Laurea specialistica in Scienza e Ingegneria dei Materiali Curriculum Scienza dei Materiali Chimica Fisica dei Materiali Avanzati Part 7b – Photophysics and photochemistry of molecular materials (excitons, energy transfer and electron transfer) Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Exciton Exciton: In some applications it is useful to consider an electronic excitation as a quasi-particles capable of migrating. This is termed an exciton. In organic materials two models are used: the band or wave model (low temperature, high crystalline order) and the hopping model (higher temperature, low crystalline order or amorphous state). Energy transfer in the hopping limit is identical with energy migration. The following consideration follows M. Kasha et al [Pure Appl. Chem. 11 (1965) 371] model of dimer exciton interaction (the band or wave model). Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Exciton model: ground state We consider a weak interaction between 2 molecules (chromophores), so that perturbation theory can be used. The ground state wave-function is and are ground state wave-functions of molecules u and v. The Hamiltonian operator is Hu and Hv are the Hamiltonians of the isolated molecules, Vuv is the intermolecular perturbation potential approximated by (point) dipole-dipole interaction term. The energy of the ground state is Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Exciton model: excited state wavefunctions If molecules u and v are the same and have identical environments and the excited state wave-functions of the molecules are denoted and , the excited dimer wavefunctions and are degenerate. Thus, the excited state wave-function of the dimer must be written with r and s coefficients to be determined. The Schrödinger equation is Solution for wave-functions (with Hamiltonian matrix elements Huu = Hvv and Hvu = Hvu) Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Exciton model: excited state energies Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Parallel transition dipoles Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

In-line dipoles Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Exciton in asymmetric dimer If the molecules in the dimer are not equivalent because of, say, local perturbations, disorder, etc., the diagonal elements of the Hamiltonian are different. The excitation energies then become: and the wavefunctions: and compete for the exciton delocalization: the first favors, the second opposes it. Corso CFMA. LS-SIMat

Main mechanisms of energy transfer Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Radiative electronic energy transfer Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Radiative energy transfer: distance dependence Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Radiative energy transfer: efficiency Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Förster mechanism from Fermi “Golden rule” Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Coulombic or dipole-dipole interaction (Förster energy transfer) Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Förster formulation of the dipole-dipole energy transfer Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Level diagrams for energy stransfer Förster mechanism Dexter mechanism Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Electronic exchange energy transfer: Dexter mechanism Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Applications of energy transfer Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Orientation factor Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

How to measure energy transfer Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Energetics of the electron transfer process Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Classical theory of electron transfer Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Marcus formulation Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Normal and inverted regions Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Marcus rate plot Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Reorganization energy Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Solvent reorganization energy (examples) Quite a substantial energy! Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Adiabatic and non-adiabatic processes Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Quantum mechanical theory Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Quantum theory - 2 Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Comparison of quantum and classical theories Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Electronic coupling and maximum ET rate Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Distance dependence of the ET rate Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Effect of solvent dynamics Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat

Photoinduced charge separation and charge recombination Corso CFMA. LS-SIMat Corso CFMA. LS-SIMat