Photochemistry
Lecture 3
Kinetics of electronically
excited states
Jablonski diagram
S0
S1
T1
Main non-reactive decay routes
following S1 excitation

Non-radiative




IC to S0 followed by vibrational relaxation.
ISC to T1 then ISC’’ to S0 with vibrational
relaxation after each step.
Collisional quenching (before or after ISC)
Radiative



Fluorescence to S0
ISC to T1 then phosphorescence to S0
Delayed fluorescence
Fluorescence and phosphorescence in
solution
Phosphorescence
Weak and slow – spin
forbidden (ms – s)
Competing collisional
processes may eliminate –
unless frozen out e.g., in
glass
Fluorescence
Rapid (10-8s) decay
- spin allowed
Mirror image of absorption and
fluorescence
absorption
Fluorescence from v=0
following vibrational
relaxation
Mirror image depends on
Molecule being fairly rigid (e.g., as in
polyaromatic systems)
 No dissociation or proton donation in
excited state


Good mirror image: anthracene,
rhodamine, fluorescein

Poor mirror image: Biphenyl, phenol,
heptane
Solvent relaxation leads to a shift of the 0-0
band
Absorption and fluorescence in organic dyes
Population inversion
between excited
electronic state and
higher vib levels of
ground state.
Fluorescence labelling and single
molecule spectroscopy

Attaching a fluorescent chromophore to
biological molecules etc

Near-field scanning optical microscopy –
optical fibre delivers laser light to spot size
50-100 nm

Maintain sufficient dilution of sample so
that single molecules are illuminated
Looking at single molecules using near
field optical microscopy / fluorescence
Single molecules of pentacene in a pterphenyl crystal
Rate of absorption; Beer Lambert Law
ℓ
dℓ
I0
dI  cId
dI



c
d

I

c = concentration, ℓ = length
It
Intensity decreases as it
passes through cell
It
ln  cl
I0
Beer Lambert Law (cont)
It
ln  cl
I0
or
It
log  cl
I0
(2.3 log x= ln x)
cl
It  I 0  I abs  I 0 exp(cl)  I 010
 is known as the molar (decadic) absorption
coefficient; it is often given units mol-1dm3 cm-1
Nb Intensity has units Js-1m-2 or Wm-2 and is the
light energy per second per unit area
Limit of very dilute concentrations
I 0  I abs  I 0 (1  cl)
 I abs  I 0cl
 I abs  0.434I 0cl
Rate of absorption only proportional
to concentration when above
approximation is valid (cℓ « 1).
Absorption spectrum of chlorophyll in solution
Some values for max /(L




C=C (* )
C=0 (* n)
C6H5- (* )
[Cu(H2O)6]2+
-1
mol
-1
cm )
15000 at 163 nm (strong)
10-20 at 270- 290nm
200
at 255 nm
10
at 810 nm
max

Integrated absorption coefficient
 varies with
wavenumber
A
˜) d˜

(


band
Integrated absorption coefficient proportional to
square of electronic transition moment
A
 fi N A Rif
2
3 0 c
Rif    i d
*
f
But from lecture 1, Einstein coefficient of absorption
 dN i
dt
 N i Bif  ( Eif )  N f B fi  ( Eif )  N f A fi
A fi 
8h 3fi
c
3
B fi
Bif 
Rif
2
6 0  2
Determining spontaneous emission rates

By measuring the area under the
absorption profile, we can determine the
transition probability and hence the rate
coefficients for stimulated
absorption/emission (Bif ), and also for
spontaneous emission (Aif ).
Flash Photolysis

Use a short pulse of light to produce a
large population of S1 state.

Follow decay of S1 after excitation switched
off



Fluorescence in real time
Delayed ‘probe’ pulse to detect ‘product’
absorption (e.g., T1  T2).
Choose light source according to timescale
of process under study




Conventional flashlamp
Q switched laser
Mode locked laser
Colliding pulse mode locked laser
ms - s
ns - s
ps – ns
fs - ps
Modern flash
photolysis
setup
Fluorescence lifetimes


Following pulsed
excitation
fluorescence would
follow first order
decay in absence of
other processes.
kf is equivalent to the
Einstein A coefficient
of spontaneous
emission
Rif    *f d

d [ S1 ]
dt
 k f [S1 ]
typically kf  108 s-1
kf  A 
16 3 3 ( Rif ) 2
3h 0c
3
= frequency of transition
i and f are the initial and
final states
First order decay
d S1 

 k f dt
S1 
[ S1 ]t  [ S1 ]0 exp(k f t )
Define fluorescence lifetime f
as time required, after
switching off excitation
source, for fluorescence to
reduce to 1/e (=0.368) times
original intensity.
1
 f  
kf
0
f
If there are no competing
processes, then the
fluorescence lifetime is equal
to the true radiative lifetime
f
Observed fluorescence lifetime

But if there are
competing processes:
d [ S1 ]

 k f [ S1 ]  kisc [ S1 ]  kic [ S1 ]....
dt
 k '[ S1 ]
S1 t  S1 0 exp(k ' t )
abs
S 0  h I
S1
f
S1 
S 0  h
k
kisc
S1 
T1
S1  S 0
kic
Decay is still first order but as the rate of
fluorescence is proportional to [S1] the
observed fluorescence lifetime is reduced to
1
f 
k f  kisc  kic  ....
Branching ratio and quantum yield
The fraction of molecules undergoing fluorescence
(branching ratio into that decay channel), is equal
to the rate of fluorescence divided by the rate of
all processes.
f 
k f [ S1 ]
(k f  kisc  kic  ...)[S1 ]
In the present case the above quantity is equal
to the quantum yield f – see below.
Quantum Yield

Definition:
rate of specified process

rate of photonabsorption
Fluorescence quantum yields show strong
dependence on type of compound excited
Fluorescence quenching and the Stern
Volmer equation
Continuous illumination
S0  h  S1
Iabs
S1  S0  h
kf[S1]
S1  T1
kisc[S1]
S1  Q  S0  Q
kQ[S1][Q]
Apply SSA
I abs
S1  
k f  kisc  kQ [Q]
Fluorescence quantum yield
f 
k f [ S1 ]
I abs

kf
k f  kisc  kQ [Q]
kQ
kisc
 1  [Q] 
f
kf
kf
1
Can determine ratios of kQ/kf and
kisc/kf from suitable plot.
Chemical actinometer

To determine a fluorescence quantum
yield need an accurate measure of photon
intensity

A chemical actinometer uses a reaction
with known quantum yield, and known
absorption coefficient at a given
wavelength to determine the light
intensity.
Chemical actinometer systems
Fluorescence quantum yield
f 
k f [ S1 ]
I abs

kf
k f  kisc  kQ [Q]
Alternatively; define f0 as the fluorescence
quantum yield in the absence of quencher
f 
0
Thus
kf
k f  kisc
f 0 I f
kQ
Q
 0  1
f
k f  kisc
If

If assume diffusion limited rate constant
for kQ ( 5 x 109 M-1s-1) then can
determine kf + kisc.

Alternatively can recognise 1/(kf+kisc) as
the observed fluorescence lifetime; if this
is known can measure kQ.
The quantum yield represents a
branching ratio
Fraction of molecules initially
excited to S1 that
subsequently fluoresce; for
the scheme on the right
f 
k f S1 
k f S1  kisc S1 

kf
k f  kisc
 k f
Thus the fraction passing on to
T1 state is 1- f
abs
S 0  h I
S1
S1  S 0  h
kf
k isc
S1 
T1
isc '
T1 k
S0
T1  S 0  h '
kp
kp
Fraction of T1 molecules

undergoing phosphorescence k  k
p
isc '
Thus
 p  (1   f )k p '
’ is observed phosphorescence
lifetime