Transcript M s

MODULE 21(701)
M
DE-ACTIVATION
(RAD/NON-RAD)
ABS
1M*
SECONDARY
SPECIES
LATER
SPECIES
FINAL
PRODUCTS
BIOLOGICAL
EVENTS
The Nature and
Properties of Excited
States
The absorption of a
photon by a molecule
can set in train a series
of processes, chemical
or physical, that
terminate when thermal
equilibrium has been
regained (unless a
subsequent biological
change is possible).
MODULE 21(701)
All processes after the primary one may involve other species
present in the sample
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.
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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?
MODULE 21(701)
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.
Virtually all organic 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 generated by photon absorption is also
of singlet multiplicity, and the nature of such singlet states has
been the focus of our attention to now.
Now it is useful to remind ourselves of the concept of multiplicity.
MODULE 21(701)
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.
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The magnitude of spin angular
momentum vector is
{ s( s  1)}1/ 2
a
and the z component is msħ , and
limited to 2s+1 values according to
ms  s, s  1, s  2..., s
b
For electrons the only value of s
that is allowed is 1/2.
Then the magnitude of the spin
angular momentum is
1
2
{s( s  1)}
1 3 12
1
( x ) 
3
2 2
2
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The spin vector can take up 2s +1
= 2 different orientations
with respect to the z-axis.
a
One corresponds to ms = +1/2;
the other ms = -1/2.
b
These are also referred to as a; b,
or spin-up; spin-down.
Not only are the ms components
opposed but also the vectors are
shown out of phase by 180o.
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In multi-electron systems, the electrons occupy orbitals according
to energy requirements (aufbau principle) and to the Pauli
exclusion principle (same orbital-spins opposed).
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.
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# of electrons
S
1
½
13 111 1 11 3 11 5 3 1
12
 ,,1
,0 
 ,012,1,
, 1,00 , ,
2 222 2 22 2 22 2 2 2
2
1 1 1 1
 ,   1  1, 0
2 2 2 2
3
1
1 3 1
1 , 0   ,
2
2 2 2
4
3 1 1 1
 ,   2,1, 0
2 2 2 2
5
1
1
1 5 3 1
2  ,1  , 0   , ,
2
2
2 2 2 2
MODULE 21(701)
Multi-electron systems are frequently described by their (spin)
multiplicity.
Multiplicity has never been designated with a label.
It takes values of 2S + 1
S
2S + 1
Multiplicity
0
1
singlet
1/2
2
doublet
1
3
triplet
3/2
4
quartet
2
5
quintet
MODULE 21(701)
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.
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Intersystem Crossing: a re-phasing
mechanism
The unique sub-state of the singlet was
represented earlier and in an analogous
way the three sub-states of the triplet
may be represented vectorially.
FIG. 21.2
The center pair of vectors shows
similarity to the pair in earlier Figure,
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 a spins, the Ms =1 level, and
coupling the bottom vector with the next
up yields the Ms = -1 level.
MODULE 21(701)
Thus the conversion of singlet to triplet (or the inverse) requires
only a re-phasing of vectors in the Ms = 0 sub-level.
Nearby inhomogeneous magnetic fields, such as a heavy metal
center, can accomplish this re-phasing  ISC.
In an energy sense, ISC proceeds iso-thermally from v = 0 of S1
(for example) to v’ > 0 of T1.
The excess vibr energy is subsequently lost by IC 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).
ISC applies also to triplet-quintet and doublet-quartet interconversions.
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Delayed Fluorescence
S1
ISC
T1
S0
Photo-excitation to S1 (v’ = n) is rapidly followed by IC to v’ = 0.
Now fluorescence and ISC processes are in competition.
Following ISC there is internal conversion in the T manifold until
T1 (v’ = 0) is reached.
The triplet is “metastable” because the downward path to S0 is
spin forbidden.
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The long-lived T1 state can be thermally repopulated (subject to
the Boltzmann condition) into an upper vibrational level of T1.
Then ISC can regenerate S1, which can then undergo the
fluorescence process.
This triplet state deactivation path is termed "delayed
fluorescence".
Requires singlet-triplet energy gaps that are small, and thus it is
relatively easy to thermally repopulate S1.
Delayed fluorescence has the same spectrum as prompt version
but its lifetime follows that of the triplet state (  M  T ).
This type of unimolecular-delayed fluorescence is "E-type"
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Another delayed fluorescence mechanism is called "P-type" (after
pyrene).
This arises from the bimolecular mutual annihilation of a pair of
triplet states.
M *  3 M *  1M *  M
3
3 *
*
M * 1 M
M* M1M hv
M
3
1
M  M  hvF
F
*
The P-type mechanism requires 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.
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Phosphorescence
S T
T S
The radiative transitions
since total electron spin is not conserved.
1
0
0
1
are forbidden
Values of kPT are very low ( 10-3 s-1 or less).
The triplet quantum yield is a property of the singlet state
TM  kTM / i ki
(in the absence of quenchers)
The phosphorescence quantum efficiency is defined by
qPT  kPT / kT
where kT is the sum of the unimolecular rate constants that are
deactivating the triplet state.
MODULE 21(701)
The phosphorescence quantum yield
The ratio of the number of phosphorescence photons emitted to
the number of molecules excited into S1, or
 PT  qPT
ABSORPTION
FLUORESCENCE
I
nm
TM
PHOSPHORESCENCE
MODULE 21(701)
The quantum efficiency of phosphorescence is the total number of
emitted photons per photon absorbed.


0
0
qPT   P(v )dv   F (v )dv  qFM
Just as we use the S1S0 radiative process (fluorescence) to learn
about the chemistry of S1 states, so we can use the T1S0
radiative transition (phosphorescence) to learn about the
chemistry of T1 states. BUT…
kPT , qPT  kFM , qFM
and phosphorescence is very weak in comparison to fluorescence
and in fluid solutions at room temperature the denominator in
qPT  k PT / (k PT  kGT  ...)
is dominated by kGT and phosphorescence signals are extremely
weak and often blend into the baseline noise, or into the long red
tail of the fluorescence Lorentzian.
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Because of the forbidden nature of the TS transition,
phosphorescence lifetimes are usually much longer than
fluorescence lifetimes, even in fluid media.
Thus time resolved experiments can be used to discriminate
between the short-lived fluorescence and the longer-lived
phosphorescence.
Unfortunately signal-to-noise discrimination is usually poor.
MODULE 21(701)
In low temperature (77 K) glassy matrices, kGT is diminished and
kPT can become more significant.
Such measures lead to measurable phosphorescence signals and
spectra are attainable which are very useful in estimating the
spectroscopic energy of triplet states.
However triplet state studies in immobilized media are not useful
for bimolecular reaction studies since there is no diffusion
We need another approach for detecting and measuring the timedependent concentrations of triplet states.
MODULE 21(701)
Consider the excitation-decay scheme:
M
hn
1M*
VARIOUS PROCESSES
INCLUDING
FLUORESCENCE
3M*
M(S0) + hnP
M(S0) + D
R+D
Bimolecular
processes
MODULE 21(701)
Assume that we excite our sample with a flash of light of zero
width, and [Q] = 0, and that we can measure [T(t)]:
d 3 *
[ M ]  kTM [1 M * ]  kT [3 M * ]
dt
kT  k PT  kGT  k RT  ...
kGT is the first order rate parameter describing all the
intramolecular (except the radiative one) and solvent-induced
processes deactivating T1
kRT represents a putative intramolecular reaction that leaves the
system on a product surface (e.g. a Norrish type II reaction).
The solution of the differential equation is :
kTM [1 M * ]0
[ M ]t 
(exp( kT t )  exp ( k M t ))
k M  kT
3
*
MODULE 21(701)
Singlet states are very short-lived species and in most cases
k M  kT
[3 M * ]t 
kTM 1 *
[ M ]0 exp ( kT t )
kM
Thus, with these limitations, T1 decays exponentially with a rate
constant kT
When Q is added, the term kQM[Q] augments the rate of triplet
decay and the multiplier of time in the exponential becomes:
kobs  kT  kQM [Q ]
where kobs is the observed first order rate constant describing the
triplet decay.
kQM can be obtained by plotting kobs vs. [Q].
MODULE 21(701)
BEWARE!!
Under excitation conditions where high concentrations of 3T* are
generated (> 10-5M, for example) then a bimolecular triplet-triplet
annihilation reaction can also contribute to the triplet decay.
3
M* M
kT
3
M *  3 M *  1M *  M
kTT
This is a kinetically second order process so the observed kinetics
will be mixed second and first order.
This effect is largest when the intrinsic triplet lifetime (T = 1/kT)
is particularly long.
MODULE 21(701)
Triplet-triplet absorption spectrophotometry
T3
S1
T2
T1
S0