Download Chemistry 3211 – Coordination Chemistry Part 4 Electronic Spectra

Chemistry 3211 – Coordination Chemistry Part 4
Electronic Spectra of Transition Metal Complexes
Introduction to Atomic Term Symbols
Transition metal complexes often have vibrant colours, whereas most (although certainly not all)
organic compounds are nearly colourless. The colour of substances arises from the excitation of
electrons within the molecular orbitals of the substance (their ground state) to orbitals of higher
energy, generating an excited state. This requires the absorption of energy, usually in the form of light.
When white light strikes a substance, only specific wavelengths of light are absorbed since only
specific quanta of energy are required to excite the electron based on the energy difference between the
two states. Since any remaining frequencies of light are not absorbed, the substance reflects them back.
This phenomenon of electronic spectra confounded physicists at the early part of the 20th century and
was a major impetus for the development of the new Quantum Theory. Albert Einstein worked on this
problem by studying and eventually explaining the photoelectric effect, for which he won the Nobel
Prize (no, it was not for his work on relativity, i.e. E = mc2). Therefore, according to the phenomenon
of complementary colours, the colour a substance exhibits informs us of the actual frequencies
absorbed by the excitation of electrons. A substance that appears violet (400 to 450 nm) actually
absorbs yellow light (550 to 580 nm) and a substance that appears red (650 to 700 nm) absorbs green
light (490 to 550 nm).
Also, the relaxation of the electron back to its lower energy ground state can be accompanied by the
emission of photons of wavelength (or frequency) corresponding approximately to the energy
associated with that transition. This radiative decay process is called fluorescence. The particular
energy of the photons emitted may be slightly lower than the energy of the incident photons because
non-radiative decay may also occur, such as energy transfer into the vibrational, rotational and
translational motion of the molecules. Because most of these non-radiative processes are thermal
degradations by transfer of heat energy to the environment (ie. bonds, solvents, other molecules), their
energies lie in the infrared region and can be measured using IR spectroscopic techniques. The
electronic transitions mentioned above are usually higher in energy and can be measured in the
ultraviolet or visible regions of the spectrum (i.e. using UV-vis spectroscopy).
The Beer-Lambert Law
The absorption of light by a substance in a solution is proportional to the concentration of the substance
in a solvent and the path length (the distance the light must travel through the solution). This
relationship is defined by the Beer-Lambert Law where light of intensity I0 at a given wavelength
passes through a solution containing a species that absorbs light, the light emerges with intensity I,
which may be measured by a suitable detector. The overall absorbance, A, is related by the following
equation:
The resulting absorbance is equated to the path length through the solution, l (in cm), the concentration
of the solution, c (in mol L-1), and the molar absorptivity, ε (in L mol-1 cm-1), which is also known as
the molar extinction coefficient. Note that absorbance is dimensionless, hence an absorbance of 1.0
corresponds to 90% absorption at a given wavelength and an absorbance of 2.0 corresponds to 99%
absorption. The molar absorbtivity, ε, is characteristic for a particular species and, in addition to the
wavelength associated with the absorption, can be used to identify the nature of the transition.
1 Defining Electronic Transitions
Absorptions result in the excitation of electrons from lower to higher states of energy. Because these
states are quantized, we observe absorption in bands. These bands can be determined from
interactions or coupling of electrons in terms of their orbital angular momenta (their ml values) and spin
angular momenta (their ms values). This is called Russell-Saunders coupling (LS coupling). In a free
atom (one in the absence of a ligand field) these interactions produce atomic states called microstates,
which are the detailed electronic configuration of the atom or ion.
Consider these quantum numbers and their orbitals:
s orbital
l=0
ml = 0
p orbital
l=1
ml = −1, 0, +1
d orbital
l=2
ml = −2, −1, 0, +1, + 2
For a given electron configuration we can determine the Russell-Saunders coupling by determining the
absolute magnitude of L (the total angular momentum, absolute sum of all possible l values) and S (the
total spin angular momentum, absolute sum of all possible electron spins). For example, if we have two
electrons in a 2p orbital, we would call it a 2p2 electron configuration. This is ok, but it doesn’t tell us
anything about the details. For example, are the two electrons in the same p orbital? Hund’s Rule says
the lowest energy configuration is to put them into different orbitals, but we have three choices (ml =
−1, 0, +1) so is there a preference? Also, Hund only predicts ground states… what about higher
energy excited states? Also, are the electrons paired or unpaired? Again, Hund says they should have
parallel spins, but to have two electrons in different p orbitals with one being spin “up” and the other
being spin “down” is allowed, but it’s just higher in energy, again, an excited state. We need a new
way of writing electron configurations that allows us to not only describe the ground state, but any
possible excited states as well. We can do this by describing the electronic state according to its orbital
and spin degeneracy.
For two electrons in a p orbital, we can say that electron 1 will have quantum numbers l1, s1 and l2, s2.
For the pair of electrons, their L values (L = |l1 + l2|) can be described by 1+1 = 2, 1+0 = 1, 0+0 = 0.
Remember, L (like quantum number l) cannot be negative, so we must use absolute values. The S
values are given by (+½) + (+½) = 1 and (+½) + (-½) = 0. This makes sense because we can have
either two unpaired electrons, or two paired electrons. The value of S cannot be negative because it
only describes the total number of spins, not their direction. So, the total angular momentum, L, and the
total spin angular momentum, S, describes the collections of microstates. There are therefore three
ways of putting an electron into a p orbital (it is triply degenerate), and two ways of aligning their
spins. The quantum numbers L and S describe the collections of microstates. We now need to find the
individual microstates themselves. These are given by different quantum numbers, ML (which is Σml)
and MS (which is Σms). The q. n. MS tells us specifically whether the net electron spin is up or down,
rather than just whether we have paired or unpaired electrons. Remember, S is an absolute value. The
relationship of ML to L is the same as ml to l, namely ML = -L…0…+L. So when L = 2, ML = -2, -1, 0,
+1, +2. An L value of 2 gives us five possible values of ML. Remember that degeneracy (also known at
the orbital multiplicity) is given by the 2L + 1 rule. When L = 2, 2L + 1 = 5, so we say that “the total
orbital angular momentum of L equal to 2 is five-fold degenerate,” or, that it has a “quintet orbital
degeneracy”.
2 With this new notation in hand, we can describe the detailed atomic electron configuration for a 2p2
electron configuration. We must describe the two electrons according to their orbital angular
momentum and their spins in relation to one another. For this, values of L correspond to atomic states
described by the labels S, P, D, F, G and higher, much like we describe s, p, d and f orbitals based on
the values of their quantum number, l. These labels will form part of the atomic term symbol which
will describe the atomic electron configuration.
So, for the following total orbital angular momenta, we apply the following labels:
L=
0
1
2
3
4
etc.
Label =
S
P
D
F
G
etc.
2L + 1 =
1
3
5
7
9
etc.
This means that a P atomic term describes three possible orbital arrangements, while a D atomic term
describes five possible orbital arrangements. This does not imply that the electrons are in a p or a d
orbital! The capitalized S, P, D, etc. notations have nothing to do with the orbital itself. This notation
only describes the number of ways a particular orbital can be filled with a given number of electrons.
The given number of electrons is defined by the atomic spin.
The atomic spin is described in the atomic term symbol as the atom’s spin multiplicity, or 2S + 1.
So, for the following electron arrangements:
# unpaired electrons, n =
0
1
2
3
4
etc.
n×½=S=
0
1/2
1
3/2
2
etc.
2S + 1 =
1
2
3
4
5
etc.
Therefore, if all electrons are paired (no unpaired electrons) we say the atomic term possesses a
singlet spin multiplicity. For two unpaired electrons, the atom or ion exhibits a triplet spin
multiplicity.
So, for a 2p2 electronic configuration, we combine the orbital and spin components to give us a
complete label for this electronic state. We know that the ground state electronic configuration has the
two electrons unpaired with parallel spins (n = 2; S = 1; 2S + 1 = 3), therefore a triplet spin state. Since
they are ideally placed in separate p orbitals, there are three ways that this arrangement can be
achieved:
+1
0
-1
+1
0
-1
+1
0
-1
The orbital arrangement is therefore triply degenerate. If 2L + 1 = 3, then L must be 1, which
corresponds to the total orbital angular momentum label P. Note also, that the absolute sum of the
individual p orbital ml quantum numbers in which we have put electrons is equal to 1. The label of the
electronic state is called the atomic term symbol, which for the above electron configuration is written
3 3
P (read triplet P) where P means a 3-fold orbital degeneracy and 3 means a 3-fold spin degeneracy. In
total, there are 3×3= 9 microstates that are described by this atomic term.
What are the other possible microstates for a 2p2 electron configuration? There are 15 possible ways of
populating the three 2p orbitals without violating the Pauli Exclusion Principle. The possible orbital
and spin orientations are shown below, with their corresponding ML and MS values shown to the right.
Remember that ML is the sum of the individual ml values for populated orbitals and MS is the sum of
the spins taking into account the direction of the net spin as well (+ or -).
ML M S
+1
0
-1
+1
0
-1
+1
0
-1
+1
0
-1
+1
0
-1
1
1
2
0
1
0
1
-1
1
0
ML MS
ML MS
+1
0
-1
+1
0
-1
+1
0
-1
+1
0
-1
+1
0
-1
1
1
0
0
0
0
0
-1
0
0
+1
0
-1
+1
0
-1
+1
0
-1
+1
0
-1
+1
0
-1
-1
1
-2
0
-1
0
-1
-1
-1
0
We can group the resulting microstates in the following table, where each X represents a configuration
that possesses the indicated ML and MS values. When ML equals +2 or -2, this is part of the L = 2 total
orbital angular momentum term, which is labeled a D term. There is only one microstate defined for a
ML state of +2 (we ignore the -2 state since it is just a reflection of the +2 state) and that microstate has
a MS value of 0, therefore it is possesses a singlet spin degeneracy. The atomic term symbol for this
configuration is 1D (singlet D) and describes 5 microstates (a D state is 5-fold degenerate, so 5 × 1 = 5).
ML↓ \ MS →
D
+2
P
+1
S
0
P
-1
D
-2
-1
X
X
X
0
X
XX
XXX
XX
X
+1
X
X
X
The next level is P (ML = +1, therefore L = 1). There are three MS possibilities for that term (one of the
MS = 0 states is part of the D term) so the next atomic term is 3P and describes 9 microstates. Lastly, we
have a S term with one remaining MS = 0 state. This gives a 1S term which describes one microstate.
Therefore, a 2p2 configuration contains 15 microstates that are grouped into the atomic terms 1D, 3P
and 1S.
4 Energies of Atomic Terms
What about their energies? Use Hund’s Rule of Maximum Multiplicities for both spin and orbitals.
These will lead to the ground state atomic terms. The term with the greatest spin multiplicity lies lowest
in energy (it has the least electron-electron repulsion by putting the fewest electrons in the same
orbital), so a triplet term will be lower in energy than a doublet or singlet spin state. The greater the
value of L, the lower the energy, therefore, a D term is lower in energy than a P or a S term. Why?
When L is high, the electrons of the same spin are further apart; therefore there are less coulombic
interactions.
Consider a 3d3 electron configuration. We can obtain the ground state atomic term by applying the
Pauli Principle and Hund’s Rules (i.e. maximize spin multiplicity and maximize orbital multiplicity).
+2
+1
0
-1
-2
The above configuration has 3 upe, hence maximizes spin to give a quartet spin state (S = 3×½ = 3/2,
2S + 1 = 4). The sum of the ml values gives ML of 3 (2+1+0), therefore L = 3 (and F term). The ground
state atomic term is 4F (quartet F). The F term is a seven-fold degenerate orbital state, and combined
with the quartet spin state, this term defines 28 microstates.
The repulsion between electrons means the different term states of an electron configuration have
different energies. Until this point, we have been looking at atomic term symbols, that is, atoms or ions
in the absence of a ligand field. What happens to these atomic terms when the degeneracy of the
orbitals is affected by a ligand field? Consider the simplest electron configuration for a transition metal,
3d1. We have only one electron, so the spin can only be S = 1, so a doublet spin state. In the absence of
a ligand field, all five of the d orbitals are degenerate with ml values of +2, +1, 0, -1, -2. The maximum
ML value is +2, so the L value is 2, a D term, therefore our atomic term is 2D. What if the atomic term
experiences an octahedral ligand field? The orbitals will split. So, just as a set of d-orbitals split into a
t2g set and an eg set, a D state will split in the same manner. It will give a new series of molecular ion
terms different from the atomic ion terms. The molecular ion terms arising from a D atomic term are
labeled T2g and Eg. It is important to note that while electronic states can, by analogy, split to the
corresping orbitals in a ligand field, the spin degeneracy remains unchanged. That is, a doublet spin
state (like in 2D being discussed here) can only generate other doublet spin states, namely 2T2g (doublet
tee two gee) and 2Eg (doublet ee gee). When electrons move from a lower energy state to a higher
energy one, “allowed” transitions can only occur between states of the same spin multiplicity. This is
one of the “selection rules”, which will be discussed in more detail later.
In multielectron ions, the effects of e--e- repulsion are summarized by the Racah Parameters, A, B and
C. These are in fact mathematical representations of Hund’s Rules. The energies of the terms are
therefore related by:
E(1S) = A + 14B + 7C
E(1G) = A + 4B + 2C
E(1D) = A – 3B + 2C
E(3P) = A + 7B
E(3F) = A – 8B
5 A is common to all, therefore if we only want relative energies, we can ignore it. Also, we can ignore C
if we are interested only in triplet terms (anyway, C ≈ 4B). Basically, we are left with the Racah
parameter, B, which in an octahedral complex is related to the ligand field splitting parameter, Δo.
Perhaps more appropriately, it is in fact a mathematical way of weighing out how strong a ligand is in
terms of its affect on the splitting (namely, is it strong or weak field) in combination with certain
electron configurations. We’ll get back to these Racah parameters in a moment.
So, if a D atomic term splits into a T2g and an Eg molecular term, just like a d orbital splits into t2g and
eg sets of orbitals in an octahedral ligand field, how do other terms split? We mentioned before that s
orbitals are of a1g symmetry in an octahedral ligand field; S atomic terms therefore give A1g molecular
terms only. P states give rise to T1g terms in a molecule. Note that the p orbitals are actually t1u
symmetry, i.e. ungerade. The molecular term arising from a P atomic term is T1g (gerade) because the
electrons are actually in d orbitals, which are centrosymmetric in an octahedron (remember, the atomic
term labels have nothing to do with the orbitals they may share a letter with).
What about F states? Firstly, f orbitals are seven-fold degenerate and possess three symmetry types. In
fact, there are two mathematical ways to represent f orbitals, so you may hear them referred to as the
“general set” or the “cubic set” of f orbitals. Anyway, in an octahedral field, f orbitals split into three
symmetry groups, t1u. t2u and a2u. Therefore, an F term will split into the following molecular terms:
T1g. T2g and A2g.
So, in an octahedral complex, the number of states and the molecular terms derived from atomic terms
are given below:
Atomic Terms
S
P
D
F
G
Number of microstates
1
3
5
7
9
Molecular Terms
A1g
T1g
T2g + Eg
T1g + T2g + A2g
A1g + Eg + T1g + T2g
The number of states represented by the individual molecular terms are 1 for an A term (an orbital
singlet), 2 for an E term (an orbital doublet) and 3 for a T term (an orbital triplet). Because the spins of
the molecular terms cannot change from that of the atomic term from which they originate, a 3F term
(3×7 = 21 microstates) becomes 3A2g, 3T1g and 3T2g in an octahedral molecule, giving (3×1)+(3×3)+
(3×3) = 21 microstates.
Of course, as the strength of the ligand field increases, so does the splitting in energy between the
individual molecular terms. These are described using Correlation Diagrams. There are many different
versions of these diagrams, but the most widely used are the Tanabe-Sugano Diagrams, which relate
energy, E, and ΔO with respect to the Racah parameter, B. The ground state term is given as the
horizontal baseline on the x axis. The diagram has two y axes. On the left are the atomic term symbols.
These correspond to a zero crystal field with no ligands, therefore only the metal atom which is
described by the atomic term symbol. As we go left to right along the x axis, ΔO increases (stronger
ligand field) so the atomic terms split into their molecular ion terms, which are given on the right of the
Tanabe-Sugano Diagram. These diagrams are extremely useful for estimating ΔO for a complex from
its spectroscopic properties.
6 Below is a Tanabe-Sugano diagram for a d3 ion:
This axis lists the molecular
term symbols for a d3 ion
when ΔO > 0 (an octahedral
field of ligands is present).
The ground state molecular
term is at the baseline, with
terms representing excited
states going up in relative
energy. Notice that as ΔO
increases, the splitting
between most states
increases as well. Also, note
that molecular terms can
only possess the same spin
multiplicity as the atomic
term from which they
originate. 4F gives 4A2g, 4T2g
and 4T1g (on the diagram the
“g” parity label is removed
for clarity).
This axis lists the
atomic term
symbols for a d3 ion
when ΔO = 0 (no
ligands present). The
ground state atomic
term is at the
baseline, with terms
representing excited
states going up in
relative energy
A Tanabe-Sugano Diagram for a d5 ion:
+2
6
+1
0
-2
-1
5
S atomic state (L = 0) hs d
+2
+1
0
-2
-1
2
I atomic state (L = 6!) ls d5
eg
6
A
t2g
eg
2
t2g
T
Because ions d4 to d7 electron configurations have high or low spin configurations, the molecular ground state depends on the strength of the ligand field. Weak ligand fields (small ΔO) are given to the left of the vertical line while strong ligand fields lie to the right. For hs d5, the atomic term is 6S, which gives a 6A molecular state. Once ΔO becomes large enough, the ls d5 case is favoured, which has a 2T molecular term arising from a 2I atomic state. 7 Spectroscopic Characterization of Electronic Transitions
Electronic spectroscopy (e.g. UV-vis) is very useful for studying the transition of electrons, or more
specifically electronic states, from low energy (usually ground state) configurations to higher energy
excited states. A UV-vis spectrum tells us two main pieces of information: the wavelength (or
frequency) of the transition, which corresponds to the energy of the transition, and the intensity of the
absorption, which basically tells us how frequently this transition is occurring.
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