 -
a b s o rb a n c e
1 .0
[C rO 4 ]2 -
Doct
0 .8
0 .6
Nonbonding
Metal d MO’s
0 .4
0 .2
0 .0
250
350
450
550
w a ve le n g th (n m )
650
750
850
[CrO4]2-
t2 orbitals
(more antibonding)
e orbitals
(antibonding)
CT
Energy
Metal (Cr) d-orbitals
Nonbonding
Oxygen 2p MO’s
e orbitals
(bonding)
t2 orbitals
(bonding)
12 Oxygen 2p orbitals
(4 oxygens x 3 p orbitals)
Absorption Spectra CrO42- Solutions
Antibonding Cr 3d orbitals
1 .4
[C r(H 2 O )6 ]3 +
1 .2
[C r(O H )4 (H 2 O )2 ]1 -
a b s o rb a n c e
1 .0
[C rO 4 ]2 -
0 .8
CT1
0 .6
0 .4
0 .2
0 .0
250
350
450
550
w a ve le n g th (n m )
650
750
850
Nonbonding
Oxygen 2p MO’s
Absorption Spectra CrO42- Solutions
Antibonding Cr 3d orbitals
1 .4
[C r(H 2 O )6 ]3 +
1 .2
[C r(O H )4 (H 2 O )2 ]1 -
a b s o rb a n c e
1 .0
[C rO 4 ]2 -
CT2
0 .8
0 .6
0 .4
0 .2
0 .0
250
350
450
550
w a ve le n g th (n m )
650
750
850
Nonbonding
Oxygen 2p MO’s
Charge Transfer Salts, ACrO4
The absorbance of SrCrO4 is similar to a concentrated solution of CrO42- ions.
Charge Transfer Excitations and
Periodic Trends
We can expect charge transfer transitions
when we have a d0 cation in a high oxidation
state. How does the charge transfer change as
we move around the periodic table?
CrO42- vs. MnO42-
Antibonding (e)
Cr dx2-y2, dz2
CT
Antibonding (e)
Mn dx2-y2, dz2
CT
Nonbonding O 2p
Nonbonding O 2p
[CrO4]2-
[MnO4]-
As the cation oxidation state increases [i.e. Cr(VI)  Mn(VII)]
d-orbitals become more electronegative (lower in energy)
CT Energy Gap decreases
Absorption shifts to longer wavelengths
SrMoO4 – SrCrO4 Series
S rC rO 4 - S rM o O 4 K ris te n
100
90
a b s o rb a n c e
80
2-
60
S rC rO 4
[C rO 4 ]
R e fle c ta n c e
70
50
S rC r0 .9 M o 0 .1 O 4
S rC r0 .8 M o 0 .2 O 4
40
S rC r0 .5 M o 0 .5 O 4
S rC r0 .2 M o 0 .8 O 4
30
S rC r0 .1 M o 0 .9 O 4
S rM o O 4
20
C rO 4 (2 -)
10
0
SrMoO4
250
350
450
550
W a ve le n g th (n m )
650
750
SrCrO4
Orbital Radii – Group 6
Cr 4s
r = 1.63 Å
Mo 5s
Cr 3d
r = 0.46 Å
Mo 4d
r = 1.75 Å
r = 0.73 Å
W 6s
W 5d
r = 1.65 Å
r = 0.78 Å
The d orbitals
are always
much smaller
than the s
and p, but the
3d orbitals
are
particularly
small
Antibonding (e)
Cr dx2-y2, dz2
CT
Nonbonding O 2p
[CrO4]2-
Antibonding (e)
Mo dx2-y2, dz2
CT
Nonbonding O 2p
[MoO4]2-
Mo 4d orbitals are larger than the Cr 3d orbitals
d-orbitals interact more with O 2p orbitals – more antibonding
CT Energy Gap increases
Absorption shifts to shorter wavelengths
2nd & 3rd Row Transition Metals
eg (s*)
2nd and 3rd row
transition metals
•d-orbitals are larger
•Metal-ligand antibonding
interactions are stronger
•eg (s*) orbitals are more
antibonding
•Low spin configurations
are always observed
[Co(H2O)6]3+
D = 2.25 eV
[Rh(H2O)6]3+
D = 4.23 eV