The document appears to be describing the magnetic properties of inorganic complexes. It discusses how ligand field theory can be used to predict whether a complex will be paramagnetic or diamagnetic based on whether it forms a low-spin or high-spin configuration. Low-spin complexes tend to be diamagnetic due to having more paired electrons, while high-spin complexes are often paramagnetic since they have more unpaired electrons. The magnitude of the crystal field splitting parameter Δ depends on factors like the metal ion, its oxidation state, and the identity and geometry of the ligands.

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2. Submitted to:
Dr. Ali Mohsin
Submitted by:
Adina Tatheer
10060607-050
BS Chemistry (V)
Section ‘A’

3. Q no. 1: Describe the magnetic properties of complex.
Magnetic properties can be determined by looking at a compound's electron configuration
and the size of its atoms. Since Magnetism is created by the spin of electrons, we can
look at how many unpaired electrons are present in a specific compound and determine
how magnetic the compound is. For this purpose we will be evaluating the d-block
elements or Transition Metals* (TMs) because they tend to have a large number of
unpaired electrons.
Introduction:
The magnetism discussed in this article is paramagnetism. Paramagnetism occurs when
there are one or more unpaired electrons in a compound. (The opposite, when all
electrons are paired, is called diamagnetism). Di- and para-magnetism are often affected
by the presence of coordination complexes, which the transition metals (d-block) readily
form.
Singular electrons have a spin, denoted by the quantum number ms as +(1/2) or –(1/2).
This spin is negated when the electron is paired with another, but creates a slight
magnetic field when the electron is unpaired. The more unpaired electrons, the more
likely paramagnetic a material is. The electron configuration of the transition metals (d-
block) changes when in a compound. This is due to the repulsive forces between
electrons in the ligands and electrons in the compound. Depending on the strength of the
ligand, the compound may become paramagnetic or diamagnetic.
Ferromagnetism:
Some paramagnetic compounds are capable of becoming ferromagnetic. This means that
the compound shows permanent magnetic properties rather than exhibiting them only in
the presence of a magnetic field. In a ferromagnetic element, electrons of atoms are
grouped into domains, where each domain has the same charge. In the presence of a
magnetic field, these domains line up so that charges are parallel throughout the entire
compound. Whether a compound can be ferromagnetic or not depends on how many
unpaired electrons it has and on its atomic size.

4. Small atoms pair up too easily and their charges cancel.
Large atoms are difficult to keep together, their charge interaction is too weak.
Therefore, only the right sized atoms will work together to group themselves into
domains. Elements with the right size include: Fe, Co, Ni. That means that Fe, Co and Ni
are paramagnetic with the capability of permanent magnetism; they are also
ferromagnetic.
Ligand Field Theory Background
An element can have up to 10 d electrons in 5 d-orbitals, dxy, dxz, dyz, dz2, and dx2-
y2. During the formation of a complex, the degeneracy (equal energy) of these orbitals is
broken and the orbitals are at different energy levels.
(Assuming a 6-ligand compound)
In an octahedral complex, the ligands approach along the x, y, and z axes, so the
repulsion is strongest in the orbitals along these axes (dz2 and dx2-y2). As a result, the
dz2 and dx2-y2 orbitals are higher in energy than the dxy, dxz, and dyz orbitals. In a tetrahedral

5. complex, the splitting is opposite, with the dxy, dxz, and dyz orbitals higher in energy to
avoid the ligands approaching between the axes. The splitting in a square planar complex
has four levels (lowest to highest): dyz and dxz, dxy, dz2, dx2-y2.
Depending on the strength of the ligand, the splitting energy between the different d-
orbitals may be large or small. Ligands producing a smaller splitting energy are called
‘weak field’ ligands, and those with a larger splitting energy are called ‘strong field’
ligands.
Filling of d-orbitals in a complex:
Hunds' Rule states that electrons will fill all available orbitals with single electrons before
pairing up, while maintaining parallel spins (paired electrons have opposing spins). For a
set of degenerated d-orbitals (not in a complex), electrons fill all orbitals before pairing to
conserve the pairing energy, otherwise needed. With the addition of ligands, the situation
becomes more complicated. The splitting energy between the d-orbitals means that
additional energy is required to place single electrons into the higher-energy orbitals.
Once the lower-energy orbitals have been half-filled (one electron per orbital), an

6. electron can either be placed in a higher-energy orbital (preserving Hund’s rule) or pair
up with an electron in a lower-energy orbital (when the splitting energy is greater than the
pairing energy). The strength of the ligands determine which option is chosen.
With a strong-field ligand, the splitting energy is very large and low-spin complexes are
usually formed. With a weak-field ligand, the electrons can easily enter the higher-energy
orbitals before pairing (high-spin).
How does this relate to magnetism?
Low-spin complexes contain more paired electrons since the splitting energy is larger
than the pairing energy. These complexes, such as [Fe(CN)6]3-, are more often
diamagnetic or weakly paramagnetic. High-spin complexes usually contain more
unpaired electrons since the pairing energy is larger than the splitting energy. With more
unpaired electrons, high-spin complexes are often paramagnetic.
The unpaired electrons in paramagnetic compounds create tiny magnetic fields, similar to
the domains in ferromagnetic materials. The higher the number of unpaired electrons
(often the higher-spin the complex), the stronger the paramagnetism of a coordination
complex. We can predict paramagnetiism and its relative strength by determining
whether a compound is a weak field ligand or a strong field ligand. Once we have
determined whether a compound has a weak or a strong ligand, we can predict its
magnetic properties:

8. Q no. 2: Explain the CF in the octahedral and tetrahedral symmetry also
explain the factors affecting the magnitude of ∆.
CF theory:
CF theory tried to describe the effect of the electrical field
of neighboring ions on the energies of the valence orbitals of an ion in a crystal. Crystal
field theory was developed by considering two compounds: manganese(II) oxide, MnO,
and copper(I) chloride, CuCl.
Octahedral Crystal Fields:
Each Mn2+ ion in manganese(II) oxide is surrounded by six O2- ions arranged toward the
corners of an octahedron, as shown in the figure below. MnO is therefore a model for
an octahedral complex in which a transition-metal ion is coordinated to six ligands.
What happens to the energies of the 4s and 4p orbitals on an Mn2+ ion when this ion is
buried in an MnO crystal? Repulsion between electrons that might be added to these
orbitals and the electrons on the six O2- ions that surround the metal ion in MnO increase
the energies of these orbitals. The three 4p orbitals are still degenerate, however. These
orbitals still have the same energy because each 4p orbital points toward two O2- ions at
the corners of the octahedron.
Repulsion between electrons on the O2- ions and electrons in the 3d orbitals on the metal
ion in MnO also increases the energy of these orbitals. But the five 3d orbitals on the
Mn2+ ion are no longer degenerate. Let's assume that the six O2-ions that surround each
Mn2+ ion define an XYZ coordinate system. Two of the 3d orbitals (3dx2-y2 and 3dz2) on
the Mn2+ion point directly toward the six O2- ions, as shown in the figure below. The
other three orbitals (3dxy, 3dxz, and 3dyz) lie between the O2- ions.

9. The energy of the five 3d orbitals increases when the six O2- ions are brought close to the
Mn2+ ion. However, the energy of two of these orbitals (3dx2-y2 and 3dz2) increases much
more than the energy of the other three (3dxy, 3dxz, and 3dyz), as shown in the figure
below. The crystal field of the six O2- ions in MnO therefore splits the degeneracy of the
five 3d orbitals. Three of these orbitals are now lower in energy than the other two.
By convention, the dxy, dxz, and dyz orbitals in an octahedral complex are called
the t2g orbitals. The dx2-y2 and dz2 orbitals, on the other hand, are called the eg orbitals.

10. The easiest way to remember this convention is to note that there are three orbitals in
the t2g set.
t2g: dxy, dxz, and dyz eg: dx2-y2 and dz2
The difference between the energies of the t2g and eg orbitals in an octahedral complex is
represented by the symbol o. This splitting of the energy of the d orbitals is not
trivial; o for the Ti(H2O)63+ ion, for example, is 242 kJ/mol.
The magnitude of the splitting of the t2g and eg orbitals changes from one octahedral
complex to another. It depends on the identity of the metal ion, the charge on this ion, and
the nature of the ligands coordinated to the metal ion.
Tetrahedral Crystal Fields:
Each Cu+ ion in copper(I) chloride is surrounded by four Cl- ions arranged toward the
corners of a tetrahedron, as shown in the figure below. CuCl is therefore a model for
a tetrahedral complex in which a transition-metal ion is coordinated to four ligands.
Once again, the negative ions in the crystal split the energy of the d atomic orbitals on the
transition-metal ion. The tetrahedral crystal field splits these orbitals into the
same t2g and eg sets of orbitals as does the octahedral crystal field.
t2g: dxy, dxz, and dyz eg: dx2-y2 and dz2
But the two orbitals in the eg set are now lower in energy than the three orbitals in
the t2g set, as shown in the figure below.

11. To understand the splitting of d orbitals in a tetrahedral crystal field, imagine four ligands
lying at alternating corners of a cube to form a tetrahedral geometry, as shown in the
figure below. The dx2-y2 and dz2 orbitals on the metal ion at the center of the cube lie
between the ligands, and the dxy, dxz, and dyz orbitals point toward the ligands. As a
result, the splitting observed in a tetrahedral crystal field is the opposite of the splitting in
an octahedral complex.
Because a tetrahedral complex has fewer ligands, the magnitude of the splitting is
smaller. The difference between the energies of the t2g and eg orbitals in a tetrahedral
complex ( t) is slightly less than half as large as the splitting in analogous octahedral
complexes ( o).
t = 4/9 o
Factors effecting the magnitude of Δ:

12. The size of the gap Δ between the two or more sets of orbitals depends on several factors,
including the ligands and geometry of the complex. Some ligands always produce a small
value of Δ, while others always give a large splitting. The reasons behind this can be
explained by ligand field theory. The spectrochemical series is an empirically-derived list
of ligands ordered by the size of the splitting Δ that they produce (small Δ to large Δ; see
also this table):
-
I− < Br− < S2− < SCN− < Cl− < NO3− < N3− < F− < OH < C2O42−
< H2O < NCS− < CH3CN < py < NH3 < en < 2,2'-
bipyridine < phen <NO2− < PPh3 < CN− < CO
It is useful to note that the ligands producing the most splitting are those that can engage
in metal to ligand back-bonding.
The oxidation state of the metal also contributes to the size of Δ between the high and
low energy levels. As the oxidation state increases for a given metal, the magnitude of Δ
increases. A V3+ complex will have a larger Δ than a V2+ complex for a given set of
ligands, as the difference in charge density allows the ligands to be closer to a V3+ ion
than to a V2+ ion. The smaller distance between the ligand and the metal ion results in a
larger Δ, because the ligand and metal electrons are closer together and therefore repel
more.
Crystal field stabilization energy:
The crystal field stabilization energy (CFSE) is the stability that results from placing a
transition metal ion in the crystal field generated by a set of ligands. It arises due to the
fact that when the d-orbitals are split in a ligand field (as described above), some of them
become lower in energy than before with respect to a spherical field known as the
barycenter in which all five d-orbitals are degenerate. For example, in an octahedral case,
the t2g set becomes lower in energy than the orbitals in the barycenter. As a result of this,
if there are any electrons occupying these orbitals, the metal ion is more stable in the
ligand field relative to the barycenter by an amount known as the CFSE. Conversely,
the eg orbitals (in the octahedral case) are higher in energy than in the barycenter, so
putting electrons in these reduces the amount of CFSE.

13. Octahedral crystal field stabilization energy
If the splitting of the d-orbitals in an octahedral field is Δoct, the three t2g orbitals are
stabilized relative to the barycenter by2/5 Δoct, and the eg orbitals are destabilized
by 3/5 Δoct. As examples, consider the twod5 configurations shown further up the page.
The low-spin (top) example has five electrons in the t2g orbitals, so the total CFSE is 5
x 2/5 Δoct = 2Δoct. In the high-spin (lower) example, the CFSE is (3 x 2/5Δoct) - (2
x 3/5 Δoct) = 0 - in this case, the stabilization generated by the electrons in the lower
orbitals is canceled out by the destabilizing effect of the electrons in the upper orbitals.
Crystal Field stabilization is applicable to transition-metal complexes of all geometries.
Indeed, the reason that many d8 complexes are square-planar is the very large amount of
crystal field stabilization that this geometry produces with this number of electrons.
Tetrahedral
Octahedral

14. Q no. 3: How pi bonding is explained by MOT and give the experimental
evidence for pi bonding?
Pi Bonding and MO Theory:
Pi-bonding also exists for tetrahedral and square planar complexes. The MO treatment
for these systems is very similar to what is observed for an octahedral system. First,
there are four plausible L-M pi-interactions: pπ-dπ, dπ-dπ, π*-dπ, σ*-dπ.
The pπ-dπ interaction involves ligand-to-metal pi donation while the other three are
metal-to-ligand pi donations. Pi-bonds will involve the t2g set, not the eg*. This is
because the eg* orbitals point directly at the ligands and are set up for σ overlap. The
direction of electron donation and the energy levels of ligand pi-bonding orbitals will
have a pronounced effect on molecules. We will consider a molecule with six pi-donor
ligands (e.g. halide ions) and then 6 pi-acceptor ligands (e.g. CO).
MX6n- :
The halide p orbitals are lower in energy than the metal d orbitals and they are filled,
while metal d orbitals may or may not contain electrons. Thus:
When the MOs form the ligand p electrons fill the t2g orbitals, thus metal t2g
electrons go into the t2g* MOs. The result of this type of interaction is a small ∆O.
M(CO)6:
The CO pi* orbitals are empty and are high in energy (remember CO bond
energy).

15. Since the CO pi* orbitals are empty, the t2g MO is filled with metal t2g electrons and
promotion is then a relatively high energy process. These diagrams explain the relative
placements of the halides and CN-/CO in the spectrochemical series. In an electrostatic
model, the reverse would be expected.
Experimental Evidence For Pi Bonding:
So what evidence is there for π-bonding (i.e. what do we look for)? We
begin by asking what would the interaction look like without π-bonding? Then what
happens with full π-bonding:
M-L → M=L
Since the bonding between metal and ligand changes between these forms, bonding
within the ligand must change. If electron density is fed into a pi or σ orbital on the
metal, a bond within the ligand will be weakened. The strongest evidence for pi- bonding
comes from metal-carbonyl complexes. Crystallography - The greater the extent of pi-
back bonding, the more M=C character there will be and the more C≡O will resemble
C=O. The difference in C≡O and C=O bond lengths is about 0.1 Å and should be useable
for quantification. Unfortunately, this has not been observed. In contrast, M-C bond
lengths do change. Consider the complexes Cr(CO)6 and Cr(CO)5(PR3). In the absence
of π-backbonding the Cr-C bond lengths should be the same. If it does occur, then the
bond lengths should be shorter in Cr(CO)5(PMe3). Why? Two reasons: PMe3 is at best
a very poor pi-acceptor so only 5 COs are competing for electron density from the metal,
not 6; and PR3 is a very good σ donor, CO is not. Thus, the Cr has more electron density
to share with fewer acceptors. One other trend is expected. The Cr-C(O) bond trans to
PR3 should be shorter than those cis. This is because the trans CO will bind to the same
d-orbital as the PR3 and the effect will be greatest there.
Infrared Spectroscopy:

16. Evidence for C=O character is most clearly seen in IR spectroscopy. ν(CO) for
C≡O is about 2150 cm-1, while in R2C=O ν(C=O) is about 1700 cm-1. Thus, the greater
the extent of backbonding the lower the expected ν(C≡O). This is seen dramatically for
two series of complexes M(CO)6n+/- and M(CO)4n+/- .This can also be seen when a CO is
substituted for by another ligand as seen in crystallography. The only problem with using
this technique is that the CO stretching band is almost always split into several
components making interpretation difficult.
Q no. 4:Explain the Electroneutrality and BackBonding with suitable
examples?
Electroneutrality:
It is assumed; that is, that there is no measurable charge excess in any side of the
membrane. So, although there is an electric potential across the membrane due to charge
separation, there is no actual measurable difference in the global concentration of positive
and negative ions across the membrane, that is, there is no actual measurable charge
excess in either side. That occurs because the effect of charge on electrochemical
potential is hugely greater than the effect of concentration so an undetectable change in
concentration creates a great change on electric potential.
Example:
Nature seems to strongly discourage any process that would lead to an excess of positive
or negative charge in matter. Suppose, for example, that we immerse a piece of zinc
metal in pure water. A small number of zinc atoms go into solution as Zn2+ ions, leaving
their electrons behind in the metal:
Zn(s) → Zn2+ + 2e–
As this process goes on, the electrons which remain in the zinc cause a negative
charge to build up within the metal which makes it increasingly difficult for additional
positive ions to leave the metallic phase. A similar buildup of positive charge in the
liquid phase adds to this inhibition. Very soon, therefore, the process comes to a halt,
resulting in a solution in which the concentration of Zn2+ is still too low (around 10–10 M)
to be detected by ordinary chemical means.

17. Figure 1. Transport of zinc ions from the metal to water; the build-up of negative
charge in the metal (and positive charge in the solution) soon brings the process to a
halt.
There would be no build-up of this opposing charge in the two phases if the excess
electrons could be removed from the metal or the positive ions consumed as the
electrode reaction proceeds. For example, we could drain off the electrons left behind
in the zinc through an external circuit that forms part of a complete electrochemical
cell. Another way to remove these same electrons is to bring a good electron acceptor
(that is, an oxidizing agent) into contact with the electrode. A suitable acceptor would
be hydrogen ions; this is why acids attack many metals. For the very active metals
such as sodium, water itself is a sufficiently good electron acceptor.
The degree of charge unbalance that is allowed produces differences in electric
potential of no more than a few volts, and corresponds to unbalances in the
concentrations of oppositely charged particles that are not chemically significant.
There is nothing mysterious about this prohibition, known as the electroneutrality
principle; it is a simple consequence of the thermodynamic work required to separate
opposite charges, or to bring like charges into closer contact. The additional work
raises the free energy change of the process, making it less spontaneous.
The only way we can get the oxidation of the metal to continue is to couple it with
some other process that restores electroneutrality to the two phases. A simple way to
accomplish this would be to immerse the zinc in a solution of copper sulfate instead
of pure water. As you will recall if you have seen this commonly-performed

18. experiment carried out, the zinc metal quickly becomes covered with a black coating
of finely-divided metallic copper. The reaction is a simple oxidation-reduction
process, a transfer of two electrons from the zinc to the copper:
Zn(s) → Zn2+ + 2e–
Cu2+ + 2e– → Cu(s)
The dissolution of the zinc is no longer inhibited by a buildup of negative charge in
the metal, because the excess electrons are removed from the zinc by copper ions that
come into contact with it. At the same time, the solution remains electrically neutral,
since for each Zn ion introduced to the solution, one Cu ion is removed. The net
reaction
Zn(s) + Cu2+ → Zn2+ + Cu(s)
quickly goes to completion.
Back bonding:
It is a type of bonding which take place between atoms in a compound ;in which one
atom has lone pair of electron and other has vacant orbital placed adjacent to each
other.
A compound which posses back bonding has pi bonding character because it occurs
after formation of sigma bond.
Usually ; back bonding causes molecule to get stable as it completes octet.
for ex. in borontriflouride ,
back bonding causes decrease in bond length and increase in bond order.
pi backbonding:

19. (Top) the HOMO and LUMO of CO. (Middle) an example of a sigma bonding orbital
in which CO donates electrons to a metal's center from its HOMO. (Bottom) an
example where the metal center donates electrons through a d orbital to CO's LUMO.
NOTE in this depiction the y axis has no relation to energy levels.
π backbonding, also called π backdonation, is a concept from chemistry in which
electrons move from an atomic orbital on one atom to a π* anti-bonding orbital on
another atom or ligand. It is especially common in the organometallic
chemistry of transition metals with multi-atomic ligands such as carbon
monoxide, ethylene or the nitrosonium cation. Electrons from the metal are used to
bond to the ligand, in the process relieving the metal of excess negative charge.
Compounds where π backbonding occurs include Ni(CO) and Zeise's
salt. IUPAC offers the following definition for backbonding:
A description of the bonding of π-conjugated ligands to a transition metal which
involves a synergic process with donation of electrons from the filled π-orbital or lone
electron pair orbital of the ligand into an empty orbital of the metal (donor–acceptor
bond), together with release (back donation) of electrons from an nd orbital of the
metal (which is of π-symmetry with respect to the metal–ligand axis) into the empty
π*-antibonding orbital of the ligand.
Metal carbonyls, nitrosyls, and isocyanides:
The electrons are partially transferred from a d-orbital of the metal to anti-bonding
molecular orbitals of CO (and its analogues). This electron-transfer (i) strengthens the

20. metal-C bond and (ii) weakens the C-O bond. The strengthening of the M-CO bond is
reflected in increases of the vibrational frequencies for the M-C bond (often outside of
the range for the usual IR spectrophotometers). Furthermore, the M-CO bond length is
shortened. The weakening of the C-O bond is indicated by a decrease in the frequency of
the νCO band(s) from that for free CO (2143 cm−1) often by more than 200 cm−1. For this
reason, IR spectroscopy is an important diagnostic technique in metal-carbonyl
chemistry. The article infrared spectroscopy of metal carbonyls discusses this in detail.
Many ligands other than CO are strong "backbonders". Nitric oxide is an even stronger π-
acceptor than is CO and νNO is a diagnostic tool in metal-nitrosyl chemistry. In the case
of isocyanide complexes, the degree of π-bonding is again indicated by shortening of the
M-CNR bond and by decrease in νCN. For the isocyanides however, an additional
parameter is the MC=N-C angle, which deviates from 180° in highly electron-rich
systems. Other ligands have weak π-backbonding abilities, which creates a labilization
effect of CO, which is described by the cis effect.
Metal-alkenes and alkyne complexes:
As in metal-carbonyls, electrons are partially transferred from a d-orbital of the metal to
anti-bonding molecular orbitals of the alkenes and alkynes. This electron-transfer (i)
strengthens the metal-ligand bond and (ii) weakens the C-C bonds within the ligand. In
the case of metal-alkenes and alkynes, the strengthening of the M-C2R4 and M-C2R2 bond
is reflected in bending of the C-C-R angles which assume greater sp3 and sp2 character,
respectively. Thus strong pi-backbonding causes a metal-alkene complex to assume the
character of a metallacyclopropane. Electronegative substituents exhibit greater pi
backbonding. Thus strong pi backbonding ligands
are tetrafluoroethylene, tetracyanoethylene, and hexafluoro-2-butyne.
Metal-phosphine complexes:

21. R3P–M σ bonding
R3P–M π backbonding
Phosphines accept electron density from metal p or d orbitals into combinations of P–C
σ* antibonding orbitals that have π symmetry. When phosphines bond to electron-rich
metal atoms, backbonding would be expected to lengthen P–C bonds as P–C σ* orbitals
become populated by electrons. The expect lengthening of the P–C distance is often
hidden by an opposing effect: as the phosphorus lone pair is donated to the metal, P(lone
pair)-R(bonding pair) repulsions decrease, which acts to shorten the P–C bond. The two
effects have been deconvoluted by comparing the structures of pairs of metal-phosphine
complexes that differ only by one electron. Oxidation of R3P–M complexes results in
longer M–P bonds and shorter P–C bonds, consistent with π-backbonding. In early work,
phosphine ligands were thought to utilize 3d orbitals to form M-P pi-bonding, but it is
now accepted that d-orbitals on phosphorus are not involved in bonding as they are too
high in energy.

22. References:
1) http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Crystal_Field_Theory/Crys
tal_Field_Theory/Magnetic_Properties_of_Coordination_Complexes_(CFT)
2) http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch12/crystal.php
3) Principles of structure and reactivity, James E Huheey, Ellen A. Keiter, Richard L Keiter,
4th edition.