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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 = 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 Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

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

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

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

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

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

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