DR. S. VALARSELVAN, Ph.

D
ASST.PROFESSOR OF CHEMISTRY

II-M.Sc CHEMISTRY

SUBJECT CODE : 18PCHE3

TITLE OF THE PAPER: PHYSICAL METHODS IN CHEMISTRY

UNIT I

Electronic Spectra of Transition metal complexes

Spectroscopic ground states, spectral terms, R-S coupling and J-J
couplings- term symbol – selection rules—microstates—Pigeon hole diagram for
p2 and d2 configuration. Orgel and Tanabe – sugano diagrams for transition metal
completes (d1-d9 states) electronic spectra of transition metal complexes—
calculation of Dq values -- Racah parameters and Beta parameters, Nephelexatic
effect, charge transfer spectra.
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ELECTRONIC SPECTRA OF COMPLEXES

INTRODUCTION

Spectra is due to the transition of an electron from one energy level to another.
Types:

1. Absorption Spectra : It shows the particular wavelength of light

absorbed (ie) particular amount of energy required to promote an
electron from one energy level to higher level.

2. Emission spectra: It shows the energy emitted when the electron

falls from the excited level to the lower level.

The electronic transitions are high-energy transitions. In the course of this

transition, other smaller energy (vibrational and rotational transition) also takes
place. But the energy difference is small in vibrational and rotational transition.
Therefore difficult to resolve.

The electronic transition is governed by selection rules. The transition

which obeys the selection rules are called as the allowed transition and the
transition disobeys the selection rule, are called forbidden transition

Allowed transition quite common (high intensity)

Forbidden transition Not common (low intensity)

d-d transitions: This actually is electron transition from t2g to eg. orbital. In
this, charge distribution between excited and ground states are same. These
transitions occur in visible or near U.V region. This appears to be the simple
explanation for the colour in the transition metal complexes.

The absorption spectra of octahedral complexes show the molar

absorbance of such d-d transition are low. This is because of selection rules. The
electron transition are of high energy transition. In addition much lower energy,
vibrational and rotational transition always occur. The vibrational and rotational
level are too close in energy, to be resolved into separate absorption bands, but
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they result in considerable broadening of electronic absorption bands in d-d

spectra. Band widths are commonly found to be the order of 1000 – 3000 cm-1

Selection rules: Not all the theoretically possible transition are actually observed.
The selection rule distinguish allowed and forbidden transition. Allowed
transitions are common but forbidden transition less frequently occur. They are
of much low intensity.

A. Laporte orbital selection rules: Transitions involving a change in

subsidiary quantum number l = ± 1 are, laporte allowed transition and
therefore they have high absorbance.

e.g as S2 S1 P1 (changes by +1) and moral absorption co-efficient is

 = 5000 – 10000 l//cm.

In contrast: d-d transitions are lapore forbidden transition because l=0

and therefore have a lower absorbance. But spectra of much lower absorbance
are observed, because of slight relaxation in the laporte rule. This enable the
transition metal complex to have bright coloured.

B. In cpxes with a centre of symmetry the only allowed transitions are those
with a change of parity. i.e gerade to ungerade . u g are allowed, but not
g g and u u. Since all d orbitals have gerade symmetry, all d-d transitions
are forbidden.

Types of Relaxation:

1. A molecule with no centre of symmetry (E.g) Td →[CoCl4]2-,

[MnBr4]2- also unsymmetrically substituted octahedral complexes e.g.
[Co(NH3) 5Cl]2+ are coloured, in such cases mixing of d and p ortritals may occur
in which case transitions are no longer pure d-d in nature. Therefore transitions
can take place between d-orbitals having different p-character and such
transitions are called as partially-allowed transitions.

2. Mixing do not occur in octahedral complexes which have a centre

of symmetry such as [Co(NH3) 6]3+ (or) [Cu(H2O)6] 2+. Here the M-L bonds vibrate
so that for a fraction of time, the d-p mixing will be possible. Thus, a very small
amount of mixing occurs and low intensity spectra are observed. These
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transitions are said to be vibrationally allowed transitions and the effect is

described as vibronic coupling. The intensity of band is roughly proportional to
the extent of mixing.

3. Spin selection Rules: During the transition between energy levels,

the spin of the electrons does not change but remains the same [ S = 0] Spin-
forbidden transitions have very weak intensity (S 0) (can be ignored). Eg.
[Mn(H2O)6]2+. So many Mn2 compounds are flesh coloured or colourless . Spin –
allowed transitions have very high intensity

Sl. No Laporte orbital Spin Type of = A/cl Example

spectra

1 Allowed Allowed Charge 10,000 [Ti Cl6] 2-

transfer
2. Party allowed Allowed d–d 500 [Co Cl4] 2-
some d-p mixing
3. Forbidden Allowed d–d 8 -10 [Ti (H2O) 6]3+
4. Partly allowed Forbidden d–d 4 [Mn Br4]2-
some d-p mixing
5. Forbidden Forbidden d-d 0.02 [Mn(H2O)6]2+

Electronic transitions in complexes:

The electron (orbital motion) revolves round the nucleus. When a charge
species revolves round the nucleus, a magnetic field is produced. Also, the
electron spin around its own axis. So another type of magnetic field is generated.

1. Thus, even though the p-orbitals are degenerate and have the same
energy, the electrons present in them interact with each other and
result in the formation of ground state (lower energy) and one (or)
more excited states due to electrostatic repulsion.

2. There can be interaction (or) coupling between the magnetic field

produced as a result of orbital motion.

3. There can be a coupling (or) interaction between the magnetic field

produced by the spin of electrons around its own axis.

If for 1-p e-, there are 6 possible ways of placing e-s in the ‘p-orbital’.
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For 2p e-s, there are 15 possible ways of placing the e-s in the p orbital.

These electronic arrangement can be divided into 3 main groups of

different energy called 3 energy states. They are labelled as term symbol.

Definition of term symbol:

Term symbol is an abbreviated description of the energy, angular

momentum and spin multiplicity of an atom in a particular state.

Term states for dn ion: When several electrons occupy a sub shell the energy
states obtained, depends upon the result of the orbital angular quantum number
of each electron. The resultant of all the l-values is demonstrated by a new
quantum number ‘L’ which defines the energy state for the atom

L = 0, 1, 2, 3, 4, 5, 6, 7, 8……

State = S P D F G H I K L

(The letter J is omitted since this is used for another quantum number)

Spin – multiplicity value = (2s + 1)

S  Spin quantum number

No of e-s present = 12345.......

(2s + 1) = 23456.......

Orbital quantum number (L) = (mlxl)

Rules for determing the term symbols:

1. The e-s should be unpaired as much as possible and occupy

different orbital (ground state) of low energy.

2. The spin multiplicity value must be maximum to be stable

3. The orbital angular momentum L value should be large (or ) the

highest (ground state).

Total angular momentum quantum number (J)

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L and S values couple to give J value. Magnetic effects of L and S couple to

give J value .

4. If sub shell is more than half filled – Smallest J value is more stable
(L-S)

If the sub shell is less than half filled – Highest J value is more stable
(L + S)

Derivation of term Symbols:

1 For C 1S2 2S2 2P2 (G.S)

1S 2S + 0 -1 L=mlxl =1x1 = 1

XX XX X X S = 1 (2s + 1) = 3 Term symbol 3P triplet

2. For B 1S2 2S2 2P1

L=mlxl =1x1 = 1 S = 1/2 ; 2S+1=2

Term symbol 2P Doublet

For transition metals : Here the e-s go to the d orbital

+2 +1 0 -1 -2

For d1 system x L=2 S=1/2; 2S+1 = 2

T.S = 2D

+2 +1 0 -1 -2

d2 System x x L= 2+1=3 S=1/2+1/2 =1 (2s+1) = 3

T.S = 3F
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+2 +1 0 -1 -2

d3 x x x L = 2+1+0 = 3 S=3/2 (2s+1) = 4

T.S = 4F

+2 +1 0 -1 -2

d4 x x x X L = 2+1+0-1 = 2 S=2, (2s+1) = 5

T.S = 5D

Similarly for d5 T.S = 6S, d6 =5D d 7 =4F, d8 = 3F

d9 =2D d10 =1S

Note: According to CFT

s orbital is completely symmetric and so does not split

p orbital all interact equally and so does not split

d orbital is split by oh field into t2g and eg orbital

f orbital is split by oh field into t1g, t2g and a2g

Orgel diagram:

The orgel diagram is the quantum mechanically calculated energy of the

term level (as ordinate) against an increasing value of field strength, the ligand
field splitting parameter.

Octahedral field Tetrahedral field

d1 system Ex – [Ti Cl6]3-, [Ti(H20)6]3+ d1 system: Here also the ground state
here the ground state of the free ion is of the free ion is described by the
described by the term symbol 2D. The term symbol 2D.
degenerate ‘d’ orbitals or levels are The degenerate d orbitals are split
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split into T2g and eg in the presence of into doublet eg and triplet t2g in the
octahedral field presence of a tetrahedral field.

The lower T2g state corresponds to The lower E corresponds to the single
the single d electron occupying one of d electron occupying one of the eg
the T2g orbital and 2eg state orbital and 2T2g, state corresponds to
corresponds to the electron the electron occupying one of the t2g
occupying one of the eg orbitals. orbital.

Note:

The magnitude of splitting o depends on the nature of the ligand and

hence affects the energy of transition. As the ligand is changed, Dq varies and
the colour of the complex also varies.

Note:

In d1 case, there is a single electron in the lower t2g level while in the d9
case there is a single hole in the upper eg level.

Thus, the transition of the d1 case is the promotion of an electron from t2g
to eg level, while in d9 ion, it is simpler to consider as the transfer of a hole from
eg to t2g. Thus the energy level diagram for d9 is therefore the inverse of that for a
d configuration.

For d9 system (octahedral) For d9 system tetrahedral

In the octahedral field the term In the tetrahedral field the term symbol
symbol 2D is split as 2Eg and 2T2g 2D is split as 2E and 2T2.
0.6Δo below and 0.4 Δo above
degenerate states
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For d4 system term symbol For d4 system, term symbol 2D is split

into 5T2 and 5E
5D is split into 5Eg & 5T2g.

For d6 system For d6 system

Here in the octahedral field, the 5D is split as 5E and 5T2
term symbol 5D is split as 5T2g
and 5Eg

Note: d6 is inverse of that for d4 configuration. From the above energy diagrams
we can come to conclusion that d1 and d9 are inverse. Similarly d4 and d6 are
inverse (or) we can say that d1 is similar to d6 and d9 is similar to d4.
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We can also state that d1 (Td) and d9 (oh) complexes have similar orgel
diagram.

So d1, d9, d4 and d6 diagrams can be combined to a single orgel diagram.

(fig 4)

The spectra of these complexes have only one band due to the single d-d
transition, that occur is assigned as E  T2.

Hole Formalism: When a subshell is more than half filled it is simpler and
more convenient to work out the terms by considering the holes (ie the
vacancies) rather than considering the large number of electrons actually present.

By considering the holes, the terms which arises for pairs of atom with p n
and p6-n and dn and d10-n give rise to identical terms.

Electronic configuration G.S terms Other term

1) p1, p5 2P 1S 1D

2) p2, p4 3P 2P 2D

3) p3 4S

4) p6 1S

5) d1, d9 2D

d2, d8 3F 3P, 1G, 1D, 1S

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d3, d7 4F 4p, 2H, 2G, 2F,3G, 3H, 3F,

d4, d6 5D 3P,1F,1D,1S

d5 6S 4G, 4F, 4D, 4P,

d10 1S 2G, 2F, 2D, 2P

Transformation of Spectroscopic symbols into mulliken symbols

Splitting of d terms in an octahedral and Tetrahedral field

Spectroscopic terms Mulliken Symbols

Octahedral field Tetrahedral field

(1) S A1g A1

(2) P T1g T1

(3) D Eg, T2g E, T2

(4) F A2g, T1g, T2g A2, T1, T2

(9) G A1g, Eg, T1g, T2g A1, E1, T1, T2

(11) H T1g, T1g, T2g, Eg T1, T2, T2, E

(13) I A1g, A2g, Eg, T1g, T2g, T2g A1, T1, T2, T2, T1

d2, d7, d3, d8 configuration

+2 +1 0 -1 -2 L=3, S=1, 2S+1 = 3

3
d2 case 1 1 Term Symbol F

Here We have two possibilities

1) Parallel Spin

2) Anti Parallel Spin

For parallel spin (2S+1) = 3 (Triplet)

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For anti parallel spin (2S+1) = 1 (Singlet)

So, the ground state  3F

Excited State  3P, 1G, 1D, 1S

Here 1G, 1D, 1S states contain electrons with opposite spin. The transition
from the ground state to 1G, 1D, 1S are spin-forbidden and will be very weak and
can be ignored.

So, the only important transition is from 3F to 3P

In the octahedral ligand field, the P state, transforms into a T1g Mulliken
term and the F state splits into 3 terms, namely, A2g, T1g and T2g.

The energy level diagram of d2 complex ion. [V(H2O)6]3+ can be shown in

the figure (5).

Here it can be seen that 3 transitions are possible from the ground states,
hence three peaks should occur in the spectrum.

Note: 1) In d1, d4, d6, d9 system only one transition occurs (because there are only
2 energy levels)

2) In d2 systems, nothing common. So energy can cross (ie) Crossing is

allowed also spin allowed transition.

The first excited state 3T2g + 3T1g(p) if the second electron also excited 3A2g
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d8 System Eg [Ni(H2O)6]2+, [Ni(NH3)6]2+

The complex with d8 configuration in an octahedral field may be regarded

as having two holes in the eg level hence promotion of an electron from the lower
t2g level to the eg level is similar to transfer of a hole from eg to t2g. So this is
inverse of d2 case. Using the same arrangement applied to d1 case, we can say
that

d2 d7 d2 d7

Oh Oh Td Td

d8 d3 d8 d3

Oh Oh Td - Td

So combined orgel diagram for 2 electron and 2 hole configuration is

shown Fig(7).

d5 system Ex [Mn(H2O)6]SO4

In orgel diagram d5 configuration is left out because of the following reason.

i) It is spin forbidden transition. The compound is almost colourless. So

weak intensity is observed in the spectra.

Orgel diagram for low spin complex

Orgel diagram can be modified to take into account low spin complex
also. But generally orgel diagram treats only the weak field (or) high spin case.
So in these cases the excited state is not included.

Example
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For d6 system : Ex Co3+ for the free ion 1I has higher energy compared to
quintet 5D. So 1I (one of the exited state) is least important.

But in the presence of ligand a ligand field or crystal field the state 1I split
into several terms. Out of these several terms 1A1g drops in energy as the
strength of the field increases and at a certain stage (critical point) A1g cross over
(get stabilised) 5T2g and becomes the ground state.

Note : After the critical point the complex would be low spin. For low spin
complex theoretically 5 transitions are possible, but we observe only two
transition in spectra.

For d5 system

Here 2I ie of higher energy compared to sextet S. For the free ion 2I is not
important. But in the presence of ligand (or) crystal field the 2I state splits into
several terms. Out of these 2T2g drops in as the strength of the field increases and
at a certain stage (critical pts) 2T2g cross over. So becomes ground state

Evaluation of Dq and B value for octahedral cpx of Nickel

For high spin octahedral cpx of Nickel, the energies of the states are given
by equations

For 3T2g E = -2Dq

For 3A2g E = -12Dq

For 3T1g (F) and 3t1g (P)

[ 6 Dq p – 16 (Dq)2] + [-6 Dq – P] E + E2 = 0

1 = A2g  T2g = 10Dq

2 = A2g  T1g (F) = 7.5 B’ + 15 Dq – ½ [225B2 + 100Dq2-180B’Dq] ½

3 = A2g  T1g (P) = 7.5 B’+ 15Dq – ½ [225 B2 + 100 Dq2 – 180 B’ Dq]2

1) Ni II Epx [Ni (NH3)6]2+ show the following transition.

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1 2 3

10750 cm -1 17500 cm-1 28200 cm-1

Calculate the value of 10 Dq and B?

 = 10 Dq = 10750 cm-1 Dq = 1075 cm-1

B = (2 + 3 - 31) / 15.

= (17500 + 28200 – 3 x 10750) / 15 = 896.7

Tanaube – Sugano diagram

The tanaube and sugano diagrams are plots of the energies of the levels in
a system in units of B (ie) E/B (as ordinate) against the ligand field strength, in
dn
units of Dq/B (as abscissa). The ground state of the metal ion is always plotted
as the abscissa, in the diagram.

For systems having more than 3 electrons and less than 8 electrons, a
change in ground state can occur as we progress from weak to strong fields.

In order to treat fully the problem of interpretation of spectra including

both H. Spin complex and L.spin complex.

For d1 system fig (8)

For d4 system
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There will be a considerable difference between the spectra of low spin

and of high spin d4 complexes. In high spin complexes, we expect only one spin
allowed band and a series of forbidden quintet  Triplet transition of low
intensity. In low spin complexes, the transition to the triplet levels become spin
allowed and a rich spectrum is expected.

So the combined diagram (both low and high spin) can be drawn as
follows.

Theoretically 4 transitions are possible but in practice 2 or 3 are observed.

Note: Where there is a crossing in orgel diagram, there will be a change in

direction of Tanaube-Sugano diagram.

After the critical point pt we observe generally low spin complexes.

For d5 system fig(10)

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For d6 system

Eg. CO2+  d7

CO3+  d6 Eg. [CoF6]3-, [Co(CN)6]3-

Here the 5D split by the increasing octahedral field strength into 5T2g in G.S
and an excited state 5Eg.

The next excited state as 1I (singlet I) which is very high energy in the free
ion is split by the application of the ligand field into several terms. Only one of
which is important. The term A1g is greatly stabilized by the ligand field and
drops rapidly becoming the ground state at 10Dq/B = 20. At this point spin
pairing takes place and hence there is a discontinuity in the diagram showing by
a vertical line. Beyond this point, the low spin A1g term is the ground state.

Weak and Strong Field

When the crystal field is fairly weak, it may be combined as a perturbation

of the free ion levels. It is justifiable to calculate the free ion energy levels, and
then to consider how these will be affected by the crystal field. This method is
known as weak field approach. [Effectively the inter electronic repulsion is
considered first and then the crystal field is super imposed on the levels so
produced].

If the crystal field is fairly strong, it may induce electron pairing (spin
paired complexes). Under such conditions, the field is important than the inter
electronic repulsion since it over-rides the correlation forces trying to maintain
maximum spin. [Therefore it is reasonable to consider the energy level in the
crystal field environment first and then to super impose the effect of inter
electronic repulsion.

1) Weak field approach

In the weak field approach we assume that the effect of the crystal field is
less than inter electronic repulsion. The electron couple together to give the
various spectroscopic terms of the free ion. If the free ion is now placed into a
crystal field, the degeneracy of the spectroscopic terms may be partially or
wholly lifted, to give a new terms which are described by group theoretical
representation.
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Eg. d2

1 1 3
F, 3P, 1G, 1D, 1S

1S 1Alg

3T
3P 1g

3A
Singlet 1D 12g , 1Eg Triplet
2g

3F 3T
2g

1T2g 3T
1g

1G
1T1g

1E1g

S–S L–L Crystal

Change transfer spectra 1Alg Coupling Coupling Coupling

The absorption of light is to cause an electronic transition within an atom

or molecule. It is essential that the absorption results in a charge density
displacement. This displacement may be localized on one atom (as it is, to first
approximation, in the d-d spectra) or it may be the displacement of charge from
one atom to another, so in electronic transition electrons move between orbitals
that have predominantly metal d-orbital character. Thus the charge distribution
is about the same in the ground state and excited state. There is another
important class of transition in which the electron moves from a M.O centered
mainly on the ligand to one centered mainly on the metal atom and vice versa.
In these the charge distribution is different, considerably from ground state and
excited state and so they are called as charge transfer transition.

Differences between d-d and charger-transfer transition

d-d transition Charge-Transfer-Transistion

1. Here electron moves from one d- This arises when an electron from
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orbitals to another results in the d-d one atom goes into another atom
transition. It is forbidden transition within the same molecule. The
against selection rule g-g (forbidden) transition is not against any selection
rule (g  u) allowed.

2. The Charge distribution between The charge distribution between the

the ground state and excited state ground state and excited state
remains the same. different because of this we say this
is as charge transfer spectra.

3. Intensity () value is normally  value is high 10,000 [Eg] [Ti Cl4]2-
below 100 and have weak intensity.

4. Mostly they occur in the visible The bands are usually obtained is
and near uv region. near uv region and often overlap
with d-d transition because of this
we do not get full d-d spectrum of
complex.

There are two possibilities of charge transfer process in metal complexes.

Electron from metal goes to ligand (ie) M  L transition (oxidation) electron
from ligand goes to metal (ie) L  M transition (reduction).

[I] Metal  Ligand (oxidation)

Here the electron from t2g (or) eg orbital of metal may go to the  *of ligand. The
direction of transition depends on the energy of the ligand and metal orbital and
also on the occupancy of orbital.

(i) M  L transition will occur when the metal is in the lower oxidation

state.

(ii) The ligand orbitals should be empty and also of lower energy.

(iii) More the reducing power of the metal the lower will be the energy of
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transition.

The energy of this type of transition probably occurs in the aqua ions of
divalent metal of the first transition series (first half) because they have valency
ions and reducing power. So they give deeply coloured complex with electron
acceptor ligand like o – phenanthrene, pyridine (neutral) due to delocalized 
electrons they are of intense colour Intense colour is absent in Ni2+ and C03+
(Higher oxdn state). (Here the metal has more reducing property and more the
oxidizing ligand- lower the energy of transition).

(II) Ligand  metal (reduction)

Here the electrons from  orbital of ligand may go to t2g or eg. (Note:
Electron from    transition is intra ligand transition)

(i) L  M transition will occur when the metals are in the higher oxidation
states.

(ii) The ligand orbital should be filled and also of higher energy.

(iii) Higher the oxidizing power of the metal lower will be the energy of
transition.

Thus charge transfer absorption in the visible spectrum is more common

in complexes of Iron (III) than in those of Cr (III). This accounts for the use of
iron (III) in colour tests in organic chemistry. Eg. Phenols and hydroxamic acid
gives neutral FeCl3 test.

Metal – Metal Charge transfer

Mn+ M(n+1)

1. A number of inorganic compounds contain a metal in two valence states.

Eg. (i) Prussina blue K(Fe (III) { Fe(II) } (CN)6). Here Fe (III) is high spin and
Fe(II) is low spin as shown by the study of mosbauier effect. Here the charge
transfer occurs from the t2g orbitals of Fe (III) to Fe (II) via interfering CN

Ligand – Ligand Charge transfer

A ligand such as SCN- has internal charge transfer transition usually

located in the u-v region of the spectrum, corresponding transition occur in co-
 20

ordinated ligand, but can be usually identified by comparison with spectras of

the free ligand.

1) M- L (oxidation) Charge transfer transition

This type of transition can only be expected when ligands possess low-
lying empty orbitals and the metal ion has filled orbitals lying higher than the
highest filled ligand orbitals. The best examples are provided by complexes
containing CO, CN- or aromatic amines (pyridine, or phenanthroline) as ligands.
In the case of octahedral metal carbonyls Cr(CO)6 and Mo (CO)6 pairs of intense
bands at 35,800 and 44,500 cm-1 for the former and 35,000 and 43,000 cm-1 for the
latter have been assigned to transition from the bonding to the anti bonding
(Ligand  * ) components due to metal-ligand  bonding intraction.

For [Ni(CN)4]2- there are 3 medium to strong bands at 32,000,

35,200 and 37,600 cm-1 which have been assigned as transition from the three
types of filled metal d-orbitals [dxy, and (dxz, dyz)] to the lowest energy orbitals
formed from the  * orbitals of the set of CN- groups.

SPIN – ORBIT COUPLING

There is a magnetic interaction between the election spin magnetic

moment (ms = + 1/2) and the magnetic moment due to the orbital motion of an
election. The charged electron circles the nucleus and this is equivalent in effect
to placing the election in the middle of a coil of wire carrying current. As
moving charge in a circle creates a magnetic field in the centre, the orbital motion
causes a magnetic field at the electronic position. This magnetic field can interact
with the spin magnetic moment of the election giving rise to spin-orbit
interaction. For two electrons the various type of interactions possible are
between

i) The two spins (s1,s2)

ii) The orbital moment (l,l2)

iii) The spin of the e- and the orbital moment of the same e- (termed spin-
orbit coupling s1,l1)

iv) The spin of the one e- and orbital moment of the other (S1,S2) normally the
last one is negligible.
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The two extreme situations are,

i) s1, s2 > l1, l2 > s1, l1 = for lighter elements up to 1st row transition series

ii) s1l1 > s2l2, l1 : l2 = for heavier elements (j-j coupling)

The energy difference between adjacent J values

J  and J   1 is ( J   1)   J    

Where  is the spin-orbit coupling constant

L

2S

Example 1). For p1 ion

2
L = 1, S = ½, T.S = P

Here L & S couple, they give raise to 2 levels corresponding to

J=L+S…L-S

J = 3/2 and 1/2

Thus 2 P term split into 2 P 3/2 and 2

P 1/2 level under the influence of
magnetic field. J split into (2J+1) levels

The magnitude of spilling between two 2p states depends upon the

strength of L-S coupling. It may be represented in terms of spin-orbit coupling
parameter (  ) zeta. The value of zeta is expressed in cm-1.

2) For d1 ion

L = 2, S = ½ , T.S = 2D

J = 5/2 ……. 3/2

Note

 value increases with oxidation number but not very sensitive to change in
oxidation state so the impact of S.O.C on spectra is very small
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The effect of Spin orbit coupling

The spin allowed d-d bands dominate the visible spectrum of complex of
many transition metal. It should be pointed that S.O.C treats the phenomenon as
one of the coupling of two angular momentum rather than bar magnet. It causes
the splitting of degeneracies in the orbital energy level diagram. For eg 4T1g state
split into the 12 fold degenerate levels. Some spin orbit arrangements are stable
than the other. It is more important in the assignment of weak spin forbidden
transition.

Magnetic Properties of Complexes

When an atom or molecule is placed in a magnetic field any spin

degeneracy and orbital degeneracy may be removed. So a level which is
orbitally non-degenerate but which is a spin doublet maybe split. The splitting
produced are very small which is directly proportional to the magnetic field.

Molecules with closed shell are therefore repelled by a magnetic field and
said to be diamagnetic. If an e-n is considered as a hard sphere carrying a
negative charge and involve orbital rotation around nucleus in a closed path, it
will generate a spin moment and an orbital moment which continue to give
paramagnetism. It is expressed in bohr magnetion (B.M)

Paramagenetic Behaviour

Free radicals or ionic system which contain one or more unpaired e-ns will
possess a permanent magnetic moment that arises from the residual spin and
angular momentum of the unpaired e-n. When a paramagnetic substance is
placed in a external magnetic field it will be attracted and there will be negative
increase in magnetic susceptibility which is independent of the applied field, but
dependent on temperature. (Since as the temperature is increased there is
opposition to the proper alignment because of thermal agitation which results in
the decrease in the effectiveness of attraction). Hence the effectiveness of the
magnetic field will diminish with increasing temperature.

Mathemedically, this dependence has been expressed by the curie’s law:

 = C/T

(or) Curie – Weiss law :  = C/T-

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C = Curie Constant,  = Weiss Constant

Factors affecting the paramagnetic behaviour of cpxes:

1. Number of unpaired electrons

2. The spectroscopic ground state and the next high excited state

3. Ligand field strength

Types of paramagnetic behaviour:

1. Large multiplet separation: (Energy difference is large)

2. Small multiplet separation: (Energy difference is small)

Large multiplet separation

Eg : Lanthanides : The paramagnetic character is due to the unpaired e-ns in f-

shell. Here the unpaired e-ns are well shielded from external ligand field (not
exposed to environment) or covalent bonding forces, and the S.O.C is very large.
The ground state is very well separated from the next excited state, by an energy
difference which is large, compared to KT (200cm-1). Therefore only ground state
is populated and not the excited state (because thermal energy cannot promote
the e-n to excited state)

Under these circumstances S.O.C is significant and for a given state of

L+S, J-will take all values from L+S to L-S.

The magnetic moment in this case is given by

 = g J (J  1) B.M , g = Gyro magnetic ratio

In lanthanides:

This sort of behavior is met when there is a well defined single J value.

In Actinides:

1. R-S coupling or L-S coupling is inadequate for actinides, so we

have to go for j-j coupling
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2. In the case of actinides the 5f e-ns are not deeply seated but to some
extent affected by the external field. So it is difficult to explain.

Small multiplet separation:

Eg: d-block elements

Here the 4s and the next orbitals lie close in energy and the difference in
energy is comparable with kt at room temperature. Therefore both levels are
equally populated therefore the effect of S.O.C is small, So one can ignore the
coupling and treat L&S as to interact independently with external field and the
wave mechanics shows that,

 = S+L = 4S ( S  1)  L ( L  1) B.M

In transition metals:-

Here we find that the orbital contribution is quenched with the result of
spin contribution. Thus only the spin angular momenturm determines the
magnetic moment.

 - S = 4S (S  1) B.M  spin only formula

Spin only formula hold good only for I-row of transition series.