Inorganic Chemistry
Sixth Edition
Chapter 7- PART B
Chapter 20
d Metal complexes:
electronic structure and
properties
Modified By Dr. Cheng-Yu Lai
PHYSICAL CHEMISTRY:
MATTER,
AND CHANGE
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PETER ATKINS|
JULIO DE PAULA | RONALD FRIEDMAN
INORGANIC
CHEMISTRYQUANTA,
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WELLER|
OVERTON
| ROURKE
| ARMSTRONG
©2014
W. H.
H. FREEMAN
FREEMAN AND
D COMPANY
©2014
W.
COMPANY
Figure 20.1 (a) The six ML vectors of an octahedral complex [ML6]n can be defined to lie
along the x, y and z axes. (b) The five d orbitals; the dz2 and dx2−y2 atomic orbitals point
directly along the axes, but the dxy, dyz and dxz atomic orbitals point between them.
(c) The formation of a dz2 orbital from a linear combination of dx2−y2 and dz2−x2
orbitals. The orbitals have been generated using the program Orbital Viewer [David
Manthey, www.orbitals.com/orb/index.html].
Basis for Bonding Theories
Models for the bonding in transition metal
complexes must be consistent with observed
behavior. Specific data used include stability
(or formation) constants, magnetic
susceptibility, and the electronic (UV/Vis)
spectra of the complexes.
Bonding Approaches
Valence Bond theory provides the
hybridization for octahedral complexes. For the
first row transition metals, the hybridization can
be: d2sp3 (using the 3d, 4s and 4p orbitals), or
sp3d2 (using the 4s, 4p and 4d orbitals).
The valence bond approach isn’t used
because it fails to explain the electronic spectra
and magnetic moments of most complexes.
Crystal Field Theory is an electrostatic model.
Coulomb Interactions
–attraction between metal ion and ligand electrons
–repulsion between metal electrons and ligand electrons
deciquanta
means 10 quantum of energy.
d orbitals
splitting
d Orbital Splitting
In some texts and articles, the gap in the d
orbitals is assigned a value of 10Dq. The upper (eg)
set goes up by 6Dq, and the lower set (t2g) goes
down by 4Dq.
The actual size of the gap varies with the metal
and the ligands.
__ __ e
g
dz2 dx2-y2
__ __ __ __ __
0.6∆o
Spherical field
0.4∆o
__
dxy
__ __ t
2g
dxz dyz
Octahedral field
∆o
Ligands, viewed as point
charges, at the corners of an
octahedron affect the various d
orbitals differently.
Strong ligand
d Orbital Splitting
The colors exhibited by most transition metal
complexes arises from the splitting of the d orbitals.
As electrons transition from the lower t2g set to the
eg set, light in the visible range is absorbed.
The Spectrochemical Series
Based on measurements for a given metal ion,
the following series has been developed:
I-<Br-<S2-<Cl-<NO3-<N3-<F-<OH-<C2O42-<H2O
<NCS-<CH3CN<pyridine<NH3<en<bipy<phen
<NO2-<PPh3<CN-<CO
+ Pairing Energy
Ligand Field Stabilization Energies for Octahedral Complexes
Octahedral crystal field stabilization energies (CFSE) for dn configurations;
pairing energy, P, terms are included where appropriate (see text). High- and lowspin octahedral complexes are shown only where the distinction is appropriate.
Table 20.3
High Spin
Low Spin
Due to small splitting
(-3/5 ΔT for an e orbital and +2/5 ΔT for a t2 orbital).
Dt = 4/9Do
Crystal field splitting diagrams for octahedral (left-hand side) and
tetrahedral (right-hand side) fields. The splittings are referred to a common
barycentre. See also Fig. 20.2.
Figure 20.8
Why do d8 metal compounds often form square planar compounds
z
Thought experiment: Make a square planar
compound by removing two ligands from an
octahedral compound
L
L
L
M
L
y
L
L
dx2-y2
dz2
x
L
L
M
L
L
dx2-y2
dxy
dxy
dxz,dyz
dz2
dxz,dyz
Octahedral
Square Planar
dx2-y2
dx2-y2
dz2
dxy
dxz,dyz
dxy
dxy
dxz,dyz
dx2-y2
dz2
H2O
H2O
Ni
2
OH2
Cl
OH2
H2O
Octahedral
Coordination number =6
Ni(II) d8 S = 1
dxz,dyz
Tetrahedral
Octahedral
OH2
dz2
Cl
Square Planar
2-
N
N
Cl
C
C
Ni
2-
Ni
Cl
Tetrahedral (CN=4)
C
N
C
N
Square Planar (CN=4)
Ni(II) d8 S =1
Ni(II) d8 S = 0
Crystal field splitting diagrams for some common fields referred to a
common barycentre. Splittings are given with respect to oct.
Figure 20.11
Ligand Field Theory
Crystal Field Theory completely ignores the
nature of the ligand, treating ligands as point
charges and does not take into account the
overlap ligands and metal- atom orbitals. As a
result, it cannot explain the spectrochemical
series.
Sigma bond approach only .
Ligand Field Theory uses a molecular orbital
approach. Initially, the ligands can be viewed as
having a hybrid orbital or a p orbital pointing
toward the metal to make σ bonds.
Metal orbital
Symmetry
label
Degeneracy
S
a1g
1
px, py, pz
t1u
3
dxy, dyz, dzx
t2g
3
Ligand Field Theory
Consider the group orbitals of all six ligands
in octahedral geometry.
Oh
E
Γσ
6
8C3 6C2 6C4
0
0
2
3C2
i 6S4 8S6 3σh 6σd
2
(=C4 )
2
0
This reduces to A1g + Eg + T1u
0
0
4
2
Ligand Field Theory
The A1g group
orbitals have the
same symmetry as
an s orbital on the
central metal.
Ligand Field Theory
The T1u group
orbitals have the
same symmetry as
the p orbitals on the
central metal.
(T
representations are
triply degenerate.)
Ligand Field Theory
The Eg group
orbitals have the
same symmetry as
the dz2 and dx2-y2
orbitals on the
central metal.
(E representations
are doubly
degenerate.)
Ligand Field Theory
Since the ligands
don’t have a
combination with t2g
symmetry, the dxy, dyz
and dxy orbitals on the
metal will be nonbonding when
considering σ
bonding.
Ligand Field Theory – σ bond only
The molecular
orbital diagram is
consistent with the
crystal field
approach.
Note that the
t2g set of orbitals is
non-bonding, and
the eg set of
orbitals is
antibonding.
Ligand Field Theory
The electrons
from the ligands (12
electrons from 6
ligands in octahedral
complexes) will fill
the lower bonding
orbitals.
{
9 Bonding orbitals –
18 electrons capacity
Ligand Field Theory
{
The electrons
from the 4s and
3d orbitals of
the metal (in the
first transition
row) will occupy
the middle
portion of the
diagram.
σ bond only ; t2g non- bonding
Nature of the Ligands- Considering π Bonding
Crystal field theory and ligand field theory
differ in that LFT considers the nature of the
ligands. Thus far, we have only viewed the
ligands as electron pairs used for making σ
bonds with the metal. Many ligands can also
form π bonds with the metal. Group theory
greatly simplifies the construction of
molecular orbital diagrams.
Considering π Bonding
To obtain Γred for π bonding, a set of
cartesian coordinates is established for each
of the ligands. The direction of the σ bonds is
arbitrarily set as the y axis (or the py orbitals).
The px and pz orbitals are used in π bonding.
x
x
z
z
z
y
y
z
y
x
y
x
z
y
x y
z
x
Oh E 8C3 6C2 6C4
Γπ 12
0
0
6 Px + 6 Pz = 12 vectors
0
Considering π
Bonding
Consider only the px and
pz orbitals on each of
the ligands to obtain Γπ.
3C2
i 6S4 8S6 3σh 6σd
2
(=C4 )
-4
0
0
0
0
0
Considering π Bonding
Oh E 8C3 6C2 6C4
Γπ 12
0
0
0
3C2
i 6S4 8S6 3σh 6σd
2
(=C4 )
-4
0
0
0
0
0
This reduces to T1g + T2g + T1u + T2u. The T2g set has
the same symmetry as the dxy, dyz and dxz orbitals on
the metal. The T1u set has the same symmetry as the
px, py and pz orbitals on the metal.
Considering π Bonding
π reduces to: T1g + T2g + T1u + T2u.
• The T1g and T2u group orbitals for the ligands don’t
match the symmetry of any of the metal orbitals.
• The T1u set has the same symmetry as the px, py and pz
orbitals on the metal. These orbitals are used primarily
to make the σ bonds to the ligands.
• The T2g set has the same symmetry as the dxy, dyz and
dxz orbitals on the metal.
π Bonding
The main source of π bonding is between
the dxy, dyz and dxz orbitals on the metal and
the d, p or π* orbitals on the ligand.
π Bonding
The ligand may have empty d or π* orbitals
and serve as a π acceptor ligand, or full p or d
orbitals and serve as a π donor ligand.
π Bonding
The empty π antibonding orbital on CO can
accept electron density from a filled d orbital
on the metal. CO is a pi acceptor ligand.
filled d
orbital
empty π*
orbital
π Donor Ligands (LM)
All ligands are σ donors. Ligands with filled
p or d orbitals may also serve as pi donor
ligands. Examples of π donor ligands are I-, Cl-,
and S2-. The filled p or d orbitals on these ions
interact with the t2g set of orbitals (dxy, dyz and
dxz) on the metal to form bonding and
antibonding molecular orbitals.
π Donor Ligands (LM)
The bonding orbitals,
which are lower in
energy, are primarily
filled with electrons from
the ligand, the and
antibonding molecular
orbitals are primarily
occupied by electrons
from the metal.
Key points: π-Donor ligands decrease O whereas π-acceptor ligands increase O; the
spectrochemical series is largely a consequence of the effects of π bonding when such
bonding is feasible.
σ Bonding vs.  Bonding
π Donor Ligands (LM)
The size of ∆o
decreases, since it is now
between an antibonding
t2g orbital and the eg*
orbital.
This is confirmed by
the spectrochemical
series. Weak field ligands
are also pi donor ligands.
π Acceptor Ligands (ML)
Ligands such as CN,
N2 and CO have empty
π antibonding orbitals
of the proper
symmetry and energy
to interact with filled d
orbitals on the metal.
π Acceptor Ligands (ML)
The metal uses the
t2g set of orbitals (dxy,
dyz and dxz) to engage
in pi bonding with the
ligand. The π* orbitals
on the ligand are
usually higher in
energy than the d
orbitals on the metal.
π Acceptor Ligands (ML)
The metal uses the
t2g set of orbitals (dxy,
dyz and dxz) to engage
in pi bonding with the
ligand. The π* orbitals
on the ligand are
usually higher in
energy than the d
orbitals on the metal.
π Acceptor Ligands (ML)
The interaction
causes the energy of
the t2g bonding
orbitals to drop
slightly, thus increasing
the size of ∆o.
Summary
1. All ligands are σ donors. In general, ligands
that engage solely in σ bonding are in the
middle of the spectrochemical series. Some
very strong σ donors, such as CH3- and H- are
found high in the series.
2. Ligands with filled p or d orbitals can also
serve as π donors. This results in a smaller
value of ∆o.
Summary
3. Ligands with empty p, d or π* orbitals can also
serve as π acceptors. This results in a larger value
of ∆o.
— increasing ∆O →
π donor weak π donor
no π effects
π
acceptor
π donor
weak π donor no π effects
π acceptor
I, Br, Cl, F
H2O
PR3, CO
NH
I-<Br-<Cl-<F-<H2O<NH3<PPh3<CO
π donor< weak π donor<σ only< π acceptor