Flexible Surface Hopping Approach to Model the Crossover from Hopping to Band-like Transport in Organic Crystals

Thermoelectric transport in molecular crystals driven by gradients of thermal electronic disorder

Thermoelectric materials convert a temperature gradient into a voltage. This phenomenon is relatively well understood for inorganic materials but much less so for organic semiconductors (OSs). These materials present a challenge because the strong thermal fluctuations of electronic coupling between the molecules result in partially delocalized charge carriers that cannot be treated with traditional theories for thermoelectricity. Here, we develop a quantum dynamical simulation approach revealing in atomistic detail how the charge carrier wave function moves along a temperature gradient in an organic molecular crystal. We find that the wave function propagates from hot to cold in agreement with the experiment, and we obtain a Seebeck coefficient in good agreement with experimental measurements that are also reported in this work. Detailed analysis reveals that gradients in thermal electronic disorder play an important role in determining the magnitude of the Seebeck coefficient, opening unexplored avenues for the design of OSs with improved Seebeck coefficients.

Charge transport in organic semiconductors from the mapping approach to surface hopping

We describe how to simulate charge diffusion in organic semiconductors using a recently introduced mixed quantum-classical method, the mapping approach to surface hopping. In contrast to standard fewest-switches surface hopping, this method propagates the classical degrees of freedom deterministically on the most populated adiabatic electronic state. This correctly preserves the equilibrium distribution of a quantum charge coupled to classical phonons, allowing one to time-average along trajectories to improve the statistical convergence of the calculation. We illustrate the method with an application to a standard model for the charge transport in the direction of maximum mobility in crystalline rubrene. Because of its consistency with the equilibrium distribution, the present method gives a time-dependent diffusion coefficient that plateaus correctly to a long-time limiting value. The resulting mobility is somewhat higher than that of the relaxation time approximation, which uses a phenomenological relaxation parameter to obtain a non-zero diffusion coefficient from a calculation with static phonon disorder. However, it is very similar to the mobility obtained from Ehrenfest dynamics, at least in the parameter regimes we have investigated here. This is somewhat surprising because Ehrenfest dynamics overheats the electronic subsystem and is, therefore, inconsistent with the equilibrium distribution.

A stochastic Schrödinger equation and matrix product state approach to carrier transport in organic semiconductors with nonlocal electron-phonon interaction

Evaluation of the charge transport property of organic semiconductors requires exact quantum dynamics simulation of large systems. We present a numerically nearly exact approach to investigate carrier transport dynamics in organic semiconductors by extending the non-Markovian stochastic Schrödinger equation with complex frequency modes to a forward-backward scheme and by solving it using the matrix product state (MPS) approach. By utilizing the forward-backward formalism for noise generation, the bath correlation function can be effectively treated as a temperature-independent imaginary part, enabling a more accurate decomposition with fewer complex frequency modes. Using this approach, we study the carrier transport and mobility in the one-dimensional Peierls model, where the nonlocal electron-phonon interaction is taken into account. The reliability of this approach was validated by comparing carrier diffusion motion with those obtained from the hierarchical equations of motion method across various parameter regimes of the phonon bath. The efficiency was demonstrated by the modest virtual bond dimensions of MPS and the low scaling of the computational time with the system size.

Spin relaxation of electron and hole polarons in ambipolar conjugated polymers

The charge-transport properties of conjugated polymers have been studied extensively for opto-electronic device applications. Some polymer semiconductors not only support the ambipolar transport of electrons and holes, but do so with comparable carrier mobilities. This opens the possibility of gaining deeper insight into the charge-transport physics of these complex materials via comparison between electron and hole dynamics while keeping other factors, such as polymer microstructure, equal. Here, we use field-induced electron spin resonance spectroscopy to compare the spin relaxation behavior of electron and hole polarons in three ambipolar conjugated polymers. Our experiments show unique relaxation regimes as a function of temperature for electrons and holes, whereby at lower temperatures electrons relax slower than holes, but at higher temperatures, in the so-called spin-shuttling regime, the trend is reversed. On the basis of theoretical simulations, we attribute this to differences in the delocalization of electron and hole wavefunctions and show that spin relaxation in the spin shuttling regimes provides a sensitive probe of the intimate coupling between charge and structural dynamics.

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.

Electron-phonon interaction toward engineering carrier mobility of periodic edge structured graphene nanoribbons

Graphene nanoribbons have many extraordinary electrical properties and are the candidates for semiconductor industry. In this research, we propose a design of Coved GNRs with periodic structure ranged from 4 to 8 nm or more, of which the size is within practical feature sizes by advanced lithography tools. The carrier transport properties of Coved GNRs with the periodic coved shape are designed to break the localized electronic state and reducing electron-phonon scattering. In this way, the mobility of Coved GNRs can be enhanced by orders compared with the zigzag GNRs in same width. Moreover, in contrast to occasional zero bandgap transition of armchair and zigzag GNRs without precision control in atomic level, the Coved GNRs with periodic edge structures can exclude the zero bandgap conditions, which makes practical the mass production process. The designed Coved-GNRs is fabricated over the Germanium (110) substrate where the graphene can be prepared in the single-crystalline and single-oriented formants and the edge of GNRs is later repaired under "balanced condition growth" and we demonstrate that the propose coved structures are compatible to current fabrication facility.

Surface hopping modeling of charge and energy transfer in active environments

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.

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.

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

Surface hopping dynamics in periodic solid-state materials with a linear vibronic coupling model

We report a surface hopping approach in which the implemented linear vibronic coupling Hamiltonian is constructed and the electronic wavefunction is propagated in the reciprocal space. The parameters of the linear vibronic coupling model, including onsite energies, phonon frequencies, and electron-phonon couplings, are calculated with density-functional theory and density-functional perturbation theory and interpolated in fine sampling points of the Brillouin zone with maximally localized Wannier functions. Using this approach, we studied the relaxation dynamics of the photo-excited hot carrier in a one-dimensional periodic carbon chain. The results show that the completeness of the number of Hilbert space k points and the number of phonon q points plays an important role in the hot carrier relaxation processes. By calculating the relaxation times of hot carriers under different reciprocal space sampling and extrapolating with the stretched-compressed exponential function, the relaxation times of hot electrons and holes in the quasi-continuous energy band are obtained. By considering the feedback effect in the hopping processes and analyzing the time-dependent phonon energy in different normal modes, we found that the long-wave longitudinal optical phonons play a major role in the relaxation dynamics of hot electrons and holes. We, therefore, provided herein an efficient and accurate approach for modeling the photophysical processes in periodic solid-state material systems.

Multilayer Subsystem Surface Hopping Method for Large-Scale Nonadiabatic Dynamics Simulation with Hundreds of Thousands of States

We present a multilayer subsystem surface hopping (MSSH) method to deal with nonadiabatic dynamics in large-scale systems. A small subsystem instead of the full system is adopted for surface hopping and is updated on-the-fly to achieve a reliable description of important adiabatic states and the wave function evolution. Additional subsystems for molecular dynamics and statistical description are introduced to further improve the simulation reliability. The global flux hopping probabilities with optimal state assignments are utilized to treat the complex surface crossings. As demonstrated in a series of one- and two-dimensional Holstein models with up to hundreds of thousands of states, MSSH shows weak parameter dependence in all investigated systems. Especially, the computational costs are reduced by 2-6 orders of magnitude compared to traditional surface hopping simulations in full systems, and size-independent results are achieved with a large time-step size of 2-5 fs. The new method is compatible with different decoherence correction strategies and achieves a much better balance between efficiency and reliability, thus promising for applications in general charge and exciton dynamics simulations.

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.

Nitrogen-Containing Perylene Diimides: Molecular Design, Robust Aggregated Structures, and Advances in n-Type Organic Semiconductors

ConspectusOrganic semiconductors (OSCs) have attracted much attention because of their potential applications for flexible and printed electronic devices and thus have been extensively investigated in a variety of research fields, such as organic chemistry, solid-state physics, and device physics and engineering. Organic thin-film transistors (OTFTs), a class of OSC-based devices, have been expected to be an alternative of silicon-based metal oxide semiconductor field-effect transistors (MOSFETs), which is the indispensable element for most of the current electronic devices. However, the noncovalently aggregated, van der Waals solid nature of the OSCs, by contrast to covalently bound silicon, conventionally exhibits lower carrier mobilities, limiting the practical applications of OTFTs. In particular, electron-transporting (i.e., n-type) OSCs lag behind their hole-transporting (p-type) counterparts in carrier mobility and ambient stability as OTFTs. This is primarily because of the difficulty in achieving compatibility between the aggregated structure exhibiting excellent carrier mobility and that with enough electron affinity. Recent understandings of carrier transport in OSCs explain that large and two-dimensionally isotropic transfer integrals coupled with small fluctuations are crucial for high carrier mobilities. In addition, from a practical point of view, the compatibility with practical device processes is highly required. Rational molecular design principles, therefore, are still demanded for developing OSCs and OTFTs toward high-end device applications.Herein, we will show our recent progress in the development of n-type OSCs with the key π-electron core (π-core) of benzo[de]isoquinolino[1,8-gh]quinolinetetracarboxylic diimide (BQQDI) on the basis of single-crystal OTFT technologies and the band-transport model enabled by two-dimensional molecular packing arrangements. The critical point is the introduction of electronegative nitrogen atoms into the π-core: the nitrogen atoms in BQQDI not only deepen the molecular orbital energies but also allow hydrogen-bonding-like attractive intermolecular interactions to control the aggregated structures, unlike the conventional role of the nitrogen introduced into OSCs only for the former role. Hence, the BQQDI analogues exhibit air-stable OTFT behavior and two-dimensional brickwork packing structures. Specifically, phenethyl-substituted analogue (PhC₂-BQQDI) has been shown as the first principal BQQDI-based material, demonstrating solution-processable thin-film single crystals, fewer anisotropic transfer integrals, and an effective suppression of molecular motions, leading to band-like electron-transport properties and stress-durable n-channel OTFT performances, in conjunction with the support of computational calculations. Insights into more fundamental points of view have been found by side-chain derivatization and OTFT studies on polycrystalline and single-crystal films. We hope that this Account provides readers with new strategies for designing high-performance OSCs by two-dimensional control of the aggregated structures.

Thermally activated intra-chain charge transport in high charge-carrier mobility copolymers

Disordered or even seemingly amorphous, donor–acceptor type, conjugated copolymers with high charge-carrier mobility have emerged as a new class of functional materials, where transport along the conjugated backbone is key. Here, we report on non-adiabatic molecular dynamics simulations of charge-carrier transport along chains of poly (indacenodithiophene-co-benzothiadiazole), within a model Hamiltonian parameterized against first-principles calculations. We predict thermally activated charge transport associated with a slightly twisted ground-state conformation, on par with experimental results. Our results also demonstrate that the energy mismatch between the hole on the donor vs the acceptor units of the copolymer drives localization of the charge carriers and limits the intra-chain charge-carrier mobility. We predict that room-temperature mobility values in excess of 10 cm2 V−1 s−1 can be achieved through proper chemical tuning of the component monomer units.

All-Atom Nonadiabatic Dynamics Simulation of Hybrid Graphene Nanoribbons Based on Wannier Analysis and Machine Learning

Trajectory surface hopping combined with ab initio electronic structure calculations is a popular and powerful approach for on-the-fly nonadiabatic dynamics simulations. For large systems, however, this remains a significant challenge because of the unaffordable computational cost of large-scale electronic structure calculations. Here, we present an efficient divide-and-conquer approach to construct the system Hamiltonian based on Wannier analysis and machine learning. In detail, the large system under investigation is first decomposed into small building blocks, and then all possible segments formed by building blocks within a cutoff distance are found out. Ab initio molecular dynamics is carried out to generate a sequence of geometries for each equivalent segment with periodicity. The Hamiltonian matrices in the maximum localized Wannier function (MLWF) basis are obtained for all geometries and utilized to train artificial neural networks (ANNs) for the structure-dependent Hamiltonian elements. Taking advantage of the orthogonality and spatial locality of MLWFs, the one-electron Hamiltonian of a large system at arbitrary geometry can be directly constructed by the trained ANNs. As demonstrations, we study charge transport in a zigzag graphene nanoribbon (GNR), a coved GNR, and a series of hybrid GNRs with a state-of-the-art surface hopping method. The interplay between delocalized and localized states is found to determine the electron dynamics in hybrid GNRs. Our approach has successfully studied GNRs with >10 000 atoms, paving the way for efficient and reliable all-atom nonadiabatic dynamics simulation of general systems.

Spin-Dependent Polaron Dynamics in Organic Ferromagnets

The spin-dependent polaron dynamics in organic ferromagnets under driven electric fields are investigated by using the extended Su-Schrieffer-Heeger (SSH) model coupled with a nonadiabatic dynamics method. It is found that the spin-down polaron with the same spin orientation as the radicals drifts faster than the spin-up one under the same driven electric field. In an applicable range of driven electric fields, the velocity of the spin-down polaron is about 3.4 times that of the spin-up one. The dynamical property of the polaron with each spin (up or down) is asymmetric upon the reversal of the driven electric fields. The diverse dynamical properties of polarons with specific spins can be attributed to the spin nondegenerate polaron energy levels, the dipole moment generated by the asymmetrical polaron charge distributions and the strong electron-lattice coupling in organic ferromagnets. Our findings are expected to be useful for improving organic ferromagnet based spintronic devices.

A reciprocal-space formulation of surface hopping

Surface hopping has seen great success in describing molecular phenomena where electronic excitations tend to be localized, but its application to materials with band-like electronic properties has remained limited. Here, we derive a formulation of fewest-switches surface hopping where both the quantum and classical equations of motion are solved entirely in terms of reciprocal-space coordinates. The resulting method is directly compatible with band structure calculations and allows for the efficient description of band-like phenomena by means of a truncation of the Brillouin zone. Using the Holstein and Peierls models as examples, we demonstrate the formal equivalence between real-space and reciprocal-space surface hopping and assess their accuracy against mean-field mixed quantum-classical dynamics and numerically exact results. Having very similar equations of motion, reciprocal-space surface hopping can be straightforwardly incorporated in existing (real-space) surface hopping implementations.

Temperature-Dependent Structural Phase Transition in Rubrene Single Crystals: The Missing Piece from the Charge Mobility Puzzle?

Accurate structural models for rubrene, the benchmark organic semiconductor, derived from synchrotron X-ray data in the temperature range of 100-300 K, show that its cofacially stacked tetracene backbone units remain blocked with respect to each other upon cooling to 200 K and start to slip below that temperature. The release of the blocked slippage occurs at approximately the same temperature as the hole mobility crossover. The blocking between 200 and 300 K is caused by a negative correlation between the relatively small thermal expansion along the crystallographic b-axis and the relatively large widening of the angle between herringbone-stacked tetracene units. DFT calculations reveal that this blocked slippage is accompanied by a discontinuity in the variation with temperature of the electronic couplings associated with hole transport between cofacially stacked tetracene backbones.

Comparing the Expense and Accuracy of Methods to Simulate Atomic Vibrations in Rubrene

Atomic vibrations can inform about materials properties from hole transport in organic semiconductors to correlated disorder in metal-organic frameworks. Currently, there are several methods for predicting these vibrations using simulations, but the accuracy-efficiency tradeoffs have not been examined in depth. In this study, rubrene is used as a model system to predict atomic vibrational properties using six different simulation methods: density functional theory, density functional tight binding, density functional tight binding with a Chebyshev polynomial-based correction, a trained machine learning model, a pretrained machine learning model called ANI-1, and a classical forcefield model. The accuracy of each method is evaluated by comparison to the experimental inelastic neutron scattering spectrum. All methods discussed here show some accuracy across a wide energy region, though the Chebyshev-corrected tight-binding method showed the optimal combination of high accuracy with low expense. We then offer broad simulation guidelines to yield efficient, accurate results for inelastic neutron scattering spectrum prediction.

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.

Efficient energy transport in an organic semiconductor mediated by transient exciton delocalization

Efficient energy transport is desirable in organic semiconductor (OSC) devices. However, photogenerated excitons in OSC films mostly occupy highly localized states, limiting exciton diffusion coefficients to below ~10^-2 cm²/s and diffusion lengths below ~50 nm. We use ultrafast optical microscopy and nonadiabatic molecular dynamics simulations to study well-ordered poly(3-hexylthiophene) nanofiber films prepared using living crystallization-driven self-assembly, and reveal a highly efficient energy transport regime: transient exciton delocalization, where energy exchange with vibrational modes allows excitons to temporarily re-access spatially extended states under equilibrium conditions. We show that this enables exciton diffusion constants up to 1.1 ± 0.1 cm²/s and diffusion lengths of 300 ± 50 nm. Our results reveal the dynamic interplay between localized and delocalized exciton configurations at equilibrium conditions, calling for a re-evaluation of exciton dynamics and suggesting design rules to engineer efficient energy transport in OSC device architectures not based on restrictive bulk heterojunctions.

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.

Analysis of External and Internal Disorder to Understand Band-Like Transport in n-Type Organic Semiconductors

Charge transport in organic semiconductors is notoriously extremely sensitive to the presence of disorder, both internal and external (i.e., related to interactions with the dielectric layer), especially for n-type materials. Internal dynamic disorder stems from large thermal fluctuations both in intermolecular transfer integrals and (molecular) site energies in weakly interacting van der Waals solids and sources transient localization of the charge carriers. The molecular vibrations that drive transient localization typically operate at low-frequency (<a-few-hundred cm^-1 ), which makes it difficult to assess them experimentally. Hitherto, this has prevented the identification of clear molecular design rules to control and reduce dynamic disorder. In addition, the disorder can also be external, being controlled by the gate insulator dielectric properties. Here a comprehensive study of charge transport in two closely related n-type molecular organic semiconductors using a combination of temperature-dependent inelastic neutron scattering and photoelectron spectroscopy corroborated by electrical measurements, theory, and simulations is reported. Unambiguous evidence that ad hoc molecular design enables the electron charge carriers to be freed from both internal and external disorder to ultimately reach band-like electron transport is provided.

Nonadiabatic Excited-State Molecular Dynamics Methodologies: Comparison and Convergence

Direct atomistic simulation of nonadiabatic molecular dynamics is a challenging goal that allows important insights into fundamental physical phenomena. A variety of frameworks, ranging from fully quantum treatment of nuclei to semiclassical and mixed quantum-classical approaches, were developed. These algorithms are then coupled to specific electronic structure techniques. Such diversity and lack of standardized implementation make it difficult to compare the performance of different methodologies when treating realistic systems. Here, we compare three popular methods for large chromophores: Ehrenfest, surface hopping, and multiconfigurational Ehrenfest with ab initio multiple cloning (MCE-AIMC). These approaches are implemented in the NEXMD software, which features a common computational chemistry model. The resulting comparisons reveal the method performance for population relaxation and coherent vibronic dynamics. Finally, we study the numerical convergence of MCE-AIMC algorithms by considering the number of trajectories, cloning thresholds, and Gaussian wavepacket width. Our results provide helpful reference data for selecting an optimal methodology for simulating excited-state molecular dynamics.

Influences of dynamic and static disorder on the carrier mobility of BTBT-C12 derivatives: a multiscale computational study

The role of dynamic and static disorder has been widely discussed for carrier transport in organic semiconductors. In this work, we apply a multiscale approach by combining molecular dynamics simulations, quantum mechanics calculations and kinetic Monte-Carlo simulations to study the influence of dynamic and static disorder on the hole mobility of four didodecyl[1]benzothieno[3,2-b]benzothiophene (BTBT-C12) isomers. It is found that the dynamic disorder of transfer integral tends to decrease the mobility for quasi-1D (quasi one-dimensional) BTBT1 and BTBT4 isomers and increase the mobility for 2D (two-dimensional) BTBT2 and BTBT3 isomers, while the dynamic disorder of site energy tends to decrease mobility for all the four isomers; however, the reduction in 2D molecules is much less than that in quasi-1D molecules. Results show that trap defects could reduce the mobility for both the quasi-1D and 2D molecular structures significantly, even to several orders of magnitude. In addition, our work also reveals that there might exist two kinds of oxidation defects of the scatter type for the concerned isomers, which thus leads to greater reduction in mobility for the quasi-1D molecular structures than the 2D molecular structures. The study shows that the 2D molecular structures are favored over the quasi-1D or 1D molecular structure, and it is expected that these results could be used to shed light on device design in organic electronics.

A Simple Solution to Trivial Crossings: A Stochastic State Tracking Approach

We present a new state tracking algorithm based on a stochastic state reassignment that reflects the quantum mechanical interpretation of the state time-overlaps. We assess the new method with a range of model Hamiltonians and demonstrate that it yields the results generally consistent with the deterministic min-cost algorithm. However, the stochastic state tracking algorithm reduces magnitudes of the state population fluctuations as the quantum system evolves toward its equilibrium. The new algorithm facilitates the thermalization of quantum state populations and suppresses the population revivals and oscillations near the equilibrium in many-state systems. The new stochastic algorithm has a favorable computational scaling, is easy to implement due to its conceptual transparency, and treats various types of state identity changes (trivial or avoided crossings and any intermediate cases) on equal footing.

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

When nonadiabatic dynamics are described on the basis of trajectories, severe trajectory branching occurs when the nuclear wave packets on some potential energy surfaces are reflected while those on the remaining surfaces are not. As a result, the traditional Ehrenfest mean field (EMF) approximation breaks down. In this study, two versions of the branching corrected mean field (BCMF) method are proposed. Namely, when trajectory branching is identified, BCMF stochastically selects either the reflected or the nonreflected group to build the new mean field trajectory or splits the mean field trajectory into two new trajectories with the corresponding weights. As benchmarked in six standard model systems and an extensive model base with two hundred diverse scattering models, BCMF significantly improves the accuracy while retaining the high efficiency of the traditional EMF. In fact, BCMF closely reproduces the exact quantum dynamics in all investigated systems, thus highlighting the essential role of branching correction in nonadiabatic dynamics simulations of general systems.

Applying Marcus theory to describe the carrier transports in organic semiconductors: Limitations and beyond

Marcus theory has been successfully applied to molecular design for organic semiconductors with the aid of quantum chemistry calculations for the molecular parameters: the intermolecular electronic coupling V and the intramolecular charge reorganization energy λ. The assumption behind this is the localized nature of the electronic state for representing the charge carriers, being holes or electrons. As far as the quantitative description of carrier mobility is concerned, the direct application of Marcus semiclassical theory usually led to underestimation of the experimental data. A number of effects going beyond such a semiclassical description will be introduced here, including the quantum nuclear effect, dynamic disorder, and delocalization effects. The recently developed quantum dynamics simulation at the time-dependent density matrix renormalization group theory is briefly discussed. The latter was shown to be a quickly emerging efficient quantum dynamics method for the complex system.

Design Rules to Maximize Charge-Carrier Mobility along Conjugated Polymer Chains

The emergence of polymeric materials displaying high charge-carrier mobility values despite poor interchain structural order has spawned a renewal of interest in the identification of structure-property relationships pertaining to the transport of charges along conjugated polymer chains and the subsequent design of optimized architectures. Here, we present the results of intrachain charge transport simulations obtained by applying a robust surface hopping algorithm to a phenomenological Hamiltonian parametrized against first-principles simulations. Conformational effects are shown to provide a clear signature in the temperature-dependent charge-carrier mobility that complies with recent experimental observations. We further contrast against molecular crystals the evolution with electronic bandwidth and electron-phonon interactions of the room-temperature mobility in polymers, showing that intrachain charge-carrier mobility values in excess of 100 cm²/(V s) can be achieved through a proper chemical engineering of the backbones.

Weak-field polaron dynamics in organic ferromagnets

With a nonadiabatic dynamical method the polaron dynamics in organic ferromagnets with spin radicals is investigated under weak electric fields. The results reveal two novel phenomena different from those in normal polymers due to the existence of spin radicals. One is that the velocity of the polaron is asymmetric upon the reversal of the applied electric field, which is explained from the asymmetric polarity of the polaron charge density in different directions of the field, and hence its effect on the lattice distortion. The other is the 'intermittent rebound' of the polaron, where the polaron intermittently moves against the electric field force during a short interval behaving like a negative current. The details of lattice distortion and charge distribution of the polaron during the process have been revealed. We further found that there exist different critical fields for the above two phenomena. With an increase of the electric field, the 'intermittent rebound' of the polaron vanishes first and subsequently the asymmetric polaron velocity. This work demonstrates the unique properties of polaron transport in organic ferromagnets, and will be helpful in the future design of organic ferromagnetic devices.

Finite-Temperature TD-DMRG for the Carrier Mobility of Organic Semiconductors

A large number of nonadiabatic dynamical studies have been applied to reveal the nature of carrier transport in organic semiconductors with different approximations. We present here a "nearly exact" graphical-process-unit-based finite-temperature time-dependent density matrix renormalization group (TD-DMRG) method to evaluate the carrier mobility in organic semiconductors, as described by the electron-phonon model, in particular, in rubrene crystal, one of the prototypical organic semiconductors, with parameters derived from first-principles. We find that (i) TD-DMRG is a general and robust method that can bridge the gap between hopping and band pictures, covering a wide range of electronic coupling strengths and (ii) with realistic parameters, TD-DMRG is able to account for the experimentally observed "band-like" transport behavior (∂μ/∂T < 0) in rubrene. We further study the long-standing puzzle of the isotope effect for charge transport and unambiguously demonstrate that the negative isotope effect (∂μ/∂m < 0 where m is the atomic mass) should be universal.

Anharmonic Lattice Vibrations in Small-Molecule Organic Semiconductors

The intermolecular lattice vibrations in small-molecule organic semiconductors have a strong impact on their functional properties. Existing models treat the lattice vibrations within the harmonic approximation. In this work, polarization-orientation (PO) Raman measurements are used to monitor the temperature-evolution of the symmetry of lattice vibrations in anthracene and pentacene single crystals. Combined with first-principles calculations, it is shown that at 10 K, the lattice dynamics of the crystals are indeed harmonic. However, as the temperature is increased, specific lattice modes gradually lose their PO dependence and become more liquid-like. This finding is indicative of a dynamic symmetry breaking of the crystal structure and shows clear evidence of the strongly anharmonic nature of these vibrations. Pentacene also shows an apparent phase transition between 80 and 150 K, indicated by a change in the vibrational symmetry of one of the lattice modes. These findings lay the groundwork for accurate predictions of the electronic properties of high-mobility organic semiconductors at room temperature.

Molecular Semiconductors for Logic Operations: Dead-End or Bright Future?

The field of organic electronics has been prolific in the last couple of years, leading to the design and synthesis of several molecular semiconductors presenting a mobility in excess of 10 cm² V^-1 s^-1 . However, it is also started to recently falter, as a result of doubtful mobility extractions and reduced industrial interest. This critical review addresses the community of chemists and materials scientists to share with it a critical analysis of the best performing molecular semiconductors and of the inherent charge transport physics that takes place in them. The goal is to inspire chemists and materials scientists and to give them hope that the field of molecular semiconductors for logic operations is not engaged into a dead end. To the contrary, it offers plenty of research opportunities in materials chemistry.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

How to calculate charge mobility in molecular materials from surface hopping non-adiabatic molecular dynamics - beyond the hopping/band paradigm

Charge transport in high mobility organic semiconductors is in an intermediate regime between small polaron hopping and band transport limits. We have recently shown that surface hopping non-adiabatic molecular dynamics is a powerful method for prediction of charge transport mechanisms in organic materials and for near-quantitative prediction of charge mobilities at room temperature where the effects of nuclear zero-point motion and tunneling are still relatively small [S. Giannini et al., Nat. Commun., 2019, 10, 3843]. Here we assess and critically discuss the extensions to Tully's original method that have led to this success: (i) correction for missing electronic decoherence, (ii) detection of trivial crossings and (iii) removal of decoherence correction-induced spurious charge transfer. If any one of these corrections is not included, the charge mobility diverges with system size, each for different physical reasons. Yet if they are included, convergence with system size, detailed balance and good internal consistency are achieved.

Spatially Resolved Photogenerated Exciton and Charge Transport in Emerging Semiconductors

We review recent advances in the characterization of electronic forms of energy transport in emerging semiconductors. The approaches described all temporally and spatially resolve the evolution of initially localized populations of photogenerated excitons or charge carriers. We first provide a comprehensive background for describing the physical origin and nature of electronic energy transport both microscopically and from the perspective of the observer. We introduce the new family of far-field, time-resolved optical microscopies developed to directly resolve not only the extent of this transport but also its potentially temporally and spatially dependent rate. We review a representation of examples from the recent literature, including investigation of energy flow in colloidal quantum dot solids, organic semiconductors, organic-inorganic metal halide perovskites, and 2D transition metal dichalcogenides. These examples illustrate how traditional parameters like diffusivity are applicable only within limited spatiotemporal ranges and how the techniques at the core of this review,especially when taken together, are revealing a more complete picture of the spatiotemporal evolution of energy transport in complex semiconductors, even as a function of their structural heterogeneities.

Quantum localization and delocalization of charge carriers in organic semiconducting crystals

Charge carrier transport in organic semiconductors is at the heart of many revolutionary technologies ranging from organic transistors, light-emitting diodes, flexible displays and photovoltaic cells. Yet, the nature of charge carriers and their transport mechanism in these materials is still unclear. Here we show that by solving the time-dependent electronic Schrödinger equation coupled to nuclear motion for eight organic molecular crystals, the excess charge carrier forms a polaron delocalized over up to 10-20 molecules in the most conductive crystals. The polaron propagates through the crystal by diffusive jumps over several lattice spacings at a time during which it expands more than twice its size. Computed values for polaron size and charge mobility are in excellent agreement with experimental estimates and correlate very well with the recently proposed transient localization theory.

Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function

In an adiabatic mixed quantum-classical simulation, the avoided crossing of weakly coupled eigenstates can lead to unphysical discontinuities in wave function dynamics, otherwise known as the trivial crossing problem. A standard solution to the trivial crossing problem eliminates spatial discontinuities in wave function dynamics by imposing changes to the eigenstate of the wave function. In this paper, we show that this solution has the side effect of introducing transient discontinuities in the nodal symmetry of the wave function. We present an alternative solution to the trivial crossing problem that preserves both the spatial and nodal structure of the adiabatic wave function. By considering a model of exciton dynamics on conjugated polymer systems, we show that failure to preserve wave function symmetry yields exciton dynamics that depends unphysically on polymer system size. We demonstrate that our symmetry-preserving solution to the trivial crossing problem yields more realistic dynamics and can thus improve the accuracy of simulations of larger systems that are prone to the trivial crossing problem.

Subspace Surface Hopping with Size-Independent Dynamics

We present a subspace surface hopping strategy to deal with complex surface crossings in nonadiabatic dynamics. By focusing on only important adiabatic states, we make subspace crossing correction (SCC) in the framework of the standard fewest switches surface hopping (FSSH) and the global flux surface hopping (GFSH). The resulting SCC-FSSH and SCC-GFSH approaches show much better performance than the counterparts using all adiabatic states for surface hopping. As demonstrated in a series of Holstein models with up to over 1000 molecular sites, both SCC-FSSH and SCC-GFSH show excellent size independence with a large time step size of 1 fs. Especially, SCC-GFSH does not refer to nonadiabatic couplings at all and gives a more proper description of superexchange, and thus, it is promising for realistic applications with complex potential energy surfaces.

Crossover from hopping to band-like transport in crystalline organic semiconductors: The effect of shallow traps

We show a crossover from coherent to incoherent behavior of charge transport in crystalline organic semiconductors by considering the effect of shallow traps within the dynamical disorder model. The mixed quantum-classical system is treated by the Ehrenfest dynamics method complementing with instantaneous decoherence corrections and energy relaxation, which has been shown to properly make the system close to equilibrium. The shallow traps, which are incorporated by a static diagonal disorder, are shown to play a central role in the crossover. Temperature dependence of charge-carrier mobility is shown to be changed from being negative to positive with the strength of shallow traps increasing, which implies that there is a crossover from hopping to band-like transport. A higher electric field helps to recover the charge-carrier band-like transport behavior from the traps-caused hopping transport. In this way, a unified physical picture of the charge transport in crystalline organic semiconductors is proposed.