Download 5.04, Principles of Inorganic Chemistry II Lecture 13: Frontier MO`s

5.04, Principles of Inorganic Chemistry II
MIT Department of Chemistry
Lecture 13: Frontier MO’s… -Ligands
-donors: in addition to donating electron density to a metal via a -bond, e-s provided to
metal via a -symmetry interaction
py
X
pz
(halide)
pz
X
-
-donation
py
px
X
and
px
donation
NR2
-
R
N
R
(amide)
2b2
2e'
4a1
2a1'
1b1
a2"
3a1
R
R
2a1
R
R
1b2
1e"
N
M
N
-donation
-donation
1a1
1a1'
z
y
x
H
H
+
N
H
-H
H
H
x
N
z
(note, z axis reoriented…descent
in symmetry)
y
other - donor ligands: sulfide (S2-), oxide (O2-), alkoxide (RO-)
5.04, Principles of Inorganic Chemistry II
Lecture 13
Page 1 of 5
acceptors: donate e-’s from a orbital and accept e-’s from the metal into an empty *
orbital. CO is the archetype of this ligand class. Other -acceptors: NO+, CN-, CNR.
Consider the MO diagram of CO below… the HOMO is filled and of -symmetry, the LUMO is
empty and of * symmetry.
C
CO
C
O
donation
C
O
and
O
C
O
-accepting
this orbital interaction responsible
for designation of these ligands as
-acids.
3
1 1
LUMO
2p
metal d orbitals situated between
and * L orbitals.
3
HOMO
2p
1
2s
2
2
C
Figure removed due to
copyright considerations.
1
CO
2s
O
5.04, Principles of Inorganic Chemistry II
Lecture 13
Page 2 of 5
General Rules for the Construction of MO Diagrams of Metal Complexes
Revisiting the energy level diagram for Lewis acid-base adduct formation:
E+
Energy
EM
M
EL
L
E-
b
Solving the above problem,
= CMM + CL L
H = E
H E
= H E CMM + CL L = 0
Left-multiplying by m and L
CM M H E M + CL M H E L = 0
CM L H E M + CL L H E L = 0
EM E
HML ESML
=
HLL E
HML ESML
HMM E
HML ESML
HML ESML
=0
EL E
Solving the above secular determinant (with the expansion for
E+ = EM
(H
+
ML
EMSML
2
)
EML
5.04, Principles of Inorganic Chemistry II
ML
EMSML
1
x ... ),
2
2
)
EML
=
=
*
E = EL
(H
1+ x = 1+
Lecture 13
Page 3 of 5
Applying the Wolfsberg Hemholz approximation,
HML = SML (EL + EM)
then,
2
E =
EM SML
EML
2
2
E * =
EL SML
EML
2
The derivation highlights the following general rules in the construction of MO
diagrams:
1. M - L atomic orbital mixing is proportional to overlap
… corollary 1’: only orbitals of correct symmetry can mix and give a
nonzero interaction energy (i.e. SML 0)
… corollary 1”: -interactions typically give rise to larger interaction energies
than those resulting from interactions more directional
and thus SML() > SML()
2. M–L atomic orbital mixing is inversely proportional to energy difference of
mixing orbitals (i.e. EML).
Other rules:
3. The order of the Coulomb energies (i.e. EL and EM) are taken as: (L) < (L) < nd < (n+1)s < (n+1)p
*L
depending on ligand
This energy ordering comes directly from Valence Orbital Ionization Energies
(VOIE) of atoms and PES spectra of ligands… consider the following:
5.04, Principles of Inorganic Chemistry II
Lecture 13
Page 4 of 5
VOIE’s of metal atoms:
Atom
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
3dn-14s 3dn-24s
3d
4.7
5.6
6.3
7.2
7.9
8.7
9.4
10.0
10.7
3dn-14s 3dn-1
4s
5.7
6.1
6.3
6.6
6.8
7.1
7.3
7.6
7.7
3dn-14p 3d n-1
4p
3.2
3.3
3.5
3.5
3.6
3.7
3.8
3.8
4.0
VOIE’s of ligand atomic orbitals and PES spectra of selected ligands:
Atom
H
C
N
O
F
Si
P
S
Br
Energies
1s
13.6
2s
2p
19.4
25.6
32.3
40.2
10.6
13.2
15.8
18.6
Note: S orbitals too low in energy to
participate (EML is too large) relative
to p orbitals.
3s
3p
14.9
18.8
20.7
7.7
10.1
11.6
4s
4p
24.1
12.5
are in eVs. Note, a VOIE is simply the opposite of the ionization energy
Figure removed due to copyright considerations.
5.04, Principles of Inorganic Chemistry II
Lecture 13
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