Charge carrier mobility in one-dimensional aligned π-stacks of conjugated small molecules with a benzothiadiazole central unit

Abstract

A theoretical study is applied to gain insight into the microscopic electron and hole transport in benzothiadiazole-cored molecular semiconductors either with furan or thiophene flanks arranged in π-stacks. For the characterization of the energetics of the reduction and oxidation processes and their impact on the molecular geometry, the internal reorganization energy is defined for isolated molecules in the gas phase. The outer-shell reorganization energy is evaluated within the frequency-resolved cavity model and as an electrostatic contribution within the polarizable continuum model. The intermolecular electronic coupling interaction for the Marcus charge hopping is calculated using the energy splitting in dimer method, the generalized Mulliken-Hush approach and the fragment charge difference scheme. In order to probe the relation between the charge hopping rate/charge carrier mobility and the molecular organization within the π-stacks, different stacking modes are investigated: (i) dimers with a perfect registry, i.e. segregated stacking motif, when molecules are placed face-to-face, and (ii) dimers forming slipped cofacial orientations with longitudinal and transverse shifts, i.e. mixed stacking motif. Besides, the effects of molecular planarity and rigidity, influencing internal molecular relaxation upon charging, the effects of non-covalent interactions within stacks and the heteroatom replacement on the charge carrier mobility are studied. The results obtained in the simulations of one-dimensional aligned π-stacks of molecular semiconductors are compared with available experimental data for small conjugated benzothiadiazole-cored molecules with thiophene flanks and benzothiadiazole-quaterthiophene-based copolymers.

A comparative analysis of symmetric diketopyrrolopyrrole‐cored small conjugated molecules with aromatic flanks: From geometry to charge transport

“…The high and comparable charge carrier mobilities independently on the heteroatom of the flank are caused by the molecular symmetry of trans‐trans DPP molecules for which only parallel stacking patterns can be formed in a condense phase leading to a better electron coupling. As we found out in our previous work, such an orientation provokes better electronic coupling in the stacks as compared to anti‐parallel one, where overlap of the molecular orbitals is reduced …”

“…The reorganization energies λ are obtained using the four‐point formalism as a difference of geometry relaxation energies upon going from neutral (0) to charged‐state (±) geometry: where E ± and E 0 are the ground state energies of charged and neutral state, respectively, and , are the energies of charged states at optimized neutral‐state geometry, and vice versa …”

“…The electronic coupling V is calculated for dimer systems applying the energy splitting in dimer (ESID) method which provides an approximation from the Kohn–Sham (KS) orbital energies and the Koopmans' theorem: where V ET and V HT is the electronic coupling for electron and hole transfer, respectively, and , , , are the corresponding orbital energies. The V values are evaluated with B3LYP/6‐31G*, since M06‐2X/cc‐pVTZ functional slightly overestimates the electronic coupling …”

“…The most calculations are performed with B3LYP/6-31G* [58] functional since it gives accurate geometries and the values of band gaps (E g ), as seen in our previous studies. [47,59] The reorganization energies λ are obtained using the fourpoint formalism [47,60] as a difference of geometry relaxation energies upon going from neutral (0) to charged-state (AE) geometry:…”

“…The V values are evaluated with B3LYP/6-31G*, since M06-2X/cc-pVTZ functional slightly overestimates the electronic coupling. [60] The charge carrier mobilities for stacks are calculated via Einstein-Smoluchowski equation in one dimensional approximation at T=298 K:…”