Coordination
Chemistry II
Bonding, including crystal field theory
and ligand field theory
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
In crystal field theory, the electron pairs on
the ligands are viewed as point negative charges
that interact with the d orbitals on the central
metal. The nature of the ligand and the
tendency toward covalent bonding is ignored.
d Orbitals
Crystal Field Theory
Ligands, viewed as point charges, at the
corners of an octahedron affect the various d
orbitals differently.
Crystal Field Theory
Crystal Field Theory
The repulsion
between ligand lone
pairs and the d
orbitals on the metal
results in a splitting of
the energy of the d
orbitals.
d Orbital Splitting
__ __ e
g
dz2 dx2-y2
__ __ __ __ __
0.6∆o
Spherical field
0.4∆o
__
dxy
__ __ t
2g
dxz dyz
Octahedral field
∆o
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.
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.
d Orbital Splitting
The splitting due
to the nature of the
ligand can be
observed and
measured using a
spectrophotometer.
Smaller values of ∆o
result in colors in the
green range. Larger
gaps shift the color to
yellow.
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
The Spectrochemical Series
The complexes of
cobalt (III) show the
shift in color due to the
ligand.
(a) CN–, (b) NO2–, (c)
phen, (d) en, (e) NH3, (f)
gly, (g) H2O, (h) ox2–, (i)
CO3 2–.
Ligand Field Strength Observations
1. ∆o increases with increasing oxidation number
on the metal.
Mn+2<Ni+2<Co+2<Fe+2<V+2<Fe+3<Co+3
<Mn+4<Mo+3<Rh+3<Ru+3<Pd+4<Ir+3<Pt+4
2. ∆o increases with increases going down a group
of metals.
Ligand Field Theory
Crystal Field Theory completely ignores the
nature of the ligand. As a result, it cannot
explain the spectrochemical series.
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.
Octahedral Symmetry
http://www.iumsc.indiana.edu/morphology/sym
metry/octahedral.html
Octahedral Symmetry
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
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.
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.
Experimental Evidence for Splitting
Several tools are used to confirm the
splitting of the t2g and eg molecular orbitals.
The broad range in colors of transition metal
complexes arises from electronic transitions as
seen in the UV/visible spectra of complexes.
Additional information is gained from
measuring the magnetic moments of the
complexes.
Experimental Evidence for Splitting
Magnetic susceptibility
measurements can be
used to calculate the
number of unpaired
electrons in a compound.
Paramagnetic
substances are attracted
to a magnetic field.
Magnetic Moments
A magnetic balance can be used to
determine the magnetic moment of a substance.
If a substance has unpaired electrons, it is
paramagnetic, and attracted to a magnetic field.
For the upper transition metals, the spinonly magnetic moment, μs, can be used to
determine the number of unpaired electrons.
μs = [n(n+2)]1/2
Magnetic Moments
The magnetic moment of a substance, in
Bohr magnetons, can be related to the number
of unpaired electrons in the compound.
μs = [n(n+2)]1/2
Where n is the number of unpaired electrons
Magnetic Moments
Complexes with 4-7 electrons in the d
orbitals have two possibilities for the
distribution of electrons. The complexes can be
low spin, in which the electrons occupy the lower
t2g set and pair up, or they can be high spin. In
these complexes, the electrons will fill the upper
eg set before pairing.
High and Low Spin Complexes
If the gap between
the d orbitals is large,
electrons will pair up and
fill the lower (t2g) set of
orbitals before
occupying the eg set of
orbitals. The complexes
are called low spin.
High and Low Spin Complexes
In low spin
complexes, the size
of ∆o is greater than
the pairing energy of
the electrons.
High and Low Spin Complexes
If the gap between
the d orbitals is small,
electrons will occupy the
eg set of orbitals before
they pair up and fill the
lower (t2g) set of orbitals
before. The complexes
are called high spin.
High and Low Spin Complexes
In high spin
complexes, the size
of ∆o is less than the
pairing energy of the
electrons.
Ligand Field Stabilization Energy
The first row transition metals in water are
all weak field, high spin cases.
do
d1
d2
d3
d4 d5 d6 d7
d8
d9 d10
LFSE 0 .4Δo .8
1.2
.6
1.2
.6
0 .4 .8
0
Experimental Evidence for LFSE
The hydration energies of the first row
transition metals should increase across the period
as the size of the metal ion gets smaller.
M2+ + 6 H2O(l)  M(H2O)62+
Experimental Evidence for LFSE
The heats of
hydration show two
“humps” consistent
with the expected LFSE
for the metal ions. The
values for d5 and d10 are
the same as expected
with a LFSE equal to 0.
Experimental Evidence of LFSE
do
d1
d2 d3 d4 d5 d6 d7
LFSE 0 .4Δo .8 1.2 .6 0 .4 .8
d 8 d9
d10
1.2 .6
0
High Spin vs. Low Spin
3d metals are generally high spin complexes except
with very strong ligands. CN- forms low spin
complexes, especially with M3+ ions.
4d & 4d metals generally have a larger value of ∆o
than for 3d metals. As a result, complexes are
typically low spin.
Effect of Metal Charge
on Splitting
Nature of the Ligands
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
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.
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.
Effect of Ligand on Splitting
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.
I-<Br-<Cl-<F-<H2O<NH3<PPh3<CO
π donor< weak π donor<σ only< π acceptor
4 – Coordinate Complexes
Square planar and tetrahedral complexes are
quite common for certain transition metals. The
splitting patterns of the d orbitals on the metal
will differ depending on the geometry of the
complex.
Tetrahedral Complexes
The dz2 and dx2-y2 orbitals
point directly between the
ligands in a tetrahedral
arrangement. As a result, these
two orbitals, designated as e in
the point group Td, are lower in
energy.
Tetrahedral Complexes
The t2 set of orbitals,
consisting of the dxy, dyz, and
dxz orbitals, are directed more
in the direction of the ligands.
These orbitals will be
higher in energy in a
tetrahedral field due to
repulsion with the electrons
on the ligands.
Tetrahedral Complexes
The size of the splitting,
∆T, is considerably smaller
than with comparable
octahedral complexes. This is
because only 4 bonds are
formed, and the metal orbitals
used in bonding don’t point
right at the ligands as they do
in octahedral complexes.
Tetrahedral Complexes
In general, ∆T ≈ 4/9
∆o. Since the splitting
is smaller, all tetrahedral
complexes are weakfield, high-spin cases.
Tetragonal Complexes
Six coordinate complexes, notably those of
Cu2+, distort from octahedral geometry. One
such distortion is called tetragonal distortion, in
which the bonds along one axis elongate, with
compression of the bond distances along the
other two axes.
Tetragonal Complexes
The elongation
along the z axis causes
the d orbitals with
density along the axis to
drop in energy. As a
result, the dxz and dyz
orbitals lower in energy.
Tetragonal Complexes
The compression
along the x and y axis
causes orbitals with
density along these axes
to increase in energy.
.
Tetragonal Complexes
For complexes with
1-3 electrons in the eg set
of orbitals, this type of
tetragonal distortion may
lower the energy of the
complex.
Square Planar Complexes
For complexes with 2
electrons in the eg set of
orbitals, a d8 configuration,
a severe distortion may
occur, resulting in a 4coordinate square planar
shape, with the ligands
along the z axis no longer
bonded to the metal.
Square Planar Complexes
Square planar
complexes are quite
common for the d8 metals
in the 4th and 5th periods:
Rh(I), IR(I), Pt(II), Pd(II)
and Au(III). The lower
transition metals have large
ligand field stabilization
energies, favoring fourcoordinate complexes.
Square Planar Complexes
Square planar
complexes are rare for the
3rd period metals. Ni(II)
generally forms tetrahedral
complexes. Only with very
strong ligands such as CN-,
is square planar geometry
seen with Ni(II).
Square Planar Complexes
The value of ∆sp for a
given metal, ligands and
bond length is
approximately 1.3(∆o).
The Jahn-Teller Effect
If the ground electronic configuration of a non-linear
complex is orbitally degenerate, the complex will distort
so as to remove the degeneracy and achieve a lower energy.
The Jahn-Teller Effect
The Jahn-Teller effect predicts which
structures will distort. It does not predict the
nature or extent of the distortion. The effect is
most often seen when the orbital degneracy is in
the orbitals that point directly towards the
ligands.
The Jahn-Teller Effect
In octahedral complexes, the effect is most
pronounced in high spin d4, low spin d7 and d9
configurations, as the degeneracy occurs in the
eg set of orbitals.
d4
d7
d9
eg
t2g
The Jahn-Teller Effect
The strength of the Jahn-Teller effect is
tabulated below: (w=weak, s=strong)
# eHigh
spin
Low
spin
1 2 3
4 5 6
* *
s
*
w w -
7
8
9 10
- w w
*
*
*
-
s
-
w w -
s
*There is only 1 possible ground state configuration.
- No Jahn-Teller distortion is expected.