II A) MAGNETIC PROPERTIES OFTRANSITION METAL COMPLEXES

by Dr. A. R. Yaul

M.Sc., M.Phil., SET, Ph.D.

Department of Chemistry NARAYANRAO KALE SMRUTI MODEL COLLEGE (Arts, Commerce and Science) Karanja (GH.), Dist.- Wardha

1 1 INTRODUCTION

When substances are placed in the magnetic field, they behave differently. The bevaviour of substance in the magnetic field is called as magnetic behavior.

The transition metal complexes shows different magnetic behavior as fallows –

1. Paramagnetism –

Those substances when placed in a magnetic field, the magnetic lines of forces passing through the substance are more as compared to air. Such substances are called paramagnetic substances and phenomenon is called as paramagnetism. 2 There is increase in the intensity of magnetic field. Paramagnetic substance placed in a magnetic field it is attracted in the magnetic field. Those substances which have one or more unpaired electron show paramagnetism. e.g. Lithium, magnesium, aluminum, calcium and tungsten

3 2. Diamagnetism – Those substances when placed in a magnetic field, the magnetic lines of forces passing through the substance are less as compared to air. Such substances are called diamagnetic substances and phenomenon is called as diamagnetism. There is decrease in the intensity of magnetic field. Diamagnetic substance placed in a magnetic field it is repelled in the magnetic field. Those substances which does not have unpaired electrons shows diamagnetism. e.g. bismuth, antimony, copper, gold, quartz, mercury, water, alcohol, air and hydrogen

4 3. Ferromagnetism – Those substances which show permanent magnetism in absence of magnetic field are called ferromagnetic substances and the phenomenon is called ferromagnetism. Paramagnetic substance which contains large number of unpaired electrons with parallel spin shows ferromagnetism. The groups of unpaired electrons with parallel spin are called as domains. E.g. Iron, nickel and cobalt

In absence of magnetic field these domain are align randomly. But in presence of magnetic field these domains are aligned in the direction of magnetic field. They have strong magnetic moment.

5 4. Anti-ferromagnetism or Ferrimagnetism – These substances which have unpaired electrons but behave as diamagnetic substance at room temperature. This is because the unpaired electrons of one atom get paired with unpaired electrons of neighboring atom having opposite spin. But as the temperature increases, the electron pair breaks and becomes unpaired electron and substance behaves as a paramagnetic substance. Such behavior of substances are called anti-ferromagnetism or ferrimagnetism. 6 e.g. Alloys such as iron manganese (FeMn) and oxides such as nickel oxide (NiO)

Magnetic Susceptibility – The ratio of intensity of magnetization to strength of applied magnetic field is called as magnetic susceptibility. It is given by,  I v = H Where,

v - Volume magnetic susceptibility I – Intensity of magnetization

7 H – Strength of applied magnetic field Gram Magnetic Susceptibility –

The ratio of volume magnetic susceptibility (v) to the density of the material () is called as gram magnetic susceptibility.

It is given by, v g = 

Where,

g - Gram magnetic susceptibility

v - Volume magnetic susceptibility  - Density of material

8 Molar Magnetic Susceptibility – The product of gram magnetic susceptibility and molecular weight of substance is called as molar magnetic susceptibility.

m = g . M

Where,

m – Molar magnetic susceptibility

g – Gram magnetic susceptibility M – Molecular weight

9 Significance of Molar Magnetic Susceptibility – The product molar magnetic susceptibility is used to calculate the effective magnetic moment.

eff = 2.83 m x T Where,

eff - Effective magnetic moment

m - Molar magnetic susceptibility T – Temperature in Kelvin

The relation between effective magnetic moment and number of unpaired electron is

eff = n (n+2) B.M. Where, n - Number of unpaired electron B.M. – Bohr Magneton

Therefore by knowing the value of molar magnetic susceptibility (m), we can calculate the eff. Therefore we can determine the number of unpaired electrons (n). Thus we can determine whether complex is low spin or high spin. 10 Gouy’s Methods for Determination of Magnetic Susceptibility –

Gouy’s method is based on determination of change in mass when the substance is placed in magnetic field. When the magnetic field is on and off change in mass occurs.

The substance whose magnetic susceptibility is to be determined is filled in cylindrical glass tube. The glass tube is hang to sensitive balance by using silver wire in such a way that, lower end of the tube is lie between poles of electromagnet. The weight of glass tube is counter balanced by putting appropriate weight on the pan of the balance. The current is now switched on, the electromagnets are activated, magnetic field is exerted.

If the substance is paramagnetic, it is attracted by the magnetic field. Due to this glass tube is pulled downfield. Therefore some additional weights are to be placed on pan balanced to counter balance the tube.

If the substance is diamagnetic, it is repelled by the magnetic field. Due to this glass tube is pushed upward. Therefore some weights are to be removed from pan of balanced to counter balance the tube.

11 The difference of two weights gives change in mass (m) which is equal to magnetic force acting on substance. It is related to magnetic susceptibility.

__1 _ 2 (ms) g = [ Ps  Pa a ] AH ------1 2 s Where,

ms – Change in mass of sample g – Gravitational force Ps – Density of substance Pa – Density of air

s – Susceptibility of substance

a – Susceptibility of air A – Cross section area of glass tube H – Field strength

Similar experiment is performed with a reference substance like water, we get

__1 _ 2 (mw) g = [ Pw  Pa a ] AH ------2 2 w 12 Divide eqn 1 by eqn 2 we get,

_  ms Ps s Pa a = ------3  mw Pw w _ Pa a

–4 The value of Pa a = 0.03 x 10

Using equation 3 we can determine magnetic susceptibility of substance.

Molar susceptibility (m) can be calculated by multiplying magnetic susceptibility of substance

(s) and molecular weight (M).

(m) = m M

13 Spin and orbital contribution to the magnetic moment Each electron possesses two types of motions i) spin motion (around its own axis) & ii) orbital motion (revolve around nucleus in orbital). Due to the spin and orbital motion, electron has its own magnetic field (Magnetic moment).

In diamagnetic substances, electrons are paired with opposite spin, their magnetic field are mutually cancelled. Therefore they are not resultant magnetic field. Hence magnetic moment is zero.

In paramagnetic substances have one or more unpaired electrons. They have resultant magnetic field. Therefore they have magnetic moment.

The magnetic moment of paramagnetic substance is due to spin and orbital motion of electrons.

The magnetic moment due to spin motion of electron is called as spin magnetic moment. It is given by

spin = g S (S+1) Where, S – spin quantum number g – constant (g = 2 for free electron)

spin = 2 S (S+1) 14 The magnetic moment due to orbital motion of electron is repelled as orbital magnetic moment. It is given by orb = l (l+1)

Where, l – orbital quantum number

Therefore total magnetic moment is sum of spin and orbital magnetic moment.

 = spin + orb

 = 2 s (s+1) + l (l+1)

In case of first transition (3d-elements) metal complexes, 3d-orbitals of metal ion containing unpaired electrons are directly under the influence of surrounding ligands. The electric field if these ligands restrict the orbital motion of electrons. Therefore orbital motion of electron is partially or completely quenched. Thus orbital magnetic moment contribution is negligible.

15 Hence, magnetic moment of 3d- element metal complexes is

spin = 2 S (S+1)

For one unpaired electron S = ½

 For ‘n’ number of electrons S = n/ 2

n (n+1) spin = 2 _ _ 2 2

n (n+2) spin = 2 _ 2 2

n (n+2) spin = 2 4

spin = n (n + 2) This is spin only formula

16 In case of second and third transition metal complexes, the electric field of surrounding ligands does not restrict the orbital motion. Therefore orbital motion is not quenched. Hence magnetic moment is due to the both spin as well as orbital motion of electron.

If higher transition element and in lanthanides and actinides the spin motion and orbital motion couple together to give a quantum number J It is given by

J = L  S (When shell is less than half filled) J = L + S (When shell is half filled or more than half filled)

Where, J – Total angular momentum L – Total orbital angular momentum S – Total spin quantum number

 = g J (J + 1) Where, g – Lande splitting factor 17 J (J + 1) + S (S + 1) - L (L + 1) g = 1 + 2J (J + 1)

18 Orbital contribution of magnetic moment

In case of first transition (3d-elements) metal complexes, 3d-orbitals of metal ion containing unpaired electrons are directly under the influence of surrounding ligands. The electric field if these ligands restrict the orbital motion of electrons. Therefore orbital motion of electron is partially or completely quenched. Thus orbital magnetic moment contribution is negligible.

Hence, magnetic moment of 3d- element metal complexes is

spin = 2 S (S+1)

For one unpaired electron S = ½ n_ (n+1)_  For ‘n’ number of electrons S = n/ 2 spin = 2 2 2

n (n+2) spin = 2 _ 2 2

n (n+2) spin = 2 4

19 spin = n (n + 2) This is spin only formula In case of higher transition series elements and lanthanides and actinides, the magnetic moment is due to the both spin and orbital motion of electrons.

In order to generate orbital magnetic moment, following conditions should be satisfied- i) The orbitals should be degenerate ii) The orbitals should have similar shape so that they are transformed into one another by rotation about an axis. In octahedral complexes of 3d elements, under the influence of ligands, d-orbital split into two sets lower energy t2g set and higher energy eg set. The eg set consist of dx2-y2 and dz2 orbital. They are degenerate orbitals but have different shapes, therefore eg orbitals do not contribute to orbital magnetic moment.

t2g set consist of dxy, dyz and dxz orbitals. These are degenerate orbitals and have similar shape. They can be transformed into each other.

But when t2g set us symmetrical (t2g, eg) then transformation are not possible therefore do not contribute to orbital magnetic moment.

0 3 In tetrahedral complexes, the d-orbital split into lower energy e and higher energy t2 set. t2 and t2 symmetrical set do not contribute to orbital magnetic moment. 20 Magnetic moment of octahedral complexes with respect to CFT

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