Download - Free Documents

Chemistry / Lecture Notes
Dr. M. Gerken
Page
. Introduction to Magnetochemistry
Many transitionmetal complexes are paramagnetic, due to the presence on unpaired d
electrons. Ligand field theory can be used to account for the number of unpaired d electrons
that occur for any specific compound. The underlying principles of ligand field theory have
already been developed. In particular, magnetic measurements can distinguish between two
possible arrangements of the d electrons in the common Td and Oh geometries, called
highspin and lowspin. For example, Figure illustrates the consequences of the two
environments for an octahedral d system. Typically, highspin complexes occur when the size
of is of the same order of magnitude as the electron spinpairing energy.
OCTAHEDRAL HIGH SPIN OCTAHEDRAL LOW SPIN
eg
eg
tg t g
Figure Ligand field splitting diagram for high and low spin octahedral environments
However, when gtgt spinpairing energy, the lowspin arrangement will be preferred. For any
given metal and oxidation state, the size of is largely determined by the nature of ligand, and
especially of the identity and charge of the donor atoms in the ligands. Magnetochemistry
can be used to distinguish the two cases . Bulk magnetic behaviour Much of van Vlecks early
work on crystal field theory focused on interpreting the magnetic behaviour of transitionmetal
compounds which of course include the most important bulk magnetic materials such as iron,
cobalt, and magnetite, FeO. The origin of all magnetic phenomena can be traced to the
motion of charges. Electrons moving in a circular path in an atom or molecule are constantly
undergoing acceleration because of the circular motion, and therefore, generate a magnetic
field perpendicular to their direction of motion, the orbital magnetic moment. Electrons also
have a spin, as a simplification visualized by the rotation of the electron around its own axis,
which produces a spin magnetic moment. If the electrons are paired in a wavefunction, their
spin magnetic fields are equal and opposite spin paired. If these moving electrons are placed
into a large external magnetic field the applied magnetic field, then the external field induces
an additional current that causes a magnetic field by itself. This induced magnetic field is
opposite to the external magnetic field Lenz law. As a consequence, the magnetic field
actually, B is the magnetic flux density, H is the magnetic field strength inside the sample
Binternal will be weaker than the external field Bexternal see figure on the righthand side,
with B being negative, and the sample is repelled by the applied field. Binternal Bexternal B
This magnetic behaviour is called diamagnetism. Every paired electron contributes to the
diamagnetism of a substance. Hence, diamagnetism is present in every sample. The
equation can be rewritten in two different ways with r as the relative magnetic permeability
Binternal r Bexternal or Binternal V Bexternal and B V Bexternal with V as the magnetic
susceptibility volume susceptibility The formulation using susceptibilities is more commonly
used among magnetochemists and will be used in this course. For diamagnetic samples, V is
negative. The size of the diamagnetic susceptibility is a function of i the number of electrons
and ii the radius of the electron orbits. Instead of the additional magnetic flux density, B, the
magnetization M in A/m is generally used B M is the magnetic field constant. With Bexternal
Hexternal substitution the above equation yields M V Hexternal.
we can use the weight of the sample compared to its apparent weight in a magnetic field to
measure . The gram susceptibility is related to V dimensionless by the density. Permanent
iron magnets are common examples of ferromagnetic materials. It is possible to ascribe
paramagnetism to a diamagnetic substance if these corrections are not made . g V/ M g M
As stated above. The susceptibilities in SI units and cgs units differ by a factor of SI
cgs.Chemistry Lecture Notes Dr. Gerken Page If an orbital is singly occupied. but commonly
used cgs units of magnetic susceptibility is given in Table . Measurements are usually made
on finely ground powders. and the volume of the displaced air must be accounted for. and
glass always contains some paramagnetic impurities. which can be turned on and off. the
measurement of the bulk sample is akin to measuring the dia para average susceptibility of a
single formula unit. is defined by the equation F V V H dH dx The integration of this equation
relates the force. V. V. The magnetic susceptibility is a measure of the force with which
magnetic attractions or repulsions occur. which is related to gram susceptibility i. Since
weighing a sample is equivalent to measuring the force of gravity acting on it. we use a Gouy
balance. Several of the seemingly laborious restrictions result directly from this theory the
tube must always be suspended at exactly the same height. this sample is drawn into the
magnetic field. The relevant scale in the old. we use a standard of known measured under
identical conditions to get for our unknown material. Air contains paramagnetic oxygen. one
unpaired electron as a paramagnetic centre will overshadow the diamagnetism of all the
paired electrons in the sample. where the sample is weighed underneath the balance and
placed between the poles of a magnet. This magnetic moment aligns itself with an external
magnetic field and increases the magnetic field inside the sample see figure above. M. If
every second paramagnet in a material is aligned in an opposing fashion. the bulk material is
ferromagnetic. Macroscopic magnetic effects are caused by the additive cooperative effect of
atomic paramagnets. experienced by the sample over the integrated field strength. specific
susceptibility g cmg by the molar mass. and negative if it is diamagnetic. Table Classification
of Magnetic Behaviour Type of magnetism Diamagnetism Paramagnetism Ferromagnetism
Antiferromagnetism Susceptibility. cm mol cgs units at C. and the contents must always be
filled to exactly the same level . As a consequence.otherwise the integrated field strength will
not be the same. The paramagnetic contribution is two orders of magnitudes larger than the
diamagnetic contributions. B and the paramagnetic susceptibility are positive. M cm mol. This
causes a net attraction between paramagnets and magnetic field gradients. The volume
susceptibility. A common standard is HgCoSCN with M . Therefore the tubes themselves
must be carefully calibrated. from the molar susceptibility. a small magnetic moment is
associated with the unpaired electron. Since the unpaired electrons in a metal complex are
usually only due to a few electrons in a large molecule. This is due to the fold greater
susceptibility of paramagnetic versus diamagnetic substances. which can safely be assumed
to be totally randomly distributed. For paramagnetic substances. M is positive if the
substance is paramagnetic. When these are oriented at random. which would require the
difficult job of measuring the integrated field strength over the volume of space the sample
occupies. Diamagnetic susceptibility correction We have to distinguish between the volume
susceptibility. For such measurements. cgs units Field dependence Independent of H
Independent of H Dependent on H Often dependent on H to to The total magnetic
susceptibility of the substance is the sum of all the diamagnetic and paramagnetic
contributions from all the electrons in the sample. the bulk material is said to be
antiferromagnetic. F. If on the other hand they align in the same direction. Therefore. This
effect is called paramagnetism.e. Rather than solving this equation directly. the sum of all the
diamagnetic effects can be .
In comparison. J T. . FeCN.. / . M T para k M T N A / / Here is the Bohr magneton eh . Using
the number of unpaired electrons.. Also many metal complexes have appreciable Calculated
Experiment orbital angular momentum contributions to the magnetic moment. with given in
Bohr magneton SS Since S represents the overall spin quantum number. Conditions for this
to occur are fulfilled in Oh complexes with d. Calculated spinonly magnetic moments
Materials whose magnetic moments are not so well insulated from one another often follow a
modified temperature dependence called Ion N S / / the CurieWeiss Law. lowering the
paramagnetic contribution. With increasing temperature. the spinonly magnetic moment can
be calculated from the equation. Cr experimental value and the calculated spinonly value
shows that the . diamagnetism does not exhibit any temperature dependence. Therefore.
which gives eff in units of Bohr magnetons when paraM is expressed in cgs units. we would
have to consider the spin as well as the orbital components or some sort of coupled angular
momentum for the prediction of paramagnetism.has . so that the paramagnetic term paraM
can be extracted according to the following formula totalM paraM diaMmetal core electrons
diaMligands diaMions diaMsolvate Diamagnetic correction terms are tabulated in several
textbooks often called Pascals constants and fortunately additivity of the separate
components of the molecule can be used. Fortunately the diamagnetic contribution is
additive. d and d transitionmetal complexes deviate significantly Ti . the magnetic
susceptibility paramagnetic susceptibility varies with temperature according to the Curie Law
M C/T where C is the Curie constant. . For substances which follow the Curie law closely.
Crudely speaking. contributes to paraM. Since the cyano ligand is a strongfield ligand we
expect an electron configuration of tg with one unpaired electron. we can rewrite the first
equation in terms of the total number of unpaired electrons nn Thus the approximate value of
the magnetic moment of any transition metal immediately gives us the total number of
unpaired electrons. Especially. Bohrmagnetons. . M. is plotted against T. d. and lowspin d .
The table on the righthand side lists experimentally determined and calculated magnetic
moments. Usually. The diamagnetic susceptibility is independent of temperature. BM
predicted for one and two unpaired electrons. V . and . the effective magnetic moment is
given by eff para eff . In a d transitionmetal complex. Fe The magnetic moment of MnNCS.
Although the agreement in the above table is excellent. and each electron has a value of .
respectively. and the motion of this charge is inducing a magnetic moment. k is the
Boltzmann constant and NA is Avogadros number.. BM. For example. . There are some
important deviations from this simplified theory. The good agreement between the / .
Microscopic theory of paramagnetism For a substance consisting of noninteracting
paramagnetic centers a condition which coordination compounds approximate much better
than most other magnetic materials due to the insulating effect of the surrounding ligands.
Mn assumption of a quenched orbital momentum is valid for these cations. The
greaterthanexpected magnetic moment is explained by the contribution of orbital angular
momentum. This is directly between the . we can make the assumption that only the spin
angular momentum of the electron. this implies that the unpaired electron is circulating
through the orbitals of the complex.has been determined as . the magnetic moments
electrons will move more randomly. Strictly. n. Predict the electron configuration. . .
producing a straight line with positive slope. Gerken Page substantial.Chemistry Lecture
Notes Dr. some complexes have measured moments which are in poorer agreement. from
the spinonly value. mc Substituting the constants gives the second term. and not its orbital
angular momentum. the electric field of the ligands the ligand field usually quenches the
orbital contribution to the paramagnetism.
They may either line up in alternating arrays. Normally entropy ensures that atomic
paramagnets are randomly arranged. and there is no bulk magnetization. However. or in
collinear arrays. Significant orbital contributions occur for d. . Gerken Page and d
configurations. so we will not consider these any further at this time. Bulk magnetism Bulk
magnets consist essentially of aligned paramagnets. which is called antiferromagnetism.
which is ferromagnetism as seen in common bar magnets. M.Chemistry Lecture Notes Dr. in
certain solids the individual magnetic moments do line up. d. and f electron configurations. .
three nonbonding MOs tg. Gerken Page . Molecular orbital diagram of octahedral
coordination complexes. dxz. which is a particularly stable electron configuration. which is
strictly based on VB theory. and d orbitals. the transitionmetal valence orbitals are depicted
together with the symmetryadapted ligand orbital of appropriate symmetry. therefore. and
dyz metal orbitals. As discussed above. and tu. ag. p. Note. we have to consider only six
linear combinations of atomic ligand orbitals. the p orbitals are the orbitals of choice. The
SAOs are usually depicted as s orbitals. that there will be many deviations from this rule.
This socalled electron rule states that valence electrons are optimal for a transitionmetal
complex. tu. they have primarily ligand character. with MO theory and. and eg. and Eg/Tg
respectively. p orbitals those p orbitals that point directly towards the central atom. The
octahedral ligand field splitting is the splitting between the nonbonding tg orbitals and the
mildly antibonding eg orbitals. which have Ag. Tu. there will be electrons contributed by the
ligands. it is clear why any electron residing in the eg orbital destabilizes the complex. and
six antibonding molecular orbitals eg. When placing electrons into this bonding
scheme.Chemistry Lecture Notes Dr. The six bonding MOs represent the six dative bonds in
an octahedral complex. The s orbitals of the ligands are usually too low in energy. M. We can
easily see that no linear combination of ligand orbitals has the correct symmetry tg to interact
with the dxy. This is the transitionmetal analogue to the octet rule. If we fill the tg orbital set
completely with six electrons we reach electrons. Hence. The valence atomic orbitals that are
located on the transitionmetal centre are the s. Coordination Compounds and MO Theory .
symmetry. since deficiencies in the tg set do not alter the . since the ligating atom is usually
more electronegative than the central atom. we have three choices of ligand orbitals
sorbitals. and the sp hybrid orbitals that point towards the metal centre. The resulting MO
diagram produces six bonding MOs ag. you have to substitute the ligand s orbitals with p
orbitals. Now we can but our crude electrostatic ligandfieldsplitting picture into a broader MO
theoretical context. providing us with the correct relative signs of the orbital lobes that point
towards the central atom. On the righthand side. Ignoring any ligand orbitals. we wont use
that description. The latter mix hybridization. In principle. therefore. both sets of orbitals have
metal character and are filled with electrons supplied by the transition metal.
lt F. The ligandfield splitting. can be occupied without greatly perturbing the bonding. In
general donor ligands bases will cause small ligandfield splitting. In the presence of p orbitals
bonding orbitals on the ligands a splitting of the tg orbitals results. In contrast the bonding
orbital of CO is low in energy and is largely localized on the O atom. and N. Octahedral
coordination complexes with acceptor ligands. So far. However. interaction between these
antibonding ligand orbitals and the metal tg orbitals is possible. the metal tg orbitals have the
correct symmetry for bonding with ligand p orbitals. increases in the sequence donor lt weak
donor lt no effect lt acceptor Representative ligands that match these classes are lt PR lt CO
I. we have only considered donor ligands bases. O. In the case where empty orbitals are
accessible on the ligand. . . effectively reducing the ligandfield splitting. the donor character
of carbonbonded CO is very low. Hence. Br. CN. which have lowlying empty orbitals. HO are
filled and donate their electrons into the bonding tg MO. Octahedral coordination complexes
with donor ligands. and the eg set is only weakly antibonding. Gerken Page bonding.
unreactive metal complexes are indeed formed with metals having a d configuration.
producing bonding and antibonding tg sets that have filled p orbitals The p orbitals on the
ligand such as Cl. For CO. Nevertheless. as shown in the figure on the righthand side.lt Cl.
The electron rule becomes particularly important for complexes with large ligandfield splitting.
is increased. O. Since the energy of the tg set is lowered the ligand field splitting. which can
accept electrons from the metal.lt Br. Typical examples for acceptor ligands are CO. . The
SAOs with tg symmetry are shown below. the has its largest amplitude on the C atom.lt HO lt
NH donor lt weak donor lt no effect lt acceptor Notable examples where the bonding effect
dominates include CH. The splitting gives metalbased tg molecular orbitals and ligandbased
antibonding tg molecular orbitals. and therefore.and H.Chemistry Lecture Notes Dr. The
formerly nonbonding metal tg orbitals are elevated. some of the most stable. M. though they
are quite strongly bonded to the metal centre.
dyz. As the result. The small size of the ligand field will never force a lowspin configuration.
the energy difference between these orbitals is the ligand field splitting. Molecular orbital
diagram of tetrahedral coordination complexes. Using the character tables of the tetrahedral
point group the metal s. and dz. t. and e symmetry labels respectively. px.pz. M.py. As
mentioned above.dxz. which we derived for octahedral complexes . t. T. The a and t metal
orbitals can interact with the four symmetryadapted ligand orbitals see SAOs for Td. dxy.
Gerken Page . Try to construct a MO diagram for a squareplanar coordination. How many
valence electrons will results in a particularly stable electron configuration Does it differ from .
the e orbital set is nonbonding and one t set is weakly antibonding. the ligand field splitting in
tetrahedral complexes is / O.Chemistry Lecture Notes Dr. dxy orbitals can be labeled with the
a.