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

Decoherence ensures convergence of non-adiabatic molecular dynamics with number of states

Non-adiabatic (NA) molecular dynamics (MD) is a powerful approach for studying far-from-equilibrium quantum dynamics in photophysical and photochemical systems. Most NA-MD methods are developed and tested with few-state models, and their validity with complex systems involving many states is not well studied. By modeling intraband equilibration and interband recombination of charge carriers in MoS2, we investigate the convergence of three popular NA-MD algorithms, fewest switches surface hopping (FSSH), global flux surface hopping (GFSH), and decoherence induced surface hopping (DISH) with the number of states. Only the standard DISH algorithm converges with the number of states and produces Boltzmann equilibrium. Unitary propagation of the wave function in FSSH and GFSH violates the Boltzmann distribution, leads to internal inconsistency between time-dependent Schrödinger equation state populations and trajectory counts, and produces non-convergent results. Introducing decoherence in FSSH and GFSH by collapsing the wave function fixes these problems. The simplified version of DISH that omits projecting out the occupied state and is applicable to few-state systems also causes problems when the number of states is increased. We discuss the algorithmic application of wave function collapse and Boltzmann detailed balance and provide detailed FSSH, GFSH, and DISH flow charts. The use of convergent NA-MD methods is highly important for modeling complicated quantum processes involving multiple states. Our findings provide the basis for investigating quantum dynamics in realistic complex systems.

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

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

Exciton Transport in the Nonfullerene Acceptor O-IDTBR from Nonadiabatic Molecular Dynamics

Theory, computation, and experiment have given strong evidence that charge carriers in organic molecular crystals form partially delocalized quantum objects that diffuse very efficiently via a mechanism termed transient delocalization. It is currently unclear how prevalent this mechanism is for exciton transport. Here we carry out simulation of singlet Frenkel excitons (FE) in a molecular organic semiconductor that belongs to the class of nonfullerene acceptors, O-IDTBR, using the recently introduced FE surface hopping nonadiabatic molecular dynamics method. We find that FE are, on average, localized on a single molecule in the crystal due to sizable reorganization energy and moderate excitonic couplings. Yet, our simulations suggest that the diffusion mechanism is more complex than simple local hopping; in addition to hopping, we observe frequent transient delocalization events where the exciton wave function expands over 10 or more molecules for a short period of time in response to thermal excitations within the excitonic band, followed by de-excitation and contraction onto a single molecule. The transient delocalization events lead to an increase in the diffusion constant by a factor of 3-4, depending on the crystallographic direction as compared to the situation where only local hopping events are considered. Intriguingly, O-IDTBR appears to be a moderately anisotropic 3D "conductor" for excitons but a highly anisotropic 2D conductor for electrons. Taken together with previous simulation results, two trends seem to emerge for molecular organic crystals: excitons tend to be more localized and slower than charge carriers due to higher internal reorganization energy, while exciton transport tends to be more isotropic than charge transport due to the weaker distance dependence of excitonic versus electronic coupling.

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.

Nonadiabatic molecular dynamics with subsystem density functional theory: application to crystalline pentacene

In this work, we report the development and assessment of the nonadiabatic molecular dynamics approach with the electronic structure calculations based on the linearly scaling subsystem density functional method. The approach is implemented in an open-source embedded Quantum Espresso/Libra software specially designed for nonadiabatic dynamics simulations in extended systems. As proof of the applicability of this method to large condensed-matter systems, we examine the dynamics of nonradiative relaxation of excess excitation energy in pentacene crystals with the simulation supercells containing more than 600 atoms. We find that increased structural disorder observed in larger supercell models induces larger nonadiabatic couplings of electronic states and accelerates the relaxation dynamics of excited states. We conduct a comparative analysis of several quantum-classical trajectory surface hopping schemes, including two new methods proposed in this work (revised decoherence-induced surface hopping and instantaneous decoherence at frustrated hops). Most of the tested schemes suggest fast energy relaxation occurring with the timescales in the 0.7-2.0 ps range, but they significantly overestimate the ground state recovery rates. Only the modified simplified decay of mixing approach yields a notably slower relaxation timescales of 8-14 ps, with a significantly inhibited ground state recovery.

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.

All-Atom Photoinduced Charge Transfer Dynamics in Condensed Phase via Multistate Nonlinear-Response Instantaneous Marcus Theory

Photoinduced charge transfer (CT) in the condensed phase is an essential component in solar energy conversion, but it is challenging to simulate such a process on the all-atom level. The traditional Marcus theory has been utilized for obtaining CT rate constants between pairs of electronic states but cannot account for the nonequilibrium effects due to the initial nuclear preparation. The recently proposed instantaneous Marcus theory (IMT) and its nonlinear-response formulation allow for incorporating the nonequilibrium nuclear relaxation to electronic transition between two states after the photoexcitation from the equilibrium ground state and provide the time-dependent rate coefficient. In this work, we extend the nonlinear-response IMT method for treating photoinduced CT among general multiple electronic states and demonstrate it in the organic photovoltaic carotenoid-porphyrin-fullerene triad dissolved in explicit tetrahydrofuran solvent. All-atom molecular dynamics simulations were employed to obtain the time correlation functions of energy gaps, which were used to generate the IMT-required time-dependent averages and variances of the relevant energy gaps. Our calculations show that the multistate IMT could capture the significant nonequilibrium effects due to the initial nuclear state preparation, and this is corroborated by the substantial differences between the population dynamics predicted by the multistate IMT and the Marcus theory, where the Marcus theory underestimates the population transfer. The population dynamics by multistate IMT is also shown to have a better agreement with the all-atom nonadiabatic mapping dynamics than the Marcus theory does. Because the multistate nonlinear-response IMT is straightforward and cost-effective in implementation and accounts for the nonequilibrium nuclear effects, we believe this method offers a practical strategy for studying charge transfer dynamics in complex condensed-phase systems.

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.

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.

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.

Stabilized coupled trajectory mixed quantum-classical algorithm with improved energy conservation: CTMQC-EDI

Coupled trajectory mixed quantum-classical (CTMQC) dynamics is a rigorous approach to trajectory-based non-adiabatic dynamics, which has recently seen an improvement to energy conservation via the introduction of the CTMQC-E algorithm. Despite this, the method's two key quantities distinguishing it from Ehrenfest dynamics, the modified Born-Oppenheimer momentum and the quantum momentum, require regularization procedures in certain circumstances. Such procedures in the latter can cause instabilities, leading to undesirable effects, such as energy drift and spurious population transfer, which is expected to become increasingly prevalent when the system gets larger as such events would happen more frequently. We propose a further modification to CTMQC-E, which includes a redefinition of the quantum momentum, CTMQC-EDI (double intercept), such that it has no formal divergences. We then show for Tully models I-III and the double arch model that the algorithm has greatly improved total energy conservation and negligible spurious population transfer at all times, in particular in regions of strong non-adiabatic coupling. CTMQC-EDI, therefore, shows promise as a numerically robust non-adiabatic dynamics technique that accounts for decoherence from first principles and that is scalable to large molecular systems and materials.

On-off conduction photoswitching in modelled spiropyran-based metal-organic frameworks

Materials with photoswitchable electronic properties and conductance values that can be reversibly changed over many orders of magnitude are highly desirable. Metal-organic framework (MOF) films functionalized with photoresponsive spiropyran molecules demonstrated the general possibility to switch the conduction by light with potentially large on-off-ratios. However, the fabrication of MOF materials in a trial-and-error approach is cumbersome and would benefit significantly from in silico molecular design. Based on the previous proof-of-principle investigation, here, we design photoswitchable MOFs which incorporate spiropyran photoswitches at controlled positions with defined intermolecular distances and orientations. Using multiscale modelling and automated workflow protocols, four MOF candidates are characterized and their potential for photoswitching the conductivity is explored. Using ab initio calculations of the electronic coupling between the molecules in the MOF, we show that lattice distances and vibrational flexibility tremendously modulate the possible conduction photoswitching between spiropyran- and merocyanine-based MOFs upon light absorption, resulting in average on-off ratios higher than 530 and 4200 for p- and n-conduction switching, respectively. Further functionalization of the photoswitches with electron-donating/-withdrawing groups is demonstrated to shift the energy levels of the frontier orbitals, permitting a guided design of new spiropyran-based photoswitches towards controlled modification between electron and hole conduction in a MOF.

Vitality of Intralayer Vibration in hBN for Effective Long-Range Interlayer Hole Transfer across High Barriers in MoSe2/hBN/WSe2 Heterostructures

Introducing the two-dimensional (2D) hexagonal boron nitride (hBN) between 2D transition metal dichalcogenide (TMD) layers promises convenient manipulation of the interlayer exciton (IX) and interlayer charge transfer in TMD/hBN/TMD heterostructures, while the role of inserted hBN layers during IX formation is controversial. Employing ab initio nonadiabatic molecular dynamics (NAMD) simulations and the electron-phonon coupling model, we systematically investigate interlayer hole transfer in MoSe2/WSe2 bilayers intercalated by hBN layers with various thicknesses. The conventional direct hole transfer from MoSe2 to WSe2 is decelerated by 2-3 orders of magnitude after the hBN insertion. Meanwhile, a novel channel intermediated by a deeper hole of WSe2 becomes dominant, where the intralayer shear mode of hBN plays a crucial role by reducing the energy barriers for this new channel. The unique role of hBN layers is revealed for the first time, enriching the knowledge of the underlying microscopic mechanisms and providing instructive guidance to practical van der Waals optoelectronic devices.

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.

Multistate Reaction Coordinate Model for Charge and Energy Transfer Dynamics in the Condensed Phase

Constructing multistate model Hamiltonians from all-atom electronic structure calculations and molecular dynamics simulations is crucial for understanding charge and energy transfer dynamics in complex condensed phases. The most popular two-level system model is the spin-boson Hamiltonian, where the nuclear degrees of freedom are represented as shifted normal modes. Recently, we proposed the general multistate nontrivial extension of the spin-boson model, i.e., the multistate harmonic (MSH) model, which is constructed by extending the spatial dimensions of each nuclear mode so as to satisfy the all-atom reorganization energy restrictions for all pairs of electronic states. In this work, we propose the multistate reaction coordinate (MRC) model with a primary reaction coordinate and secondary bath modes as in the Caldeira-Leggett form but in extended spatial dimensions. The MRC model is proven to be equivalent to the MSH model and offers an intuitive physical picture of the nuclear-electronic feedback in nonadiabatic processes such as the inherent trajectory of the reaction coordinate. The reaction coordinate is represented in extended dimensions, carrying the entire reorganization energies and bilinearly coupled to the secondary bath modes. We demonstrate the MRC model construction for photoinduced charge transfer in an organic photovoltaic caroteniod-porphyrin-C60 molecular triad dissolved in tetrahydrofuran as well as excitation energy transfer in a photosynthetic light-harvesting Fenna-Matthews-Olson complex. The MRC model provides an effective and robust platform for investigating quantum dissipative dynamics in complex condensed-phase systems since it allows a consistent description of realistic spectral density, state-dependent system-bath couplings, and heterogeneous environments due to static disorder in reorganization energies.

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

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

A comprehensive review on the behavior and evolution of oil droplets during oil/water separation by membranes

Membrane separation technology has significant advantages for treating oil-in-water emulsions. Understanding the evolution of oil droplets could reveal the interfacial and colloidal interactions, facilitate the design of advanced membranes, and improve the separation performances. This review on the characteristic behavior and evolution of oil droplets focuses on the advanced analytical techniques, and the subsequent fouling as well as demulsification effects during membrane separation. A detailed introduction is provided on microscopic observations and numerical simulations of the dynamic evolution of oil droplets, featuring real-time in-situ visualization and accurate reconstruction, respectively. Characteristic behaviors of these oil droplets include attachment, pinning, wetting, spreading, blockage, intrusion, coalescence, and detachment, which have been quantified by specific proposed parameters and criteria. The fouling process can be evaluated using Hermia and resistance models. The related adhesion force and intrusion pressure as well as droplet-droplet/membrane interfacial interactions can be accurately quantified using various force analysis methods and advanced force measurement techniques. It is encouraging to note that oil coalescence has been achieved through various effects such as electrostatic interactions, mechanical actions, Laplace pressure/surface free energy gradients, and synergistic effects on functional membranes. When oil droplets become destabilized and coalesce into larger ones, the functional membranes can overcome the limitations of size-sieving effect to attain higher separation efficiency. This not only bypasses the trade-off between permeability and rejection, but also significantly reduces membrane fouling. Finally, the challenges and potential research directions in membrane separation are proposed. We hope this review will support the engineering of advanced materials for oil/water separation and research on interface science in general.

Learning Decoherence Time Formulas for Surface Hopping from Quantum Dynamics

Surface hopping simulations have achieved great success in many different fields, but their reliability has long been limited by the overcoherence problem. We here present a general machine learning assisted approach to identify optimal decoherence time formulas for surface hopping using exact quantum dynamics as references. In order to avoid computationally expensive force calculations, we use the nuclear kinetic energy and the adiabatic energy difference to iteratively generate the descriptor space. Through multilayer screening of the candidate descriptors and discrete optimization of the relevant parameters, we obtain new energy-based decoherence time formulas. As benchmarked in thousands of diverse multilevel systems and six standard scattering models, surface hopping with our new decoherence time formulas nearly reproduces the exact quantum dynamics while maintaining high efficiency. Thereby, our approach provides a promising avenue for systematically improving the accuracy of surface hopping simulations in complex systems from quantum dynamics data.

Zeno and Anti-Zeno Effects in Nonadiabatic Molecular Dynamics

Decoherence plays an important role in nonadiabatic (NA) molecular dynamics (MD) simulations because it provides a physical mechanism for trajectory hopping and can alter transition rates by orders of magnitude. Generally, decoherence effects slow quantum transitions, as exemplified by the quantum Zeno effect: in the limit of infinitely fast decoherence, the transitions stop. If the measurements are not sufficiently frequent, an opposite quantum anti-Zeno effect occurs, in which the transitions are accelerated with faster decoherence. Using two common NA-MD approaches, fewest switches surface hopping and decoherence-induced surface hopping, combined with analytic examination, we demonstrate that including decoherence into NA-MD slows down NA transitions; however, many realistic systems operate in the anti-Zeno regime. Therefore, it is important that NA-MD methods describe both Zeno and anti-Zeno effects. Numerical simulations of charge trapping and relaxation in graphitic carbon nitride suggest that time-dependent NA Hamiltonians encountered in realistic systems produce robust results with respect to errors in the decoherence time, a favorable feature for NA-MD simulations.

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.

Jumping Kinetic Monte Carlo: Fast and Accurate Simulations of Partially Delocalized Charge Transport in Organic Semiconductors

Developing devices using disordered organic semiconductors requires accurate and practical models of charge transport. In these materials, charge transport occurs through partially delocalized states in an intermediate regime between localized hopping and delocalized band conduction. Partial delocalization can increase mobilities by orders of magnitude compared to those with conventional hopping, making it important for the design of materials and devices. Although delocalization, disorder, and polaron formation can be described using delocalized kinetic Monte Carlo (dKMC), it is a computationally expensive method. Here, we develop jumping kinetic Monte Carlo (jKMC), a model that approaches the accuracy of dKMC for modest amounts of delocalization (such as those found in disordered organic semiconductors), with a computational cost comparable to that of conventional hopping. jKMC achieves its computational performance by modeling conduction using identical spherical polarons, yielding a simple delocalization correction to the Marcus hopping rate that allows polarons to jump over their nearest neighbors. jKMC can be used in regimes of partial delocalization inaccessible to dKMC to show that modest delocalization can increase mobilities by as much as 2 orders of magnitude.

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.

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.

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.

Recent Progress of Organic Semiconductor Materials in Spintronics

Spintronics, a new discipline focusing on the spin-dependent transport process of electrons, has been developing rapidly. Spin valves are the most significant carriers of spintronics utilizing the spin freedom of electrons. It is expected to pierce "Moore's Law" and become the core component in processors of the next generation. Organic semiconductors advance in their adjustable band gap, weak spin-orbit coupling and hyperfine interaction, excellent film-forming property, having enormous promise for spin valves. Here, the principle of spin valves is introduced, and the history and progress in organic spin injection and transport materials are summarized. Then we analyze the influence of spinterface on device performance and introduce reliable methods of constructing organic spin valves. Finally, the challenges for spin valves are discussed, and the future is proposed. We aim to draw the attention of researchers to organic spin valves and promote further research in spintronics through this paper.

Tunneling-to-Hopping Transition in Multiheme Cytochrome Bioelectronic Junctions

Multiheme cytochromes (MHCs) have attracted much interest for use in nanobioelectronic junctions due to their high electronic conductances. Recent measurements on dry MHC junctions suggested that a coherent tunneling mechanism is operative over surprisingly long long distances (>3 nm), which challenges our understanding of coherent transport phenomena. Here we show that this is due to (i) a low exponential distance decay constant for coherent conduction in MHCs (β = 0.2 Å^-1) and (ii) a large density of protein electronic states which prolongs the coherent tunneling regime to distances that exceed those in molecular wires made of small molecules. Incoherent hopping conduction is uncompetitive due to the large energy level offset at the protein-electrode interface. Removing this offset, e.g., by gating, we predict that the transport mechanism crosses over from coherent tunneling to incoherent hopping at a protein size of ∼7 nm, thus enabling transport on the micrometer scale with a shallow polynomial (∼1/r) distance decay.

Time-Dependent Charge Carrier Transport with Hall Effect in Organic Semiconductors for Langevin and Non-Langevin Systems

The time-dependent charge carrier transport and recombination processes in low-mobility organic semiconductor diodes are obtained through numerical simulations using the finite element method (FEM). The application of a Lorentz force across the diode alters the charge transport process leading to the Hall effect. In this contribution, the Hall effect parameters, such as the Hall voltage and charge carrier concentration with varying magnetic fields, are computed for both Langevin and non-Langevin type recombination processes. The results indicate the charge carrier concentration within the diode for the Langevin system is about seven and fourteen times less while the maximum amount of extracted charge is nearly five and ten times less than that in the non-Langevin system of 0.01 and 0.001, respectively. The Hall voltage values obtained for the steady-state case are similar to the non-Langevin system of ββL=0.01. However, the values obtained for the Langevin and non-Langevin systems of ββL=1 and 0.001 exhibit anomalies. The implications of these findings advance the understanding of the charge transport and Hall effect measurements in organic semiconductors that underpins the device's performance.

Structural Disorder in Higher-Temperature Phases Increases Charge Carrier Lifetimes in Metal Halide Perovskites

Solar cells and optoelectronic devices are exposed to heat that degrades performance. Therefore, elucidating temperature-dependent charge carrier dynamics is essential for device optimization. Charge carrier lifetimes decrease with temperature in conventional semiconductors. The opposite, anomalous trend is observed in some experiments performed with MAPbI₃ (MA = CH₃NH₃⁺) and other metal halide perovskites. Using ab initio quantum dynamics simulation, we establish the atomic mechanisms responsible for nonradiative electron-hole recombination in orthorhombic-, tetragonal-, and cubic MAPbI₃. We demonstrate that structural disorder arising from the phase transitions is as important as the disorder due to heating in the same phase. The carrier lifetimes grow both with increasing temperature in the same phase and upon transition to the higher-temperature phases. The increased lifetime is rationalized by structural disorder that induces partial charge localization, decreases nonadiabatic coupling, and shortens quantum coherence. Inelastic and elastic electron-vibrational interactions exhibit opposite dependence on temperature and phase. The partial disorder and localization arise from thermal motions of both the inorganic lattice and the organic cations and depend significantly on the phase. The structural deformations induced by thermal fluctuations and phase transitions are on the same order as deformations induced by defects, and hence, thermal disorder plays a very important role. Since charge localization increases carrier lifetimes but inhibits transport, an optimal regime maximizing carrier diffusion can be designed, depending on phase, temperature, material morphology, and device architecture. The atomistic mechanisms responsible for the enhanced carrier lifetimes at elevated temperatures provide guidelines for the design of improved solar energy and optoelectronic materials.

All-Atom Nonadiabatic Semiclassical Mapping Dynamics for Photoinduced Charge Transfer of Organic Photovoltaic Molecules in Explicit Solvents

Direct all-atom simulation of nonadiabatic dynamics in disordered condensed phases like liquid solutions and amorphous solids has been challenging. The first all-atom simulation of the photoinduced charge-transfer dynamics of a prototypical organic photovoltaic carotenoid-porphyrin-C₆₀ molecular triad in explicit tetrahydrofuran is presented. Based on the Meyer-Miller mapping Hamiltonian, various semiclassical and mixed quantum-classical dynamics are employed, including the linearized semiclassical, symmetrical quasiclassical, mean-field Ehrenfest, classical mapping model, and spin-mapping model approaches. The all-atom nonadiabatic dynamics were compared to multi-state harmonic models with a globally shared bath, and the models built using the ensemble averages on the initial electronic state could reproduce the all-atom results. The solvent effect was found to be critical for the photoinduced charge transfer, and the time-dependent solute-solvent radial distribution functions revealed that only the nonadiabatic dynamics started with the effective forces on the initial electronic state could capture the correct nuclear dynamics. The proposed strategy for modeling condensed-phase nonadiabatic dynamics with atomistic details is readily applied to complex condensed-phase systems.

Exciton Dissociation in a Model Organic Interface: Excitonic State-Based Surface Hopping versus Multiconfigurational Time-Dependent Hartree

Quantum dynamical simulations are essential for a molecular-level understanding of light-induced processes in optoelectronic materials, but they tend to be computationally demanding. We introduce an efficient mixed quantum-classical nonadiabatic molecular dynamics method termed eXcitonic state-based Surface Hopping (X-SH), which propagates the electronic Schrödinger equation in the space of local excitonic and charge-transfer electronic states, coupled to the thermal motion of the nuclear degrees of freedom. The method is applied to exciton decay in a 1D model of a fullerene-oligothiophene junction, and the results are compared to the ones from a fully quantum dynamical treatment at the level of the Multilayer Multiconfigurational Time-Dependent Hartree (ML-MCTDH) approach. Both methods predict that charge-separated states are formed on the 10-100 fs time scale via multiple "hot-exciton dissociation" pathways. The results demonstrate that X-SH is a promising tool advancing the simulation of photoexcited processes from the molecular to the true nanomaterials scale.

A New Frontier in Exciton Transport: Transient Delocalization

Efficient exciton transport is crucial to the application of organic semiconductors (OSCs) in light-harvesting devices. While the physics of exciton transport in highly disordered media is well-explored, the description of transport in structurally and energetically ordered OSCs is less established, despite such materials being favorable for devices. In this Perspective we describe and highlight recent research pointing toward a highly efficient exciton transport mechanism which occurs in ordered OSCs, transient delocalization. Here, exciton-phonon couplings play a critical role in allowing localized exciton states to temporarily access higher-energy delocalized states whereupon they move large distances. The mechanism shows great promise for facilitating long-range exciton transport and may allow for improved device efficiencies and new device architectures. However, many fundamental questions on transient delocalization remain to be answered. These questions and suggested next steps are summarized.

Detailed Balance and Independent Electron Surface-Hopping Method: The Importance of Decoherence and Correct Calculation of Diabatic Populations

We benchmark and improve the independent electron surface-hopping (IESH) method developed by J. C. Tully's group for nonadiabatic simulations near metal surfaces. We have incorporated decoherence within the IESH method as well as implemented a scheme for the accurate calculation of diabatic populations. We benchmark the original IESH method with the above inclusions for a model system to calculate rate constants and long-time populations. The original IESH method fails to capture the detailed balance for some of the parameters, which is corrected with the inclusion of decoherence and accurate calculation of diabatic populations. Total rate constants are well captured both within the original IESH method as well as within our modified IESH.

New Opportunities for Organic Semiconducting Polymers in Biomedical Applications

The life expectancy of humans has been significantly elevated due to advancements in medical knowledge and skills over the past few decades. Although a lot of knowledge and skills are disseminated to the general public, electronic devices that quantitatively diagnose one’s own body condition still require specialized semiconductor devices which are huge and not portable. In this regard, semiconductor materials that are lightweight and have low power consumption and high performance should be developed with low cost for mass production. Organic semiconductors are one of the promising materials in biomedical applications due to their functionalities, solution-processability and excellent mechanical properties in terms of flexibility. In this review, we discuss organic semiconductor materials that are widely utilized in biomedical devices. Some advantageous and unique properties of organic semiconductors compared to inorganic semiconductors are reviewed. By critically assessing the fabrication process and device structures in organic-based biomedical devices, the potential merits and future aspects of the organic biomedical devices are pinpointed compared to inorganic devices.

Electron-Volt Fluctuation of Defect Levels in Metal Halide Perovskites on a 100 ps Time Scale

Metal halide perovskites (MHPs) have gained considerable attention due to their excellent optoelectronic performance, which is often attributed to unusual defect properties. We demonstrate that midgap defect levels can exhibit very large and slow energy fluctuations associated with anharmonic acoustic motions. Therefore, care should be taken classifying MHP defects as deep or shallow, since shallow defects may become deep and vice versa. As a consequence, charges from deep levels can escape into bands, and light absorption can be extended to longer wavelengths, improving material performance. The phenomenon, demonstrated with iodine vacancy in CH₃NH₃PbI₃ using a machine learning force field, can be expected for a variety of defects and dopants in many MHPs and other soft inorganic semiconductors. Since large-scale anharmonic motions can be precursors to chemical decomposition, a known problem with MHPs, we propose that materials that are stiffer than MHPs but softer than traditional inorganic semiconductors, such as Si and TiO₂, may simultaneously exhibit excellent performance and stability.

Nonadiabatic Molecular Dynamics with Extended Density Functional Tight-Binding: Application to Nanocrystals and Periodic Solids

In this work, we report a new methodology for nonadiabatic molecular dynamics calculations within the extended tight-binding (xTB) framework. We demonstrate the applicability of the developed approach to finite and periodic systems with thousands of atoms by modeling "hot" electron relaxation dynamics in silicon nanocrystals and electron-hole recombination in both a graphitic carbon nitride monolayer and a titanium-based metal-organic framework (MOF). This work reports the nonadiabatic dynamic simulations in the largest Si nanocrystals studied so far by the xTB framework, with diameters up to 3.5 nm. For silicon nanocrystals, we find a non-monotonic dependence of "hot" electron relaxation rates on the nanocrystal size, in agreement with available experimental reports. We rationalize this relationship by a combination of decreasing nonadiabatic couplings related to system size and the increase of available coherent transfer pathways in systems with higher densities of states. We emphasize the importance of proper treatment of coherences for obtaining such non-monotonic dependences. We characterize the electron-hole recombination dynamics in the graphitic carbon nitride monolayer and the Ti-containing MOF. We demonstrate the importance of spin-adaptation and proper sampling of surface hopping trajectories in modeling such processes. We also assess several trajectory surface hopping schemes and highlight their distinct qualitative behavior in modeling the excited-state dynamics in superexchange-like models depending on how they handle coherences between nearly parallel states.

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.

Implementation and Validation of Constrained Density Functional Theory Forces in the CP2K Package

Constrained density functional theory (CDFT) is a powerful tool for the prediction of electron transfer parameters in condensed phase simulations at a reasonable computational cost. In this work we present an extension to CDFT in the popular mixed Gaussian/plane wave electronic structure package CP2K, implementing the additional force terms arising from a constraint based on Hirshfeld charge partitioning. This improves upon the existing Becke partitioning scheme, which is prone to give unphysical atomic charges. We verify this implementation for a variety of systems: electron transfer in (H₂O)₂⁺ in a vacuum, electron tunnelling between oxygen vacancy centers in solid MgO, and electron self-exchange in aqueous Ru²⁺–Ru³⁺. We find good agreement with previous plane-wave CDFT results for the same systems, but at a significantly lower computational cost, and we discuss the general reliability of condensed phase CDFT calculations.

Exciton transport in molecular organic semiconductors boosted by transient quantum delocalization

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