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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat1 Chimica Fisica dei Materiali Avanzati Part 7a – Molecular photophysics and photochemistry Laurea specialistica in Scienza e Ingegneria dei Materiali Curriculum Scienza dei Materiali

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat2 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

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat3 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 is the frequency in s 1 is the molar extinction coefficient in M 1 cm 1

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat4 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. 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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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat5 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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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat6 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 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 and – electronic wave-functions of reactant and product – electronic Hamiltonian operator and – nuclear (vibrational) wave-functions of reactant and product – Franck-Condon factor

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat7 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)

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat8 Jablonski diagram

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat9 Time scales

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat10 Single molecule and ensemble of molecules By the ergodic principle, time averaging is equivalent to averaging over the micro-canonical ensemble Uncertainty principle

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat11 Emission 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

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat12 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 broadening 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

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat13 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.

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat14 Excited state decay and lifetime Population of the excited state,, decays by: Reactions: Kinetic equation: relaxation rate Solution of the equation: excited state lifetime

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat15 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

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat16 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

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat17 Relaxation dynamics of singlet excited state

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat18 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:

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat19 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. S 1 -S 0, f = 1, at = cm 1 (500 nm) 3×10 8 s 1 For forbidden transition, e.g. T 1 -S 0, f = 10 8, at = cm 1 3 s 1

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat20 Absorption and emission spectra:coumarin

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat21 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.

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat22 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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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat23 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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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat24 Excimers and exciplexes: molecular orbitals (HOMO) A (LUMO) A (HOMO) B (LUMO) B

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U NIVERSITA DEGLI S TUDI DI P ADOVA Corso CFMA. LS-SIMat25 Excimers and exciplexes: reaction scheme

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