Charge transfer excitons in π -stacked thiophene oligomers and P3[Alkyl]T crystals: CIS calculations and electroabsorption spectroscopy

Abstract

Poly(3-alkylthiophenes), P3[Alkyl]T, exhibit high mobility and efficiency of formation of polaronic chargecarriers generated by light absorption which gives them applications in field effect devices. Excited states ofπ -stacked dimers of tetra-thiophene oligomers (T4), infinite isolated polythiophene (PT) chains and P3[Alkyl]Tcrystals are modeled using configuration interaction singles (CIS) calculations. Excited states in cofacial T4dimers are mostly localized, Frenkel (FR) states except for two low energy CT exciton states which become theionization potential and electron affinity levels of T4 molecules at large dimer separation. The lowest excitedstates in infinite, isolated PT chains and P3[Alkyl]T crystals are intra-chain excitons where the electron and holeare localized on the same chain. The next lowest excited states are inter-chain, CT excitons in which electronand hole reside on neighboring chains. The former capture almost all optical oscillator strength and the lattermay be a route to efficient formation of polaronic charge carriers in P3[Alkyl]T systems. Changes in opticalabsorption energies of T4 dimers are explained as a function of molecular separation using CIS calculations withfour frontier orbitals in the active space. Shifts in optical absorption energy observed on going from isolatedchains to P3[Alkyl]T lamellar structures are already present in single-particle transition energies induced bydirect π - π interactions at short range. The electroabsorption spectrum of T4 dimers is calculated as a functionof dimer separation and states which are responsible for parallel and perpendicular components of the spectrumare identified.

Spectroscopic Identification of the Charge Transfer State in Thiophene/Fullerene Heterojunctions: Electroabsorption Spectroscopy from GW/BSE Calculations

“…Chemist's notation is used for two-electron integrals (ij|kl), in which orbitals i and j share the same electron coordinate and k and l share the other electron coordinate. Diagonal and off-diagonal (ij|ab) twoelectron matrix elements have the following approximate forms, 19 The Hamiltonian in eq 5 accounts for the Coulombic behavior of FR and CT state energies as a function of the dimer separation for triplet states. The Hamiltonian for singlet states in this model has the term 2(ia|jb), in addition to terms in eq 5.…”

“…The odd/even symmetry of the molecular wave functions with respect to the center of inversion means that only four off-diagonal terms in the Hamiltonian are nonzero. 19 The Hamiltonian in eq 5 accounts for the Coulombic behavior of FR and CT state energies as a function of the dimer separation for triplet states. The Hamiltonian for singlet states in this model has the term 2(ia|jb), in addition to terms in eq 5.…”

“…The degenerate triplet FR state energy is ε ai −((AA| CC)+(BB|DD))/2 and the degenerate triplet CT state energy is ε ai −((AA|DD)+(BB|CC))/2. The corresponding wave functions for the first eigenvalue 19 are,…”

“…Frenkel states are denoted as FR1 and FR2. The corresponding wave functions for the eigenvalue ε ai −((AA|DD)+(BB|CC))/ 2 19 are,…”

“…CT states in oligothiophene/C 60 and similar systems have been modeled using time-dependent density functional theory (TDDFT) applied to single donor–acceptor pairs. ,− We reported EA calculations on tetrathiophene dimers and found that the main features arise from the main 1B 1 u thiophene FR transition and the CT state; the former exhibits a first derivative EA line shape and the latter a second derivative shape. Both are observed in experiment on polycrystalline P3HT .…”