NON BONDING ELECTRONS

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Models describing Bonding

• VBT A covalent bond is formed when orbitals

of two atoms overlap.• CFT• Modified CFT, known as Ligand Field Theory• MOT

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CFT- Assumptions

• Interactions between metal ions and ligands are purely electrostatic or ionic.

• Ligands: point charges. Negatively charged: ion-ion interaction. Positively charged: ion-dipole interaction.

• Due to repulsion by ligand electrons, electrons on metal occupy d-orbitals which are farthest from the direction of ligand approach.

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Symmetric field• d orbitals are degenerate for an isolated gaseous atom.• If a spherically symmetric field of negative charges is

placed around the metal, these orbitals remain degenerate, but are raised in energy due to repulsion between the negative charges on the ligands and in d orbitals.

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Octahedral field• If discrete point charges (ligands)

interact with metal, degenercy of d-orbitals is destroyed.

• Splitting of d-orbitals takes place.

• All d-orbitals do not interact in a similar way with the ligands.

• Orbitals lying along the axis i.e., x2-y2, z2 will be destabilized more in comparison to orbitals lying in between the axis.

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CFT- Octahedral Complexes

• For Oh , difference between Eg and T2g is Δ₀ (10 Dq).• The baricentre must be conserved on going from

spherical to octahedral field, so the extent of destabilization of Eg should be equal to the extent of stabilization of T2g .

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For more than 1 electron in d-orbital, e‾ ─ e‾ interactions must be taken into account

For d1 –d3 systems : Hund’s rule predicts that electrons will not pair and occupy T2g set.

For d4-d7 systems :• Put all electrons in T2g and pair them (Low spin or Strong field, Δ₀

high)• Put electrons in Eg set which lies higher in energy i.e., firstly all

the orbitals are singly occupied and then pairing takes place (High spin or Weak Field, Δ₀ small).

Two important parameters should be considered:– Pairing energy (P)– Eg - T2g Splitting ( Δ₀ , CFSE)

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Pairing Energy, P

The pairing energy, P, is made up of two parts.

1) Columbic repulsion energy caused by having two electrons in same orbital. Destabilizing energy contribution of Pc for each doubly occupied orbital.

2) Exchange stabilizing energy for each pair of electrons having the same spin and same energy. Stabilizing contribution of Pe for each pair having same spin and same energy

P = sum of all Pc and Pe interactions

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CFSE for an Octahedral Complex

CFSE= -0.4 x n(T2g) + 0.6 x n(Eg) Δ₀

If CFSE> P, Pairing occursIf CFSE< P, no Pairing

Δ₀ Δ₀

d5 system

LS Complex High Spin Complex9

Δ₀ Depends upon:

1. Nature of ligand2. Charge on metal ion.3. Principal Quantam No. of d-orbital (3d,4d,5d) Δ₀(5d)> Δ₀(4d)> Δ₀(3d)

Spectrochemical series:I− < Br− < S2− < SCN− < Cl− < N3

−, F− < urea, OH− < ox, O2− <H2O < NCS− < py, NH3 < en < bpy, phen < NO2

− < CH3−, C6H5

−< CN− < CO. 10

Applications of CFT

1. Ionic Radii:- For a given oxidation state, ionic radii decreases

steadily on going from left to right in transition series (dotted line).

Trivalent transition metal ions show a similar trend.

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Eg, Ti-O bonds are shorter than Ca-O bonds due to larger interaction between Ti+2 and bonding electrons.

Applications of CFT

2. Lattice energy:-Crystal field splitting of d-orbitals results in CFSE and increased lattice energies of ionic compounds. Occurrence of CFSE leads to an increased lattice energy.

Lattice energy of fluorides of first row transition elements. 12

Jahn-Teller Distortion• If both the eg orbitals are symmetrically filled - all ligands are

repelled equally. Result: regular octahedron• If asymmetrically filled – some ligands are repelled more than the

other. Result: Distorted octahedron• for the case of Cu, d9 configuration. Doubly occupied orbitals will

face stronger repulsions than singly occupied.

Consider eg configuration: (dz2 )1 , ( dx2 − y2 )2

Ligands along x, -x, y, -y will be repelled more and bonds will be elongated i.e. the octahedron will be compressed along the z axis.

Consider eg configuration: : (dz2 )2 , ( dx2 − y2 )1

Ligands along z, -z will be repelled more and bonds elongated. i.e. the octahedron will be elongated along the z axis. 13

The effect of JT

distortions is best

documented for Cu(II)

complexes (with 3e ˉ

in eg)

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Square Planar Coordination• For understanding square planar complexes, consider their d

energy level diagram in octahedral and distorted octahedral fields.• d8 configuration, 2 electrons in the eg orbitals • The effect of distorted octahedron:

– For small elongations along z axis P> energy between two eg

orbitals.– For large elongations P< energy between two eg orbitals

• Distortion is now sufficiently large.• It results in a 4-coordinate square planar shape, with the ligands

along the z axis no longer bonded to the metal.• Square planar complexes are quite common for the d8 metals in

the 4th and 5th periods: Rh(I), IR(I), Pt(II), Pd(II) and Au(III).• Square planar complexes are rare for the 3rd period metals. Ni(II)

generally forms tetrahedral complexes. With very strong ligands such as CN- square planar geometry is seen with Ni(II).

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Tetrahedral field

• Imagine a tetrahedral molecule inside a cube with ligands occupying alternate corners and metal at the centre of the cube.

• The two ‘e’ orbitals point towards the axis.• The three ‘t2’ orbitals point in between the axis, i.e.,

nearer to the direction of approach of ligands and hence these orbitals are of higher energy.

• Magnitude of splitting is less as none of the d-orbitals point directly towards the approaching ligands.

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Tetrahedral Field

Δt < Δ₀18

Tetrahedral Field

• There are only 4 ligands in tetrahedral complex, so ligand field is roughly 2/3 of octahedral field.

• All tetrahedral complexes are high spin since CFSE is normally smaller than pairing energy.

• If a very strong field ligand is present, square planar geometry will be favoured.

Δt = 4/9 Δ₀

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• Most transition metals prefer octahedral coordination or distorted octahedral coordination. Large CFSE.

• High spin d5 ions, d0 and d10 have no particular preference for octahedral or tetrahedral as their CFSE is zero.

• Ions such as Cr+3, Ni+2, Mn+3 show preference for octahedral coordination.

• Coordination preferences of ions are shown by the type of spinel structure they adopt.– Normal– Inverse– Intermediate between normal and inverse

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General Facts

Spinels – Use of CFSE• Spinel is the name given to mineral MgAl2O4 .

• General formula AB2O4 .

Normal Spinel :- Oxygens form ccp array. Mg(II) (A type) occupy tetrahedral sites. Al(III) (B-type) occupy octahedral sites.

[MII]tet[MIIIMIII]ohO4

Inverse spinel :- Half of the trivalent ions swap with divalent ions. Mg(II) occupies octahedral sites.

[MIII]tet[MIIMIII]ohO421

Spinels – Use of CFSE

• Several transition metal oxides with the formula AB2O4 .

• CFSE is highly useful in determining whether a structure would be normal or inverse.

• If M3+ ion has a higher CFSE in an octahedral field compared to M2+ ion : Normal spinel.

• If M2+ ion has a higher CFSE in an octahedral field compared to M3+ ion: Inverse spinel.

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Inert Pair Effect

• Heavy post transition elements exhibit this effect.• Eg. Tl, Sn, Pb,Sb.• Lower oxidation states are stable for elements as

we go down the group.

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