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Corso CFMA. LS-SIMat 1
Chimica Fisica dei Materiali AvanzatiChimica Fisica dei Materiali Avanzati
Part 7a – Molecular photophysics and Part 7a – Molecular photophysics and photochemistryphotochemistry
Laurea specialistica in Scienza e Ingegneria dei MaterialiCurriculum Scienza dei Materiali
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Corso CFMA. LS-SIMat 2
Spontaneous and stimulated transitionsSpontaneous 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
3
3
21
21
2112
8
c
h
B
A
BB
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Corso CFMA. LS-SIMat 3
Transition dipole moment and oscillator Transition dipole moment and oscillator strengthstrength
For transition from state 1 to state 2, the transition dipole moment is
M is the dipole moment operator, and are the wave-functions of states 1 and 2.
Einstein coefficient and transition dipole moment
2112 M
1 2
212212 3
2
B
Oscillator strengthOscillator strength
22
219
3
810319.4
he
mdf e
is the frequency in s1 is the molar extinction coefficient in M1 cm1
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Corso CFMA. LS-SIMat 4
Potential energy curvePotential energy curve
Potential energy curveA curve describing the variation of the potential energy of the systemof atoms that make up the reactants and products of a reaction as a
function of one geometric coordinate, and corresponding to theenergetically easiest passage from reactants to products.
Potential energy curveA curve describing the variation of the potential energy of the systemof atoms that make up the reactants and products of a reaction as a
function of one geometric coordinate, and corresponding to theenergetically 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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Corso CFMA. LS-SIMat 5
Reaction coordinate, potential energy Reaction coordinate, potential energy surfacesurface
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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Corso CFMA. LS-SIMat 6
Franck-Condon principle and reaction rateFranck-Condon principle and reaction rate
Franck-Condon principle
Because the nuclei are so much more massive than the electrons, anelectronic transition takes place very much faster than the nuclei can respond
Franck-Condon principle
Because the nuclei are so much more massive than the electrons, anelectronic transition takes place very much faster than the nuclei can respond
Reaction rate
and – electronic wave-functions of reactant and product
– electronic Hamiltonian operator
and – nuclear (vibrational) wave-functions of reactant and product
– Franck-Condon factor
22
prper Hk
r p
eH
r p2
pr
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Corso CFMA. LS-SIMat 7
Diabatic and adiabatic photoreactionsDiabatic and adiabatic photoreactions
Diabatic photoreaction: Within the Born
Oppenheimer approximation, a reaction
beginning on one excited state potential-
energy 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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Corso CFMA. LS-SIMat 8
Jablonski diagramJablonski diagram
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Corso CFMA. LS-SIMat 9
Time scalesTime scales
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Corso CFMA. LS-SIMat 10
Single molecule and ensemble of Single molecule and ensemble of moleculesmolecules
By the ergodic principle, time averaging is equivalent to averaging over the micro-canonical ensemble
Uncertainty principle tE
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Corso CFMA. LS-SIMat 11
Emission bandwidthEmission bandwidth
Single molecule If the lifetime of an excited state is = 10 ns
(10−8 s)
the emission bandwidth from uncertainty principle, , is or
For a band at = 500 nm,
Ensemble of molecules
Typical bandwidth for organic dye molecules
in solution is 5-50 nm
E 21 n
cn 22max
max nm 10 6 n
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Corso CFMA. LS-SIMat 12
Homogeneous broadening the same transition energy (0) for all molecules
the same line-shape (A()) for all molecules
Homogeneous broadening the same transition energy (0) for all molecules
the same line-shape (A()) for all molecules
Homogeneous and inhomogeneous Homogeneous and inhomogeneous broadeningbroadening
Homogeneous broadening mechanisms: motion (Doppler effect) collisions interaction with environment temperature ...
Inhomogeneous broadening
Some distribution of transition energies (0) around average value ( )
The total line shape is a superposition of individual molecule line-shapes
Inhomogeneous broadening
Some distribution of transition energies (0) around average value ( )
The total line shape is a superposition of individual molecule line-shapes
0
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Corso CFMA. LS-SIMat 13
Single molecule fluorescence Single molecule fluorescence spectroscopyspectroscopy
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 molecules.
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Corso CFMA. LS-SIMat 14
Excited state decay and lifetimeExcited state decay and lifetime
Population of the excited state, , decays by: Reactions:
Kinetic equation:
relaxation rate
Solution of the equation:
excited state lifetime
tSS 11
11
01
01
3.
2.
1.
TS
SS
hSS
isc
ic
r
k
k
k
iscicr
iscicr
kkkk
kSSkSkSkdt
dS
with
11111
010
1
001
tSA
k
eAeAtSt
kt
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Corso CFMA. LS-SIMat 15
Fluorescence quantum yieldFluorescence quantum yield
Fluorescence intensity (number of photons emitted per unit time)
Total number of emitted photons
Fluorescence quantum yield is the ratio of the number of emitted photons to the number of excited molecules
rate of non radiative relaxation
ktrrfl eSktSkti 011
0
1 0k
kSdttiI r
flfl
iscicnr
rrnrr
rrflfl
kkk
kkk
k
k
k
S
I
with
01
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Corso CFMA. LS-SIMat 16
Quantum yield for triplet state processesQuantum yield for triplet state processes
For the process :
The quantum yield of intersystem crossing is
11 TS isck
0
111
11
0
at thus
k
kSdttSkT
t
tSkdt
tdT
iscisc
isc
isc
iscisc k
k
k
S
T
01
1
Triplet state decay Radiative:
Non radiative: Rate equation:
Assuming ,
Phosphorescence quantum yield
phk hST
Tr 01
01 STTnrk
111 TkTk
dt
dT Tnr
Tr
Tnr
Trisc kkk
tkk Tnr
TreTtT 011
iscTnr
Tr
Tr
ph kk
k
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Corso CFMA. LS-SIMat 17
Relaxation dynamics of singlet excited Relaxation dynamics of singlet excited statestate
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Corso CFMA. LS-SIMat 18
Steady state fluorescenceSteady state fluorescence Processes:
Light absorption:
Fluorescence:
Non radiative decay:
Kinetic equation:
10 ShS aka
flk hSS r 01
01 SS nrk
photons. ofdensity theis where
101
ex
nrrexa SkkSkdt
dS
For low excitation intensity (no depletion of the ground state)
The steady state solution ( ) is:
The fluorescence intensity is:
section) cross absorption theis ( ; const; 00 aaISkS exexa
01 dtdSnrr
ex
kk
aIS
1
flexnrr
rexrfl aI
kk
kaISkI
1
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Corso CFMA. LS-SIMat 19
Radiative rate and oscillator Radiative rate and oscillator strengthstrength
According to the classical theory
– radiative rate (in s−1)
– energy of the transition (in cm−1)
f – oscillator strength of the transition
For allowed transition, e.g. S1-S0, f = 1, at = 20000 cm−1 (500 nm)
3×108 s−1
For forbidden transition, e.g. T1-S0, f = 10−8, at = 20000 cm−1
3 s−1
fdkr2
02
09 7.0103
rk
0
0
rk
rk
0
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Corso CFMA. LS-SIMat 20
Absorption and emission Absorption and emission spectra:coumarinspectra:coumarin
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Corso CFMA. LS-SIMat 21
Stokes shiftStokes 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.
2/Δ
energytion reorganiza :
statesbetween differenceenergy :
emabs
em
abs
EEG
λ
G
GE
GE
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Corso CFMA. LS-SIMat 22
De-excitation processesDe-excitation processes
Most common processes responsible for quenching of the excited state
Reactions can be inter-molecular or intra-molecular
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Corso CFMA. LS-SIMat 23
Excimer and exciplexExcimer 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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Corso CFMA. LS-SIMat 24
Excimers and exciplexes: molecular Excimers and exciplexes: molecular orbitalsorbitals
(HOMO)A
(LUMO)A
(HOMO)B
(LUMO)B
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Corso CFMA. LS-SIMat 25
Excimers and exciplexes: reaction schemeExcimers and exciplexes: reaction scheme
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