Module-I

Coordination chemistry
 Metal Complexes
➢ A metal complex is a central metal atom bonded to
a group of molecules or ions.
Donor atom
➢ If it’s charged, it’s a complex ion. (Lewis base)
➢ Compounds containing complexes are coordination ligand
compounds

Ligands
Acceptor atom (Lewis acid)
➢ The molecules or ions coordinating to the
Metal ions
metal are the ligands.
➢ They are usually anions or polar molecules.
➢ The must have lone pairs to interact with
metal
A chemical mystery:
Same metal, same ligands, different number of ions when dissolved

• Many coordination compounds are brightly colored, but again, same metal,
same ligands, different colors.
 Werner’s theory of coordination compounds
Metals exert two types of linkages;
• (i) the primary or ionizable links which are satisfied
by negative ions and equal the oxidation state of the
metal, and
• (ii) the secondary or nonionizable links which can
be satisfied by neutral or negative ions/groups. The
secondary linkages equal the coordination number
of central metal atom/ion. This number is fixed for a
metal.
• The ions/groups bound by the secondary linkages
have characteristic spatial arrangements
[Co(NH3)6]Cl3
corresponding to different co-ordination numbers. In
the modern terminology, such spatial arrangements
are called coordination polyhedra.
 Ligands
❑ The ligands are the ions or molecules bound to the central atom/ion in the coordination
entity.
❑ This is better visualized as the combination of a Lewis acid (the central atom/ion) with a
number of Lewis bases (ligands).
❑ The atom in the Lewis base that forms the bond to the Lewis acid (central atom/ion) is
called the donor atom (because it donates the pair of electrons required for bond
formation).
❑ The central atom/ ion is the acceptor atom/ion (because it receives the electron pairs from
the ligands).
❑ Some of the common ligands in coordination compounds are Br–, Cl–, CN–, OH–, O2–,
CO32–, NO2–, C2O42–, NH3, CO, H2O, NH2CH2CH2NH2 (1,2- ethylenediamine).
 Ligands
Ambidentate ligands
❖Ligands which can ligate through two different atoms present in it are called
ambidentate ligands.
❖Examples of such ligands are the NO2– and SCN– ions.
❖NO2– ion can coordinate through either the nitrogen or the oxygen atoms to a central
metal atom/ion.
❖Similarly, SCN– ion can coordinate through the sulphur or nitrogen atom. Such
possibilities give rise to linkage isomerism in coordination compounds.
 Ligands
Denticity of the ligand
“The denticity of the ligand is defined as the number of pairs of electrons shared with
the metal atom or ion.”

Types of ligands

Monodentate Bidentate/didentate Polydentate

 Ligands
• Monodentate ligand
This will coordinate with the only site of a metal ion. In other words, it can donate only one pair of electrons to
the metal ion.
Example: Cl-, Br-, SO42-, NH2NH3+, NH3, H2O

• Bidentate ligand
This will occupy two sites of a metal ion. That is, it can attach itself to two positions of a metal ion. Example:
 Ligands
Polydentate ligands
These ligands occupy many sites of the same metal ion.
 Isomerism in Coordination Compounds
Two or more different compounds having the same formula are called isomers.
1. Stereoisomerism. 2. Structural Isomerism.
a) Geometrical isomerism a) Coordination isomerism
b) Optical isomerism b) Ionization isomerism
c) Hydrate isomerism
d) Linkage isomerism
Some terms & their definitions:
❖Enantiomer: Stereoisomers not superimposable on their mirror images are called
enantiomers.
❖Diastereoisomers: Stereoisomers that do not possess mirror image relation are called
diastereoisomers.
❖Asymmetric molecule: A molecule without any symmetry (except c1) is classified as
an Asymmetric molecule.
 Geometric Isomerism
Geometric Isomers differ in the spatial arrangement of atoms within the same structural framework. It is
also called cis-trans-isomerism.

Geometric Isomerism for coordination no. 4

 Geometric Isomerism
Geometric Isomerism for coordination no.6
 Optical Isomerism
A chiral complex is optically active if its structure cannot be superimposed on its mirror image.
➢ The condition necessary for a molecule to exhibit Optical isomerism is the absence of a rotation
reflection axis (Sn).
➢ Easy judgment for optical activity implies the absence of a plane or center of symmetry.
 Structural Isomerism
1. Ionization Isomerism: Ionisation isomerism involves the exchange of ions inside and
outside the coordination sphere. These isomers give different ions in solution, hence it is
called ionisation isomerism.
➢ The ionization isomers [Co(NH3)5Br]SO4 and [Co(NH)5SO4]Br dissolve in water to
yield different ions and thus react differently to various reagents:

[Co(NH3)5Br]SO4 + Ba2+ BaSO4 (s)

[Co(NH)5SO4]Br + Ba2+ No reaction

[Co(NH3)5Br]SO4+ Ag+ No reaction

[Co(NH)5SO4]Br + Ag+ AgBr(s)

 Structural Isomerism
2. Solvate/hydrate isomerism: Solvate isomerism is known as 'hydrate isomerism' in case
where water is involved as a solvent.
➢ Solvate isomers differ by whether or not a solvent molecule is directly bonded to the metal
ion or merely present as free solvent molecules in the crystal lattice.
The best known example involves isomers of
"chromic chloride hydrates," of which three are
known: [Cr(H2O)6]Cl3, [Cr(H2O)5Cl]Cl2.H2O,
and [Cr(H2O)4Cl2]Cl.2H2O, These differ in their
reactions:

dehydr. over H SO
[Cr(H2O)6]Cl3 2 4 [Cr(H2O)6]Cl3 (no change)

dehydr. over H SO
[Cr(H2O)5Cl]Cl2.H2O 2 4 [Cr(H2O)5Cl]Cl2

[Cr(H2O)4Cl2]Cl.2H2O dehydr. over H2SO4 [Cr(H2O)5Cl]Cl2

 Structural Isomerism
3. Coordination Isomerism: Coordination compounds made up of cationic and anionic
coordination entities show this type of isomerism due to the interchange of ligands between
the cation and anion entities. Some of the examples are:

(i) [Co(NH3)6][Cr(CN)6] and[Cr(NH3)6][Co(CN)6]

(ii) [Cu(NH3)4][PtCl4] and [Pt(NH3)4] [CuCl4]

4. Linkage isomerism: Linkage isomerism occurs with ambidentate ligands. These ligands
are capable of coordinating in more than one way. The best-known cases involve the
monodentate ligands SCN- / NCS- and NO2- / ONO-.
For example:
[Co(NH3)5ONO]Cl the nitrito isomer -O attached
[Co(NH3)5NO2]Cl the nitro isomer - N attached.
 Bonding Theories for Coordination complexes
a) Valance Bond Theory (VBT)
❖ The central metal cation or atom makes available a number of vacant s, p, and or d-orbitals
equal to its coordination number to form coordinate covalent bonds with ligands.
❖ These vacant atomic orbitals of metal are hybridized to form a new set of equivalent bonding
orbitals, called hybrid orbitals. These orbitals have the same geometry, energy and definite
directional properties.
❖ The bonding in metal complexes arises when a filled ligand orbital containing a lone pair of
electrons overlaps a vacant hybrid orbital on the metal cation or atom to form a coordinate
covalent bond.
 Valance Bond Theory (VBT)
❖Each ligand has at least one orbital containing a lone pair of electrons.
➢ Pauling classified the ligands into two categories (i) Strong ligands like CN–, CO– etc.
(ii) weak ligands like F–, Cl– etc.
❖Strong ligands have a tendency to pair up the d-electrons of a metal cation/atom to
provide the necessary orbitals for hybridization. While, weak ligands do not have a
tendency to pair up the d-electrons.

❖The d orbital used in hybridization may be either inner (n-1) d-orbitals or outer n d-
orbitals. The complex formed by inner (n-1) d-orbitals, is called inner orbital
complex whereas the complex formed by outer d-orbital is called outer orbital complex.

❖If unpaired electrons are present within the complex, then complex is paramagnetic in
nature while if all the electrons are paired then complex is diamagnetic in nature.
Valance Bond Theory (VBT)
 Valance Bond Theory (VBT)
(a) Inner Orbital Complexes: [Co(CN)6]3- ion
➢ In this complex, the oxidation state of cobalt is +3.
➢ The valence shell electronic configuration of Co3+ is 3d6.
➢ The CN– ligands are strong and therefore cause pairing of 3d-electrons.
➢ All six 3d-electrons are therefore paired and occupy three of the five 3d orbitals.
➢ The vacant 3d- orbitals combine with the vacant 4s and 4p orbitals to form six d2sp3-hybrid orbitals.
➢ These six hybrid orbitals overlap with six filled orbitals of ligands to form six-coordinate covalent bonds.
 Valance Bond Theory (VBT)
(b) Outer Orbital Complexes: [Fe(F)6]3- ion:
➢ In this complex, the oxidation state of Iron(Fe) is +3.
➢ The valence shell electronic configuration of Fe3+ is 3d5.
➢ The F- ligands are weak and therefore cause no pairing of 3d-electrons.
➢ All five 3d-electrons are therefore occupied on five 3d orbitals.
➢ The vacant 4s- orbitals combine with the vacant 4p and two vacant 5d orbitals mixed with each other to form
six sp3d2-hybrid orbitals.
➢ These six hybrid orbitals overlap with six filled orbitals of ligands to form six-coordinate covalent bonds.
 Valance Bond Theory (VBT)
Examples of tetrahedral complexes: [NiCl4]2- ion
➢ In this complex ion, the oxidation state of Ni is +2.
➢ The valence shell electronic configuration is 3d8.
➢ Since Cl– is a weak ligand, therefore no pairing of electrons will occur in 3d-orbitals.
➢ None of the five 3d-orbitals is vacant.
➢ Vacant 4s and 4p orbitals combine to give four sp3 hybrid orbitals.
➢ These four hybrid orbitals form bonds with four ligands by sharing four pairs of electrons.
 Valance Bond Theory (VBT)
Examples of tetrahedral complexes:
[Ni(CO)4]
 Valance Bond Theory (VBT)
Inner Orbital Complexes: [Co(NH3)6]3+ ion
➢ The cobalt ion is in +3 oxidation state and has the electronic configuration 3d6.
➢ Six pairs of electrons, one from each NH3 molecule, occupy the six hybrid orbitals.
➢ Diamagnetic octahedral complex.
 Valance Bond Theory (VBT)
Examples of Square planner complexes: [NiCl4]2- ion
➢ In this complex ion, the oxidation state of Ni is +2.
➢ The valence shell electronic configuration is 3d8.
➢ Since CN– is a strong ligand, therefore these ligands cause to pair up the two unpaired electrons in one d-orbital
resulting in a vacant 3d-orbital.
➢ This vacant 3d-orbital gets hybridized with the vacant 4s and two 4p orbitals to give four dsp2 hybrid orbitals.
➢ These four hybrid orbitals form bonds with four ligands by sharing four pairs of electrons.
Module-I
Lecture-8
 Valance Bond Theory (VBT)
Limitation of the VBT:
➢ It could not explain the nature of ligands.
➢ It is not helpful to predict the mystery behind the formation of outer or inner orbital
coordination complex.
➢ VBT fails to predict any distortion in the shapes of the coordination complexes from
regular geometry.
➢ Fail to explain the color & characteristics of absorption spectra of complex
compounds.
➢ It could not explain reaction rates and the mechanism of reactions of complexes.
➢ This theory does not provide any quantitative interpretation data about the
thermodynamic and kinetic stability of coordination complexes.
 Crystal Field Theory
(Bonding theory of coordination complexes)
Metal-ligand connections are electrostatic interactions between a central metal ion and a set of
negatively charged ligands (or ligand dipoles) arranged around metal ion.

Assumption of CFT
➢ The metal-ligand bond is ionic arising purely from the electrostatic interactions between
the metal ions and ligands.
➢ CFT considers anions as point charges and neutral molecules as dipoles.
Crystal Field Theory
Shape of s, p, and d-orbital

➢ When transition metals are not bonded to any

ligand, their s, p, and d orbitals degenerate
that is they have the same energy.
➢ When they start bonding with other ligands,
due to different symmetries of the d orbitals
and the inductive effect of the ligands on the
electrons, the d orbitals split apart and
become non-degenerate in octahedral and
tetrahedral fields.
➢ No net effect on s and p orbitals in octahedral
and tetrahedral fields and they remain non-
degenerate.
 Crystal Field Theory
Approach of ligands in Oh and Td field
 Crystal Field Theory
Approach of ligands in Oh and Td field

➢ Orbitals 𝒅𝒙𝟐 −𝒚𝟐 and 𝒅𝒛𝟐 will face direct ➢ None of the d-orbital will face direct interaction
interaction with the incoming electron cloud of the with the incoming electron cloud of the ligand.
ligand and thus raise in energy ➢ Orbitals 𝒅𝒙𝟐 −𝒚𝟐 and 𝒅𝒛𝟐 will face less closer
➢ dxy, dyz, and dzx are placed between the axis and approach towards incoming electron cloud of the
thus don’t face direct interaction with the ligand as compared to dxy, dyz, and dzx and thus dxy,
incoming electron cloud of the ligand and thus dyz, and dzx raise in energy while 𝒅𝒙𝟐 −𝒚𝟐 and 𝒅𝒛𝟐
lower in energy. lowered in energy.
Crystal Field Theory
(Octahedral crystal field splitting)
Crystal Field Theory
(Tetrahedral crystal field splitting)
 Crystal Field Theory
Tetrahedral complexes
The magnitude of the crystal field splitting ∆𝒕 is considerably less than the octahedral fields.
There are two main reason for this
▪ There are only four ligands instead of six, so the ligand field is only (2/3)rd of size; hence the
crystal field splitting is also (2/3)rd of size
▪ The direction of orbital doesn’t coincide with the direction of ligands. This reduces the crystal
field splitting by approximately further by (2/3)rd

𝟐 𝟐 𝟒
∆𝒕 = ( × )∆𝟎 = ∆𝟎
𝟑 𝟑 𝟗
 Crystal Field Theory
Tetrahedral complexes
 Crystal Field Theory
Crystal field stabilization energy (CFSE)
“defined as the change in energy due to the splitting of the d-orbitals of metal cation under the influence of
ligand field in a complex.”
In other words, “CFSE is the gain in energy achieved by the preferential filling up of orbitals by electrons.”
• The stability of the complex increases as the amount of CFSE increases which is the
magnitude of the energy difference between the two sets (t2g and eg ) orbitals.

CFSE = {- 0.4 ∆𝟎 × (no. of electrons in t2g set) + 0.6 ∆𝟎 × (no. of electrons in t2g set)} + P

∆𝟎 = 10 Dq

CFSE = {- 4 𝑫𝒒 × (no. of electrons in t2g set) + 6 𝑫𝒒 × (no. of electrons in t2g set)} + P

P = pairing energy
 Crystal Field Theory
The magnitude of o depends on three factors:
➢ Nature of the ligands:
Spectrochemical series: experimentally observed order of the crystal field splitting energies
(o) produced by different ligands.
Strong-field ligands (large o) Weak-field ligands (less o)
CN−, CO > NO2− > en > NH3 > H2O > ox > OH− > F− > SCN−, Cl− > Br− > I−

➢ Charge on metal ions: o(M2+) <o(M3+) < o(M4+)

➢ Nature metal ions: o(3d Mn+) < o(4d Mn+) < o(5d Mn+); n+ is constant

Spin Pairing Energy (p)

Spin pairing energy (p): is an increase in energy due to electrostatic repulsions when an e- is put into
an occupied orbital.”
o > p : Low Spin complex (LSC)
o < p : High Spin complex (HSC)
 Crystal Field Theory
Crystal field stabilization energy (CFSE)

1.

3. [Co(CN)6]3- (d6) LSC

2. [CoF6]3-
Co : 3d74S2
CFSE = {(-0.4 × 6) + (0.6 × 0)} ∆𝟎 + 3p
Co3+ : 3d64S0 (d6) HSC o
= - 2.4 ∆𝟎 + 3p
= - 24 Dq + 3p
eg
o
t2g [Co(CN)6]3-
CFSE = {(-0.4 × 4) + (0.6 × 2)} ∆𝟎 + p (d6) LSC
= - 0.4 ∆𝟎 + p = - 4 Dq + p
 Crystal Field Theory
Crystal field splitting of d6 ions under weak and strong field

Magnetism:
o o
𝝁𝒔 = 𝒏 𝒏 + 𝟐 ; n= no. of unpaired electron
Energy

[CoF6 ]3- [CoF6]3-: n=4; 𝝁𝒔 = 5.3 BM; Paramagnetic

(d6) HSC [Co(CN)6]3-: n=4; 𝝁𝒔 = 0; Diamagnetic
o < p [Co(CN)6]3-
(d6) LSC
o > p
Crystal Field Theory (CFT)
 Crystal Field Theory (CFT)
Experimental determination of CFSE value

UV-visible for Ti(H2O)3+

Energy

𝝀𝒎𝒂𝒙
𝟒𝟗𝟓 𝒏𝒎

𝝀𝒎𝒂𝒙 = 495 nm

𝒉𝒄
E= = 243 kJ/mol = o
𝝀𝒎𝒂𝒙

CFSE = - 0.4 × o = - 97 kJ/mol

 Tetragonal distortion in octahedral complexes
Jahn–Teller distortion (JT): “Any non-linear molecule in degenerate electronic ground state will undergo a
geometrical distortion that removes its degeneracy, and lower its energy.”

t2g eg Distortion HSC (WFL) Distortion LSC () Distortion

S S No d1 t2g1eg0 Yes (less) t2g1eg0 Yes (less)
A S Yes (less) d2 t2g2eg0 Yes (less) t2g2eg0 Yes (less)
S A Yes (more) d3 t2g3eg0 No t2g3eg0 No
d4 t2g3eg1 Yes (more) t2g4eg0 Yes (less)
S : Symmetric d5 t2g3eg2 No t2g5eg0 Yes (less)
A: Asymmetric d6 t2g4eg2 Yes (less) t2g6eg0 No
HSC --High Spin complex d7 t2g5eg2 Yes (less) t2g6eg1 Yes (more)
WFL---Weak Field Ligands d8 t2g6eg2 No t2g6eg2 No
LSC--Low Spin complex d9 t2g6eg3 Yes (more) t2g6eg3 Yes (more)
SFL---Strong Field Ligands d10 t2g6eg4 No t2g6eg4 No

Significant Jahn-Teller effects are observed in complexes of high-spin Cr(II) (d4), Mn(III) (d4), Cu(II) (d9), Ni(III) (d7),
and low-spin Co(II) (d7).
 Tetragonal elongation
If the 𝒅𝒛𝟐 orbital contain one more electron than 𝒅𝒙𝟐 −𝒚𝟐 orbital then the ligands approaching along +z and
–z direction will encounter greater repulsion than the other four ligands, which result in elongation of the
octahedral along z direction and commonly known as tetragonal elongation.

➢ When an octahedral complex exhibits elongation,

the axial bonds are longer than the equatorial
bonds.
➢ Tetragonal elongation is much more common as
compared to tetragonal compression.
 Tetragonal elongation in Cu(II)-d9 system
For example, trans-Cu(NH3)4(H2O)2]2+ is readily formed in an aqueous solution as a distorted
octahedron with two water molecules at greater distances than the ammonia ligands; liquid ammonia
is the required solvent for [Cu(NH3)6]2+ formation. The formation constants for these reactions show
the difficulty of putting the fifth and sixth ammonia on the metal:
 Tetragonal compression
If the 𝒅𝒙𝟐 −𝒚𝟐 orbital contain one more electron than 𝒅𝒛𝟐 orbital then the ligands approaching along +x, +y
and –x, -y- direction will encounter greater repulsion than the other two ligands, which result in elongation
of the octahedral along x and y direction as compared to z axis and commonly known as tetragonal
compression.
➢ When an octahedral complex exhibits compression, the equatorial bonds are longer than the axial
bonds.
Tetragonal elongation and formation of square planner complex

𝒅𝒙𝟐 −𝒚𝟐
𝒅 𝒛𝟐
(𝒅𝒛𝟐 ,𝒅𝒙𝟐 −𝒚𝟐 ) 𝒅𝒙𝟐 −𝒚𝟐
𝒅𝒙𝟐 −𝒚𝟐 eg
Energy 𝒅 𝒛𝟐
𝒅𝒙𝒚
𝒅𝒚𝒛 , 𝒅𝒛𝒙
t2g 𝒅𝒙𝒚
𝒅 𝒛𝟐
𝒅𝒙𝒚 (𝒅𝒙𝒚 , 𝒅𝒚𝒛 , 𝒅𝒛𝒙 )

(Octahedral 𝒅𝒚𝒛 , 𝒅𝒛𝒙 𝒅𝒚𝒛 , 𝒅𝒛𝒙

Tetragonal
Compression Field) Tetragonal
d8 Systems
elongation
Ti(H2O)3+, d1 Square planar
Cu2+ , d9 arrangement
(weak/strong
field) Pt2+, Au3+
 Square planner complex
Ions that form square planner complex

Electronic configuration Ions Type of filed No. of unpaired electrons

d4 Cr(+II) weak 4
d6 Fe(+II) Haem 2
d7 Co(+II) Strong 1
d8 Ni(+II), Rh(+I), Ir(+I), Strong 0
Pd(+II), Pt(+II), Au(+III) Strong and weak 0
d9 Cu(+II), Ag(+II) Strong and weak 1
 Spinels
The spinel structure consists of an fcc array of O2– ions in which the A ions reside in one-
eighth of the tetrahedral holes and the B ions inhabit half the octahedral holes; this
structure is commonly denoted A[B2]O4, where the atom type in the square bracket
represents that occupying the octahedral sites.

A[B2]O4 A(II) and B(III)

𝟏 𝟏
( )th of Td sites ( )th of Oh sites
𝟖 𝟐

In the inverse spinel structure, the cation distribution is B[AB]O4, with the more
abundant B-type cation distributed over both coordination geometries.
B[AB]O4 A(II) and B(III)
𝟏 𝟏
( )th of Td sites ( )th of Oh sites
𝟖 𝟐
 Spinels
The occupation factor, λ, of a spinel is the fraction of B atoms in the tetrahedral sites: λ = 0 for a normal
spinel and λ = ½ for an inverse spinel, B[AB]O4; intermediate λ values indicate a level of disorder in the
distribution

▪ Determination of spinels vs Inverse Spinels by CFSE

Normal Spinels Inverse Spinels A(II) and B(III)

A[B2]O4 B[AB]O4
𝟏 𝟏
( )th of Td sites ( )th of Oh sites 𝟏 𝟏
𝟖 𝟐 ( )th of Td sites ( )th of Oh sites
𝟖 𝟐
▪ CFSE of B(III) in Oh site > CFSE of B(III) in Td site ▪ CFSE of B(III) in Oh = 0 & CFSE of A(II) in Oh site >
or, when CFSE of A (II) and B(III) = 0 CFSE of A(II) in Td site

Ions d-electronic CFSE

MgAl2O4 configuration
Mg2+ d0 0 (Td sites)
Normal Spinels
Al3+ d0 0 (Oh sites)
 Spinels
Fe3O4 = Fe(II)Fe2(III)O4 Ions d-electronic CFSE
configuration
{Fe : 3d64s2} Fe2+ d6 Max in Oh sites
Fe3+ d5 0 (Oh /Tdsites)

CFSE of d6 ions in Td = CFSE of d6 ions in Oh =

d6 in Td field: e3t23 d6 in Oh field: t2g4eg2
CFSE = {3× −𝟎. 𝟔 + 𝟑 × +𝟎. 𝟒 }∆𝒕 CFSE = {4× −𝟎. 𝟒 + 𝟐 × +𝟎. 𝟔 }∆𝟎
𝟒 𝟏.𝟔
= -0.4 ∆𝒕 = (-0.4 × ) ∆𝟎 = - ∆𝟎 = -0.4 ∆𝟎
𝟗 𝟗
= -0.178 ∆𝟎

CFSE of Fe2+ (d6) ion in Oh > CFSE of Fe2+ (d6) ion in Td

⇒ Fe2+ (d6) ion will goes to Oh sites to maximize its CFSE
⇒ half- of the d5 (Fe3+) ions will goes to Td sites.
⇒ Then the formulae is: Fe3+[Fe3+Fe2+]O4 of B[AB]O4⇒ Inverse spinels
 Spinels
Mn3O4 = Mn(II)Mn2(III)O4 Ions d-electronic CFSE
configuration
{Mn : 3d54s2} Mn2+ d5 0 (Oh /Td sites)
Mn3+ d4 Max in Oh sites

CFSE of d4 ions in Td = CFSE of d4 ions in Oh =

d6 in Td field: e2t22 d6 in Td field: t2g3eg1
CFSE = {2× −𝟎. 𝟔 + 𝟐 × +𝟎. 𝟒 }∆𝑡 CFSE = {3× −𝟎. 𝟒 + 𝟏 × +𝟎. 𝟔 }∆0
𝟒 𝟏.𝟔
= -0.4 ∆𝑡 = (-0.4 × ) ∆0 = - ∆0 = -0.6 ∆0
𝟗 𝟗
= - 0.178 ∆0

CFSE of Mn3+(d4) ion in Oh > CFSE of Mn3+ (d4) ion in Td

⇒ Mn3+(d4) ion will goes to Oh sites to maximize its CFSE
⇒ Mn2+(d5) ion will goes to Td sites.
⇒ Then the formulae is: Mn2+[(Mn3+)2]O4 of A[B2]O4⇒ Normal spinels
 Spinels
NiFe2O4 = Ni(II)Fe2(III)O4 Ions d-electronic CFSE
configuration
{Fe : 3d64s2 Ni : 3d84s2}
Ni2+ d8 Max in Oh sites
Fe3+ d5 0 (Oh /Td sites)

CFSE of d8 ions in Td = CFSE of d8 ions in Oh =

d8 in Td field: e4t24 d8 in Oh field: t2g6eg2
CFSE = {4× −𝟎. 𝟔 + 𝟒 × +𝟎. 𝟒 }∆𝒕 CFSE = {6× −𝟎. 𝟒 + 𝟐 × +𝟎. 𝟔 }∆𝟎
𝟒 𝟑.𝟐
= -0.8 ∆𝒕 = (-0.8 × ) ∆𝟎 = - ∆𝟎 = -1.2 ∆𝟎
𝟗 𝟗
= -0.36 ∆𝟎

CFSE of Ni2+(d8) ion in Oh > CFSE of Ni2+(d8) ion in Td

⇒ Ni2+(d8) ion will goes to Oh sites to maximize its CFSE
⇒ Fe2+(d5) ion will goes to Td sites.
⇒ Then the formulae is: Fe3+[Fe3+Ni2+]O4 of B[AB]O4⇒ Inverse spinels
 Spinels
The inverse spinels of formula AFe2O4 are sometimes classified as ferrites

Occupation factor, λ, in some spinels.

 Spinels
Special case of Co3O4 Co3O4 = Co(II)Co2(III)O4
• O2- will behave as typical SFL ligand {Co : 3d74s2}
• So Co2+/Co3+ will exhibit low spin complex Ions d-electronic CFSE
configuration
Co2+ d7 Max in Oh sites
CFSE of d7 ions in Td (LSC)= Co3+ d6 Max in Oh sites
d8 in Td field: e4t23 CFSE of d6 ions in Td (LSC)=
CFSE = {4× −𝟎. 𝟔 + 𝟑 × +𝟎. 𝟒 }∆𝒕 d8 in Td field: e4t22
𝟒 𝟒.𝟖
= -1.2 ∆𝒕 = (-1.2 × ) ∆𝟎 = - ∆𝟎 CFSE = {4× −𝟎. 𝟔 + 𝟐 × +𝟎. 𝟒 }∆𝒕
𝟗 𝟗 𝟒 𝟔.𝟒
= -0.53 ∆𝟎 = -1.6 ∆𝒕 = (-1.6 × ) ∆𝟎 = - ∆𝟎 = -0.72 ∆𝟎
𝟗 𝟗

CFSE of d7 ions in Oh (LSC)= CFSE of d6 ions in Oh (LSC)=

d8 in Oh field: t2g6eg1 d8 in Oh field: t2g6eg0
CFSE = {6× −𝟎. 𝟒 + 𝟏 × +𝟎. 𝟔 }∆𝟎 CFSE = {6× −𝟎. 𝟒 + 𝟎 × +𝟎. 𝟔 }∆𝟎
= -1.8 ∆𝟎 = -2.4 ∆𝟎
Preference is given for trivalent Co3+ cation, hence Co3+ goes to Oh site and structure is normal Spinel.
 Magnetic properties of coordination complex

The theoretical paramagnetic moment for such a complex is given by

Where J is the total angular momentum quantum number and g is the L and splitting factor for the electron, defined as

The value of J depends on the total orbital angular momentum quantum number L and the total spin angular momentum
quantum number S.
 Magnetic properties of coordination complexes
For complexes in which spin-orbit coupling is non-existent or negligible but spin and orbital contributions
are both significant, the predicted expression for µ is

When the orbital contribution is minimal and could be ignored. Hence, L = 0 and in this condition, the
previous equation reduces to

µ= [4S(S + 1)]½ = 2[S(S + 1)]½ BM

This is known as the spin-only formula for magnetic moment.

Since, S = n/2, the expression may be further simplified to

𝝁𝒔 = 𝒏 𝒏 + 𝟐 ; n= no. of unpaired electron

𝝁𝒔 = 𝟎; 𝑫𝒊𝒂𝒎𝒂𝒈𝒏𝒆𝒕𝒊𝒄,
𝝁𝒔 ≠ 𝟎; 𝑷𝒂𝒓𝒂𝒎𝒂𝒈𝒏𝒆𝒕𝒊𝒄
 Magnetic properties of coordination complex
1. Co3+ Oh complex with strong field ligand 2. Co3+ Oh complex with Weak field ligand
{Co : 3d74s2} Co3+ : 3d6
Co3+ : 3d6 Co3+ Oh(HSC) : t2g4eg2
Co3+ Oh(LSC) : t2g6eg0
eg
eg

t2g
t2g

n=4
𝝁𝒔 = 𝒏 𝒏 + 𝟐 ; n= no. of unpaired electron 𝝁𝒔 = 𝒏 𝒏 + 𝟐 BM
n=0 ⇒ 𝝁𝒔 = 𝟒 𝟒 + 𝟐 BM
𝝁𝒔 = 0 ⇒ 𝝁𝒔 = 𝟐𝟒 BM = 4.9 BM

Diamagnetic complex Paramagnetic complex

 Magnetic properties of coordination complex
3. Co2+ Td complex with strong/weak field ligand 4. Co2+ Square planner (SP) complex with
Co2+ : 3d7 strong/weak field ligand
Co2+ Td: e4t23 Co2+ : 3d7
Co2+ SP: (𝒅𝒚𝒛 ≈ 𝒅𝒛𝒙 )4 (𝒅𝒛𝟐 )2(𝒅𝒙𝒚 )1
t2 𝒅𝒙𝟐 −𝒚𝟐

eg
𝒅𝒙𝒚
n=3
𝝁𝒔 = 𝒏 𝒏 + 𝟐 BM
𝒅 𝒛𝟐
⇒ 𝝁𝒔 = 𝟑 𝟑 + 𝟐 BM t2g
⇒ 𝝁𝒔 = 𝟏𝟓 BM = 3.87 BM n=1
𝝁𝒔 = 𝒏 𝒏 + 𝟐 BM 𝒅𝒚𝒛 , 𝒅𝒛𝒙
Paramagnetic complex ⇒ 𝝁𝒔 = 𝟏 𝟏 + 𝟐 BM
⇒ 𝝁𝒔 = 𝟑 BM = 1.732 BM

Paramagnetic complex
 Electronic Structures of Metal Complexes
Color: observed color is complimentary to what was absorbed.

Colour of light Approx. 𝝀 Colour of light

absorbed ranges/nm transmitted
Red 700-620 Green
Orange 620-580 Blue
Yellow 580-560 Violet
Green 560-490 Red
Blue 490-430 Orange
Violet 430-380 Yellow
 Electronic Structures of Metal Complexes
Energy of absorption
𝒉𝒄
𝑬=
𝝀
• If less ∆E ⇒ 𝒂𝒃𝒔𝒐𝒓𝒃 𝒍𝒊𝒈𝒉𝒕 𝒐𝒇 high 𝝀
𝑹𝒆𝒅 𝒓𝒆𝒈𝒊𝒐𝒏 𝒐𝒇 𝒗𝒊𝒔𝒊𝒃𝒍𝒆 𝒔𝒑𝒆𝒄𝒕𝒓𝒂
eg
Energy

• If high ∆E ⇒ 𝒂𝒃𝒔𝒐𝒓𝒃 𝒍𝒊𝒈𝒉𝒕 𝒐𝒇 less 𝝀

𝑩𝒍𝒖𝒆 𝒓𝒆𝒈𝒊𝒐𝒏 𝒐𝒇 𝒗𝒊𝒔𝒊𝒃𝒍𝒆 𝒔𝒑𝒆𝒄𝒕𝒓𝒂
t2g
[CrF6]3-
[Cr(H2O)6]3+
Green
Violet [Cr(CN)6]3-

Yellow

Absorbed
light
Red Yellow Violet
 Electronic spectra of TiCl3

➢ We observe the appearance of a shoulder in the case of [Ti(H2O)6]3+.

➢ Perfectly octahedral [Ti(H2O)6]3+ should give only one d-d Transition.
➢ However, distortion occurs to eliminate the degeneracy of the system.
➢ If a complex distorts from regular octahedral geometry, the t2g and eg levels are split,
the consequence of which is the appearance of a shoulder as shown in the figure right.
 Electronic transitions
Lambert – Beer’s law
Lambert's law stated that absorbance of a material sample is directly proportional to its thickness (path length).
Beer's law stated that absorbance is proportional to the concentrations of the species in the material sample.

if 𝜺 𝒐𝒇 𝒄𝒐𝒎𝒑𝒐𝒖𝒏𝒅 𝒊𝒔 𝒉𝒊𝒈𝒉
⇒ it’s absorptivity is high
⇒ compound will be intense in colour
 Selection rules for electronic transitions
To explain the absorption spectra of coordination complexes, it is necessary to know the selection
rules that govern electronic transitions.
Any transition in violation of selection rule is said to be ‘forbidden’,

The Laporte Rule.

In a molecule or ion possessing a centre of symmetry, transitions are not allowed between orbitals of the same
parity. For example d to d.

In other words, there must be change in parity (∆l=±1), i.e. the orbital quantum number should differ by 1.

The forbidden transitions are

s (l=0)→ s (l=0) → ∆l=0,
d (l=2)→ d (l=2) → ∆l=0,
p (l=1)→ f (l=3) → ∆l=±2.

The allowed transitions are

s (l=0)→ p (l=1) → ∆l=±1
p (l=1)→ d (l=2) → ∆l=±1
 Selection rules for electronic transitions
The Laporte Rule.
➢ The geometries affected by this rule include octahedral and square-planar complexes.
➢ The rule is not applicable to tetrahedral complexes as it does not contain a center of
symmetry.
 Selection rules for electronic transitions
➢ The key element here is that there are mechanisms by which selection rules can be relaxed so that
transitions can occur, even if only at low intensities.
➢ Unsymmetrical vibrations of an octahedral complex can transiently destroy its center of symmetry and
allow transitions that would otherwise be Laporte forbidden.
➢ In cases where the rule applies, the colors of the complexes are usually relatively pale.
 Selection rules for electronic transitions
Question:
Explain:[Cu(H2O)6]2+which is a rather pale blue color vs [Cu(NH3)4]2+which is an intense dark blue.

Cu : 3d104s1
Cu2+: 3d94s0 4s 4p 4d
Possible transition
[Cu(H2O)6]2+ ×× ×× ×× ×× ×× ×× d (l=2)→ d (l=2) → ∆l=0
Octahedral Laporte forbidden
3d
complex
sp3d2 Intensity of colour will be less
4s 4p 4d

[Cu(NH3)4]2+ ×× ×× ×× ×× Possible transition

Square Planner p (l=1)→ d (l=2) → ∆l=±1
3d
complex Laporte allowed
dsp2 Intensity of colour will be high
 Selection rules for electronic transitions
The Laporte Rule.
Spin Allowed - Spin Forbidden
“Any transition for which ∆S≠0 is strongly forbidden; that is, in order to be allowed, a transition must involve
no change in spin state”

Consider the case of the high spin d5complex [Mn(H2O)6]2+.

Electronic transition is not only Laporte forbidden but also spin forbidden. Absorptions that are doubly forbidden
transitions are extremely weak. Therefore, dilute solutions of Mn(II) are colorless.
 Charge-Transfer (CT) Bands
“ Similar to d-d transitions, charge-transfer (CT) transitions also involve the metal d-orbitals. CT bands are
observed if the energies of empty and filled ligand- and metal-centered orbitals are similar.”

i) Ligand to-Metal charge transfer (LMCT) like in MnO4-, CrO42- etc. For MnO4-, the d-electron count
on Mn(VII) is d0. The origin of the color in this species is not due to d-d transition, rather, charge transfer
from O2- to Mn(VII), described as LMCT band.

ii) Metal-to Ligand charge transfer (MLCT) like in [Fe(bpy)3]2+: In this complex the charge transfer
occurs from Fe(II) to the empty π* orbitals of bpy ligand.

****************************