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Subject Chemistry

Paper No and Title CH-201: Inorganic Chemistry-II

Module No and Title 1. Electronic Spectra and Magnetic Properties of

Transition Metal Complexes

Module Tag PG-326

Content Writer:-

Dr. Archana Chahar

Asst. Professor and Head,

Dept. of Chemistry,

Kisan PG College, Simbhaoli

TABLE OF CONTENTS:

1. Spectroscopic ground states, correlation,

2. Orgel and Tanabe-Sugano diagrams for transition metal complexes (d1-d

9

states),

3. Calculations of Dq, B and β parameters,

4. Charge transfer spectra,

5. Spectroscopic method of assignment of absolute configuration in

optically active metal chelates and their stereochemical information,

6. Anomalous magnetic moments,

7. Magnetic exchange coupling and spin crossover

1. Spectroscopic ground states, correlation

The spectra of transition metal complexes is not as simple as it appears

from just the splitting of d-orbitals with electrons get promoted from the lower

energy orbital set to a higher energy orbital set. Actually, energy levels of a

transition metal atom or ion with a particular electronic configuration are

described not only by the electronic configuration itself but also by different

types of electronic interactions such as spin-spin, orbital-orbital or spin-orbital

which can be categorised by some special symbols, called as term symbols. The

ground state term symbol is predicted by the Hund's rule. In other words, the

term symbol in quantum mechanics is an abbreviated description of the total

angular momentum quantum numbers in a multi-electron atom. However, the

quantum mechanical states of a single electron can also be described by a term

symbol.

➢ Calculation of Microstates in a Particular Electronic Configuration

Various overall arrangement of electronic cloud around the nucleus for a

particular configuration are not same as far the energy or angular momentum

are concerned. These different electronic arrangements can be classified on the

basis of overall spin, orbital or total angular momentum.

The term microstates may be defined as the overall electronic arrangements of

a particular electronic configuration which can be differentiated in terms of

energy or angular momentum.

➢ Atomic Term Symbols

Atomic term symbols may be defined as the symbolic representations of

various electronic states having different resultant angular momentums resulting

from spin-spin, orbital-orbital or spin-orbital interactions and the transitions

between two different atomic states may also be represented using their term

symbols, to which certain rules apply.

The term symbol for a particular atomic state is written as follows:

Term symbol = 2S+1

Lj

Where,

2S+1 = spin multiplicity

S - resultant spin angular momentum quantum number

L = resultant orbital angular momentum quantum number

J = resultant total angular momentum quantum number

For L = 0, 1, 2, 3, 4, ……..symbol are S, P, D, F, G,……..respectively.

2. Orgel and Tanabe-Sugano diagrams for transition metal complexes

(d1-d

9 states)

Orgel Diagrams:

Orgel Diagrams are correlation diagrams which show the relative energies of

elecronic terms in transition metal complexes. They are named after their

creator, Leslie Orgel. Orgel diagrams are restricted to weak ligand fields (i.e.

high-spin complexes). Because Orgel diagrams are qualitative, no energy

calculations can be performed from these diagrams.

Orgel diagrams only show the symmetry states of the highest spin multiplicity

instead of all possible terms, unlike a Tanabe-Sugano diagram. Orgel diagrams

will, however, show the number of spin allowed transitions, along with their

respective symmetry designations.

In an Orgel diagram, the parent term (P, D, or F) in the presence of no ligand

field is located in the center of the diagram, with the terms due to that electronic

configuration in a ligand field at each side.

Orgel diagrams are useful for showing the energy levels of both high spin

octahedral and tetrahedral transition metal ions. They only show the spin-

allowed transitions. For complexes with D ground terms only one electronic

transition is expected and the transition energy corresponds directly to D.

Hence, the following high spin configurations are dealt with: d1, d

4, d

6 and d

9.

D Orgel diagram

On the left hand side d1, d

6 tetrahedral and d

4, d

9 octahedral complexes are

covered and on the right hand side d4, d

9 tetrahedral and d

1, d

6 octahedral. For

simplicity, the g subscripts required for the octahedral complexes are not

shown.

For complexes with F ground terms, three electronic transitions are expected

and D may not correspond directly to a transition energy. The following

configurations are dealt with: d2, d

3, high spin d

7 and d

8.

F and P Orgel diagram

On the left hand side, d2, d

7 tetrahedral and d

3, d

8 octahedral complexes are

covered and on the right hand side d3, d

8 tetrahedral and d

2 and high spin

d7 octahedral. Again for simplicity, the g subscripts required for the octahedral

complexes are not shown.

On the left hand side, the first transition corresponds to D, the equation to

calculate the second contains expressions with both D and C.I. (the

configuration interaction from repulsion of like terms) and the third has

expressions which contain D, C.I. and the Racah parameter B.

4T2g

4A2g transition energy = D

4T1g(F)

4A2g transition energy = 9/5 *D - C.I.

4T1g(P)

4A2g transition energy = 6/5 *D + 15B' + C.I.

On the right hand side, the first transition can be unambiguously assigned as:

3T2g

3T1g transition energy = 4/5 *D + C.I.

But, depending on the size of the ligand field (D) the second transition may be

due to:

3A2g

3T1g transition energy = 9/5 *D + C.I. for a weak field or

3T1g(P) <---

3T1g transition energy = 3/5 *D + 15B' + 2 * C.I. for a strong

field.

Example: d2, d

8

The free ion term energies for these configurations are identical. The angular

momentum of the d8 ion can be considered to arise from two positively charged

„holes‟ in the closed d10

shell (which has no angular momentum). The terms that

arise from this angular moment, and the repulsion energy between the holes, are

just the same as for two electrons. However the strong field diagram for d8 is

different. In the octahedral field the configurations are t2g, 6eg2, t2g,

5eg3, t2g,

4eg4.

Applying the same methods as for d2, there is only one triplet state compatible

with t2g, eg2, namely

3A2g (notice the absence of any orbital degeneracy in the half-filled eg set). The

d8 correlation diagram that we get like this is:

Notice how the crossing implied by the dotted lines has been avoided in the

actual 3T1 states whose energies are shown by the full lines. Compared to the

d- ion the ligand field splitting of the free ion terms has been reversed. We can

interpret this as the action of the ligands on the two „holes‟ in the filled d10

shell. Because they are positively charged, the sign of the splitting is inverted.

This result is even simpler for d1 and d9, but is generally true for all high-spin

dn and d10-n ions.

Now replace the octahedral field by the tetrahedral field. The strong field side of

all the correlation diagrams inverts because the splitting of the t2 and e orbitals

inverts. Taken with the relationship between dn and d10-n, this means that the

same diagram will describe dn in an octahedron to be plotted with either sign

relative to the free ion term energies, which means that it can describe the four

possible combinations of dn and d10-n ions in tetrahedral and octahedral fields.

d1/d

9case:

From this, it can be seen that d1 (right hand side) has a Ground State of T2. This

implies the t2g

energy level.

Thus, for d1, there is a single transition from t2g to eg, written as

2Eg2T2g. The

energy gap corresponds to 1Δo. The spectra would appear as a single peak,

perhaps with some peak-splitting due to Jahn-Teller distortions. However, d9

(left hand side) has a ground state of E, which corresponds to the eg level.

Increasing the number of d-electrons:

It can be seen from these that d2 and d

8 show several transitions, while d4 is

only one.

Note also that there is repulsion (bending) between the lines of the same

symmetry. This prevents crossing over (non-crossing rule).

d4 –

5T2g

5Eg at Δo is the only transition, but there will be Jahn-Teller

distortions in 5Eg.

d2 – Several transitions each corresponding to a peak. They are:

3A2g T1g (F) at 1.8Δo.

3T2g T1g (F) at 0.8Δo.

3T1g (P) T1g (F). Value here would be dependent on the Racah Parameter.

d8 – three transitions again.

3T2g

3A2g at Δo.

3T1g (F)

3A2g. Would be at 1.8Δo, but repulsions (bending) alters value.

3T1g (P)

3A2g. This is again Racah dependent.

Orgel diagrams for d2, d

3, d

4, d

6)d

1, d

9 :

Tanabe-Sugano Diagrams

Tanabe-Sugano diagrams are used in coordination chemistry to predict

electromagnetic absorptions of metal coordination compounds of tetrahedral

and octahedral complexes. The analysis derived from the diagrams can also be

compared to experimental spectroscopic data. Armed with spectroscopic data,

an approximation to the crystal field splitting energy (10Dq), generated by

ligands attached to a metal center, can be found.

Tanabe–Sugano diagrams can be used for both high spin and low spin

complexes, unlike Orgel diagrams, which apply only to high spin complexes.

Tanabe–Sugano diagrams can also be used to predict the size of the ligand field

necessary to cause high-spin to low-spin transitions.

In a Tanabe–Sugano diagram, the ground state is used as a constant reference,

in contrast to Orgel diagrams. The energy of the ground state is taken to be zero

for all field strengths, and the energies of all other terms and their components

are plotted with respect to the ground term.

Racah Parameters

Racah parameters were generated as a means to describe the effects of

electron-electron repulsion within the metal complexes. The Racah parameters

are A, B and C. In the case of Tanabe-Sugano diagrams each electron

configuration split has an energy that can be related by the B value. A is ignored

because it is roughly the same for any metal center and C generally

approximated as being 1/4B. What B represents is an approximation of the bond

strength between the ligand and metal.1 Comparisons between tabulated free

ion B and B of a coordination complex is called the nephelauxetic ratio (the

effect of reducing electron-electron repulsion via ligands). This effect is what

gives rise to the spectrochemical series of ligands described later.

Parameters

The x-axis in a Tanabe-Sugano diagram is in terms of the crystal field

splitting parameter, 10Dq, or Δoct, scaled by the B Racah Parameter. The y-axis

is in terms of energy of a electronic transition, E, scaled by B. Each line

represents the energy of an electronic state while varying the strength of

octahedral ligand field. And while only a few electronic states are spin allowed

the spin forbidden electron transitions are included since spin forbidden

transitions can appear in spectrum. Each term symbol is created from the

splitting of term symbols from spherical to octahedral symmetry. With the

relative energy ordering of the states are determined via Hund's rules.

Diagrams for d4, d

5, d

6, and d

7 metal ions have a discontinuity in energies as the

ligand field is varied. The discontinuity, shown with the vertical line, represents

complexes changing from high-spin to low-spin complexes. At the line, the spin

pairing energy is equal to the crystal field splitting energy. To the left of the line

metal complexes are high-spin as the spin pairing energy is greater than that of

the ligand field splitting. To the right of the line metal complexes are low-spin

as the spin pairing energy is less than that of the ligand field splitting energy.

Diagrams

D

2Tanabe-Sugano diagram D

3Tanabe-Sugano diagram

D4 Tanabe-Sugano diagram D

5Tanabe-Sugano diagram

D6 Tanabe-Sugano diagram D

7 Tanabe-Sugano diagram

D8 Tanabe-Sugano diagram

How to use the Diagrams

1. Before looking at the diagrams the d-configuration of the metal ion must

be determined.

2. Choose the appropriate Tanabe-Sugano diagram matching the d-

configuration.

3. Take a spectrum of the complex and identify λmax for spin-allowed

(strong intensity) and spin forbidden (weak intensity) transitions.

4. Convert λmax to wavenumbers and generate energy ratios relative to the

lowest allowed transition. (i.e. E2/E1and E3/E1)

5. Using a ruler, slide it across the printed diagram until the E/B ratios

between lines is equivalent to the ratios found in step 4.

6. Solve for B using the E/B values (y-axis, step 4) and Δoct/B (x-axis, step

5) to yield the ligand field splitting energy 10Dq.

Nephelauxetic Effect

Imagine you had an abundance of V(H2O)63+

(d2) which has two absorptions.

If you had no other available metal centers, but an abundance of ligands, the

complex's absorption spectrum (therefore its color) could be changed via

application of the spectrochemical series:

I− < Br− < S2− < SCN− < Cl− < NO3− < N3− < F− < OH− < C2O42− ≈ H2O

< NCS− < CH3CN < py (pyridine) < NH3 < en (ethylenediamine) < bipy (2,2'-

bipyridine) < phen (1,10-phenanthroline) < NO2− < PPh3 < CN− ≈ CO

If you wanted higher energy absorptions (shift toward purple colors) you use

ligands to the right of H2O and if you wanted redder colors attach ligands to the

left of H2O. Here you could measure the nephelauxetic ratio of the ligands to

compare how each ligand modifies the B Racah parameter. The series of

complexes would also serve as a very good demonstration for a classroom. The

reason behind modifying metal ligands has implications for commercial

products. Unique colors in ceramics and glass products can be traced back to

many metal compounds.

3. Calculation of Dq, B and β Parameters

B: Racah parameter for a metal ion

B′: Racah parameter for a complex

Racah parameter B′ for a complex is generally smaller than that for the free ion

B

B′ < B

Reason: The e–

- e–- repulsion is smaller in a complex this is called the

nephelauxetic effect (d electrons are delocalized onto ligands; are separated

more from each other in a complex, cloud-expansion)

The ratio β= B′/B < 1 is the nephelauxetic parameter

bis a measure for covalency of the M-L bonds

β ≥ 0 (almost) pure covalent bond

β ≥ 1 (almost) pure ionic bond

Example B/cm–1 B′/cm–1

Cr3+

1030

[Cr(en)3]3+

622 (=> Tanabe-Sugano-Diagramm)

β = 622/1030 = 0.60

β ≥ The Cr3+-N-bonds have some covalent character

Nephelauxetic effect can be factorized (into functions of ligand and metal)

nephelauxetic row of ligands

large B‟ small B‟ (covalency increases)

hL: F¯< H2O < NH3< en < ox2–< NCS¯< Cl¯< CN¯< Br¯< I¯

trend: B‟ decreases with decreasing electronegativity; the less electronegative

the ligand, the more it reduces the electron repulsion between d electrons on the

metal nephelauxetic row of TM ions

large B‟ small B‟ (covalency increases)

kM: Mn2+

< Ni2+

~ Co2+

< Mn3+

< Fe3+

< Cr3+

< Mn4+

< Pt4+

trend: B‟ decreases from 3d to 5d,

trend: B‟ decreases with oxidation state of M

4. Charge Transfer Transitions

Charge Transfer Transitions can be ligand to metal, metal to ligand, and

intervalence charge transfer (metal to metal) in mixed valence systems. The

occurrence of these is very widespread. Famous examples are Fe(SCN)62+

(blood red), Fe(phen)32+

(blood red), and Prussian Blue, which are respectively

examples of ligand to metal, metal to ligand metal to metal charge transfer.

These transitions are typified by compounds such as MnO4 -, where there are no

d electrons, yet this appears as a deep purple colour.

Ligand-to-metal transitions occur in all complexes, not only transition metals. In

complexes with dd transitions LMCT transitions can often be seen at higher

energy and identified by their much stronger intensity. Sometimes they obscure

some of the predicted d-d bands. In d0 complexes such as MnO4- they are the

only transitions seen. LMCT can be regarded as an internal redox transition, the

metal being reduced and the ligand oxidised. It is therefore possible to correlate

LMCT energies with the redox properties of metals and ligands. The

comparison of two metal ions with the same ligands is shown below. Lowering

the energy of empty metal orbitals gives an ion that is more easily reduced

hence more strongly oxidising and is expected to correlate with a lower LMCT

energy.

Figure: Ligand to metal charge transfer transition

For a given ligand LMCT transitions generally follow the trends below:

(i) Increase 3d < 4d < 5d as oxidising power decreases.

(ii) Decrease with metal oxidation state.

(iii) Decrease from left to right along the series as Zeff increases.

Exceptions to trend (iii) sometimes occur when there is a change of electron

configuration.

Variation with Metal:-

Ability to receive or release electrons is obviously dependent on electron

configuration. If the

metal has a full t2g then Ligand to Metal Charge Transfer will have to put

electrons into the antibonding eg, which is likely to be very high in energy.

Similarly, for the classic MnO4-, the orbitals are empty so an electron is easily

transferred into the lowest energy orbitals.

From this, it is obvious that Ligand to Metal Charge Transfer is more likely to

occur for high oxidation state (low d electron count) metals. Similarly, Metal to

Ligand Charge Transfer would require many d-electrons, and vacant orbitals on

the ligand to receive them (usually π*).

Comparing metals with different oxidation states, for a higher oxidation state,

the d-orbitals are lower in energy, since the increased charge of the nucleus

stabilises them. Thus, the energy gap is reduced, and the Transition Energy is

lower.

Moving down a Group, 4d and 5d transition metals, the 4d and 5d orbitals are

higher in energy and so the Transition Energy is increased.

Moving across the Period, the d-orbitals decrease in energy, reducing the

Transition Energy.

However, d-electrons are increasingly populating these orbitals, and this can

have important consequences. For example, the energy of transition for Pd is

higher than for Ru because the electron has to enter an eg orbital instead of t2g,

so the energy gap is larger.

Figure: Metal to ligand charge transfer transition

Variation with Ligands:-

Comparing Ligands, again orbital energy is the key to the transition energies.

For example, down the halides, their non-bonding orbitals increase in energy,

giving:

Thus, the Transition Energy will decrease for lower halides.

These processes resemble redox reactions drive by photons, which transfer

electrons between atoms. The energies nicely follow the expected redox

properties. For a given metal ion, LMCT energies reflect the redox properties of

the ligand. A lower LMCT energy corresponds to a more easily oxidising

ligand. Thus FeF3 is light green, because the F and Fe charge transfer occurs in

the ultraviolet. However, the colours of FeCl3 (brown) and FeBr3 (red-black)

and the nonexistence of FeI3, are indicative of a progressive lowering of the

charge transfer energy which eventually becomes possible thermally. There are

many examples, e.g. HgCl2 (white), HgBr2 (yellow), HgI2 (red).

Most of the colours used in analytical chemistry are charge transfer transitions,

because their high intensity enables the determination of very small

concentrations of material. Examples are the use of Ni(IV) in an oxidised

dimethylglyoximate complex, which is red, and the determination of platinum

metals using sulphur-containing ligands. Apart from Prussian blue, the mixed

iron oxides (black), Ag(I)Ag(III)O2 (brown-black), and Cs2Au(I)Au(III)Cl6 are

good examples of mixed valence species.

Energies:-

If the orbitals are substantially of one-centre in type, the charge-transfer nergies

are closely related to the sum of the ionisation energy of the donor centre and

the electron-affinity of the acceptor centre.

• The well defined shifts for the series CoX42-

and NiX42-

shows the difference

between the halides as well as the more oxidising properties of Ni(II) as

compared to Co(II) consistent with their effective nuclear charge.

• The series of compounds with the formula Co(NH3)5X2+

demonstrate how

large the changes in charge transfer energies are compared to the shifts due to

the difference in their ligand field parameters.

• Changes in the metal can have a similarly profound influence. It has been

shown that the energy decreases with increasing formal charge on the metal.

Higher energies in the second and third transition series reflect the well-known

increase in stability of higher oxidation states of these metals.

EXAMPLE:

a) LMCT energies of d0 oxoanions follow the orders:

VO43-

> CrO42-

> MnO4-

MnO4- < TcO4

- < ReO4

-

b) LMCT energies of some [MCl6]2-

complexes of 5d series metals follow the

order:

[OsCl6]2-

> [IrCl6]2-

< [PtCl6]2-

The ground state electron configurations in these low-spin complexes are t2g4,

t2g5, t2g

6 respectively. In the first two an electron can be excited into a t2g orbital

and the order follows the expected trend with increasing Zeff. However in the

[PtCl6]2-

the t2g orbitals are full and the transition is into the higher energy eg

which leads to a reversal of the normal trend.

EXAMPLE:

The energies of LMCT bands of some tetrahedral Co2+

complexes follow the

order:

[CoCl4]2-

> [CoBr4]2-

> [CoI4]2-

as expected from the ease of oxidation of Cl- < Br

- < I

-.

Metal-to-ligand charge transfer occurs in complexes where the ligands have

empty antibonding orbitals at relatively low energy, for example in carbonyls

and with O and N-donor ligands attached to unsaturated π-systems. Generally

they follow the reverse order expected for LMCT, e.g. there is an increase in

energy as the metal Zeff increases, because the ions are less easily oxidised.

6. Anomalous Magnetic Moment

Anomalous magnetic moment is the magnetic moment for a metal ion in

a discrete molecular species having a value which falls outside the range of

values predicted from the spin and orbital angular momentum in ligand fields of

given strength and symmetry. The discrete molecular species means that there is

no secondary magnetic interaction between the neighboring molecules. In other

words, these do not have any ferromagnetic or antiferromagnetic interactions, or

magnetically dilute. Let us briefly try to understand the meaning of „anomalous‟

magnetic moment by taking some simple examples.

Octahedral Complexes

1. Nickel (II) Complexes

Under regular octahedral geometry, the 3A2g ground state term for Ni (II)

acquires some orbital contribution from the next higher 3T2g state term due to

spin-orbit coupling. Overall magnetic moment is dependent of Δ value and λ.

Assuming Δ = 8000 cm-1

and λ = 75 % of the free ion value, 𝜇off can be

calculated by using the following equation,

[

]

The value of α is 2 for Eg and 4 for an A2g ground state term. The calculated 𝜇off

is about 3.3 B.M. which is fairly above the spin-only moment of 2.83. This also

includes a small temperature-independent paramagnetism contribution.

Generally, 𝜇off is in the range of 3.0-3.3 B.M., however observed values are

slightly higher than this value. Fe(II), Fe(III), and Co(II) also show similar

trends however, in some instances orbital angular momentum for the ground

state for these ions in firm octahedral symmetry are not quenched and the

expression for 𝜇off is more complicated. For these systems there also exists the

possibility of „high spin‟ (H.S.) and „low spin‟ (L.S.) complexes with variation

in the ligand field strength. For the high-spin octahedral cases of Fe (II), Fe

(III), and Co (II); there is a rather complicated dependence on λ. and on kT.

2. Iron (II) Complexes

The free ion term for Fe (II) is a 5D state and the absence of adjacent higher

terms of the same multiplicity simplifies the calculations. The ground state in

octahedral symmetry is 5T2g and 𝜇off is expected to have a value of 5.6 B.M. at

room temperature. Experimental value of the moments fall in the range 5.1-5.7

B.M. Fe (III) under weak ligand fields has a 6Al ground state arising from a free

ion 6S state and the moments are in the order of 5.9 B.M.

3. Cobalt (II) Complexes

For high-spin octahedral Co (II) complexes, the ground-state configuration is

T1g resulting from a free ion F ground state. Following two cases are

considered for the calculation of 𝜇off

(1) The ligand field is small compared with the inter-electronic interactions

(2) The field is large compared with inter-electronic interactions.

The calculated 𝜇off is in the range 4.7- 5.1 B.M. Depending on the ligand field

strength and the amount of distortion from octahedral symmetry; experimental

values lies in the range of 4.7-5.2 B.M.

Tetrahedral Complexes

Relatively large contributions to the observed moments from orbital angular

momentum are expected and observed for Ni(II) in tetrahedral fields with

ground state in an orbitally degenerate T state. For regular tetrahedral

complexes; 𝜇off should be within the range of 3.5-4.0 B.M. Tetrahedral Co(II)

complexes usually exhibit moments closer to the spin-only values and these are

of the order 4.2-4.4 B.M.

Square Planar Complexes

Square planar Ni(II) complexes have no unpaired electron and essentially

exhibit zero moments or small contributions due to the temperature-independent

paramagnetism. Square planar Co(II) species having slightly large orbital

contributions than low-spin octahedral complexes are, however, paramagnetic

and reported to exhibit moments in the range 2.1-2.9 B.M.

Factors Responsible for Anomalous Magnetic Moment

A variety of models has been proposed to account for the anomalous

magnetic moments of various metal complexes. These may be discussed under

the following categories:

(1) Equilibrium between two spin states

(2) Magnetically non-equivalent sites in the unit cell

(3) Solute-solvent interaction

(4) Solute-solute interaction

(5) Configurational equilibrium

7. Magnetic exchange coupling and spin crossover

Magnetic Exchange Coupling

The magnetic materials can be broadly classified into two categories;

magnetically dilute and magnetically concentrated. Magnetically dilute

substances simply refer to the magnetic materials in which individual

paramagnetic centres cannot interact with each other due to large distance of

separation. On the other hand, the total-electron-spin of paramagnetic centres do

interact through direct-exchange or super exchange interactions in magnetically

concentrated substances, which is obviously due to the small inter-

micromagnetic separation. In the direct-exchange, there is a coupling between

nearest neighbouring cations without involving any intermediary anion; while

the superexchange is generally a strong magnetic exchange interaction between

two nearest neighbouring cations through a non-magnetic anion. Now although

the orbital contribution to the magnetic moment can be of considerable

magnitude, it can be neglected in magnetically concentrated materials for a

simplified approach to the rationalization of overall magnetic profile. Therefore,

we will consider the spin-only magnetic moment (µs.o.) as the effective

magnetic moment (µrff) in these cases.

The energy of total-spin interactions of paramagnetic centres (AE) in

magnetically concentrated material can be given by the following relation.

ΔE = 2J(S)t(S)k

Where J is the exchange-coupling constant and is a measure of the magnitude of

total electron spin interaction between various paramagnetic centres. The

symbols (S)t and (S)k simply represent the total-electron-spin of ith and k

th metal

centres, respectively. For ferromagnetic substances, the value of J is positive

which simply implies that the total electronic spins of all paramagnetic centres

are aligned parallel to each other. For antiferromagnetic substances, the value of

J is negative which simply indicates that the total electronic spins of all

paramagnetic centres are aligned antiparallel to each other.

Spin crossover

Spin Crossover (SCO) is a phenomenon that occurs in some metal

complexes wherein the spin state of the complex changes due to an external

stimulus. The stimulus include temperature, pressure, Spin crossover is

sometimes referred to as spin transition or spin equilibrium behavior. The

change in spin state usually involves interchange of low spin (LS) and high spin

(HS) configuration.

Spin crossover is commonly observed with first row transition metal complexes

with a d4 through d

7 electron configuration in an octahedral ligand geometry.

Spin transition curves typically plot the high-spin molar fraction vs. T. Often a

gradual spin transition is followed by an abrupt (ΔT = 10K) transition with

hysteresis and a two-step transition. The abruptness with hysteresis indicates

cooperativity, or “communication”, between neighboring metal complexes. In

the latter case, the material is bistable and can exist in the two different spin

states with a different range of external stimuli (temperature in this case) for the

two phenomena, namely LS → HS and HS → LS. The two-step transition is

relatively rare but is observed, for example, with dinuclear SCO complexes for

which the spin transition in one metal center renders the transition in the second

metal center less favorable. Several types of spin crossover have been

identified; some of them are light induced excited spin-state trapping (LIESST),

ligand-driven light induced spin change (LD-LISC), and charge transfer induced

spin transition (CTIST).

Light-induced spin-crossover of [Fe(pyCH2NH2)3]2+

, which switches from high and low-spin

Calculation of Magnetic moments of transition metal atoms

Case-II

Problems

1. For a d7 metal ion determine the energy ratios for allowed transitions at

Δoct/B of 20.

2. For a d6metal ion of Δoct/B = 30 and B=530 cm-1 what would the

energies of the 5 allowed transitions be? How many are in the UV-Vis

range? How many are in the IR range?

3. Write out the allowed transitions for a d5 metal ion in a E/B> 28 ligand

field.

4. A d4 complex exhibits absorptions at 5500 cm

-1 (strong) and 31350 cm

-1

(weak). What are the transitions that are being exhibited in the complex?

What is the corresponding Δoct for the complex?

5. A spectrum of d7 metal complex seemingly exhibits only two intense

transitions. What is the Δoct/B that this situation occurs? Please use

reference to specific transitions and energy splitting.

Answers

1. Δoct/B of 20 yields E/B values of 38, 32, 18. Ratios then are 2.11 and 1.78

2. Δoct/B = 30 yields E/B heights of 27, 40, 57, 65, 85. Energies are then

14310, 21200, 30210, 34450 and 45050 cm-1

. All are in the UV-Vis

range. *note you need to infer the E/B value for the last transition as the

diagram does not extend that far up.

3. 2A2g<-

2T2g,

2T1g<-

2T2g,

2Eg<-

2T2g, and

2A1g<-

2T2g.

4. 31,350/5,500 gives a ratio of 5.7/1. The only Δoct/B value that matches is

at 10. B value is then 550 cm-1

. Δoct equals 5500 cm-1

.

5. Three transitions are generated at low Δoct/B. However, at about a value

of Δoct/B = 13 the transitions 4A2g<-

4T1g, and

4T1g<-

4T1g have the same

energies which results in the appearance of only two absorptions.