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Handout-6
Course 201N
1st Semester 2006-2007
Inorganic Chemistry
Instructor: Jitendra K. Bera
Contents
2. Coordination Complexes of Transition Metal Ions
Magnetic properties of coordination complexes
Molecular Orbital Theory of Coordination Complexes
Magnetization and Magnetic Susceptibility
If a body is placed in a homogeneous field, H0, the field within the body varies from the
free space value. The scheme below defines some of the terms that are often used in the
field of magnetochemistry. Chemists often prefer to measure mass rather than volume,
and to use moles rather than grams. Hence, molar magnetic susceptibility χM is usually
reported.
The sign of the induced magnetization (M) defines two basic types of magnetic behavior.
If M (or χ) is negative, it is Diamagnetism; if M (or χ) is positive, it is Paramagnetism. In
a field gradient, diamagnet moves out of field to lower energy (χ < 0) and paramagnet
moves in to field to lower energy. Compounds with only paired electrons are
diamagnetic and compounds with unpaired electrons are paramagnetic. The
ferromagnetism, anti-ferromagnetism and ferrimagnetism are special forms of
paramagnetism that are outside the scope of this course.
Typically χpara values are higher than χdia. The χM values of diamagnetic N2 and
paramagnetic O2 illustrate this fact. All substances have a diamagnetic component to the
susceptibility. The observed χobs includes the contribution from both χpara and χdia.
Paramagnetism: It arises from the interaction between H0 and the magnetic field of the
unpaired e’s associated with their spin and orbital angular momenta. In a hypothetical
free ion or atom, both the orbital and spin angular momenta give rise to a magnetic
moment
and
contribute
to
paramagnetism. When the atom or
the ion is part of a complex, orbital
angular
momentum
may
be
eliminated (or quenched). We shall
discuss the quenching of the orbital
contribution later. However, the spin
angular momentum survives and
gives rise to spin-only paramagnetism which is characteristic of many d-metal
complexes. The magnitude of the spin magnetic moment of an electron is provided in the
right.
Curie Law: The Curie law relates the molar magnetic susceptibility χM as a function of
temperature. In Curie equation, N is Avogardro’s number, k is Boltzmann constant, g is
the gyromagnetic ratio, and β is Bohr magneton. A simplified form of Curie Law: χM =
C/T which describe the inverse dependence of χM with temperature T. Here C is a
constant that is characteristic of the substance and known as Curie constant.
The values of C for different ‘S’ values
can be calculated from the Curie
equation. For S=½, 1, 3/2, 2 and 5/2,
the calculated values of C are 0.375,
1.0, 1.88, 3.0 and 4.375 emu K/mol.
Experimentally, if we measure χM of a
substance at different temperature and
plot χMT values against T, we shall
obtain a straight line that would
intersects the y-axis at the value C.
The experimental C value would
provide information on the number of
unpaired electrons in the system.
Effective magnetic moment: It is a convenient parameter (µeff) (hugely popular among
inorganic chemists) that is related to χM. The ‘µeff’ is defined as:
(µ
µeff)2 = g2 S(S+1) β2
If g=2,
It can also be expressed in terms of number of unpaired electrons:
The µeff is related to the χMT values:
To recapitulate, one first makes a direct measurement of the volume susceptibility of a
substance from which χM is calculated, and the above equation allows one to deduce the
magnetic moment of the ion, atom or molecule responsible for the paramagnetism.
The µeff, however, can be calculated very easily if we know the number of unpaired
electrons in the system.
Ion
Ti3+
V3+
Cr3+
Mn3+
Fe3+
# of unpaired
electrons (n)
1
2
3
4
5
S
½
1
3/2
2
5/2
Predicted µeff values
√3 = 1.73
√8 = 2.83
√15 = 3.87
√24 = 4.90
√35 = 5.92
Inferring electron configuration from magnetic moment:
1. The magnetic moment of an octahedral co(II) complex is 4.0 BM. What is its electron
configuration? Answer: A Co(II) complex is d7 system. The two possible configurations
are t2g5eg2 (high-spin) with three unpaired electrons or t2g6eg1 (low-spin) with one
unpaired electron. The spin-only values would be 3.87 and 1.73 BM. Therefore, the only
consistent assignment is the configuration t2g5eg2, which means a high-spin complex.
2. The magnetic moment of the complex [Mn(NCS)6]4- is 6.06 BM. What is its electron
configuration? - A Mn(II) complex is d5 system. The magnetic moment value suggests an
electron configuration t2g3eg2, that means it is a high-spin complex.
3. The anion [Ni(SPh)4]2- is tetrahedral. Explain why it is paramagnetic. – The Ni(II) is d8
system. In a tetrahedral environment the electron configuration should be e4t24 containing
two unpaired electrons. Hence it is paramagnetic. On contrary, [Ni(CN)4]2- is diamagnetic
as it adopts a square planar geometry and all eight d-electrons are paired up.
4. The complexes NiCl2(PPh3)2 and PdCl2(PPh3)2 are paramagnetic and diamagnetic
respectively. The structure of these two complexes can be assigned from the magnetic
data. Both the Ni(II) and Pd(II) are d8 ions. The PdCl2(PPh3)2 should have a square-planar
geometry and NiCl2(PPh3)2 have a tetrahedral structure with two unpaired electrons.
5. Take two examples of K3[CoF6] and [Co(NH3)6]Cl3. The first one is a high-spin
complex with ground state electron configuration t2g4eg2 and the complex is
paramagnetic. The second complex is diamagnetic indicating it as a low-spin complex
with electron configuration t2g6eg0.
Orbital contribution to magnetic moments: From a quantum mechanics viewpoint, the
magnetic moment is dependent on both spin and orbital angular momentum
contributions. The spin-only formula used is given as: µs.o. = √{4S(S+1)} and this can be
modified to include the orbital angular momentum as follows:
For orbital angular momentum to contribute, and hence for the paramagnetism to differ
significantly from the spin-only value, the orbital in which electron resides must be able
to transform the orbital it occupies into an
equivalent and degenerate orbital by a simple
rotation (it is the rotation of the electrons which
induces the orbital contribution). In a free ion, the
five d-orbitals are degenerate and some orbitals
can be transformed into others by rotations. The
figure at right illustrates that a 90° or 45° rotation
about z-axis transform dxz↔dyz and dxy↔dx2-y2
orbitals respectively. In an octahedral complex,
due to crystal field splitting, the degeneracy
between the dxy and dx2-y2 orbitals is lifted. It
causes the partial quenching of the orbital
contribution. There is a further factor that needs to
be taken into consideration: if all the t2g orbitals are singly occupied, an electron in, say,
dxz orbital cannot be transferred into dyz orbital because it already contains an electron
having the same spin quantum number as the incoming electron; if all the t2g orbitals are
doubly occupied the transfer is not possible. Thus only configurations which have t2g
electron other than three or six electrons make orbital contributions to the magnetic
moments of octahedral complexes: for high-spin complexes, only the configurations t2g1,
t2g2, t2g4eg2 and t2g5eg2. Note that eg electrons do not contribute to orbital moment. For
tetrahedral geometry it is easily shown that the configurations giving rise to an orbital
contribution are e2t21, e2t22, e4t24 and e4t25.
It is evident from this discussion that in most cases the orbital moments are quenched in
metal complexes and magnetic moments are close to the spin-only value. The tables
below give a list of spin-only and spin+orbital magnetic moments with experimental data
for d1 to d9 configurations.
An example helps to understand the quenching of orbital moment in different metal
complexes. Lets consider Ni(II) (d8) complex. As a free ion, the total magnetic moment
µs+o is calculated to be 4.47. In octahedral d8 complex, the orbital contribution is zero. On
the contrary, d8 tetrahedral complex will have contribution from the orbital magnetic
moment. Hence, although both complexes have two unpaired electrons, the [Ni(H2O)6]2+
has magnetic moment close to the spin-only value but the magnetic moment in [NiCl4]2is higher than the spin-only value.
Orbital contribution zero.
Magnetic moment is close
to the spin-only value.
Magnetic moment is higher
than the spin-only value as
there is positive orbital
contribution
Molecular Orbital Theory of Coordination Complexes
Limitations of Crystal Field Theory.
Although Crystal Field theory accounts for many features of complexes including
their color it still leaves some facts unexplained. The color of compounds like
KMnO4 (Mn7+ has no d electrons) cannot be explained.
One of the important experimental facts is the spectrochemical series where many
anionic ligands turn out to be quite weak field ligands (H2O > OH-).
Also quite strangely neutral ligands and very weak or even poor Lewis bases (for
example CO) turn out to be extremely strong field ligands.
The above is quite contrary to the Crystal field theory assumption of an electrostatic
interaction between the metal ion and the ligand.
In addition there is direct experimental evidence that suggests quite strongly that in
fact the metal orbitals overlap with the ligand orbitals. One such evidence is found
from EPR (Electron Paramagnetic Resonance) experiments. EPR is very similar to
NMR except that instead of the nuclear spin the electron spin is the focus of
investigation. Thus a species with one unpaired electron would behave in a very
similar way as nucleus with a spin of ½. If the crystal field theory is correct, an
unpaired electron present on a metal should be localized on it (remember that CFT
does not permit overlap between metal and ligand orbitals) and a single absorption
should be seen. If however, the electron is delocalized (even partly) into the ligand
orbitals also, and if the ligand atoms can couple with the electron spin, a hyperfine
structure should be seen in the EPR spectrum. In fact this is what is observed in a
number of cases. This means that it is important to look into the overlap between the
metal and the ligand orbitals. This can be done by looking at the molecular orbital
picture of metal complexes.
Complexes in which metal-ligand σ-bonding is involved.
As an example for the above type of situation let us choose the complex [Co(NH3)6]3+.
This complex contains NH3 as the ligand which can only participate as a σ-donor to the
metal ion (The nitrogen atom does not have any low lying orbitals to participate in any
additional type of bonding). How do we construct the molecular orbital diagram for this
complex? We can use simple symmetry arguments to come out with a picture that would
be understandable. Let us first consider the metal orbitals. The valence orbitals available
are 3d, 4s, and 4p. So a total of 9 orbitals are available. Which of these orbitals are
suitable to be used in σ-bonding? Remember that we are constructing a molecular
orbital diagram for an octahedral complex. This means that the orbitals that we can use
should have their lobes pointed along the axes (In order to have a positive and head-on
overlap with the ligand orbitals). Obviously the 4s orbital is quite suitable. This is labeled
a1g (look handout-4 for the interpretation of different representation symbols). All the 4p
orbitals are also suitable (px, py, pz are along the x, y and z directions). These are labeled
as t1u. Now let us inspect the 3d orbitals. Only two of them are suitable. The orbitals dx2-y2
and dz2 are suitable since they have the lobes along the axes. These are labeled eg ; we
have seen them before!!!) However, the orbitals dxz, dyz and dxy are not suitable since
ligand orbitals cannot overlap with them to give a positive overlap. These cannot be,
therefore, utilized by the metal for σ-bonding. These remain non-bonding and are labeled
as t2g.
Thus we conclude that of the 9
valence orbitals of the metal
six are suitable for forming σbonding (a1g, t1u, eg) and three
are non-bonding orbitals (t2g).
Let us assume that by a linear
combination of the ligand
orbitals (one from each ligand)
we are able to generate six
orbitals of similar symmetry,
called as ligand group orbitals (LGO’s) as that of the six metal bonding orbitals . These
orbitals on the metal and the ligand now can combine to afford the M. O diagram as
shown below.
The salient features of the above M. O. diagram can be summarized as follows:
The lowest energy orbitals a1g, t1u, eg are closer in energy to the ligand orbitals.
The t2g orbitals remain non-bonding and their energy is not changed after forming the
M.O.’s
The higer energy orbitals a1g*, t1u*, eg* are closer in energy to the metal orbitals.
The energy separation between the non-bonding t2g and the eg* orbitals represents the
∆o of the crystal field diagram. As before, if this separation is large, low-spin
complexes are formed. If the separation is small, high spin complexes are formed.
Thus, [Co(NH3)6]3+ ( Co3+ has six electrons; six ammonia ligands contribute twelve
electrons) has the electronic configuration, a1g2, t1u6, eg4, t2g6. In contrast [CoF6]3- has
the configuration a1g2, t1u6, eg4, t2g4 eg*2. Notice that the filling of the lower energy
orbitals a1g2, t1u6, eg4is reminiscent of the valence bond treatment and the filling of the
higher energy orbitals t2g6 (for the cobalt hexammine complex) or t2g4 eg*2 (for the
cobalt hexafluoride) is reminiscent of the crystal field treatment.
π-bonding involving π-donor ligands
Ligands like halides or hydroxide, in spite of being ionic, are found in the lower end of
the spectrochemical series. The M. O. theory has a more satisfactory answer to their
position. Consider, F-. In addition to acting as a σ-donor this ligand can also act as a πdonor. We have already seen the σ-bonding picture. If we have to utilize the metal
orbitals for π-bonding we have seen that only the t2g orbitals are available. These can be
utilized for π-bonding by forming LGO’s of the same symmetry. However, note that the
t2g set of LGO’s will be lower in energy in comparison with the metal orbitals, because of
the greater electronegativity of F- ligands. Consequently, the π-overlap between the
metal and ligand orbitals will give rise to an energy diagram where the metal t2g orbitals
will be raised in energy (now they will be called t2g*). As a result the gap between these
orbitals and the eg* orbitals is decreased compared to the pre π-bonding situation.
Because of this, high spin complexes result.
π-bonding involving π-acceptor ligands
Ligands such as CO, PR3 etc., can form σ-bonds with metals similar to ammonia. Unlike
ammonia, which does not have any vacant orbitals to receive electron density, CO and
PR3, however have vacant orbitals of the suitable symmetry to form π-bonds with the
metal. However, since these orbitals are empty, they will be higher in energy in
comparison to the metal t2g orbitals with which they have to overlap to form the π-bonds.
Consequently the metal t2g orbitals are lowered in energy after formation of the π-bonds.
The result is that the energy separation between the t2g and the eg* orbitals is increased
after π-bond formation. Note that although the t2g orbitals (LGO’s) of the ligand are
raised after the π-bond formation it does not matter as these remain empty. Thus the
formation of the π-bond explains quite readily the intriguing fact that neutral and weakly
Lewis Basic ligands such as CO and PR3 are found in the higher end of the
spectrochemical series.
A single scheme below illustrate the effect of both the π-donor and π-acceptor ligands.