1. Laurea specialistica in Scienza e Ingegneria dei Materiali
Curriculum Scienza dei Materiali
Chimica Fisica dei Materiali Avanzati Part 7a – Molecular photophysics and photochemistry
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

2. 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
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

3. Transition dipole moment and oscillator strength
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
Oscillator strength
n is the frequency in s-1
is the molar extinction coefficient in M-1 cm-1
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

4. 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
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

5. 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.
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

6. Franck-Condon principle and reaction rate
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
and – electronic wave-functions of reactant and product
– electronic Hamiltonian operator
and – nuclear (vibrational) wave-functions of reactant and product
– Franck-Condon factor
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

7. Diabatic 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)
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

8. Jablonski diagram
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

9. Time scales
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

10. Single molecule and ensemble of molecules
By the ergodic principle, time averaging is equivalent to averaging over the micro-canonical ensemble
Uncertainty principle
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

11. Emission bandwidth Single molecule Ensemble of molecules
If the lifetime of an excited state is t = 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
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

12. Homogeneous and inhomogeneous broadening
the same transition energy (n0) for all molecules
the same line-shape (A(n)) for all molecules
Inhomogeneous broadening
Some distribution of transition energies (n0) around average value ( )
The total line shape is a superposition of individual molecule line-shapes
Homogeneous broadening mechanisms:
motion (Doppler effect)
collisions
interaction with environment
temperature ...
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

13. 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 molecules.
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

14. Excited state decay and lifetime
Population of the excited state, , decays by:
Reactions:
Kinetic equation:
 relaxation rate
Solution of the equation:
 excited state lifetime
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

15. Fluorescence 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
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

16. Quantum yield for triplet state processes
For the process :
The quantum yield of intersystem crossing is
Triplet state decay
Radiative:
Non radiative:
Rate equation:
Assuming ,
Phosphorescence quantum yield
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

17. Relaxation dynamics of singlet excited state
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

18. Steady state fluorescence
Processes:
Light absorption:
Fluorescence:
Non radiative decay:
Kinetic equation:
For low excitation intensity (no depletion of the ground state)
The steady state solution ( ) is:
The fluorescence intensity is:
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

19. Radiative rate and oscillator strength
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 = cm−1 (500 nm)
3×108 s−1
For forbidden transition, e.g. T1-S0, f = 10−8, at = cm−1
3 s−1
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

20. Absorption and emission spectra:coumarin
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

21. 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.
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

22. De-excitation processes
Most common processes responsible for quenching of the excited state
Reactions can be inter-molecular or intra-molecular
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

23. 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.
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

24. Excimers and exciplexes: molecular orbitals
(LUMO)A
(LUMO)B
(HOMO)A
(HOMO)B
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat

25. Excimers and exciplexes: reaction scheme
Corso CFMA. LS-SIMat
Corso CFMA. LS-SIMat