Quantum Dynamics of Electron–Hole Separation in Stacked Perylene Diimide-Based Self-Assembled Nanostructures

Abstract

We report on high-dimensional quantum dynamical simulations of electron−hole separation in self-assembled mesomorphic nanostructures composed of donor−acceptor conjugated co-oligomers. The latter are based on perylene diimide (PDI) acceptor units combined with fluorene-thiophene-benzothiadiazole donor units, which form highly ordered, stacked structural motifs upon self-assembly. Simulations are shown for a first-principles parametrized model lattice of 25 stacked PDI units under the effects of an applied external field and temperature. The simulations are carried out with the multilayer multiconfiguration timedependent Hartree (ML-MCTDH) method with nearly 900 vibrational degrees of freedom and 25 electronic states. Temperature effects are included using the thermofield dynamics approach. A transition between a short-time coherent dynamics and a kinetic regime is highlighted. From a flux-over-population analysis, electron−hole dissociation rates are obtained in the range of 5−20 ns −1 in the absence of static disorder, exhibiting a moderate field and temperature dependence. These results for electron−hole separation rates can be employed as a benchmark to calibrate the parametrization of kinetic Monte Carlo simulations applied to much larger lattice sizes.

Electron–Hole Separation in Perylene Diimide Based Self-Assembled Nanostructures: Microelectrostatics Analysis and Kinetic Monte Carlo Simulations

“…3 for a detailed discussion). This definition coincides with the boundary employed in our recent quantumdynamical study 5 where a flux-over-population approach [58][59][60] was used to compute the eh dissociation rate. Indeed, the computation of escape rates based upon the MFPT vs. flux-over-population approaches have been shown to be equivalent for Kramers escape type problems under rather general conditions.…”

“…Complemented by KMC calculations based upon the ME-based on-site energies, a full picture of the e-h dissociation process in the present material is obtained. This treatment is complementary to our recent work 5 where a quantum-dynamical study of e-h separation was carried out within a reduced one-dimensional model representing an isolated PDI stack.…”

“…As for the theoretical description of charge separation in organic solar-cell materials, quantum dynamical and quantum-classical simulations of coupled electrons and holes have been successfully applied to describe the first steps of charge separation on the ultra-fast 2 timescale. [1][2][3][4][5][6] On the other hand, the process of splitting into free charges has been the playground for phenomenological models -specifically Onsager-Braun (OB) theory 7,8 and its improved versions [9][10][11][12] -or for kinetic Monte Carlo (KMC) simulations. [13][14][15][16][17][18] The latter are well suited for multiscale simulations, as KMC can be fed with rates from non-adiabatic electron transfer theories, such as the popular Marcus theory, its Marcus-Levich-Jortner (MLJ) extension, along with the related Fermi's Golden Rule (FGR) approach, [19][20][21] whose parameters can be obtained from accurate quantum chemistry calculations.…”

“…As for the theoretical description of charge separation in organic solar-cell materials, quantum dynamical and quantum-classical simulations of coupled electrons and holes have been successfully applied to describe the first steps of charge separation on the ultrafast time scale. − On the other hand, the process of splitting into free charges has been the playground for phenomenological modelsspecifically Onsager–Braun (OB) theory , and its improved versions (see refs − )or for kinetic Monte Carlo (KMC) simulations. − The latter are well suited for multiscale simulations, as KMC can be fed with rates from nonadiabatic electron-transfer theories, such as the popular Marcus theory, its Marcus–Levich–Jortner (MLJ) extension, and the related Fermi’s Golden Rule (FGR) approach, − whose parameters can be obtained from accurate quantum chemistry calculations. The adoption of realistic morphologies for materials and interfaces obtained with atomistic molecular dynamics, and the description of long-range electrostatic effects on the energy landscape, have been paths explored by researchers in the field to improve the realism in the simulation of electronic processes in photovoltaic materials.…”

“…Second, on the basis of the ME analysis, we carry out KMC calculations to predict field-dependent electron–hole (e–h) dissociation rates and yields. The KMC simulations were calibrated with the help of a recent quantum dynamical analysis for a one-dimensional model adapted to preferential transport in the PDI stacking direction . Even though the present analysis is carried out for a system exhibiting a moderate PCE in photovoltaic applications, the present approach can be transposed to a broad class of novel nonfullerene acceptor (NFA) materials that often comply with highly ordered morphologies. , …”