universita` degli studi di padova - Dipartimento di Scienze Chimiche

UNIVERSITA’ DEGLI STUDI DI PADOVA
Laurea specialistica in Scienza e Ingegneria dei Materiali
Curriculum Scienza dei Materiali
Chimica Fisica dei Materiali Avanzati
Part 7a – Molecular photophysics and photochemistry
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Spontaneous and stimulated transitions
Stimulated emission: emission which is induced by a resonant
perturbing electromagnetic field
Spontaneous emission: emission which occurs even in the
absence of a perturbing external electromagnetic field
Einstein coefficients
B12  B21
A21 8h 3

B21
c3
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Transition dipole moment and oscillator strength
 For transition from state 1 to state 2, the transition dipole
moment is
12   1 M  2
M is the dipole moment operator,  1 and
functions of states 1 and 2.
 2 are the wave-
 Einstein coefficient and transition dipole moment
B12 
2 2

2 12
3
Oscillator strength
2
8

me 2
f  4.319  1019    d 

2
3he
 is the frequency in s1
    is the molar extinction coefficient in M1 cm1
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Potential energy curve
Potential energy curve
A curve describing the variation of the potential energy of the system
of atoms that make up the reactants and products of a reaction as a
function of one geometric coordinate, and corresponding to the
energetically easiest passage from reactants to products.
The very notion of potential
energy curve implies the
adiabatic (Born-Oppenheimer)
approximation whereby
electronic and nuclear motions
are treated separately
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Reaction coordinate, potential energy surface
Reaction coordinate: A geometric parameter that changes during the
conversion of one (or more) reactant molecular entities into one
(or more) product molecular entities and whose value can be
taken for a measure of the progress of an elementary reaction
(for example, a bond length or bond angle or a combination of
bond lengths and/or bond angles; it is sometimes approximated
by a non-geometric parameter, such as the bond order of some
specified bond).
Potential energy surface: A geometric hypersurface on which the potential
energy of a set of reactants is plotted as a function of the
coordinates representing the molecular geometries of the system.
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Franck-Condon principle and reaction rate
Franck-Condon principle
Because the nuclei are so much more massive than the electrons, an
electronic transition takes place very much faster than the nuclei can respond
Reaction rate
k   r He  p
2
r  p
2
 r and  p – electronic wave-functions of reactant and product
H e – electronic Hamiltonian operator
 r and  p – nuclear (vibrational) wave-functions of reactant and product
r  p
2
– Franck-Condon factor
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Diabatic and adiabatic photoreactions
Diabatic photoreaction: Within the Born
Oppenheimer approximation, a reaction
beginning on one excited state potentialenergy surface and ending, as a result of
radiationless transition, on another
surface, usually that of the ground state.
Also called non-adiabatic.
Adiabatic photoreaction: Within the Born
Oppenheimer approximation, a reaction of
an excited state species that occurs on a
single potential-energy surface.
(IUPAC Compendium of Chemical Terminology)
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Jablonski diagram
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Time scales
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Single molecule and ensemble of molecules
 By the ergodic principle, time averaging is equivalent to
averaging over the micro-canonical ensemble
Uncertainty principle
Et  
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Emission bandwidth
 Single molecule
 If the lifetime of an excited state is t = 10 ns
(10−8 s)
the emission bandwidth from uncertainty
principle, Et   , is  n  1 2t or
n  2max 2tc
 For a band at max = 500 nm, n  10 6 nm
 Ensemble of molecules
 Typical bandwidth for organic dye molecules
in solution is 5-50 nm
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Homogeneous and inhomogeneous broadening
Homogeneous broadening
 the same transition energy (0) for all molecules
 the same line-shape (A()) for all molecules
Inhomogeneous broadening
 Some distribution of transition energies (0) around average value ( 0 )
 The total line shape is a superposition of individual molecule line-shapes
Homogeneous broadening mechanisms:
 motion (Doppler effect)
 collisions
 interaction with environment
 temperature ...
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Single molecule fluorescence spectroscopy
Compared with SPM:
• Pros: does not require contacts
• Cons: spatial resolution is
comparatively low
Displays the dynamic behavior of single
molecules not obscured by the
statistical average on the ensemble of
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molecules.
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Excited state decay and lifetime
 Population of the excited state, S1   S1 t ,
decays by:
 Reactions:
1.
kr
S1 
S0  h
2.
k ic
S1 
S0
3.
isc
S1 k
T1
 Kinetic equation:
dS1
 kr S1  kic S1  kisc S1  kS1
dt
 relaxation rate
with k  kr  kic  kisc
 Solution of the equation:
S1 t   A0e
t  k 1
 kt
 A0e

t
t
 excited state lifetime
A0  S1 t  0
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Fluorescence quantum yield
 Fluorescence intensity (number of photons emitted per unit time)
i fl t   kr S1 t   kr S1 0 e  kt
 Total number of emitted photons

I fl   i fl t dt  S1 0 
0
kr
k
 Fluorescence quantum yield is the ratio of the number of emitted
photons to the number of excited molecules
I
k
kr
t
 fl  fl  r 
  tkr
S1 0  k kr  knr t r
with
knr  kic  kisc
rate of non radiative relaxation
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Quantum yield for triplet state processes
isc
 For the process S1 k
T1 :
dT1 t 
  kisc S1 t 
dt
thus at t  
Triplet state decay
k rT
 Radiative: T1 
S0  h ph
T
k nr
 Non radiative: T1 
S0
 Rate equation:

dT1
T
 krT T1  knr
T1
dt
k
T1     kisc S1 t dt  S1 0  isc
k
0
 The quantum yield of
intersystem crossing is
isc 
T1   kisc

 tkisc
S1 0 k
T
 Assuming kisc  krT  knr
,
T1 t   T1 0e 

T
 k rT  k nr
t
Phosphorescence quantum yield
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 ph
krT
 T

T isc
kr  knr
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Relaxation dynamics of singlet excited state
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Steady state fluorescence
 Processes:
 Light absorption:
ka
S0  h a 
S1
 Fluorescence:
kr
S1 
S0  h fl
k nr
S1 
S0
 Non radiative decay:
 Kinetic equation:
dS1
 ka ex S0  kr  knr S1
dt
where ex is the density of photons.
For low excitation intensity (no depletion of the ground state)
S0  const; ka ex S0  aI ex ;
(a is the absorption cross section)
aI ex
S

The steady state solution ( dS1 dt  0 ) is: 1
kr  knr
The fluorescence intensity is:
I fl  kr S1 
aI exkr
 aI ex fl
kr  knr
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Radiative rate and oscillator strength
 According to the classical theory
kr  3  10 9 02    d  0.7 02 f
k r – radiative rate (in s−1)
 0 – energy of the transition (in cm−1)
f – oscillator strength of the transition
 For allowed transition, e.g. S1-S0, f = 1, at  0 = 20000 cm−1 (500 nm)
kr  3×108 s−1
 For forbidden transition, e.g. T1-S0, f = 10−8, at  0 = 20000 cm−1
kr  3 s−1
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Absorption and emission spectra:coumarin
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Stokes shift
 Stokes shift: The difference (usually in frequency units) between the
spectral positions of the band maxima (or the band origin) of the
absorption and luminescence arising from the same electronic
transition.
Eabs  G  
Eem  G  
G : energy difference between states
λ : reorganiza tion energy
ΔG  Eabs  Eem  / 2
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De-excitation processes
 Most common processes responsible for quenching of the
excited state
 Reactions can be inter-molecular or intra-molecular
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Excimer and exciplex
 Excimer: An electronically excited dimer, non-bonding in the
ground state. For example, a complex formed by the interaction
of an excited molecular entity with a ground state partner of the
same structure.
 Exciplex: An electronically excited complex of definite
stoichiometry, non-bonding in the ground state. For example, a
complex formed by the interaction of an excited molecular entity
with a ground state counterpart of a different structure.
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Excimers and exciplexes: molecular orbitals
(LUMO)A
(HOMO)A
(LUMO)B
(HOMO)B
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Excimers and exciplexes: reaction scheme
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