MODULE 21_03
The Nature and Properties of Excited States
In many cases the absorption of a photon by a molecule sets in train a series of processes,
chemical or physical, that terminate when thermal equilibrium has been regained (unless a
subsequent biological change is possible). The following scheme is a typical summary.
M
ABSORPTION
DE-ACTIVATION
(RADIATIVE/NON-RADIATIVE)
1
M*
SECONDARY SPECIES
LATER SPECIES
FINAL PRODUCTS
BIOLOGICAL EVENTS
All processes after the primary one may involve other species present in the sample and reactions
such as bond breaking, bond formation, atom transfer, energy transfer, electron transfer, proton
transfer, etc may be initiated.
To investigate this plethora of processes the experimental
photoscientist employs a variety of tools and techniques in order to describe, evaluate and
understand the various steps between light absorption and final product formation.
1
Questions that are addressed include:
What is the nature and reactivity of the primary excited states and states derived there from?
What are the final products, what are their yields, and what environmental factors determine
these?
What are the identities of the intermediate species in the sequence and what kinetic and
thermodynamic properties do they possess?
What factors, such as molecular structure influence the reactivity of the intermediates?
Are there any biological consequences?
Up to this point we have been mainly concerned with the absorption of light itself and the nature
and reactivity of the primary electronically excited state generated in the absorption process.
Since virtually all organic molecules and many inorganic molecules and organometallic
complexes exist as singlet (spin-paired) ground states (there are a few notable exceptions, such
as O2, NO, and complexes containing open shell transition metals), the primary excited state is
also of singlet multiplicity, and the nature of such singlet states has been the focus of our
attention to now. At this point it is useful to remind ourselves of the concept of multiplicity.
Electrons, Spin and Multiplicity
The total angular momentum of an electron in an atom/molecule is composed of contributions
from its orbital motion and from its intrinsic angular momentum, conveniently referred to as
spin. The full description of an electronic state requires a quantum number for spin angular
momentum, termed s. The symbol ms represents the quantum number for the projection of the
spin vector on the z-axis.
The
magnitude
{ s(s  1)}1/ 2

of
spin
angular
momentum
vector
is
and the z component, ms , is limited to 2s+1
values according to ms  s, s  1, s  2...,  s .
For electrons the
only value of s that is allowed is 1/2. This corresponds to a
FIG. 21.1
magnitude of the spin angular momentum of

1
2
{s( s  1)}
1 3 12
1
( x ) 
3
2 2
2
The spin vector can take up 2s +1 = 2 different orientations
2
with respect to the z-axis. One corresponds to ms = +1/2; the other ms = -1/2. These orientations
are also referred to as  and  , or  and  . See Figure 21.1 where the  and  spins are
represented. Not only are the ms components opposed but also the vectors are shown out of
phase by 180o.
In multi-electron systems, the electrons place themselves in orbitals according to energy
requirements (aufbau principle) and to the Pauli exclusion principle (same orbital-spins paired).
We define a total spin angular momentum quantum number, S (never negative), which combines
the individual s values through a Clebsch-Gordon series:
S  s1  s2 , s1  s2 1,...s1  s2
For two electrons, s = ½ + ½ = 1, or s = ½ - ½ = 0. For three electrons, we take the values of S
for two electrons and combine them with s = ½ for the additional one, and so on. The results of
this are shown in Table 21.1
# of electrons
S
1
only
2
1 1 1 1
 ,   1  1, 0
2 2 2 2
1
1 3 1
1 , 0   ,
2
2 2 2
3 1 1 1
 ,   2,1, 0
2 2 2 2
1
1
1 5 3 1
2  ,1  , 0   , ,
2
2
2 2 2 2
1
2
3
4
5
Table 21.1
Multi-electron systems are frequently described by their (spin) multiplicity, a property that has
never been designated with a character, and which has a value of 2S + 1. See Table 21.2.
3
S
0
1/2
1
3/2
2
2S + 1
Multiplicity
1
singlet
2
doublet
3
triplet
4
quartet
5
quintet
Table 21.2
Thus, a system in which all the spins are paired except for a
single electron (e.g., a free radical or a Cu2+ ion) has S = 1/2
and is a doublet state. A system in which two electrons are
unpaired has S = 1 and is a triplet state. However, this same
system may have the possibility of the two spins being
paired (if Pauli allows) when S = 0 and it becomes a singlet
state. Most organic molecule ground states have all spins
paired (singlet). Causing one of the spins to invert (in a
different orbital) produces an S = 1 system, i.e., a triplet.
Intersystem Crossing: a re-phasing mechanism
The unique sub-state of the singlet was represented in Figure
21.1 and in an analogous way the three sub-states of the
triplet may be represented vectorially as shown in Figure
21.2. The center pair of vectors shows similarity to the pair
in Figure 21.1, except now the vectors are in phase. This
represents the Ms = 0 level of the triplet state. Coupling the
top vector in the Figure with the next down gives a pair of 
spins, the Ms =1 level of the triplet, and coupling the bottom
vector with the next up yields a pair of  spins-the Ms = -1
level.
From this description, it is clear that conversion of
singlet to triplet (or the inverse) requires only a re-phasing
FIG. 21.2
4
of vectors in the Ms = 0 level of either the singlet or the triplet. The nearby presence of
inhomogeneous magnetic fields, such as a heavy metal center, can accomplish this re-phasing.
This is the process we know as intersystem crossing (ISC).
In an energy sense, ISC proceeds
iso-thermally from v  0 of S1, (for example) to v  0 of T1. The excess vibrational energy is
subsequently lost by internal conversion to T1 (v’ = 0). From there a spin inverting, forbidden
radiative decay (phosphorescence) can occur. However, the non-radiative process is usually
more efficient (in fluid solutions). The term intersystem crossing applies also to triplet-quintet
and doublet-quartet inter-conversions.
Delayed Fluorescence
Refer to the simplified Jablonski diagram in Figure 21.3.
Picture a scheme in which photo-
excitation to S1 (v’= n) is rapidly followed by internal conversion to v’ = 0 from where the
fluorescence and ISC processes are in competition.
Subsequent to ISC there is internal
conversion in the T manifold until T1 (v’ = 0) is reached. The triplet is metastable because the
downward conversion to S0 is spin forbidden
S1
ISC
T1
FIG. 21.3
S0
Under appropriate conditions the long-lived T1 state can find itself thermally repopulated
(subject to the Boltzmann condition) into an upper vibrational level of T1 from which ISC can
regenerate S1, which can then undergo the fluorescence process.
This mechanism of triplet state deactivation is termed "delayed fluorescence". Compounds
exhibiting this phenomenon have singlet-triplet energy gaps that are small, and thus it is
relatively easy to thermally repopulate S1. Delayed fluorescence has the same spectrum as the
prompt version (the transitions are the same), but its lifetime follows that of the triplet state
5
(since  M  T ). The type of unimolecular-delayed fluorescence described above is "E-type"
named after the xanthene dye, eosin, in which it was initially observed. The value of EST in the
xanthenes is in the region of 6 kcal mol-1.
There is another delayed fluorescence mechanism called "P-type" (after pyrene). This arises
from the bimolecular mutual annihilation of a pair of triplet states.
3
M *  3 M *  1M *  M
1
M *  M  hvF
P-type processes require the triplet states to have a lifetime that is long enough for the second
order, bimolecular event between two low concentration species to be able to effectively
compete with the first order decay of the triplet.
Phosphorescence:
The radiative transition, T1  S0 , as the inverse S0  T1 , is forbidden since total electron spin
is not conserved. Thus, phosphorescence has a low probability and values of
3
kPT (radiative rate
1
constant) are very low ( 10 s or less). The triplet quantum yield is a property of the singlet
state
TM  kTM / i ki
(21.1)
(in the absence of quenchers)
The phosphorescence quantum efficiency is defined by
qPT  kPT / kT
(21.2)
where kT is the sum of the unimolecular rate constants that are deactivating the triplet state.
Then the phosphorescence quantum yield is seen to be the ratio of the number of
phosphorescence photons emitted to the number of molecules excited into S1, or
PT  qPT
TM
(21.3)
Schematic spectra are shown in Figure 21.4, where we see the expected red shift due to loss of
electronic excitation as S1 converts to T1. Note that the phosphorescence intensity has been
amplified by many orders of magnitude to compare to the fluorescence intensity.
6
ABSORPTION
FLUORESCENCE
PHOSPHORESCENCE
I
WAVELENGTH
FIG. 21.4
The quantum efficiency of phosphorescence is equal to the total number of emitted photons
under the spectral envelope per photon absorbed.


0
0
qPT   P(v)dv   F (v)dv  qFM
(21.4)
Just as we use the S1->S0 radiative process (fluorescence) to inform about the nature and
chemistry of S1 states, so we ought to be able to use the T1->S0 radiative transition
(phosphorescence) to inform on nature and chemistry of T1 states.
But we know that
kPT , qPT  kFM , qFM and thus phosphorescence signals are very weak in
comparison to fluorescence signals.
denominator in
Thus, in fluid solutions at room temperature the
qPT  kPT / (kPT  kGT  ...)
is
very much dominated by kGT,
and
phosphorescence signals are extremely weak and usually blend into the baseline noise, or into
the long red tail of the fluorescence Lorentzian.
Phosphorescence lifetimes are much longer
than those of fluorescence, even in fluid media, and in principle time domain experiments should
be able to discriminate between the short-lived fluorescence and the longer-lived
phosphorescence. Again, however, the signal-to-noise discrimination is usually insufficient.
In low temperature (77 K) glassy matrices, kGT is diminished and kPT can dominate the
deactivation scheme. Such measures lead to measurable phosphorescence signals and spectra are
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attainable which are very useful in estimating the spectroscopic energy of triplet states.
Unfortunately triplet state studies in immobilized media are not useful for bimolecular reaction
studies since there is no diffusion. Such investigations require another way of probing triplet
concentrations as a function of time. Before examining the instrumentation it will be useful to
explore some kinetic principles. The scheme is as shown:
h
M
1
M*
3
M*
VARIOUS PROCESSES
INCLUDING
FLUORESCENCE
M(S0) + hP
M(S0) + 
R + 
Bimolecular
processes
From the foregoing kinetic scheme and assuming that the excitation flash is of negligibly short
duration compared to the rates of all subsequent processes and [Q] = 0:
with kT  kPT  kGT  kRT
d 3 *
[ M ]  kTM [1 M * ]  kT [3 M * ]
(21.5)
dt
 ... and where kGT is the first order rate parameter describing all the
intramolecular (except the radiative one) and solvent-induced processes contributing to returning
the system to the ground state, and kRT represents a putative intramolecular reaction that leaves
the system on a product surface (eg a Norrish type II reaction).
The solution of the differential equation is as follows:
[3 M * ]t 
kTM [1 M * ]0
(exp(kT t )  exp (kM t ))
kM  kT
Singlet states are very short-lived species and in most cases kM  kT
8
(21.6)
then
[3 M * ]t 
kTM 1 *
[ M ]0 exp ( kT t )
kM
(21.7)
Thus, under the applied conditions, the T1 state decays exponentially with a rate constant kT.
When Q is added, the term kQM[Q] is added and the multiplier of time in the exponential
becomes:
kobs  kT  kQM [Q]
(21.8)
where kobs is the observed first order rate constant governing the triplet decay. Values of kQM can
be obtained by plotting kobs vs. [Q].
In some instances, the T1 time profile departs from exponential behavior. This can arise from the
T-T annihilation process referred to above:
3
M* M
3
M *  3 M *  1M *  M
kT
kTT
then
d 3 *
[ M ]  kT [3 M * ]  kTT [3 M * ]2
dt
(21.9)
Thus, a second order term appears and the T1 decays by mixed first order and second order
3
*
kinetics. This effect only occurs at high [ M ]0 and when
9
 T 1/ kT is large.