Bonding in coordination compounds

• Alfred Werner Nobel prize 1913

• VBT
• Crystal Field Theory (CFT)
• Modified CFT, known as Ligand
Field Theory
• MOT

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How & Why?

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 Valance Bond Model
Ligand = Lewis base
Metal = Lewis acid
s, p and d orbitals give hybrid orbitals with specific geometries
Number and type of M-L hybrid orbitals determines geometry of the complex

Octahedral Complex
e.g. [Cr(NH3)6]3+

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Tetrahedral e.g. [Zn(OH)4]2- Square Planar e.g. [Ni(CN)4]2-

Limitations of VB theory
Can not account for colour of complexes
May predict magnetism wrongly
Can not account for spectrochemical series

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 Crystal Field Model
A purely ionic model for transition metal complexes.
Ligands are considered as point charge.
Predicts the pattern of splitting of d-orbitals.
Used to rationalize spectroscopic and magnetic
properties.

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d-orbitals: look attentively along the axis

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Octahedral Field

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• We assume an octahedral array of negative charges placed
around the metal ion (which is positive).
• The ligand and orbitals lie on the same axes as negative
charges.
– Therefore, there is a large, unfavorable interaction between
ligand (-) and these orbitals.
– These orbitals form the degenerate high energy pair of
energy levels.
• The dxy, dyz, and dxz orbitals bisect the negative charges.
– Therefore, there is a smaller repulsion between ligand and
metal for these orbitals.
– These orbitals form the degenerate low energy set of energy
levels.
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In Octahedral Field
dyz

dz 2

dxz

dx2-
y2 dxy
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In Tetrahedral Field

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 Crystal Field Stabilization Energy (CFSE)
• In Octahedral field, configuration is: t2gx egy
• Net energy of the configuration relative to the
average energy of the orbitals is:
= (-0.4x + 0.6y)∆O

BEYOND d3
• In weak field: ∆O < P, => t2g3eg1
• In strong field ∆O > P, => t2g4
• P - paring energy
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 Magnitude of ∆

Oxidation state of the metal ion

[Ru(H2O)6]2+ 19800 cm-1
[Ru(H2O)6]3+ 28600 cm-1

Nature of the metal ion

3d<4d<5d

Number and geometry of the ligand

∆t< ∆o (∆t = 4/9 ∆o )

Nature of the ligand

I-<S2-<SCN-<Cl-<NO3-<N3-<F-<OH-<C2O42-<H2O<…..CN-<CO
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Ground-state Electronic Configuration,
Magnetic Properties and Colour

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Ground-state Electronic Configuration,
Magnetic Properties and Colour
[Mn(H2O)6]3+
Weak Field Complex
the total spin is 4 × ½ = 2
High Spin Complex

[Mn(CN)6]3-
Strong field Complex
total spin is 2 × ½ = 1
Low Spin Complex
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 Ground-state Electronic Configuration,
Magnetic Properties and Colour

d5 ions, Oh field eg High Spin

+ 0.6 ∆oct
CFSE = 0
- 0.4 ∆oct
t2g 5 u.p.e-

eg Low Spin
+ 0.6 ∆oct CFSE =
5 x - 0.4 ∆oct + 2P
- 0.4 ∆oct = - 2.0 ∆oct + 2P
t2g
1 u.p.e-
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What is the CFSE of [Fe(CN)6]3-?
CN- = s.f.l.
C.N. = 6 ∴ Oh Fe(III) ∴ d5 h.s. l.s.
CN 3-
eg eg
CN
NC
Fe + 0.6 ∆oct
NC CN
- 0.4 ∆oct
CN t2g
t2g

CFSE = 5 x - 0.4 ∆oct + 2P = - 2.0 ∆oct + 2P

If the CFSE of [Co(H2O)6]2+ is -0.8 ∆oct, what spin state is it in?

C.N. = 6 ∴ Oh Co(II) ∴ d7 h.s. l.s.

OH2 2+ eg eg
OH2 + 0.6 ∆oct
H2O
Co
H2O OH2 - 0.4 ∆oct
t2g t2g
OH2

CFSE = (5 x - 0.4 ∆oct) CFSE = (6 x - 0.4 ∆oct)

+ (2 x 0.6 ∆oct) = - 0.8 ∆oct + (0.6 ∆oct) + P= - 1.8 ∆oct +20
P
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Magnetic dipole – magnetic moment µ = i × A [A m2]

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Atomic Motions of Electric Charges

The origins for the magnetic moment of a free atom

Motions of Electric Charges:

1. The spins of the electrons S. Unpaired spins give a paramagnetic

contribution. Paired spins give a diamagnetic contribution.

2. The orbital angular momentum L of the electrons about the

nucleus, degenerate orbitals, paramagnetic contribution.

The change in the orbital moment induced by an applied magnetic

field, a diamagnetic contribution.

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• The Bohr magneton is a fundamental quantity in

the quantum theory of magnetism. Bohr's

explanation of atomic structure was based on the

assumption that the angular momentum of

an electron circulating about the nucleus of an atom is

quantized and equal to nh/2π:, where n

is an integer and h is Planck's constant.

• That is, nh/2π = ma2ω where m is the mass of the

electron. a the radius of its orbit and ω its angular

velocity in radians. 24
• The area of the circular orbit is πa2 and the
current to which the electron circulation JS
equivalent is e x (ω/2π).
• From the theory of a current flowing through a
circular loop of wire, the magnetic moment
associated with the circulating electron is equal
to the product
Current × area = eω/2π × πa2 = ea2ω/2

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From Bohr’s postulate this equal to

ea2/2 = nh/2πma2 = n (he/4πm) = nβ. So β = he/4πm

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• The magnetic moment µ of a complex with total
spin quantum number S is:
• µ = 2{S(S+1)}1/2 µB (µB is the Bohr magneton)
• µB = eh/4πme = 9.274 ×10-24 J T-1
• Since each unpaired electron has a spin ½,
• S = (½)n, where n = no. of unpaired electrons
• µ = {n(n+2)}1/2 µB
• In d4, d5, d6, and d7 octahedral complexes,
magnetic measurements can very easily predict
weak versus strong field.
• Tetrahedral complexes - only high spin
complexes result, for ∆t << ∆O.
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 n = no. of unpaired electrons
µ = {n(n+2)}1/2 µB
Ion n S µ/µB Experimental
Calculate
d
Ti3+ 1 1/2 1.73 1.7 – 1.8
V3+ 2 1 2.83 2.7 – 2.9
Cr3+ 3 3/2 3.87 3.8
Mn3+ 4 2 4.90 4.8 – 4.9
Fe3+ 5 5/2 5.92 5.3

Similar Calculation can be done

for Low-spin Complex
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Gouy balance to
measure the magnetic
susceptibilities

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 The origin of the color of the transition
metal compounds
E2

∆E hν

E1

∆E = E2 – E1 = hν
Ligands influence ∆O, therefore the colour

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The colour can change depending on a number of factors
e.g.
1. Metal charge
2. Ligand strength

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The optical absorption spectrum of [Ti(H2O)6]3+

Assigned transition:
t2g eg
This corresponds to
the energy gap
∆O = 243 kJ mol-1
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• Spectrochemical Series: An order of ligand
field strength based on experiment:
Weak Field I- < Br-< S2-< SCN-< Cl-<
NO3-< F- < C2O42-< H2O< NCS-<
CH3CN< NH3< en < bipy< phen<
NO2-< PPh3< CN-< CO Strong Field

H2N NH2
N
N
Ethylenediamine (en)
1.10 - penanthroline (phen)

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 [CrF6]3- [Cr(H2O)6]3+ [Cr(NH3)6]3+ [Cr(CN)6]3-

As Cr3+ goes from being attached to a weak field

ligand to a strong field ligand, ∆ increases and the
color of the complex changes from green to yellow.
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 The Jahn-Teller effect

Jahn-Teller theorem:
“A degenerate system will undergo distortion to eliminate degeneracy”

Molecules will distort to eliminate the degeneracy

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 Limitations of CFT
Considers Ligand as Point charge/dipole only
Does not take into account overlap between ligand and
metal orbitals

Consequence
e.g. Fails to explain why CO is stronger ligand than CN- in
complexes having metal in low oxidation state

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 Metals in Low Oxidation States

• In low oxidation states, the electron density

on the metal ion is very high.
• To stabilize low oxidation states, we require
ligands, which can simultaneously bind the
metal center and also withdraw electron
density from it.

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Stabilizing Low Oxidation State: CO Can Do the Job

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Stabilizing Low Oxidation State: CO Can Do the Job

Ni(CO)4], [Fe(CO)5], [Cr(CO)6], [Mn2(CO)10],

[Co2(CO)8], Na2[Fe(CO)4], Na[Mn(CO)5]
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 O C M

σ orbital serves as a very weak donor to a metal atom

O C M O C M O C M

CO-M sigma bond M to CO pi backbonding CO to M pi bonding

(rare) 45
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