Charge transport in high mobility molecular semiconductors: classical models and new theories

Rapid Estimation of the Intermolecular Electronic Couplings and Charge-Carrier Mobilities of Crystalline Molecular Organic Semiconductors through a Machine Learning Pipeline

Organic semiconductors (OSC) offer tremendous potential across a wide range of (opto)electronic applications. OSC development, however, is often limited by trial-and-error design, with computational modeling approaches deployed to evaluate and screen candidates through a suite of molecular and materials descriptors that generally require hours to days of computational time to accumulate. Such bottlenecks slow the pace and limit the exploration of the vast chemical space comprising OSC. When considering charge-carrier transport in OSC, a key parameter of interest is the intermolecular electronic coupling. Here, we introduce a machine learning (ML) model to predict intermolecular electronic couplings in organic crystalline materials from their three-dimensional (3D) molecular geometries. The ML predictions take only a few seconds of computing time compared to hours by density functional theory (DFT) methods. To demonstrate the utility of the ML predictions, we deploy the ML model in conjunction with mathematical formulations to rapidly screen the charge-carrier mobility anisotropy for more than 60,000 molecular crystal structures and compare the ML predictions to DFT benchmarks.

Non-adiabatic molecular dynamics simulations provide new insights into the exciton transfer in the Fenna-Matthews-Olson complex

A trajectory surface hopping approach, which uses machine learning to speed up the most time-consuming steps, has been adopted to investigate the exciton transfer in light-harvesting systems. The present neural networks achieve high accuracy in predicting both Coulomb couplings and excitation energies. The latter are predicted taking into account the environment of the pigments. Direct simulation of exciton dynamics through light-harvesting complexes on significant time scales is usually challenging due to the coupled motion of nuclear and electronic degrees of freedom in these rather large systems containing several relatively large pigments. In the present approach, however, we are able to evaluate a statistically significant number of non-adiabatic molecular dynamics trajectories with respect to exciton delocalization and exciton paths. The formalism is applied to the Fenna-Matthews-Olson complex of green sulfur bacteria, which transfers energy from the light-harvesting chlorosome to the reaction center with astonishing efficiency. The system has been studied experimentally and theoretically for decades. In total, we were able to simulate non-adiabatically more than 30 ns, sampling also the relevant space of parameters within their uncertainty. Our simulations show that the driving force supplied by the energy landscape resulting from electrostatic tuning is sufficient to funnel the energy towards site 3, from where it can be transferred to the reaction center. However, the high efficiency of transfer within a picosecond timescale can be attributed to the rather unusual properties of the BChl a molecules, resulting in very low inner and outer-sphere reorganization energies, not matched by any other organic molecule, e.g., used in organic electronics. A comparison with electron and exciton transfer in organic materials is particularly illuminating, suggesting a mechanism to explain the comparably high transfer efficiency.

Research and Progress on Organic Semiconductor Power Devices

Organic semiconductor power devices have been attracting increasing attention due to their advantages such as flexibility, low fabrication cost, and sustainability. They have found wide applications in fields such as flexible electronic devices and biomedical devices. However, in the field of power applications, the lack of reliable organic semiconductor power devices is mainly attributed to the limited thermal stability and electrical stability of organic materials. This article provides a detailed review of the development status of organic semiconductor power devices from three aspects: device structure, organic materials, and fabrication methods. It clarifies that the future development goal is to enhance the voltage resistance and thermal stability of organic transistors through higher-performance structure design, higher-mobility materials, and higher-quality fabrication methods. The continuous innovation and development of the structures, materials, and fabrication of these devices will generate more novel devices, offering more possibilities for the application of organic semiconductor power devices. This information is of great reference value and guidance significance for engineers in related fields.

Entropy-ruled nonequilibrium charge transport in thiazolothiazole-based molecular crystals: a quantum chemical study

The charge and energy fluctuations in molecular solids are crucial factors for a better understanding of charge transport (CT) in organic semiconductors. The energetic disorder-coupled molecular charge transport is still not well-established. Moreover, the conventional Einstein's diffusion (D)-mobility (μ) relation fails to explain the quantum features of organic semiconductors, including nonequilibrium and degenerate transport systems, where kB is the Boltzmann constant, T is the temperature and q is the electric charge. To overcome this issue, a unified version of the entropy-ruled D/μ relation was proposed by Navamani (J. Phys. Chem. Lett., 2024, 15, 2519-2528) for hopping and band transport systems as where d, η and heff are the dimension (d = 1, 2, 3), chemical potential and effective entropy, respectively. Within this context, we investigate the CT properties of 2,5-bis(4-methoxyphenyl)thiazolo[5,4-d]thiazole (MOP-TZTZ) and 2,5-bis(2,4,5 trifluorophenyl)-thiazolo[5,4-d]thiazole (TFP-TZTZ) molecular solids using electronic structure calculations and the entropy-ruled method. The CT key parameters such as charge transfer integral and site energy are computed by matrix elements of the Kohn-Sham Hamiltonian. Using Marcus theory, the charge transfer rate is numerically calculated for MOP-TZTZ and TFP-TZTZ molecular crystals under different site energy disorder (ΔEij(E⃑)) situations. Using our entropy-ruled method, the exact diffusion-mobility (D/μ) and other transport quantities such as thermodynamic density of states, conductivity, and current density are calculated for these derivatives at different applied electric field values via the site energy disorder. The theoretical results show that the molecule TFP-TZTZ has good hole mobility (∼0.012 cm2 V-1 s-1) at a site energy disorder value of 90 meV. The obtained ideality factor from the Navamani-Shockley diode current density equation categorizes the typical transport as either the Langevin-type or Shockley-Read-Hall mechanism in the studied molecular solids. Our analysis clearly shows that both the electron and hole transport in these MOP-TZTZ and TFP-TZTZ molecules follow the trap-free Langevin mechanism, which is indeed ideal for designing charge-transporting molecular devices.

Is there a finite mobility for the one vibrational mode Holstein model? Implications from real time simulations

The question of whether there exists a finite mobility in the standard Holstein model with one vibrational mode on each site remains unclear. In this Communication, we approach this problem by employing the hierarchical equation of motion method to simulate model systems where the vibrational modes are dissipative. It is found that, as the friction becomes smaller, the charge carrier mobility increases significantly and a friction-free limit cannot be obtained. The current autocorrelation functions are also calculated for the friction-free Holstein model, and converged results cannot be obtained with an increase in the number of sites. Based on these observations, we conclude that a finite mobility cannot be defined for the standard Holstein model in the parameter regime explored in this work.

Morphology, dynamic disorder, and charge transport in an indoloindole-based hole-transporting material from a multi-level theoretical approach

The exponential effort in the design of hole-transporting materials (HTMs) during the last decade has been motivated by their key role as p-type semiconductors for (opto)electronics. Although structure-property relationships have been successfully rationalized to decipher optimal site substitutions, aliphatic chain lengths or efficient aromatic cores for enhanced charge conduction, the impact of molecular shape, material morphology and dynamic disorder has been generally overlooked. In this work, we characterize by means of a multi-level theoretical approach the charge transport properties of a novel planar small-molecule HTM based on the indoloindole aromatic core (IDIDF), and compare it with spherical spiro-OMeTAD. Hybrid DFT calculations predict moderate band dispersions in IDIDF associated to the main transport direction characterized by π-π stacked molecules, both between the indoloindole cores and the thiophene groups. Strongly coupled dimers show relevant non-covalent interactions (NCI), indicating that NCI surfaces are a necessary but not exclusive requirement for large electronic couplings. We evidence remarkable differences in the site energy standard deviation and electronic coupling distributions between the conduction paths of IDIDF and spiro-OMeTAD. Despite the spherical vs. planar shape, theoretical calculations predict in the static crystal strong direction-dependent charge transport in the two HTMs, with ca. one-order-of-magnitude higher mobility (μ) for IDIDF. The dynamical disorder promoted by finite temperature effects in the crystal leads to a reduction in the hole transport properties in both HTMs, with maximum μ values of 2.42 and 4.2 × 10-2 cm2 V-1 s-1 for IDIDF and spiro-OMeTAD, respectively, as well as a significant increase in the transport anisotropy in the latter. Finally, the impact of the material amorphousness in the hole mobility is analysed by modelling a fully random distribution of HTM molecules. An average (lower-bound) mobility of 1.1 × 10-3 and 4.9 × 10-5 cm2 V-1 s-1 is predicted for planar IDIDF and spherical spiro-OMeTAD, respectively, in good accord with the experimental data registered in thin-film devices. Our results demonstrate the strong influence of molecular shape, dynamic structural fluctuations and crystal morphology on the charge transport, and pose indoloindole-based HTMs as promising materials for organic electronics and photovoltaics.

Unified Entropy-Ruled Einstein's Relation for Bulk and Low-Dimensional Molecular-Material Systems: A Hopping-to-Band Shift Paradigm

We present a unified paradigm on entropy-ruled Einstein's diffusion-mobility relation (μ/D ratio) for 1D, 2D, and 3D free-electron solid state systems. The localization transport in the extended molecules is well approximated by the continuum time-delayed hopping factor within our unified entropy-ruled transport method of noninteracting quantum systems. Moreover, we generalize an entropy-dependent diffusion relation for 1D, 2D, and 3D systems as defined by D d , h e f f = D d , h e f f = 0 ⁡ exp ( ( d - 1 ) h e f f d + 2 ) , where heff and d are the effective entropy and dimension (d = 1, 2, 3), respectively. This generalized relation is valid for both equilibrium and nonequilibrium transport systems since the parameter heff is closely connected with the nonequilibrium fluctuation theorem-based entropy production rule. Importantly, we herein revisit the Boltzmann approach using an entropy-ruled method for mobility calculation for the universal quantum materials that is expressed as μ d = [ ( d d + 2 ) q d h e f f d η ] v F 2 τ 2 , where v F 2 τ 2 is the diffusion constant for band transport systems and η is the chemical potential. According to our entropy-ruled μ/D relation, the Navamani-Shockley diode equation is transformed.

Two-Step Machine Learning Approach for Charge-Transfer Coupling with Structurally Diverse Data

Electronic coupling is important in determining charge-transfer rates and dynamics. Coupling strength is sensitive to both intermolecular, e.g., orientation or distance, and intramolecular degrees of freedom. Hence, it is challenging to build an accurate machine learning model to predict electronic coupling of molecular pairs, especially for those derived from the amorphous phase, for which intermolecular configurations are much more diverse than those derived from crystals. In this work, we devise a new prediction algorithm that employs two consecutive KRR models. The first model predicts molecular orbitals (MOs) from structural variation for each fragment, and coupling is further predicted by using the overlap integral included in a second model. With our two-step procedure, we achieved mean absolute errors of 0.27 meV for an ethylene dimer and 1.99 meV for a naphthalene pair, much improved accuracy amounting to 14-fold and 3-fold error reductions, respectively. In addition, MOs from the first model can also be the starting point to obtain other quantum chemical properties from atomistic structures. This approach is also compatible with a MO predictor with sufficient accuracy.

Trap suppression in ordered organic photovoltaic heterojunctions

The high trap density (generally 1016-1018 cm-3) in organic solar cells (OSCs) brings about the localization of charge carriers and reduced charge carrier lifetime, mainly due to the weak intermolecular interactions of organic semiconductors resulting in their relatively poor crystallinity, which leads to low charge carrier mobilities and intense non-radiative recombination, thus impeding the further improvement of power conversion efficiencies (PCEs). Therefore, trap suppression is crucial to boost the performance of OSCs, and improving the crystallinity of donor/acceptor materials and enhancing the molecular order in devices can contribute to the trap suppression in OSCs. In this feature article, we summarize the recent advances of trap suppression in OSCs by material design and device engineering, and further outline possible development directions for trap suppression to enhance PCEs of OSCs.

Interlayer Charge Transport in 2D Lead Halide Perovskites from First Principles

We report on the implementation of a versatile projection-operator diabatization approach to calculate electronic coupling integrals in layered periodic systems. The approach is applied to model charge transport across the saturated organic spacers in two-dimensional (2D) lead halide perovskites. The calculations yield out-of-plane charge transfer rates that decay exponentially with the increasing length of the alkyl chain, range from a few nanoseconds to milliseconds, and are supportive of a hopping mechanism. Most importantly, we show that the charge carriers strongly couple to distortions of the Pb-I framework and that accounting for the associated nonlocal dynamic disorder increases the thermally averaged interlayer rates by a few orders of magnitude compared to the frozen-ion 0 K-optimized structure. Our formalism provides the first comprehensive insight into the role of the organic spacer cation on vertical transport in 2D lead halide perovskites and can be readily extended to functional π-conjugated spacers, where we expect the improved energy alignment with the inorganic layout to speed up the charge transfer between the semiconducting layers.

Coexistence of Incoherent and Ultrafast Coherent Exciton Transport in a Two-Dimensional Superatomic Semiconductor

Fully leveraging the remarkable properties of low-dimensional semiconductors requires developing a deep understanding of how their structure and disorder affect the flow of electronic energy. Here, we study exciton transport in single crystals of the two-dimensional superatomic semiconductor CsRe6Se8I3, which straddles a photophysically rich yet elusive intermediate electronic-coupling regime. Using femtosecond scattering microscopy to directly image exciton transport in CsRe6Se8I3, we reveal the rare coexistence of coherent and incoherent exciton transport, leading to either persistent or transient electronic delocalization depending on temperature. Notably, coherent excitons exhibit ballistic transport at speeds approaching an extraordinary 1600 km/s over 300 fs. Such fast transport is mediated by J-aggregate-like superradiance, owing to the anisotropic structure and long-range order of CsRe6Se8I3. Our results establish superatomic crystals as ideal platforms for studying the intermediate electronic-coupling regime in highly ordered environments, in this case displaying long-range electronic delocalization, ultrafast energy flow, and a tunable dual transport regime.

Transiently delocalized states enhance hole mobility in organic molecular semiconductors

Evidence shows that charge carriers in organic semiconductors self-localize because of dynamic disorder. Nevertheless, some organic semiconductors feature reduced mobility at increasing temperature, a hallmark for delocalized band transport. Here we present the temperature-dependent mobility in two record-mobility organic semiconductors: dinaphtho[2,3-b:2',3'-f]thieno[3,2-b]-thiophene (DNTT) and its alkylated derivative, C8-DNTT-C8. By combining terahertz photoconductivity measurements with atomistic non-adiabatic molecular dynamics simulations, we show that while both crystals display a power-law decrease of the mobility (μ) with temperature (T) following μ ∝ T -n, the exponent n differs substantially. Modelling reveals that the differences between the two chemically similar semiconductors can be traced to the delocalization of the different states that are thermally accessible by charge carriers, which in turn depends on their specific electronic band structure. The emerging picture is that of holes surfing on a dynamic manifold of vibrationally dressed extended states with a temperature-dependent mobility that provides a sensitive fingerprint for the underlying density of states.

Investigating the function and design of molecular materials through terahertz vibrational spectroscopy

Terahertz spectroscopy has proved to be an essential tool for the study of condensed phase materials. Terahertz spectroscopy probes the low-frequency vibrational dynamics of atoms and molecules, usually in the condensed phase. These nuclear dynamics, which typically involve displacements of entire molecules, have been linked to bulk phenomena ranging from phase transformations to semiconducting efficiency. The terahertz region of the electromagnetic spectrum has historically been referred to as the 'terahertz gap', but this is a misnomer, as there exist a multitude of methods for accessing terahertz frequencies, and now there are cost-effective instruments that have made terahertz studies much more user-friendly. This Review highlights some of the most exciting applications of terahertz vibrational spectroscopy so far, and provides an in-depth overview of the methods of this technique and its utility to the study of the chemical sciences.

Ambipolar Charge Transport in Organic Semiconductors: How Intramolecular Reorganization Energy Is Controlled by Diradical Character

The charged forms of π-conjugated chromophores are relevant in the field of organic electronics as charge carriers in optoelectronic devices, but also as energy storage substrates in organic batteries. In this context, intramolecular reorganization energy plays an important role in controlling material efficiency. In this work, we investigate how the diradical character influences the reorganization energies of holes and electrons by considering a library of diradicaloid chromophores. We determine the reorganization energies with the four-point adiabatic potential method using quantum-chemical calculations at density functional theory (DFT) level. To assess the role of diradical character, we compare the results obtained, assuming both closed-shell and open-shell representations of the neutral species. The study shows how the diradical character impacts the geometrical and electronic structure of neutral species, which in turn control the magnitude of reorganization energies for both charge carriers. Based on computed geometries of neutral and charged species, we propose a simple scheme to rationalize the small, computed reorganization energies for both n-type and p-type charge transport. The study is supplemented with the calculation of intermolecular electronic couplings governing charge transport for selected diradicals, further supporting the ambipolar character of the investigated diradicals.

Quantum-Classical Transition Analogy of the Diffusion-Mobility Relation for Hopping and Band Transport Systems: Molecules to Materials

We propose a quantum-classical transition analogy for Einstein's diffusion-mobility (D/μ) relation to reveal electron-hole dynamics in both the degenerate and nondegenerate molecular and material systems. Here, one-to-one variation between differential entropy and chemical potential (Δη/Δh_s) is the proposed analogy, which unifies quantum and classical transport. The degeneracy stabilization energy on D/μ decides whether the transport is quantum or classical; accordingly, the transformation occurs in the Navamani-Shockley diode equation.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

Charge Localization in Acene Crystals from Ab Initio Electronic Structure

The performance of Koopmans-compliant hybrid functionals in reproducing the electronic structure of organic crystals is tested for a series of acene crystals. The calculated band gaps are found to be consistent with those achieved with the GW method at a fraction of the computational cost and in excellent accord with the experimental results at room temperature, when including the thermal renormalization. The energetics of excess holes and electrons reveals a struggle between polaronic localization and band-like delocalization. The consequences of these results on the transport properties of acene crystals are discussed.

Self-assembled discotics as molecular semiconductors

With the advent of a new era of smart-technology, the demand for more economic optoelectronic materials that do not compromise with efficiency is gradually on the rise. Organic semiconductors provide greener alternatives to the conventional inorganic ones, but encounter the challenge of balancing charge carrier mobility with processability in devices. Discotic liquid crystals (DLCs), a class of self-assembling soft organic materials, possess the perfect degree of order and dynamics to address this challenge. Providing unidimensional charge carrier pathways through their nanoscale columnar architecture, DLCs can behave as efficient charge transport systems across a wide range of optoelectronic devices. Moreover, DLCs are solution-processable, thus reducing the fabrication cost. In this article, we have discussed the approaches towards developing DLCs as semiconductors, focusing on their molecular design concepts, supramolecular structures and electronic properties in the context of their charge carrier mobilities.

Efficiently predicting directional carrier mobilities in organic materials with the Boltzmann transport equation

Describing charge carrier anisotropy in crystalline organic semiconductors with ab initio methods is challenging because of the weak intermolecular interactions that lead to both localized and delocalized charge transport mechanisms. Small polaron hopping models (localized) are generally used to describe materials with small charge carrier mobilities, while periodic band models (delocalized) are used to describe materials with high charge carrier mobilities. Here, we prove the advantage of applying the constant relaxation time approximation of the Boltzmann transport equation (BTE) to efficiently predict the anisotropic hole mobilities of several unsubstituted (anthracene, tetracene, pentacene, and hexacene) and substituted (2,6-diphenylanthracene, rubrene, and TIPS-pentacene) high-mobility n-acene single crystals. Several density functionals are used to optimize the crystals, and the composite density functional PBEsol0-3c/sol-def2-mSVP predicts the most experimentally similar geometries, adequate indirect bandgaps, and the theoretically consistent n-acene charge transport mobility trend. Similarities between BTE and Marcus mobilities are presented for each crystal. BTE and Marcus charge carrier mobilities computed at the same geometry result in similar mobility trends, differing mostly in materials with more substitutions or structurally complex substituents. By using a reduced number of calculations, BTE is able to predict anisotropic carrier mobilities efficiently and effectively for a range of high-mobility organic semiconductors.

Influence of Side Chain Interdigitation on Strain and Charge Mobility of Planar Indacenodithiophene Copolymers

Indacenodithiophene (IDT) copolymers are a class of conjugated polymers that have limited long-range order and high hole mobilities, which makes them promising candidates for use in deformable electronic devices. Key to their high hole mobilities is the coplanar monomer repeat units within the backbone. Poly(indacenodithiophene-benzothiadiazole) (PIDT_C16-BT) and poly(indacenodithiophene-thiapyrollodione) (PIDT_C16-TPD_C1) are two IDT copolymers with planar backbones, but they are brittle at low molecular weight and have unsuitably high elastic moduli. Substitution of the hexadecane (C₁₆) side chains of the IDT monomer with isocane (C₂₀) side chains was performed to generate a new BT-containing IDT copolymer: PIDT_C20-BT. Substitution of the methyl (C₁) side chain on the TPD monomer for an octyl (C₈) and 6-ethylundecane (C_13B) afford two new TPD-containing IDT copolymers named PIDT_C16-TPD_C8 and PIDT_C16-TPD_C13B, respectively. Both PIDT_C16-TPD_C8 and PIDT_C16-TPD_C13B are relatively well deformable, have a low yield strain, and display significantly reduced elastic moduli. These mechanical properties manifest themselves because the lengthened side chains extending from the TPD-monomer inhibit precise intermolecular ordering. In PIDT_C16-BT, PIDT_C20-BT and PIDT_C16-TPD_C1 side chain ordering can occur because the side chains are only present on the IDT subunit, but this results in brittle thin films. In contrast, PIDT_C16-TPD_C8 and PIDT_C16-TPD_C13B have disordered side chains, which seems to lead to low hole mobilities. These results suggest that disrupting the interdigitation in IDT copolymers through comonomer side chain extension leads to more ductile thin films with lower elastic moduli, but decreased hole mobility because of altered local order in the respective thin films. Our work, thus, highlights the trade-off between molecular packing structure for deformable electronic materials and provides guidance for designing new conjugated polymers for stretchable electronics.

Computational Method for Evaluating the Thermoelectric Power Factor for Organic Materials Modeled by the Holstein Model: A Time-Dependent Density Matrix Renormalization Group Formalism

Organic/polymeric materials are of emerging importance for thermoelectric conversion. The soft nature of these materials implies strong electron-phonon coupling, often leading to carrier localization. This poses great challenges for the conventional Boltzmann transport description based on relaxation time approximation and band structure calculations. In this work, combining the Kubo formula with the finite-temperature time-dependent density matrix renormalization group (FT-TD-DMRG) in the grand canonical ensemble, we developed a nearly exact algorithm to calculate the thermoelectric power factor PF = α² σ, where α is the Seebeck coefficient and σ is the electrical conductivity, and apply the algorithm to Holstein Hamiltonian with electron-phonon coupling to model organic materials. Our algorithm can provide a unified description covering the weak coupling limit described by the bandlike Boltzmann transport to the strong coupling hopping limit.

Generalization on Entropy-Ruled Charge and Energy Transport for Organic Solids and Biomolecular Aggregates

Herein, a generalized version of the entropy-ruled charge and energy transport mechanism for organic solids and biomolecular aggregates is presented. The effects of thermal disorder and electric field on electronic transport in molecular solids have been quantified by entropy, which eventually varies with respect to the typical disorder (static or dynamic). Based on our previous differential entropy (h s )-driven charge transport method, we explore the nonsteady carrier energy flux principle for soft matter systems from small organic solids to macrobiomolecular aggregates. Through this principle, the synergic nature of charge and energy transport in different organic systems is addressed. In this work, entropy is the key parameter to classify whether the carrier dynamics is in a nonsteady or steady state. Besides that, we also propose the formulation for unifying the hopping and band transport, which provides the relaxation time-hopping rate relation and the relaxation time-effective mass ratio. The calculated disorder drift time (or entropy-weighted carrier drift time) for hole transport in an alkyl-substituted triphenylamine (TPA) molecular device is 9.3 × 10-7 s, which illustrates nuclear dynamics-coupled charge transfer kinetics. The existence of nonequilibrium transport is anticipated while the carrier dynamics is in the nonsteady state, which is further examined from the rate of traversing potential in octupolar molecules. Our entropy-ruled Einstein model connects the adiabatic band and nonadiabatic hopping transport mechanisms. The logarithmic current density at different electric field-assisted site energy differences provides information about the typical transport (whether trap-free diffusion or trap-assisted recombination) in molecular devices, which reflects in the Navamani-Shockley diode equation.

Chemical Modifications Suppress Anharmonic Effects in the Lattice Dynamics of Organic Semiconductors

The lattice dynamics of organic semiconductors has a significant role in determining their electronic and mechanical properties. A common technique to control these macroscopic properties is to chemically modify the molecular structure. These modifications are known to change the molecular packing, but their effect on the lattice dynamics is relatively unexplored. Therefore, we investigate how chemical modifications to a core [1]benzothieno[3,2-b]benzothiophene (BTBT) semiconducting crystal affect the evolution of the crystal structural dynamics with temperature. Our study combines temperature-dependent polarization-orientation (PO) low-frequency Raman measurements with first-principles calculations and single-crystal X-ray diffraction measurements. We show that chemical modifications can indeed suppress specific expressions of vibrational anharmonicity in the lattice dynamics. Specifically, we detect in BTBT a gradual change in the PO Raman response with temperature, indicating a unique anharmonic expression. This anharmonic expression is suppressed in all examined chemically modified crystals (ditBu-BTBT and diC8-BTBT, diPh-BTBT, and DNTT). In addition, we observe solid–solid phase transitions in the alkyl-modified BTBTs. Our findings indicate that π-conjugated chemical modifications are the most effective in suppressing these anharmonic effects.

Optical Anisotropy and Momentum-Dependent Excitons in Dibenzopentacene Single Crystals

High-quality single crystals of the organic semiconductor (1,2;8,9)-dibenzopentacene were grown via physical vapor transport. The crystal structure-unknown before-was determined by single-crystal X-ray diffraction; polarization-dependent optical absorption measurements display a large anisotropy in the ac plane of the crystals. The overall Davydov splitting is ∼110 meV, which is slightly lower than that in the close relative pentacene (120 meV). Momentum-dependent electron energy-loss spectroscopy measurements show a clear exciton dispersion of the Davydov components. An analysis of the dispersion using a simple 1D model indicates smaller electron- and hole-transfer integrals in dibenzopentacene as compared to pentacene. The spectral weight distribution of the excitation spectra is strongly momentum-dependent and demonstrates a strong momentum-dependent admixture of Frenkel excitons, charge-transfer excitons, and vibrational modes.

Real Temperature Model of Dynamic Disorder in Molecular Crystals

Charge carrier mobilities in ordered organic semiconductors are limited by inherent vibrational phonons that scatter carriers. To improve a material's intrinsic mobility, restricting particularly detrimental modes with molecular substitutions may be a viable strategy. Here, we develop a probabilistic temperature-dependent displacement model that we couple with the density functional dimer projection protocol to predict effective electronic coupling fluctuations. The phonon-induced deviations from the equilibrium electronic couplings are used to infer the detriment of low-frequency phonons on charge carrier mobilities in a set of organic single crystals. We show that asymmetric sliding motions in pentacene and 2,6-diphenylanthracene induce large electronic coupling fluctuations, whereas seesawlike motions cause large fluctuations in rubrene, 9,10-diphenylanthracene, and, 2,6-diphenylanthracene. Vibrational analyses revealed that the asymmetric sliding phonon in rubrene persists only in the low-mobility direction of the crystal. Therefore, rubrene's intrinsic high mobility is likely due to the absence of this source of disorder in its high-mobility conduction channels. This model can be used to identify particularly harmful or helpful phonons in crystalline materials and may provide design rules for developing materials with intrinsically low disorder.

Semiconductor Porous Hydrogen-Bonded Organic Frameworks Based on Tetrathiafulvalene Derivatives

Herein, we report on the use of tetrathiavulvalene-tetrabenzoic acid, H₄TTFTB, to engender semiconductivity in porous hydrogen-bonded organic frameworks (HOFs). By tuning the synthetic conditions, three different polymorphs have been obtained, denoted MUV-20a, MUV-20b, and MUV-21, all of them presenting open structures (22, 15, and 27%, respectively) and suitable TTF stacking for efficient orbital overlap. Whereas MUV-21 collapses during the activation process, MUV-20a and MUV-20b offer high stability evacuation, with a CO₂ sorption capacity of 1.91 and 1.71 mmol g^–1, respectively, at 10 °C and 6 bar. Interestingly, both MUV-20a and MUV-20b present a zwitterionic character with a positively charged TTF core and a negatively charged carboxylate group. First-principles calculations predict the emergence of remarkable charge transport by means of a through-space hopping mechanism fostered by an efficient TTF π–π stacking and the spontaneous formation of persistent charge carriers in the form of radical TTF^•+ units. Transport measurements confirm the efficient charge transport in zwitterionic MUV-20a and MUV-20b with no need for postsynthetic treatment (e.g., electrochemical oxidation or doping), demonstrating the semiconductor nature of these HOFs with record experimental conductivities of 6.07 × 10^–7 (MUV-20a) and 1.35 × 10^–6 S cm^–1 (MUV-20b).

Lattice Relaxation Forward Negative Coulomb Drag in Hopping Regime

Quasi-particle formed by electron and the dressed deformed lattice is important to accurately interpret the properties of various disordered/amorphous materials. However, a unified understanding of the drag effect, in particular the negative Coulomb drag in hopping systems, remains an open challenge. This work proposes a theoretic framework to account for both positive and negative Coulomb drag in dual-1D-hopping systems by considering both the electron-electron correlation and the electron-phonon correlation. It is found that lattice relaxation in the active line of the hopping system may give rise to an inverse energetic pumping force in the passive line, causing negative Coulomb drag. The mobility of the negative coulomb drag can approach the scale of 10−5cm2V−1s−1, especially at low temperature, high carrier-density, and narrow inter-spacing separation. More intriguingly, the positive drag could be recovered by varying the energy fluctuation and suppressing the electron-phonon interactions, but with a much lower magnitude. Our work could serve as a universal model for the Coulomb drag effect in the hopping system.

Charge Transport in Organic Semiconductors: The Perspective from Nonadiabatic Molecular Dynamics

Organic semiconductors (OSs) are an exciting class of materials that have enabled disruptive technologies in this century including large-area electronics, flexible displays, and inexpensive solar cells. All of these technologies rely on the motion of electrical charges within the material and the diffusivity of these charges critically determines their performance. In this respect, it is remarkable that the nature of the charge transport in these materials has puzzled the community for so many years, even for apparently simple systems such as molecular single crystals: some experiments would better fit an interpretation in terms of a localized particle picture, akin to molecular or biological electron transfer, while others are in better agreement with a wave-like interpretation, more akin to band transport in metals.

Exciting recent progress in the theory and simulation of charge carrier transport in OSs has now led to a unified understanding of these disparate findings, and this Account will review one of these tools developed in our laboratory in some detail: direct charge carrier propagation by quantum-classical nonadiabatic molecular dynamics. One finds that even in defect-free crystals the charge carrier can either localize on a single molecule or substantially delocalize over a large number of molecules depending on the relative strength of electronic couplings between the molecules, reorganization, or charge trapping energy of the molecule and thermal fluctuations of electronic couplings and site energies, also known as electron–phonon couplings.

Our simulations predict that in molecular OSs exhibiting some of the highest measured charge mobilities to date, the charge carrier forms “flickering” polarons, objects that are delocalized over 10–20 molecules on average and that constantly change their shape and extension under the influence of thermal disorder. The flickering polarons propagate through the OS by short (≈10 fs long) bursts of the wave function that lead to an expansion of the polaron to about twice its size, resulting in spatial displacement, carrier diffusion, charge mobility, and electrical conductivity. Arguably best termed “transient delocalization”, this mechanistic scenario is very similar to the one assumed in transient localization theory and supports its assertions. We also review recent applications of our methodology to charge transport in disordered and nanocrystalline samples, which allows us to understand the influence of defects and grain boundaries on the charge propagation.

Unfortunately, the energetically favorable packing structures of typical OSs, whether molecular or polymeric, places fundamental constraints on charge mobilities/electronic conductivity compared to inorganic semiconductors, which limits their range of applications. In this Account, we review the design rules that could pave the way for new very high-mobility OS materials and we argue that 2D covalent organic frameworks are one of the most promising candidates to satisfy them.

We conclude that our nonadiabatic dynamics method is a powerful approach for predicting charge carrier transport in crystalline and disordered materials. We close with a brief outlook on extensions of the method to exciton transport, dissociation, and recombination. This will bring us a step closer to an understanding of the birth, survival, and annihiliation of charges at interfaces of optoelectronic devices.

Efficient Surface Hopping Approach for Modeling Charge Transport in Organic Semiconductors

The trajectory surface hopping (TSH) method is nowadays widely applied to study the charge/exciton transport process in organic semiconductors (OSCs). In the present study, we systematically examine the performance of two approximations in the fewest switched surface hopping (FSSH) simulations for charge transport (CT) in several representative OSCs. These approximations include (i) the substitution of the nuclear velocity scaling along the nonadiabatic coupling vector (NCV) by rescaling the hopping probability with the Boltzmann factor (Boltzmann correction (BC)) and (ii) a phenomenological approach to treat the quantum feedback from the electronic system to the nuclear system (implicit charge relaxation (IR)) in the OSCs. We find that charge mobilities computed by FSSH-BC-IR are in very good agreement with the mobilities obtained by standard FSSH simulations with explicit charge relaxation (FSSH-ER), however, at reduced computational cost. A key parameter determining the charge carrier mobility is the reorganization energy, which is sensitively dependent on DFT functionals applied. By employing the IR approximation, the FSSH method allows systematic investigation of the effect of the reorganization energies obtained by different DFT functionals like B3LYP or ωB97XD on CT in OSCs. In comparison to the experiments, FSSH-BC-IR using ωB97XD reorganization energy underestimates mobilities in the low-coupling regime, which may indicate the lack of nuclear quantum effects (e.g., zero point energy (ZPE)) in the simulations. The mobilities obtained by FSSH-BC-IR using the B3LYP reorganization energy agree well with experimental values in 3 orders of magnitude. The accidental agreement may be the consequence of the underestimation of the reorganization energy by the B3LYP functional, which compensates for the neglect of nuclear ZPE in the simulations.

Efficient Intermolecular Charge Transport in π-Stacked Pyridinium Dimers Using Cucurbit[8]uril Supramolecular Complexes

Intermolecular charge transport through π-conjugated molecules plays an essential role in biochemical redox processes and energy storage applications. In this work, we observe highly efficient intermolecular charge transport upon dimerization of pyridinium molecules in the cavity of a synthetic host (cucurbit[8]uril, CB[8]). Stable, homoternary complexes are formed between pyridinium molecules and CB[8] with high binding affinity, resulting in an offset stacked geometry of two pyridiniums inside the host cavity. The charge transport properties of free and dimerized pyridiniums are characterized using a scanning tunneling microscope-break junction (STM-BJ) technique. Our results show that π-stacked pyridinium dimers exhibit comparable molecular conductance to isolated, single pyridinium molecules, despite a longer transport pathway and a switch from intra- to intermolecular charge transport. Control experiments using a CB[8] homologue (cucurbit[7]uril, CB[7]) show that the synthetic host primarily serves to facilitate dimer formation and plays a minimal role on molecular conductance. Molecular modeling using density functional theory (DFT) reveals that pyridinium molecules are planarized upon dimerization inside the host cavity, which facilitates charge transport. In addition, the π-stacked pyridinium dimers possess large intermolecular LUMO-LUMO couplings, leading to enhanced intermolecular charge transport. Overall, this work demonstrates that supramolecular assembly can be used to control intermolecular charge transport in π-stacked molecules.

Capillary-Confinement Crystallization for Monolayer Molecular Crystal Arrays

Organic single-crystalline semiconductors are highly desired for the fabrication of integrated electronic circuits, yet their uniform growth and efficient patterning is a huge challenge. Here, a general solution procedure named the "soft-template-assisted-assembly method" is developed to prepare centimeter-scale monolayer molecular crystal (MMC) arrays with precise regulation over their size and location via a capillary-confinement crystallization process. It is remarkable that the field-effect mobility of the array is highly uniform, with variation less than 4.4%, which demonstrates the most uniform organic single-crystal arrays ever reported so far. Simulations based on fluid dynamics are carried out to understand the function mechanism of this method. Thanks to the ultrasmooth crystalline orientation surface of MMCs, high-quality p-n heterojunction arrays can be prepared by weak epitaxy growth of n-type material atop the MMC. The p-n heterojunction field-effect transistors show ambipolar characteristics and the corresponding inverters constructed by these heterojunctions exhibit a competitive gain of 155. This work provides a general strategy to realize the preparation and application of logic complementary circuits based on patterned organic single crystals.

Systematic kMC Study of Doped Hole Injection Layers in Organic Electronics

Organic light emitting diodes (OLED) play an important role in commercial displays and are promising candidates for energy-efficient lighting applications. Although they have been continuously developed since their discovery in 1987, some unresolved challenges remain. The performance of OLEDs is determined by a multifaceted interplay of materials and device architectures. A commonly used technique to overcome the charge injection barrier from the electrodes to the organic layers, are doped injection layers. The optimization of doped injection layers is critical for high-efficiency OLED devices, but has been driven mainly by chemical intuition and experimental experience, slowing down the progress in this field. Therefore, computer-aided methods for material and device modeling are promising tools to accelerate the device development process. In this work, we studied the effect of doped hole injection layers on the injection barrier in dependence on material and layer properties by using a parametric kinetic Monte Carlo model. We were able to quantitatively elucidate the influence of doping concentration, material properties, and layer thickness on the injection barrier and device conductivity, leading to the conclusion that our kMC model is suitable for virtual device design.

Synergistic effects of side-functionalization and aza-substitution on the charge transport and optical properties of perylene-based organic materials: a DFT study

The physicochemical properties of organic materials are subject to the chemical structure of the molecular unit and the arrangement of molecules in a crystal.

Highly Stable Nonhydroxyl Antisolvent Polymer Dielectric: A New Strategy towards High-Performance Low-Temperature Solution-Processed Ultraflexible Organic Transistors for Skin-Inspired Electronics

Scarcity of the antisolvent polymer dielectrics and their poor stability have significantly prevented solution-processed ultraflexible organic transistors from low-temperature, large-scale production for applications in low-cost skin-inspired electronics. Here, we present a novel low-temperature solution-processed PEI-EP polymer dielectric with dramatically enhanced thermal stability, humidity stability, and frequency stability compared with the conventional PVA/c-PVA and c-PVP dielectrics, by incorporating polyethyleneimine PEI as crosslinking sites in nonhydroxyl epoxy EP. The PEI-EP dielectric requires a very low process temperature as low as 70°C and simultaneously possesses the high initial decomposition temperature (340°C) and glass transition temperature (230°C), humidity-resistant dielectric properties, and frequency-independent capacitance. Integrated into the solution-processed C8-BTBT thin-film transistors, the PEI-EP dielectric enables the device stable operation in air within 2 months and in high-humidity environment from 20 to 100% without significant performance degradation. The PEI-EP dielectric transistor array also presents weak hysteresis transfer characteristics, excellent electrical performance with 100% operation rate, high mobility up to 7.98 cm² V^-1 s^-1 (1 Hz) and average mobility as high as 5.3 cm² V^-1 s^-1 (1 Hz), excellent flexibility with the normal operation at the bending radius down to 0.003 mm, and foldable and crumpling-resistant capability. These results reveal the great potential of PEI-EP polymer as dielectric of low-temperature solution-processed ultraflexible organic transistors and open a new strategy for the development and applications of next-generation low-cost skin electronics.

Beyond Conformational Control: Effects of Noncovalent Interactions on Molecular Electronic Properties of Conjugated Polymers

Tuning the electronic properties of polymers is of great importance in designing highly efficient organic solar cells. Noncovalent intramolecular interactions have been often used for conformational control to enhance the planarity of polymers or molecules, which may reduce band gaps and promote charge transfer. However, it is not known if noncovalent interactions may alter the electronic properties of conjugated polymers through some mechanism other than the conformational control. Here, we studied the effects of various noncovalent interactions, including sulfur-nitrogen, sulfur-oxygen, sulfur-fluorine, oxygen-nitrogen, oxygen-fluorine, and nitrogen-fluorine, on the electronic properties of polymers with planar geometry using unconstrained and constrained density functional theory. We found that the sulfur-nitrogen intramolecular interaction may reduce the band gaps of polymers and enhance the charge transfer more obviously than other noncovalent interactions. Our findings are also consistent with the experimental data. For the first time, our study shows that the sulfur-nitrogen noncovalent interaction may further affect the electronic structure of coplanar conjugated polymers, which cannot be only explained by the enhancement of molecular planarity. Our work suggests a new mechanism to manipulate the electronic properties of polymers to design high-performance small-molecule-polymer and all-polymer solar cells.

Charge-Separation and Charge-Recombination Rate Constants in a Donor-Acceptor Buckybowl-Based Supramolecular Complex: Multistate and Solvent Effects

The kinetics of the nonradiative photoinduced processes (charge-separation and charge-recombination) experimented in solution by a supramolecular complex formed by an electron-donating bowl-shaped truxene-tetrathiafulvalene (truxTTF) derivative and an electron-accepting fullerene fragment (hemifullerene, C30H12) has been theoretically investigated. The truxTTF·C30H12 heterodimer shows a complex decay mechanism after photoexcitation with the participation of several low-lying excited states of different nature (local and charge-transfer excitations) all close in energy. In this scenario, the absolute rate constants for all of the plausible charge-separation (CS) and charge-recombination (CR) channels have been successfully estimated using the Marcus-Levich-Jortner (MLJ) rate expression, electronic structure calculations, and a multistate diabatization method. The outcomes suggest that for a reasonable estimate of the CS and CR rate constants, it is necessary to include the following: (i) optimally tuned long-range (LC) corrected density functionals, to predict a correct energy ordering of the low-lying excited states; (ii) multistate effects, to account for the electronic couplings; and (iii) environmental solvent effects, to provide a proper stabilization of the charge-transfer excited states and accurate external reorganization energies. The predicted rate constants have been incorporated in a simple but insightful kinetic model that allows estimating global CS and CR rate constants in line with the most generalized three-state model used for the CS and CR processes. The values computed for the global CS and CR rates of the donor-acceptor truxTTF·C30H12 supramolecular complex are found to be in good agreement with the experimental values.

Impact of Nanoscale Morphology on Charge Carrier Delocalization and Mobility in an Organic Semiconductor

A central challenge of organic semiconductor research is to make cheap, disordered materials that exhibit high electrical conductivity. Unfortunately, this endeavor is hampered by the poor fundamental understanding of the relationship between molecular packing structure and charge carrier mobility. Here a novel computational methodology is presented that fills this gap. Using a melt-quench procedure it is shown that amorphous pentacene spontaneously self-assembles to nanocrystalline structures that, at long quench times, form the characteristic herringbone layer of the single crystal. Quantum dynamical simulations of electron hole transport show a clear correlation between the crystallinity of the sample, the quantum delocalization, and the mobility of the charge carrier. Surprisingly, the long-held belief that charge carriers form relatively localized polarons in disordered OS is only valid for fully amorphous structures-for nanocrystalline and crystalline samples, significant charge carrier delocalization over several nanometers occurs that underpins their improved conductivities. The good agreement with experimentally available data makes the presented methodology a robust computational tool for the predictive engineering of disordered organic materials.

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.

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.

Free Charge Carriers in Homo-Sorted π-Stacks of Donor-Acceptor Conjugates

Inspired by the high photoconversion efficiency observed in natural light-harvesting systems, the hierarchical organization of molecular building blocks has gained impetus in the past few decades. Particularly, the molecular arrangement and packing in the active layer of organic solar cells (OSCs) have garnered significant attention due to the decisive role of the nature of donor/acceptor (D/A) heterojunctions in charge carrier generation and ultimately the power conversion efficiency. This review focuses on the recent developments in emergent optoelectronic properties exhibited by self-sorted donor-on-donor/acceptor-on-acceptor arrangement of covalently linked D-A systems, highlighting the ultrafast excited state dynamics of charge transfer and transport. Segregated organization of donors and acceptors promotes the delocalization of photoinduced charges among the stacks, engendering an enhanced charge separation lifetime and percolation pathways with ambipolar conductivity and charge carrier yield. Covalently linking donors and acceptors ensure a sufficient D-A interface and interchromophoric electronic coupling as required for faster charge separation while providing better control over their supramolecular assemblies. The design strategies to attain D-A conjugate assemblies with optimal charge carrier generation efficiency, the scope of their application compared to state-of-the-art OSCs, current challenges, and future opportunities are discussed in the review. An integrated overview of rational design approaches derived from the comprehension of underlying photoinduced processes can pave the way toward superior optoelectronic devices and bring in new possibilities to the avenue of functional supramolecular architectures.

Multi-level aggregation of conjugated small molecules and polymers: from morphology control to physical insights

Aggregation of molecules is a multi-molecular phenomenon occurring when two or more molecules behave differently from discrete molecules due to their intermolecular interactions. Moving beyond single molecules, aggregation usually demonstrates evolutive or wholly emerging new functionalities relative to the molecular components. Conjugated small molecules and polymers interact with each other, resulting in complex solution-state aggregates and solid-state microstructures. Optoelectronic properties of conjugated small molecules and polymers are sensitively determined by their aggregation states across a broad range of spatial scales. This review focused on the aggregation ranging from molecular structure, intermolecular interactions, solution-state assemblies, and solid-state microstructures of conjugated small molecules and polymers. We addressed the importance of such aggregation in filling the gaps from the molecular level to device functions and highlighted the multi-scale structures and properties at different scales. From the view of multi-level aggregation behaviors, we divided the whole process from the molecule to devices into several parts: molecular design, solvation, solution-state aggregation, crystal engineering, and solid-state microstructures. We summarized the progress and challenges of relationships between optoelectronic properties and multi-level aggregation. We believe aggregation science will become an interdisciplinary research field and serves as a general platform to develop future materials with the desired functions.

Developing molecular-level models for organic field-effect transistors

Organic field-effect transistors (OFETs) are not only functional devices but also represent an important tool for measuring the charge-transport properties of organic semiconductors (OSs). Thus, efforts to understand the performance and characteristics of OFET devices are not only useful in helping achieve higher device efficiencies but also critical to ensuring accuracy in the evaluations of OS charge mobilities. These studies rely on OFET device models, which connect the measured current characteristics to the properties of the OSs. Developing such OFET models requires good knowledge of the charge-transport processes in OSs. In device active layers, the OS thin films are either amorphous (e.g. in organic light-emitting diodes and organic solar cells) or crystalline (e.g. those optimized for charge transport in OFETs). When the electronic couplings between adjacent OS molecules or polymer chain segments are weak, the charge-transport mechanism is dominated by hopping processes, which is the context in which we frame the discussion in this Review. Factors such as disorder, mobility anisotropy, traps, grain boundaries or film morphology all impact charge transport. To take these features fully into account in an OFET device model requires considering a nano-scale, molecular-level resolution. Here, we discuss the recent development of such molecular-resolution OFET models based on a kinetic Monte Carlo approach relevant to the hopping regime. We also briefly describe the applicability of these models to high-mobility OFETs, where we underline the need to extend them to incorporate aspects related to charge delocalization.

Charge Mobility in Discotic Liquid Crystals

Discotic (disk-shaped) molecules or molecular aggregates may form, within a certain temperature range, partially ordered phases, known as discotic liquid crystals, which have been extensively studied in the recent past. On the one hand, this interest was prompted by the fact that they represent models for testing energy and charge transport theories in organic materials. However, their long-range self-assembling properties, potential low cost, ease of processability with a variety of solvents and the relative ease of tailoring their properties via chemical synthesis, drove the attention of researchers also towards the exploitation of their semiconducting properties in organic electronic devices. This review covers recent research on the charge transport properties of discotic mesophases, starting with an introduction to their phase structure, followed by an overview of the models used to describe charge mobility in organic substances in general and in these systems in particular, and by the description of the techniques most commonly used to measure their charge mobility. The reader already familiar or not interested in such details can easily skip these sections and refer to the core section of this work, focusing on the most recent and significant results regarding charge mobility in discotic liquid crystals.

Artificial neural networks for predicting charge transfer coupling

Quantum chemistry calculations have been very useful in providing many key detailed properties and enhancing our understanding of molecular systems. However, such calculation, especially with ab initio models, can be time-consuming. For example, in the prediction of charge-transfer properties, it is often necessary to work with an ensemble of different thermally populated structures. A possible alternative to such calculations is to use a machine-learning based approach. In this work, we show that the general prediction of electronic coupling, a property that is very sensitive to intermolecular degrees of freedom, can be obtained with artificial neural networks, with improved performance as compared to the popular kernel ridge regression method. We propose strategies for optimizing the learning rate and batch size, improving model performance, and further evaluating models to ensure that the physical signatures of charge-transfer coupling are well reproduced. We also address the effect of feature representation as well as statistical insights obtained from the loss function and the data structure. Our results pave the way for designing a general strategy for training such neural-network models for accurate prediction.

The influence of sorbitol doping on aggregation and electronic properties of PEDOT:PSS: a theoretical study

Many organic electronics applications such as organic solar cells or thermoelectric generators rely on PEDOT:PSS as a conductive polymer that is printable and transparent. It was found that doping PEDOT:PSS with sorbitol enhances the conductivity through morphological changes. However, the microscopic mechanism is not well understood. In this work, we combine computational tools with machine learning to investigate changes in morphological and electronic properties of PEDOT:PSS when doped with sorbitol. We find that sorbitol improves the alignment of PEDOT oligomers, leading to a reduction of energy disorder and an increase in electronic couplings between PEDOT chains. The high accuracy (r 2 > 0.9) and speed up of energy level predictions of neural networks compared to density functional theory enables us to analyze HOMO energies of PEDOT oligomers as a function of time. We find a surprisingly low degree of static energy disorder compared to other organic semiconductors. This finding might help to better understand the microscopic origin of the high charge carrier mobility of PEDOT:PSS in general and potentially help to design new conductive polymers.

Investigating structure-charge transport relationships in thiophene substituted naphthyridine crystalline materials by computational model systems

The development of novel π-conjugated charge transfer mediators is at the forefront of current research efforts and interests. Among the plethora of building blocks, diketopyrrolopyrroles have been widely employed, associated to the ease of tailoring their optoelectronic properties by systematic peripheral substitutions. It is somehow of surprise to us that their six-member ring bis-lactam analogues, naphthyridines have been overlooked and reports are scarce and almost solely limited to their use in polymeric materials. Herein we report a comprehensive theoretical analysis of the charge transfer properties of 1,5-naphthyridine-based materials by means of a number of bespoke model systems, further able to quantitatively predict experimental mobility observations. Our results imply that thiophene substituted naphthyridine crystalline materials represent a promising class of organic π-conjugated systems with an experimentally observed ability to self-assemble in the solid state conforming to one dimensional stacking motifs. These highly sought-after charge propagation channels are characterised by large wavefunction overlap and thermal integrity and have as a result the potential to outperform currently exploited alternatives. We anticipate this work to be of interest to materials scientists and hope it will pave the way towards the realisation of novel charge transfer mediators exploiting naphthyridine chemistries.

Toward a First-Principles Evaluation of Transport Mechanisms in Molecular Wires

Understanding charge transport through molecular wires is important for nanoscale electronics and biochemistry. Our goal is to establish a simple first-principles protocol for predicting the charge transport mechanism in such wires, in particular the crossover from coherent tunneling for short wires to incoherent hopping for longer wires. This protocol is based on a combination of density functional theory with a polarizable continuum model introduced by Kaupp et al. for mixed-valence molecules, which we had previously found to work well for length-dependent charge delocalization in such systems. We combine this protocol with a new charge delocalization measure tailored for molecular wires, and we show that it can predict the tunneling-to-hopping transition length with a maximum error of one subunit in five sets of molecular wires studied experimentally in molecular junctions at room temperature. This suggests that the protocol is also well suited for estimating the extent of hopping sites as relevant, for example, for the intermediate tunneling-hopping regime in DNA.