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Advanced Inorganic
Chemistry
ADVANCED INORGANIC CHEMISTRY
UV
visible
infrared
3A
3A
2g
→1Eg
[Ni(NH3)6]2+
υ, cm-1
2g
→3T2g
?
~10-18 J
• Electronic transitions
• UV and visible wavelengths
• Molecular vibrations
• Thermal infrared wavelengths
Increasing energy
• Molecular rotations
• Microwave and far-IR wavelengths
~10-23 J
• Each of these processes is quantized
• Translational kinetic energy of molecules is unquantized
ADVANCED INORGANIC CHEMISTRY
MOLECULAR ABSORPTION PROCESSES
Electronic
XPS UPS
UV-visible
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ADVANCED INORGANIC CHEMISTRY
‫ترم طیفی‬
ELECTRONIC (UV-VISIBLE) SPECTROSCOPY
c=n.l
With energy of photons
E=h.n
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ADVANCED INORGANIC CHEMISTRY
‫ترم طیفی‬
ELECTRONIC (UV-VISIBLE) SPECTROSCOPY
(2) charge transfer
metal-ligand
(MLCT)
ligand-metal
(LMCT)
ADVANCED INORGANIC CHEMISTRY
(1) metal-metal (d-d) transition
‫ترم طیفی‬
UV-visible spectroscopy
ligand p*
metal d s*
metal d n
ligand p
n
(3) ligand-centered transition
s
s s*, n s*, n p*, and p p*
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ADVANCED INORGANIC CHEMISTRY
‫ترم طیفی‬
UV-visible spectroscopy
(1) metal-metal (d-d) transition
(2) charge transfer
metal-ligand
(MLCT)
ligand-metal
(LMCT)
(3) ligand-centered transition
s s*, n s*, n p*, and p p*
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ADVANCED INORGANIC CHEMISTRY
Ferdowsi University of Mashhad
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single bonds → sigma (s) orbitals → s electrons
double bond → a sigma (s) orbital and a pi (p) molecular orbital
Pi orbitals are formed by the parallel overlap of atomic p orbitals
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ADVANCED INORGANIC CHEMISTRY
There are three types of electronic transitions:
- p, s, and n electrons
- d and f electrons
- charge transfer electrons
Selection Rules
1. Spin selection rule: DS = 0
only one electron is involved in any transition
allowed transitions: singlet  singlet or triplet 
triplet
forbidden transitions:
singlet  triplet or
triplet  singlet
Changes in spin multiplicity are forbidden
• Spin-forbidden transitions
– Transitions involving a change in the spin state of the
molecule are forbidden
– Strongly obeyed
– Relaxed by effects that make spin a poor quantum
number (heavy atoms)
Selection rules
2.
Laporte selection rule (or parity rule): there must be a change in the
parity (symmetry) of the complex
DL = ±1
Electric dipole transition can occur only between states of opposite parity.
Laporte-allowed transitions:
gu
or u  g
Laporte-forbidden transitions:
g  g or u  u
g stands for gerade – compound with a center of symmetry
u stands for ungerade – compound without a center of symmetry
Selection rules can be relaxed due to:
vibronic coupling (interaction between electron and vibrational modes)
spin-orbit coupling
geometry relaxation during transition
• Symmetry-forbidden transitions
– Transitions between states of the same parity are
forbidden
– Particularly important for centro-symmetric molecules
(ethene)
– Relaxed by coupling of electronic transitions to
vibrational transitions (vibronic coupling)
electronic transition
Laporte allowed (charge transfer)
Laporte forbidden (d-d transition)
spin allowed; noncentrosymmetiric
spin allowed; centrosymmetric
spin forbidden
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e
10000
(1000—50000)
100—200
(200—250)
5—100
(20—100)
0.01—1
(< 1)
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ADVANCED INORGANIC CHEMISTRY
‫ترم طیفی‬
selection rules
The Selection rules for electronic transitions
Charge-transfer band – Laporte and spin allowed – very intense
3A
a
2g
→1Eg
Laporte and spin forbidden – very weak
a, b, and c, Laporte
forbidden, spin
allowed, intermediate intensity
b
[Ni(H2O)6]2+
3A
c
2g
→3T2g
ADVANCED INORGANIC CHEMISTRY
ADVANCED INORGANIC CHEMISTRY
‫ترم طیفی‬
[CoCl4]2-
[Co(H2O)6]2+
[Mn(H2O)6]2+
Ferdowsi University of Mashhad
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d-d transition
crystal field splitting
5d > 4d > 3d
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ADVANCED INORGANIC CHEMISTRY
Do size and charge of the metal ion and ligands
4d metal ~50% larger than 3d metal
5d metal ~25% larger than 4d metal
d-d transition
crystal field splitting
ADVANCED INORGANIC CHEMISTRY
crystal field stabilization energy (CFSE)
spin-pairing energy
high-spin/low spin configuration d4 ~ d7
d4
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tetrahedron
octahedron
elongated
octahedron
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square
planar
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ADVANCED INORGANIC CHEMISTRY
Dt = 4/9 Do
‫ترم طیفی‬
Tetrahedral
ADVANCED INORGANIC CHEMISTRY
‫ترم طیفی‬
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ADVANCED INORGANIC CHEMISTRY
‫ترم طیفی‬
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Ferdowsi University of Mashhad
Crystal Field Splitting Energy
Forming Complex
ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory
 An energy diagram of the orbitals shows all five d orbitals
are higher in energy in the forming complex than in the free
metal ion, because of the repulsions from the approaching
ligands
Ligand field theory combines an electrostatic
model of metal-ligand interactions (crystal field
theory) and a covalent model (molecular orbital
theory).
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OH
TD
Octahedral 3d Complexes
Δo ≈ P (pairing energy)
Both low-spin (Δo ≤ P) and
high-spin (P ≥ Δo )
complexes are found
Tetrahedral Complexes
ΔTd = 4/9 Δo
hence P >> ΔTd and tetrahedral
complexes are always high spin
ELECTRONIC STRUCTURE OF HIGH-SPIN AND LOW-SPIN OH COMPLEXES
NOTE:
SOME FACTORS INFLUENCING THE MAGNITUDE OF Δ-SPLITTING
Oxidation State
Δo (M3+) > Δo(M2+)
e.g. Δo for Fe(III) > Fe(II).
The higher oxidation state is likely to be low-spin
5d > 4d >3d
e.g. Os(II) > Ru(II) > Fe(II)
All 5d and 4d complexes are low-spin.
*Crystal Field Splitting Energy - The d orbital energies are
“split” with the two dx2-y2 and dz2 orbitals (eg orbital set)
higher in energy than the dxy, dxz, and dyz orbitals (t2g
orbital set)
*The energies of the d orbitals in different environments
determines the magnetic and electronic spectral properties of
transition metal complexes.
ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory
*Strong-field ligands, such as CN- lead to larger splitting
energy
*Weak-field ligands such as H2O lead to smaller splitting
energy
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
Explaining the Colors of Transition Metals

Diversity in colors is determined by the energy
difference (D) between the t2g and eg orbital sets in
complex ions

When the ions absorbs light in the visible range,
electrons move from the lower energy t2g level to the
higher eg level, i.e., they are “excited” and jump to a
higher energy level
ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory
D E electron = Ephoton = hv = hc/l

11/21/2012
The substance has a “color” because only certain
wavelengths of the incoming white light are absorbed
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ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory
 Example – Consider the [Ti(H2O)6]3+ ion – Purple in
aqueous solution
 Hydrated Ti3+ is a d1 ion, with the d electron in one of the
three lower energy t2g orbitals
 The energy difference (DA) between the t2g and eg orbitals
corresponds to the energy of photons spanning the green
and yellow range
 These colors are absorbed and the electron jumps to one of
the eg orbitals
 Red, blue, and violet light are transmitted as purple
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
For a given “ligand”, the color depends on the oxidation
state of the metal ion – the number of “d” orbital electrons
available
A solution of [V(H2O)6]2+ ion is violet
A solution of [V(H2O)6]3+ ion is yellow

For a given “metal”, the color depends on the ligand
[Cr(NH3)6]3+ (yellow-orange)
ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory
[Cr(NH3)5]2+ (Purple)
Even a single ligand is enough to change the color
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ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory
 Spectrochemical Series
 The Spectrochemical Series is a ranking of ligands with
regard to their ability to split d-orbital energies
 For a given ligand, the color depends on the oxidation
state of the metal ion
 For a given metal ion, the color depends on the ligand
 As the crystal field strength of the ligand increases, the
splitting energy (D) increases (shorter wavelengths of
light must be absorbed to excite the electrons
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MAGNETIC PROPERTIES OF TRANSITION METAL COMPLEXES



The splitting of energy levels influence magnetic
properties
Affects the number of unpaired electrons in the metal ion
“d” orbitals
According to Hund’s rules, electrons occupy orbitals one at
a time as long as orbitals of “equal energy” are available
When “all” lower energy orbitals are “half-filled (all +½
spin state)”, the next electron can
 Enter a half-filled orbital and pair up (with a –½ spin
state electron) by overcoming a repulsive pairing energy
(Epairing)
or
 Enter an empty, higher energy orbital by overcoming the
crystal field splitting energy (D)
 The relative sizes of Epairing and (D) determine the
occupancy of the d orbitals
ADVANCED INORGANIC CHEMISTRY

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MAGNETIC PROPERTIES OF TRANSITION METAL COMPLEXES



ADVANCED INORGANIC CHEMISTRY

The occupancy of “d” orbitals, in turn, determines the
number of unpaired electrons, thus, the paramagnetic
behavior of the ion
Ex. Mn2+ ion ([Ar] 3d5) has 5 unpaired electrons in 3d
orbitals of equal energy
In an octahedral field of ligands, the orbital energies split
The orbital occupancy is affected in two ways:
 Weak-Field ligands (low D) and High-Spin complexes
 Strong-Field ligands (high D) and Low-Spin complexes
(from spectrochemical series)
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
Explanation of Magnetic Properties

Weak-Field ligands and High-Spin complexes

Ex.

A weak-field ligand, such as H2O, has a “small” crystal
field splitting energy (D)

It takes less energy for “d” electrons to move to
the “eg” set (remaining unpaired) rather than
pairing up in the “t2g” set with its higher
repulsive pairing energy (Epairing)

Thus, the number of unpaired electrons in a
weak-field ligand complex is the same as in
the free ion

Weak-Field Ligands create high-spin complexes,
those with a maximum of unpaired electrons

Generally Paramagnetic
[Mn(H2O)6]2+
Mn2+ ([Ar] 3d5)
ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory
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ADVANCED INORGANIC CHEMISTRY
TRANS
ITION
ELEME
NTS &
THEIR
COOR
DINATI
ON
COMP
OUNDS
Crystal Field Theory
 Explanation of Magnetic Properties
 Strong-Field Ligands and Low-Spin Complexes
 Ex. [Mn(CN)6]4 Strong-Field Ligands, such CN-, cause large crystal
field splitting of the d-orbital energies, i.e., higher
(D)
 (D) is larger than (Epairing)
 Thus, it takes less energy to pair up in the “t2g“ set
than would be required to move up to the “eg” set
 The number of unpaired electrons in a
Strong-Field Ligand complex is less than
in the free ion
 Strong-Field ligands create low-spin complexes,
i.e., those with fewer unpaired electrons
 Generally Diamagnetic
Fewer
unpaired electrons
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Crystal Field Theory

Explaining Magnetic Properties

Orbital diagrams for the d1 through d9 ions in octahedral
complexes show that both high-spin and low-spin
options are possible only for:
d4
d5
d6
d7
ions

With three “lower” energy t2g orbitals available, the d1,
d2, d3 ions always form high-spin (unpaired) complexes
because there is no need to pair up

Similarly, d8 & d9 ions always form high-spin
complexes because the 3 orbital t2g set is filled with 6
electrons (3 pairs)
The two t2g orbitals must have either two d8 or one d9
unpaired electron
11/21/2012
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Explaining Magnetic Properties
high spin:
weak-field
ligand
11/21/2012
low spin:
strong-field
ligand

high spin:
weak-field
ligand
low spin:
strong-field
ligand
ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory
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Magnetic moments of high-spin and low-spin states d4-d7
d4
d5
d6
d7
High
Spin
P > D
n=4
s = 4.90
n=5
s = 5.92
n=4
s = 4.90 *
n=3
s = 3.87 *
Low
Spin
D > P
n=2
s = 2.83 *
n=1
s = 1.73 *
n=0
s =0
n=1
s = 1.73
* Some additional orbital contribution to magnetic moment expected
Account for the magnetic moments of the
following complexes
[V(H2O)6]Cl3
 = 3.10
[Co(NH3)6]Br2
 = 4.55
K4[Fe(CN)6]
=0
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PRACTICE
PROBLEM
ADVANCED
INORGANIC CHEMISTRY
Iron(II) forms an essential complex in hemoglobin
For each of the two octahedral complex ions
[Fe(H2O)6]2+
[Fe(CN)6]4Draw an orbital splitting diagram, predict the number of
unpaired electrons, and identify the ion as low-spin or high
spin
Ans:
Fe2+ has the [Ar] 3d6 configuration
H2O produces smaller crystal field splitting (D) than CNThe [Fe(H2O)6]2+ has 4 unpaired electrons (high spin)
The [Fe(CN)6]4- has no unpaired electrons (low spin)

Four electron groups about the central atom

Four ligands around a metal ion also cause d-orbital
splitting, but the magnitude and pattern of the splitting
depend on the whether the ligands are in a “tetrahedral” or
“square planar” arrangement

Tetrahedral – AX4

Octahedral – AX4E2 (2 ligands along “z” axis removed)
Splitting of d-orbital energies by a
tetrahedral field of ligands
Splitting of d-orbital energies by
a square planar field of ligands.
ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory
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ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory (Splitting)
 Tetrahedral Complexes
 Ligands approach corners of a tetrahedron
 None of the five metal ion “d” orbitals is directly in the
path of the approaching ligands
 Minimal repulsions arise if ligands approach the dxy, dyz,
and dyz orbitals closer than if they approach the
dx2-y2 and dz2 orbitals (opposite of octahedral case)
 Thus, the dxy, dyz, and dyz orbitals experience more
electron repulsion and become higher energy
 Splitting energy of d-orbital energies is “less” in a
tetrahedral complex than in an octahedral complex
Dtetrahedral < Doctahedral
 Only high-spin tetrahedral complexes are known because
the magnitude of (D) is small (weak)
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ADVANCED INORGANIC CHEMISTRY
Crystal Field Theory (Splitting)
 Square Planar Complexes
 Consider an Ocatahedral geometry with the two z axis
ligands removed, no z-axis interactions take place
 Thus, the dz2, dxz an dyz orbital energies decrease
 The two ‘d” orbitals in the xy plane (dxy, dx2-y2) interact
most strongly with the approaching ligands
 The (dxy, dx2-y2) orbital has its lobes directly on the x,y
axis and thus has a higher energy than the dxy orbital
 Square Planar complexes are generally strong field – low
spin and generally diamagnetic
 D8 metals ions such as [PdCl4]2- have 4 pairs of the
electrons filling the lowest energy levels and are thus,
“diamagentic”
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