Chimica Fisica dei Materiali Avanzati Part 7a – Molecular photophysics and photochemistry

UUNIVERSITA’ DEGLI NIVERSITA’ DEGLI SSTUDI DI TUDI DI PPADOVAADOVA

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



Spontaneous and stimulated transitionsSpontaneous and stimulated transitionsStimulated emission: emission which is induced by a resonant

perturbing electromagnetic fieldSpontaneous emission: emission which occurs even in the

absence of a perturbing external electromagnetic field

Einstein coefficients

3

3

21

21

2112

8ch

BA

BB



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 strength

22

219

3810319.4

hemdf e

is the frequency in s1 is the molar extinction coefficient in M1 cm1



Potential energy curvePotential energy curvePotential energy curve

A 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



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.



Franck-Condon principle and reaction rateFranck-Condon principle and reaction rate

Franck-Condon principleBecause 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

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



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)



Jablonski diagramJablonski diagram



Time scalesTime scales



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



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



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

0



Single molecule fluorescence Single molecule fluorescence spectroscopyspectroscopy

Compared with SPM:• Pros: does not require contacts • Cons: spatial resolution is

comparatively lowDisplays the dynamic behavior of single molecules not obscured by the statistical average on the ensemble of molecules.



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

kSSkSkSkdtdS

with

11111

010

1001

tSAk

eAeAtSt

kt



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 0kkSdttiI r

flfl

iscicnr

rrnrr

rrflfl

kkk

kkk

kkk

SI

with

01



Quantum yield for triplet state processesQuantum yield for triplet state processes For the process :

The quantum yield of intersystem crossing is

11 TS isck

0111

11

0

at thus

kkSdttSkT

t

tSkdt

tdT

iscisc

isc

isc

iscisc k

kk

ST

01

1

Triplet state decay Radiative: Non radiative: Rate equation:

Assuming ,

Phosphorescence quantum yield

phk hST

Tr 01

01 STTnrk

111 TkTk

dtdT T

nrTr

Tnr

Trisc kkk

tkk Tnr

TreTtT 011

iscTnr

Tr

Tr

ph kkk



Relaxation dynamics of singlet excited Relaxation dynamics of singlet excited statestate



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 SkkSkdtdS

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

kkaIS

1

flexnrr

rexrfl aI

kkkaISkI

1



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

rk0



Absorption and emission Absorption and emission spectra:coumarinspectra:coumarin



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/Δenergytion reorganiza :

statesbetween differenceenergy :

emabs

em

abs

EEGλ

GGEGE



De-excitation processesDe-excitation processes

Most common processes responsible for quenching of the excited state

Reactions can be inter-molecular or intra-molecular



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.



Excimers and exciplexes: molecular Excimers and exciplexes: molecular orbitalsorbitals

(HOMO)A

(LUMO)A

(HOMO)B

(LUMO)B



Excimers and exciplexes: reaction schemeExcimers and exciplexes: reaction scheme

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Chimica Fisica dei Materiali Avanzati Part 7a – Molecular photophysics and photochemistry