Singlet Exciton Diffusion in Organic Crystals Based on Marcus Transfer Rates

Nonadiabatic Simulation of Exciton Dynamics in Organic Semiconductors Using Neural Network-Based Frenkel Hamiltonian and Gradients

In this study, we present a multiscale method to simulate the propagation of Frenkel singlet excitons in organic semiconductors (OSCs). The approach uses neural network models to train a Frenkel-type Hamiltonian and its gradient, obtained by the long-range correction version of density functional tight-binding with self-consistent charges. Our models accurately predict site energies, excitonic couplings, and corresponding gradients, essential for the nonadiabatic molecular dynamics simulations. Combined with the fewest switches surface hopping algorithm, the method was applied to four representative OSCs: anthracene, pentacene, perylenediimide, and diindenoperylene. The simulated exciton diffusion constants align well with experimental and reported theoretical values and offer valuable insights into exciton dynamics in OSCs.

Analysis of Site Energies and Excitonic Couplings: The Role of Symmetry and Polarization

An excitonic coupling model is developed based on an equation-of-motion coupled cluster combined with the fragment molecular orbital method. The effects of polarization and excitonic coupling on the splitting of quasi-degenerate levels in systems containing multiple chromophores are elucidated on dimers of formaldehyde, water, formic acid, hydrogen fluoride, and carbon monoxide. It is shown that the level structure is mainly determined by the mutual polarization of chromophores and to a lesser extent by the excitonic coupling. The role of symmetry in excitonic coupling in dimers is discussed. The excitonic coupling between all residues in the photoactive yellow protein (PDB: 2PHY) is analyzed.

Adsorption Structures Affecting the Electronic Properties and Photoinduced Charge Transfer at Perylene-Based Molecular Interfaces

Perylene-based organic semiconductors are widely used in organic electronic devices. Here, we studied the ultrafast excited state dynamics after optical excitation at interfaces between the electron donor (D) diindenoperylene (DIP) and the electron acceptor (A) dicyano-perylene-bis(dicarboximide) (PDIR-CN2 ) using femtosecond time-resolved second harmonic generation (SHG) in combination with large scale quantum chemical calculations. Thereby, we varied in bilayer structures of DIP and PDIR-CN2 the interfacial molecular geometry. For an interfacial configuration which contains a edge-on geometry but also additional face-on domains an optically induced charge transfer (CT) is observed, which leads to a pronounced increase of the SHG signal intensity due to electric field induced second harmonic generation. The interfacial CT state decays within 7.5±0.7 ps, while the creation of hot CT states leads to a faster decay (5.3±0.2 ps). For the bilayer structures with mainly edge-on geometries interfacial CT formation is suppressed since π-π overlap perpendicular to the interface is missing. Our combined experimental and theoretical study provides important insights into D/A charge transfer properties, which is needed for the understanding of the interfacial photophysics of these molecules.

An ab initio method on large sized molecular aggregate system: Predicting absorption spectra of crystalline organic semiconducting films

Theoretical description of electronically excited states of molecular aggregates at an ab initio level is computationally demanding. To reduce the computational cost, we propose a model Hamiltonian approach that approximates the electronically excited state wavefunction of the molecular aggregate. We benchmark our approach on a thiophene hexamer, as well as calculate the absorption spectra of several crystalline non-fullerene acceptors, including Y6 and ITIC, which are known for their high power conversion efficiency in organic solar cells. The method qualitatively predicts the experimentally measured spectral shape, which can be further linked to the molecular arrangement in the unit cell.

Mechanism of Delocalization-Enhanced Exciton Transport in Disordered Organic Semiconductors

Large exciton diffusion lengths generally improve the performance of organic semiconductor devices, because they enable energy to be transported farther during the exciton lifetime. However, the physics of exciton motion in disordered organic materials is not fully understood, and modeling the transport of quantum-mechanically delocalized excitons in disordered organic semiconductors is a computational challenge. Here, we describe delocalized kinetic Monte Carlo (dKMC), the first model of three-dimensional exciton transport in organic semiconductors that includes delocalization, disorder, and polaron formation. We find that delocalization can dramatically increase exciton transport; for example, delocalization across less than two molecules in each direction can increase the exciton diffusion coefficient by over an order of magnitude. The mechanism for the enhancement is 2-fold: delocalization enables excitons to hop both more frequently and further in each hop. We also quantify the effect of transient delocalization (short-lived periods where excitons become highly delocalized) and show that it depends strongly upon the disorder and transition dipole moments.

Relating reorganization energies, exciton diffusion length and non-radiative recombination to the room temperature UV-vis absorption spectra of NF-SMA

Understanding excited-state reorganization energies, exciton diffusion lengths and non-radiative (NR) recombination, and the overall optoelectronic responses of nonfullerene small molecule acceptors (NF-SMAs) is important in order to rationally design new materials with controlled properties. While the effects of structural modifications on the optical gaps and electron affinities of NF-SMAs have been studied extensively, analyses of their absorption spectra that carefully characterize electronic and vibrational contributions that allow comparisons of reorganization energies and their implications for exciton diffusion lengths and NR recombination have yet to be reported. Here, we study the room temperature absorption spectra of three structural classes of NF-SMAs in dilute solutions through multiparameter Franck Condon (MFC) analyses and density functional theory (DFT) calculations. We show that the absorption spectra of these NF-SMAs can be categorized based on molecular structure-spectra correlation. The absorption spectra of curved, Y6-like structures can be described using an MFC model with two electronic transitions and two effective vibrational modes. The results of MFC/DFT analyses reveal that Y6 exhibits the smallest intra-molecular reorganization energy among the materials studied. Linear ITIC-like molecular structures reveal larger reorganization energies and reduced conformational uniformity compared to Y6. Meanwhile structures such as IDTBR and IEICO, which have an extra π-conjugated moiety between the donor and acceptor moieties, have large excited-state reorganization energies and low degrees of conformational uniformity. Since the intra-molecular reorganization energy is correlated with exciton diffusion length and nonradiative voltage losses (ΔV_nr), our results highlight the power of RT absorption spectroscopy and DFT calculations as simple tools to designing improved OSCs materials with small reorganization energies, small ΔV_nr, large exciton diffusion length and low energetic disorder (due to a strongly dominant conformation).

Aggregation‐Induced Dual Phosphorescence from ( o ‐Bromophenyl)‐Bis(2,6‐Dimethylphenyl)Borane at Room Temperature

Designing highly efficient purely organic phosphors at room temperature remains a challenge because of fast non‐radiative processes and slow intersystem crossing (ISC) rates. The majority of them emit only single component phosphorescence. Herein, we have prepared 3 isomers (o, m, p‐bromophenyl)‐bis(2,6‐dimethylphenyl)boranes. Among the 3 isomers (o‐, m‐ and p‐BrTAB) synthesized, the ortho‐one is the only one which shows dual phosphorescence, with a short lifetime of 0.8 ms and a long lifetime of 234 ms in the crystalline state at room temperature. Based on theoretical calculations and crystal structure analysis of o‐BrTAB, the short lifetime component is ascribed to the T₁^M state of the monomer which emits the higher energy phosphorescence. The long‐lived, lower energy phosphorescence emission is attributed to the T₁^A state of an aggregate, with multiple intermolecular interactions existing in crystalline o‐BrTAB inhibiting nonradiative decay and stabilizing the triplet states efficiently.

Exciton transport in molecular organic semiconductors boosted by transient quantum delocalization

Designing molecular materials with very large exciton diffusion lengths would remove some of the intrinsic limitations of present-day organic optoelectronic devices. Yet, the nature of excitons in these materials is still not sufficiently well understood. Here we present Frenkel exciton surface hopping, an efficient method to propagate excitons through truly nano-scale materials by solving the time-dependent Schrödinger equation coupled to nuclear motion. We find a clear correlation between diffusion constant and quantum delocalization of the exciton. In materials featuring some of the highest diffusion lengths to date, e.g. the non-fullerene acceptor Y6, the exciton propagates via a transient delocalization mechanism, reminiscent to what was recently proposed for charge transport. Yet, the extent of delocalization is rather modest, even in Y6, and found to be limited by the relatively large exciton reorganization energy. On this basis we chart out a path for rationally improving exciton transport in organic optoelectronic materials.

Accurate Polarization-Resolved Absorption Spectra of Organic Semiconductor Thin Films Using First-Principles Quantum-Chemical Methods: Pentacene as a Case Study

Theoretical studies using clusters as model systems have been extremely successful in explaining various photophysical phenomena in organic semiconductor (OSC) thin films. But they have not been able to satisfactorily simulate total and polarization-resolved absorption spectra of OSCs so far. In this work, we demonstrate that accurate spectra are predicted by time-dependent density functional theory (TD-DFT) when the employed cluster reflects the symmetry of the crystal structure and all monomers feel the same environment. Additionally, long-range corrected optimal tuned functionals are mandatory. For pentacene thin films, the computed electronic spectra for thin films then reach an impressive accuracy compared with experimental data with a deviation of less than 0.1 eV. This allows for accurate peak assignments and mechanistic studies, which paves the way for a comprehensive understanding of OSCs using an affordable and easy-to-use cluster approach.

Long-Range Interactions Boost Singlet Exciton Diffusion in Nanofibers of π-Extended Polymer Chains

Raising the distance covered by singlet excitons during their lifetimes to values maximizing light absorption (a few hundred nm) would solve the exciton diffusion bottleneck issue and lift the constraint for fine (∼10 nm) phase segregation in bulk heterojunction organic solar cells. In that context, the recent report of highly ordered conjugated polymer nanofibers featuring singlet exciton diffusion length, L_D, in excess of 300 nm is both appealing and intriguing [Jin, X.; et al. Science 2018, 360 (6391), 897-900]. Here, on the basis of nonadiabatic molecular dynamics simulations, we demonstrate that singlet exciton diffusion in poly(3-hexylthiophene) (P3HT) fibers is highly sensitive to the interplay between delocalization along the polymer chains and long-range interactions along the stacks. Remarkably, the diffusion coefficient is predicted to rocket by 3 orders of magnitude when going beyond nearest-neighbor intermolecular interactions in fibers of extended (30-mer) polymer chains and to be resilient to interchain energetic and positional disorders.

Analytical Time-Dependent Long-Range Corrected Density Functional Tight Binding (TD-LC-DFTB) Gradients in DFTB+: Implementation and Benchmark for Excited-State Geometries and Transition Energies

The absorption and emission of light is a ubiquitous process in chemical and biological processes, making a theoretical description inevitable for understanding and predicting such properties. Although ab initio and DFT methods are capable of describing excited states with good accuracy in many cases, the investigation of dynamical processes and the need to sample the phase space in complex systems often requires methods with reduced computational costs but still sufficient accuracy. In the present work, we report the derivation and implementation of analytical nuclear gradients for time-dependent long-range corrected density functional tight binding (TD-LC-DFTB) in the DFTB+ program. The accuracy of the TD-LC-DFTB potential-energy surfaces is benchmarked for excited-state geometries and adiabatic as well as vertical transition energies. The benchmark set consists of more than 100 organic molecules taken as subsets from available benchmark sets. The reported method yields a mean deviation of 0.31 eV for adiabatic excitation energies with respect to CC2. In order to study more subtle effects, seminumerical second derivatives based on the analytical gradients are employed to simulate vibrationally resolved UV/vis spectra. This extensive test exhibits few problematic cases, which can be traced back to the parametrization of the repulsive potential.

Role of Conical Intersections on the Efficiency of Fluorescent Organic Molecular Crystals

Organic molecular crystals are attractive materials for luminescent applications because of their promised tunability. However, the link between the chemical structure and emissive behavior is poorly understood because of the numerous interconnected factors which are at play in determining radiative and nonradiative behaviors at the solid-state level. In particular, the decay through conical intersection dominates the nonadiabatic regions of the potential energy surface, and thus, their accessibility is a telling indicator of the luminosity of the material. In this study, we investigate the radiative mechanism for five organic molecular crystals which display a solid-state emission, with a focus on the role of conical intersections in their photomechanisms. The objective is to situate the importance of the accessibility of conical intersections with regards to emissive behavior, taking into account other nonradiative decay channels, namely, vibrational decay, and exciton hopping. We begin by giving a brief overview of the structural patterns of the five systems within a larger pool of 13 crystals for a richer comparison. We observe that because of the prevalence of sheet like and herringbone packing in organic molecular crystals, the conformational diversity of crystal dimers is limited. Additionally, similarly spaced dimers have exciton coupling values of a similar order within a 50 meV interval. Next, we focus on three exemplary cases, where we disentangle the role of nonradiative decay mechanisms and show how rotational minimum energy conical intersections in vacuum lead to puckered ones in the crystal, increasing their instability upon crystallization in typical packing motifs. In contrast, molecules with puckered conical intersections in vacuum tend to conserve this trait upon crystallization, and therefore, their quantum yield of fluorescence is determined predominantly by other nonradiative decay mechanisms.

Assessing the effects of increasing conjugation length on exciton diffusion: from small molecules to the polymeric limit

Organic solar cells (OSC) generally contain long-chain π-conjugated polymers as donor materials, but, more recently, small-molecule donors have also attracted considerable attention. The nature of these compounds is of crucial importance concerning the various processes that determine device performance, among which singlet exciton diffusion is one of the most relevant. The efficiency of the diffusion mechanism depends on several aspects, from system morphology to electronic structure properties, which vary importantly with molecular size. In this work, we investigated the effects of conjugation length on the exciton diffusion length through electronic structure calculations and an exciton diffusion model. By applying extrapolation procedures to thiophene and phenylene vinylene oligomer series, we investigate their electronic and optical properties from the small-molecule point of view to the polymeric limit. Several properties are calculated as a function of oligomer size, including transition energies, absorption and emission spectra, reorganization energies, exciton coupling and Förster radii. Finally, an exciton diffusion model is used to estimate diffusion lengths as a function of oligomer size and for the polymeric limit showing agreement with experimental data. Results also show that longer conjugation lengths correlate with longer exciton diffusion lengths in spite of also being associated with shorter exciton lifetimes.

Long-range exciton diffusion in molecular non-fullerene acceptors

The short exciton diffusion length associated with most classical organic semiconductors used in organic photovoltaics (5-20 nm) imposes severe limits on the maximum size of the donor and acceptor domains within the photoactive layer of the cell. Identifying materials that are able to transport excitons over longer distances can help advancing our understanding and lead to solar cells with higher efficiency. Here, we measure the exciton diffusion length in a wide range of nonfullerene acceptor molecules using two different experimental techniques based on photocurrent and ultrafast spectroscopy measurements. The acceptors exhibit balanced ambipolar charge transport and surprisingly long exciton diffusion lengths in the range of 20 to 47 nm. With the aid of quantum-chemical calculations, we are able to rationalize the exciton dynamics and draw basic chemical design rules, particularly on the importance of the end-group substituent on the crystal packing of nonfullerene acceptors.

Real-Time Propagation TDDFT and Density Analysis for Exciton Coupling Calculations in Large Systems

Photoactive systems are characterized by their capacity to absorb the energy of light and transform it. Usually, more than one chromophore is involved in the light absorption and excitation transport processes in complex systems. Linear-Response Time-Dependent Density Functional (LR-TDDFT) is commonly used to identify excitation energies and transition properties by solving the well-known Casida’s equation for single molecules. However, in practice, LR-TDDFT presents some disadvantages when dealing with multichromophore systems due to the increasing size of the electron–hole pairwise basis required for accurate evaluation of the absorption spectrum. In this work, we extend our local density decomposition method that enables us to disentangle individual contributions into the absorption spectrum to computation of exciton dynamic properties, such as exciton coupling parameters. We derive an analytical expression for the transition density from Real-Time Propagation TDDFT (P-TDDFT) based on Linear Response theorems. We demonstrate the validity of our method to determine transition dipole moments, transition densities, and exciton coupling for systems of increasing complexity. We start from the isolated benzaldehyde molecule, perform a distance analysis for π-stacked dimers, and finally map the exciton coupling for a 14 benzaldehyde cluster.

Charge transport parameters for carbon based nanohoops and donor-acceptor derivatives

The effect of donor-acceptor (D-A) moieties on magnitudes such as reorganization energies and electronic couplings in cycloparaphenylene (CPP) carbon based nanohoops (i.e. conjugated organic molecules with cyclic topology) is highlighted via model computations and analysis of the available crystalline structure of N,N-dimethylaza[8]CPP. For the sake of comparison, intra-molecular and inter-molecular charge transport parameters are concomitantly modelled for the recently determined herringbone polymorph of [6]CPP, along with [8]CPP and [12]CPP. The peculiar contribution of low frequency vibrations to intramolecular reorganization energies is also disclosed by computing the Huang-Rhys factors for the investigated [n]CPPs and the N,N-dimethylaza derivative. In contrast with most planar organic semiconductors where the layer in which molecules are herringbone arranged identifies the high-mobility plane, nanohoops disclose inter-layer electronic couplings larger than the intra-layer counterparts. Charge transfer rate constants modelled with three different approaches (Marcus, Marcus-Levich-Jortner and spectral overlap) suggest that D-A nanohoops, owing to orbital localization, may be more efficient for charge transport than [n]CPPs for suitable solid phase arrangements.

The dimer-approach to characterize opto-electronic properties of and exciton trapping and diffusion in organic semiconductor aggregates and crystals

We present the recently developed dimer approach which seems to include all main effects determining the photo-physics of organic semiconductor aggregates.

Opposite Anisotropy Effects of Singlet and Triplet Exciton Diffusion in Tetracene Crystal

We observe the diffusion anisotropy difference between singlet and triplet excitons in organic crystals; that is, singlet and triplet excitons may have completely different spatial direction preference for diffusion. This phenomenon can be ascribed to the distinct dependence of different excitonic couplings (Coulomb Förster vs. exchange Dexter) existing in singlet and triplet excitons on their intermolecular distance and intermolecular orientation. Such a discovery provides insights for understanding the fundamental photophysical process in a vast range of organic condensed-phase systems and optimizing the efficiency of organic optoelectronic materials.

A theoretical description of charge reorganization energies in molecular organic P-type semiconductors

Charge transport properties of materials composed of small organic molecules are important for numerous optoelectronic applications. A material's ability to transport charges is considerably influenced by the charge reorganization energies of the composing molecules. Hence, predictions about charge-transport properties of organic materials deserve reliable statements about these charge reorganization energies. However, using density functional theory which is mostly used for the predictions, the computed reorganization energies depend strongly on the chosen functional. To gain insight, a benchmark of various density functionals for the accurate calculation of charge reorganization energies is presented. A correlation between the charge reorganization energies and the ionization potentials is found which suggests applying IP-tuning to obtain reliable values for charge reorganization energies. According to benchmark investigations with IP-EOM-CCSD single-point calculations, the tuned functionals provide indeed more reliable charge reorganization energies. Among the standard functionals, ωB97X-D and SOGGA11X yield accurate charge reorganization energies in comparison with IP-EOM-CCSD values. © 2016 Wiley Periodicals, Inc.

Simulations of singlet exciton diffusion in organic semiconductors: a review

Recent advances in exciton diffusion simulations in conjugated materials are presented in this review.

Charge transfer properties of two polymorphs of luminescent (2-fluoro-3-pyridyl)(2,2′-biphenyl)borinic 8-oxyquinolinate

First example of polymorphism and its impact on the charge transport properties of a model borinic quinolinate system.

Effect of high pressure on the crystal structure and charge transport properties of the (2-fluoro-3-pyridyl)(4-iodophenyl)borinic 8-oxyquinolinate complex

Compression of the crystal structure and its impact on the charge transport properties of a model borinic quinolinate system.