Efficient calculation of electronic coupling integrals with the dimer projection method via a density matrix tight-binding potential

Designing organic semiconductors for practical applications in organic solar cells, organic field-effect transistors, and organic light-emitting diodes requires understanding charge transfer mechanisms across different length and time scales. The underlying electron transfer mechanisms can be efficiently explored using semiempirical quantum mechanical (SQM) methods. The dimer projection (DIPRO) method combined with the recently introduced non-self-consistent density matrix tight-binding potential (PTB) [Grimme et al., J. Chem. Phys. 158, 124111 (2023)] is used in this study to evaluate charge transfer integrals important for understanding charge transport mechanisms. PTB, parameterized for the entire Periodic Table up to Z = 86, incorporates approximate non-local exchange, allowing for efficient and accurate calculations for large hetero-organic compounds. Benchmarking against established databases, such as Blumberger's HAB sets, or our newly introduced JAB69 set and comparing with high-level reference data from ωB97X-D4 calculations confirm that DIPRO@PTB consistently performs well among the tested SQM approaches for calculating coupling integrals. DIPRO@PTB yields reasonably accurate results at low computational cost, making it suitable for screening purposes and applications to large systems, such as metal-organic frameworks and cyanine-based molecular aggregates further discussed in this work.

Modeling Molecular Emitters in Organic Light-Emitting Diodes with the Quantum Mechanical Bespoke Force Field

Combined molecular dynamics (MD) and quantum mechanics (QM) simulation procedures have gained popularity in modeling the spectral properties of functional organic molecules. However, the potential energy surfaces used to propagate long-time scale dynamics in these simulations are typically described using general, transferable force fields designed for organic molecules in their electronic ground states. These force fields do not typically include spectroscopic data in their training, and importantly, there is no general protocol for including changes in geometry or intermolecular interactions with the environment that may occur upon electronic excitation. In this work, we show that parameters tailored for thermally activated delayed fluorescence (TADF) emitters used in organic light-emitting diodes (OLEDs), in both their ground and electronically excited states, can be readily derived from a small number of QM calculations using the QUBEKit (QUantum mechanical BEspoke toolKit) software and improve the overall accuracy of these simulations.

Impact of Fluoroalkylation on the n-Type Charge Transport of Two Naphthodithiophene Diimide Derivatives

In this work, we investigate two recently synthesized naphthodithiophene diimide (NDTI) derivatives featuring promising n-type charge transport properties. We analyze the charge transport pathways and model charge mobility with the non-adiabatic hopping mechanism using the Marcus-Levich-Jortner rate constant formulation, highlighting the role of fluoroalkylated substitution in α (α-NDTI) and at the imide nitrogen (N-NDTI) position. In contrast with the experimental results, similar charge mobilities are computed for the two derivatives. However, while α-NDTI displays remarkably anisotropic mobilities with an almost one-dimensional directionality, N-NDTI sustains a more isotropic charge percolation pattern. We propose that the strong anisotropic charge transport character of α-NDTI is responsible for the modest measured charge mobility. In addition, when the role of thermally induced transfer integral fluctuations is investigated, the computed electron-phonon couplings for intermolecular sliding modes indicate that dynamic disorder effects are also more detrimental for the charge transport of α-NDTI than N-NDTI. The lower observed mobility of α-NDTI is therefore rationalized in terms of a prominent anisotropic character of the charge percolation pathways, with the additional contribution of dynamic disorder effects.

Efficient evaluation of Coulomb interactions in kinetic Monte Carlo simulations of charge transport

The application of predictive and reliable modeling techniques for the simulation of charge transport in functional materials is an essential step for the development of advanced platforms for electronics, optoelectronics, and photovoltaics. In this context, kinetic Monte Carlo (KMC) methods have emerged as a valuable tool, especially for the simulation of systems where charge transport can be described by the hopping of charge carriers across localized quantum states, as, for example, in organic semiconductor materials. The accuracy, computational efficiency, and reliability of KMC simulations of charge transport, however, crucially depend on the methods and approximations used to evaluate electrostatic interactions arising from the distribution of charges in the system. The long-range nature of Coulomb interactions and the need to simulate large model systems to capture the details of charge transport phenomena in complex devices lead, typically, to a computational bottleneck, which hampers the application of KMC methods. Here, we propose and assess computational schemes for the evaluation of electrostatic interactions in KMC simulations of charge transport based on the locality of the charge redistribution in the hopping regime. The methods outlined in this work provide an overall accuracy that outperforms typical approaches for the evaluation of electrostatic interactions in KMC simulations at a fraction of the computational cost. In addition, the computational schemes proposed allow a spatial decomposition of the evaluation of Coulomb interactions, leading to an essentially linear scaling of the computational load with the size of the system.

Exploring Disordered Morphologies of Blends and Block Copolymers for Light-Emitting Diodes with Mesoscopic Simulations

Recently, disordered blends of semiconducting and insulating polymers have been used to prepare light-emitting diodes with increased luminous efficiency. Because the thermodynamic stability of the disordered phase in blends is limited, equivalent diblock copolymers (BCPs) could be an alternative. However, the choice between disordered blends and BCPs requires understanding structural differences and their effect on charge carrier transport. Using a hybrid mesoscopic model, we simulate blends and equivalent BCPs of two representative semiconducting and insulating polymers: poly(p-phenylene vinylene) (PPV) and polyacrylate. The immiscibility is varied to mimic annealing at different temperatures. We find stable or metastable disordered morphologies until we reach the mean-field (MF) spinodal. Disordered morphologies are heterogeneous because of thermal fluctuations and local segregation. Near the MF spinodal, segregation is stronger in BCPs than in the blends, even though the immiscibility, normalized by the MF spinodal, is the same. We link the spatial distribution of PPV with electric conductance. We predict that the immiscibility (temperature at which the layer is annealed) affects electrical percolation much stronger in BCPs than in blends. Differences in the local structure and percolation between blends and BCPs are enhanced at a high insulator content.

A quantitative structure-property study of reorganization energy for known p-type organic semiconductors

Intramolecular reorganization energy (RE), which quantifies the electron-phonon coupling strength, is an important charge transport parameter for the theoretical characterization of molecular organic semiconductors (OSCs). On a small scale, the accurate calculation of the RE is trivial; however, for large-scale screening, faster approaches are desirable. We investigate the structure-property relations and present a quantitative structure-property relationship study to facilitate the computation of RE from molecular structure. To this end, we generated a compound set of 171, which was derived from known p-type OSCs built from moieties such as acenes, thiophenes, and pentalenes. We show that simple structural descriptors such as the number of atoms, rings or rotatable bonds only weakly correlate with the RE. On the other hand, we show that regression models based on a more comprehensive representation of the molecules such as SMILES-based molecular signatures and geometry-based molecular transforms can predict the RE with a coefficient of determination of 0.7 and a mean absolute error of 40 meV in the library, in which the RE ranges from 76 to 480 meV. Our analysis indicates that a more extensive compound set for training is necessary for more predictive models.

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole-Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log-log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

Effects of Structural and Energetic Disorders on Charge Transports in Crystal and Amorphous Organic Layers

Understanding charge transports in organic films is important for both fundamental science and practical applications. Here, contributions of off-diagonal (structural) and diagonal (energetic) disorders to charge transports were clarified using molecular-based multiscale simulation. These disorders, important for understanding charge transport in organic systems, are investigated by comparing crystal and amorphous aggregates of N,N'-diphenyl-N,N'-bis(1-naphthyl)-1,1'-biphenyl-4,4'-diamine (NPD). Although NPD has been used as a hole transport material, it also exhibits comparable electron mobility experimentally. The experimental mobility and its electric field dependence in amorphous layers were reasonably reproduced by the multiscale simulation, confirming the electron transport properties of NPD. We assumed that the structural disorder would lower mobilities; however, the mobilities were found to be independent of the degree of structural disorder. Energetic disorder markedly lowered charge mobility instead. Charge migration in crystals was dominated by maximum electronic coupling pairs, whereas small electronic coupling pairs significantly contributed to charge transport in amorphous aggregate.

The prediction of hole mobility in organic semiconductors and its calibration based on the grain-boundary effect

A new reliable computational model to predict the hole mobility of poly-crystalline organic semiconductors in thin films was developed. Site energy differences and transfer integrals in crystalline morphologies of organic molecules were obtained from quantum chemical calculations, in which periodic boundary conditions were efficiently applied to capture the interactions with the surrounding molecules in the crystalline organic layer. Then the parameters were employed in kinetic Monte Carlo (kMC) simulations to estimate the carrier mobility. Carrier transport in multiple directions has been considered in the kMC simulation to mimic poly-crystalline characteristics under thin-film conditions. Furthermore, the calculated mobility was corrected using a calibration equation based on microscopy images of the thin films to take the effect of grain boundaries into account. As a result, good agreement was observed between the predicted and measured hole mobility values for 21 molecular species: the coefficient of determination (R(2)) was estimated to be 0.83 and the mean absolute error was 1.32 cm(2) V(-1) s(-1). This numerical approach can be applied to any molecules for which crystal structures are available and will provide a rapid and precise way of predicting device performance.

The crucial role of a spacer material on the efficiency of charge transfer processes in organic donor-acceptor junction solar cells

Organic photovoltaic donor-acceptor junction devices composed of π-conjugated polymer electron donors (D) and fullerene electron acceptors (A) show greatly increased performance when a spacer material is inserted between the two layers (W. Y. Nie, G. Gupta, B. K. Crone, F. L. Liu, D. L. Smith, P. P. Ruden, C. Y. Kuo, H. Tsai, H. L. Wang, H. Li, S. Tretiak and A. D. Mohite, Adv. Sci., 2015, 2, 1500024.). For instance, experimental results reveal significant improvement of photocurrent when a terthiophene oligomer derivative is inserted in between π-conjugated poly(3-hexylthiophene-2,5-diyl) (P3HT) donor and C₆₀ acceptor. These results indicate favorable charge separation dynamics, which is addressed by our present joint theoretical/experimental study establishing the beneficial alignment of electronic levels due to the specific morphology of the material. Namely, based on the experimental data we have constructed extended structural interface models containing C₆₀ fullerenes and P3HT separated by aligned oligomer chains. Our time-dependent density functional theory (TD-DFT) calculations based on a long-range corrected functional, allowed us to address the energetics of essential electronic states and analyze them in terms of charge transfer (CT) character. Specifically, the simulations reveal the electronic spectra composed of a ladder of excited states evolving excitation toward spatial charge separation: an initial excitonic excitation at P3HT decomposes into charges by sequentially relaxing through bands of C₆₀-centric, oligomer → C₆₀ and P3HT → C₆₀ CT states. Our modeling exposes a critical role of dielectric environment effects and electronic couplings in the self-assembled spacer oligomer layer on the energetics of critical CT states leading to a reduced back-electron transfer, preventing recombination losses, and thus rationalizes physical processes underpinning experimental observations.

Charge Transport in Molecular Materials: An Assessment of Computational Methods

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

Simulating charge transport in organic semiconductors and devices: a review

Charge transport simulation can be a valuable tool to better understand, optimise and design organic transistors (OTFTs), photovoltaics (OPVs), and light-emitting diodes (OLEDs). This review presents an overview of common charge transport and device models; namely drift-diffusion, master equation, mesoscale kinetic Monte Carlo and quantum chemical Monte Carlo, and a discussion of the relative merits of each. This is followed by a review of the application of these models as applied to charge transport in organic semiconductors and devices, highlighting in particular the insights made possible by modelling. The review concludes with an outlook for charge transport modelling in organic electronics.

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.

Coherent Dynamics of Mixed Frenkel and Charge-Transfer Excitons in Dinaphtho[2,3-b:2'3'-f]thieno[3,2-b]-thiophene Thin Films: The Importance of Hole Delocalization

Charge-transfer states in organic semiconductors play crucial roles in processes such as singlet fission and exciton dissociation at donor/acceptor interfaces. Recently, a time-resolved spectroscopy study of dinaphtho[2,3-b:2'3'-f]thieno[3,2-b]-thiophene (DNTT) thin films provided evidence for the formation of mixed Frenkel and charge-transfer excitons after the photoexcitation. Here, we investigate optical properties and excitation dynamics of the DNTT thin films by combining ab initio calculations and a stochastic Schrödinger equation. Our theory predicts that the low-energy Frenkel exciton band consists of 8-47% CT character. The quantum dynamics simulations show coherent dynamics of Frenkel and CT states in 50 fs after the optical excitation. We demonstrate the role of charge delocalization and localization in the mixing of CT states with Frenkel excitons as well as the role of their decoherence.

A theoretical study on charge transport of dithiolene nickel complexes

The effect of chemical structures on the charge transport characteristics of dithiophene nickel complexes was studied using DFT and NEGF-DFT methods.

QM/QM approach to model energy disorder in amorphous organic semiconductors

It is an outstanding challenge to model the electronic properties of organic amorphous materials utilized in organic electronics. Computation of the charge carrier mobility is a challenging problem as it requires integration of morphological and electronic degrees of freedom in a coherent methodology and depends strongly on the distribution of polaron energies in the system. Here we represent a QM/QM model to compute the polaron energies combining density functional methods for molecules in the vicinity of the polaron with computationally efficient density functional based tight binding methods in the rest of the environment. For seven widely used amorphous organic semiconductor materials, we show that the calculations are accelerated up to 1 order of magnitude without any loss in accuracy. Considering that the quantum chemical step is the efficiency bottleneck of a workflow to model the carrier mobility, these results are an important step toward accurate and efficient disordered organic semiconductors simulations, a prerequisite for accelerated materials screening and consequent component optimization in the organic electronics industry.

25th anniversary article: organic field-effect transistors: the path beyond amorphous silicon

Over the past 25 years, organic field-effect transistors (OFETs) have witnessed impressive improvements in materials performance by 3-4 orders of magnitude, and many of the key materials discoveries have been published in Advanced Materials. This includes some of the most recent demonstrations of organic field-effect transistors with performance that clearly exceeds that of benchmark amorphous silicon-based devices. In this article, state-of-the-art in OFETs are reviewed in light of requirements for demanding future applications, in particular active-matrix addressing for flexible organic light-emitting diode (OLED) displays. An overview is provided over both small molecule and conjugated polymer materials for which field-effect mobilities exceeding > 1 cm(2) V(-1) s(-1) have been reported. Current understanding is also reviewed of their charge transport physics that allows reaching such unexpectedly high mobilities in these weakly van der Waals bonded and structurally comparatively disordered materials with a view towards understanding the potential for further improvement in performance in the future.

Can lattice models predict the density of states of amorphous organic semiconductors?

We extend existing lattice models of small-molecule amorphous semiconductors by accounting for changes in molecular polarizability upon charging or excitation. A compact expression of this contribution to the density of states is provided. Although the lattice model and the description based on a microscopic morphology both qualitatively predict an additional broadening, shift, and an exponential tail (traps) of the density of states, a quantitative agreement between the two cannot be achieved.