The Electronic Spectra of
Coordination Compounds
Introduction
Many transition metal complexes are
colored. This is due to transitions of electrons
between the molecular orbitals that are formed
largely by the d orbitals on the metal.
Many transitions are in the visible range,
with the color of the complex taking on the
complementary color of the frequency or
frequencies absorbed.
Introduction
General Features
Absorption bands in electronic spectra are
usually broad, and occur much more rapidly
than molecular vibrations. As a result, the
spectra represent a “snapshot” of molecules in
various vibrational and rotational states.
General Features
Extinction coefficients will range from <1
up to 50,000 M-1cm-1 depending upon the type
of electronic transition and whether it is
permitted based on selection rules.
Selection Rules
Electronic transitions obey the following
selection rules:
1. ∆S = 0. Electrons cannot change spin.
2. The Laporte rule states that there must be a
change in parity. Only gu or ug
transitions are allowed. Thus, all dd
transitions are forbidden by this selection rule.
The UV/Vis
spectra of
transition metal
complexes show
the transitions of
the electrons.
Analysis of
these spectra can
be quite complex.
Summary of Observations-First
Row Transition Metal Complexes
(high spin)



d1, d4, d6 and d9 complexes show one
absorption.
d2, d3, d7 and d8 complexes show three
absorptions, with the 3rd peak often obscured.
d5 complexes show very weak, sharp
absorptions.
Note that
even the single
peaks show “side
peaks” or
overlapping bands
of absorption.
Electron Spectra
The UV/Vis spectra are used to determine
the value of ∆o for the complex. The spectra
arise from electronic transitions between the t2g
and eg sets of molecular orbitals. Electronelectron interactions can greatly complicate the
spectra. Only in the case of a single electron is
interpretation of the spectrum straightforward.
Obtaining ∆o
For a d1 configuration, only a single peak is seen. It
results from the electron promotion from the t2g
orbitals to the eg orbitals. The “toothed” appearance of
the peak is due to a Jahn-Teller distortion of the excited
state. The energy of the peak = ∆o.
General
Observations
d1, d4, d6 and d9 usually
have 1 absorption, though
a side “hump” results
from Jahn-Teller
distortions.
General
Observations
d2, d3, d7 and d8
usually have 3
absorptions, one is
often obscured by a
very intense charge
transfer band.
General Observations
d5 complexes consist of very weak, relatively
sharp transitions which are spin-forbidden, and
have a very low intensity.
Electronic Transitions
Absorption of light occurs when electrons
are promoted from lower to higher energy
states. Interactions between electrons causes
more than one peak in the UV/Vis spectra of
these complexes. The electrons are not
independent of each other, and the spin angular
momenta and orbital angular momenta interact.
Electronic Transitions
The interaction of orbital angular momenta
(ml values) and spin angular momenta (ms values)
is called Russel-Saunders or LS coupling.
The lower transition metals (4d and 5d)
undergo further coupling (called j-j coupling or
spin-orbit coupling).
3d Multi-electron Complexes
The interactions produce atomic states called
microstates that are described by a new set of
quantum numbers.
ML = total orbital angular momentum =Σml
MS = total spin angular momentum = Σms
Determining the Energy States of an
Atom
A microstate table that contains all possible
combinations of ml and ms is constructed.
Each microstate represents a possible electron
configuration. Both ground state and excited
states are considered.
Energy States
Microstates would have the same energy
only if repulsion between electrons is negligible.
In an octahedral or tetrahedral complex,
microstates that correspond to different relative
spatial distributions of the electrons will have
different energies. As a result, distinguishable
energy levels, called terms are seen.
Energy States
To obtain all of the terms for a given
electron configuration, a microstate table is
constructed. The table is a grid of all possible
electronic arrangements. It lists all of the
possible values of spin and orbital orientation.
It includes both ground and excited states, and
must obey the Pauli Exclusion Principle.
Constructing a Microstate Table
Consider an atom of carbon. Its highest
occupied orbital has a p2 electron configuration.
Microstates correspond to the various
possible occupation of the px, py and pz orbitals.
Constructing a Microstate Table
ml =
+1
Configurations: ___
___
___
0
___
___
___
-1 microstate:
___ (1+,0+)
___ (0+,-1+)
___ (1+,-1+)
These are examples of some of the ground
state microstates. Others would have the
electrons (arrows) pointing down.
Constructing a Microstate Table
ml =
+1
Configurations: ___
___
___
0
___
___
___
-1 microstate:
___ (1+,1-)
___ (0+,0-)
___ (-1+,-1-)
These are examples of some of the excited
state microstates.
Microstate Table for
2
p
For the carbon atom, ML will range from +2
down to -2, and MS can have values of +1 (both
electrons “pointing up”), 0 (one electron “up”,
one electron “down), or -1 (both electrons
“pointing down”).
Microstate Table for
2
p
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
The table
includes all
possible
microstates.
Constructing a Microstate Table
Once the microstate table is complete, the
microstates are collected or grouped into atomic
(coupled) energy states.
Constructing a Microstate Table
For two electrons,
L = l1+ l2, l1+ l2-1, l1+ l2-2,…│l1- l2│
For a p2 configuration, L = 1+1, 1+1-1, 1-1.
The values of L are: 2, 1 and 0.
L is always positive, and ranges from the
maximum value of Σl.
Constructing a Microstate Table
For two electrons,
S = s1+ s2, s1+ s2-1, s1+ s2-2,…│s1- s2│
For a p2 configuration, S = ½ + ½ , ½ + ½ -1.
The values of S are: 1 and 0.
Atomic Quantum Numbers
Quantum numbers L and S describe
collections of microstates, whereas ML and MS
describe the individual microstates themselves.
Constructing a Microstate Table
The microstate table is a grid that includes all
possible combinations of L, the total angular
momentum quantum number, and S, the total
spin angular momentum quantum number.
For two electrons,
L = l1+ l2, l1+ l2-1, l1+ l2-2,…│l1- l2│
S = s1+ s2, s1+ s2-1, s1+ s2-2,…│s1- s2│
Constructing a Microstate Table
Once the microstate table is complete, all
microstates associated with an energy state with
specific value of L and S are grouped.
It doesn’t matter which specific microstates
are placed in the group. Microstates are grouped
and eliminated until all microstates are
associated with a specific energy state or term.
Term Symbols
Each energy state or term is represented by a
term symbol. The term symbol is a capitol letter
that is related to the value of L.
L=
0
1
2
3
4
Term
Symbol
S
P
D
F
G
Term Symbols
The upper left corner of the term
symbol contains a number called the
multiplicity. The multiplicity is the number of
unpaired electrons +1, or 2S+1.
Microstate Table for
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
2
p
Eliminate
microstates
with
ML=+2-2,
with Ms=0.
Microstate Table for
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
2
p
These
microstates
are associated
with the term
1D.
Microstate Table for
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
2
p
Eliminate
microstates
with
ML=+1-1,
with
Ms=+1-1
Microstate Table for
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
2
p
Eliminate
microstates
with
ML=+1-1,
with
Ms=+1-1
Microstate Table for
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
2
p
These
microstates
are associated
with the term
3P.
Microstate Table for
MS
ML
+1
0
-1
1+1-
+2:
1+0+
1+01-0+
1-0-
0:
-1+1+
-1+10+0-1-1+
-1-1-
-1:
-1+0+
-1+0-1-0+
-1-0-
+1:
-2:
-1+-1-
2
p
One
microstate
remains. It is
associated
with the term
1S.
Term States for
2
p
The term states for a p2 electron
configuration are 1S, 3P, and 1D.
The term symbol with the greatest
multiplicity and highest value of ML will be the
ground state. 3P is the ground state term for
carbon.
Determining the Relative Energy
of Term States
1. For a given electron configuration, the term
with the greatest multiplicity lies lowest in
energy. (This is consistent with Hund’s rule.)
2. For a term of a given multiplicity, the greater
the value of L, the lower the energy.
Determining the Relative Energy
of Term States
For a p2 configuration, the term
states are 3P, 1D and 1S.
The terms for the free atom should
have the following relative energies:
3P< 1D
<1S
Determining the Relative Energy
of Term States
The rules for predicting the ground state
always work, but they may fail in
predicting the order of energies for excited
states.
Energy States for a d2 Configuration
A microstate table for a d2 electron
configuration will contain 45 microstates (ML =
4-4, and MS=1, 0 or -1) associated with the
following terms:
1S, 1D, 1G, 3P, and 3F
Energy States for a d2 Configuration

Problem: Determine the ground state of a free
atom with a d2 electron configuration, and place
the terms in order of increasing energy.
1S, 1D, 1G, 3P,
and 3F
Determining the Ground State Term
We only need to know the ground state term
to interpret the spectra of transition metal
complexes. This can be obtained without
constructing a microstate table.
The ground state will
a) have the maximum multiplicity
b) have the maximum value of ML for the
configuration obtained in part (a).