Charge Transport in Molecular Materials: An Assessment of Computational Methods

Electron Localization and Mobility in Monolayer Fullerene Networks

The novel 2D quasi-hexagonal phase of covalently bonded fullerene molecules (qHP C60), the so-called graphullerene, has displayed far superior electron mobilities, if compared to the parent van der Waals three-dimensional crystal (vdW C60). Herein, we present a comparative study of the electronic properties of vdW and qHP C60 using state-of-the-art electronic-structure calculations and a full quantum-mechanical treatment of electron transfer. We show that both materials entail polaronic localization of electrons with similar binding energies (≈0.1 eV) and, therefore, they share the same charge transport via polaron hopping. In fact, we quantitatively reproduce the sizable increment of the electron mobility measured for qHP C60 and identify its origin in the increased electronic coupling between C60 units.

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 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.

Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime

Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus-Levich-Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane-anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes.

Detailed Complementary Consistency: Wave Function Tells Particle How to Hop, Particle Tells Wave Function How to Collapse

In mixed quantum-classical dynamics, the quantum subsystem can have both wave function and particle-like descriptions. However, they may yield inconsistent results for the expectation value of the same physical quantity. We here propose a novel detailed complementary consistency (DCC) method based on the principle of detailed internal consistency. Namely, the wave function along each trajectory tells the particle how to hop, while the particle tells the wave function how to collapse based on active states in the trajectory ensemble. As benchmarked in a diverse array of representative models with localized nonadiabatic couplings, DCC not only achieves fully consistent results (i.e., identical populations calculated based on wave functions and active states) but also closely reproduces the exact quantum results. Due to the high performance, our new DCC method has great potential to give a consistent and accurate mixed quantum-classical description of general nonadiabatic dynamics after further development.

Methods for the analysis, interpretation, and prediction of single-molecule junction conductance behaviour

This article offers a broad overview of measurement methods in the field of molecular electronics, with a particular focus on the most common single-molecule junction fabrication techniques, the challenges in data analysis and interpretation of single-molecule junction current-distance traces, and a summary of simulations and predictive models aimed at establishing robust structure-property relationships of use in the further development of molecular electronics.

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.

Electronic Transport Properties of Molecular Clusters Sb4O6, P4Se3, and P4O6

Inorganic molecular crystal (IMC) is a trending class of materials in which structural units comprise molecular cages or clusters bonded via van der Waal forces. The structure-property relationship in IMCs is less known due to the unusual assembly of molecular clusters in these materials. In this paper, the density functional theory-calculated electronic transport properties of the molecular clusters of antimony oxide (Sb4O6), phosphorus triselenide (P4Se3), and phosphorus trioxide (P4O6) are described in detail. The calculated values of highest occupied molecular orbital-lowest unoccupied molecular orbital gaps appeared as 5.487, 2.296, and 4.425 eV for Sb4O6, P4Se3, and P4O6, respectively. The work was carried out to explore the charge transport mechanism in IMCs in order to disclose their potential in practical applications. The calculations involved charge-transfer integral based on Marcus theory to compute the electronic coupling (V), reorganization energies (λ), and hopping rate (k) in the structures. The hopping rate for Sb4O6, P4Se3, and P4O6 is found as 8.49 × 10-12, 1.28 × 10-14, and 2.51 × 10-20 s-1, respectively. The transport properties of Sb4O6 are found better, which predicts the application of the relevant IMC for device grade applications. The findings of this study are important for future application of the IMCs in electronic and optoelectronic applications.

Accessing the electronic structure of liquid crystalline semiconductors with bottom-up electronic coarse-graining

Understanding the relationship between multiscale morphology and electronic structure is a grand challenge for semiconducting soft materials. Computational studies aimed at characterizing these relationships require the complex integration of quantum-chemical (QC) calculations, all-atom and coarse-grained (CG) molecular dynamics simulations, and back-mapping approaches. However, these methods pose substantial computational challenges that limit their application to the requisite length scales of soft material morphologies. Here, we demonstrate the bottom-up electronic coarse-graining (ECG) of morphology-dependent electronic structure in the liquid-crystal-forming semiconductor, 2-(4-methoxyphenyl)-7-octyl-benzothienobenzothiophene (BTBT). ECG is applied to construct density functional theory (DFT)-accurate valence band Hamiltonians of the isotropic and smectic liquid crystal (LC) phases using only the CG representation of BTBT. By bypassing the atomistic resolution and its prohibitive computational costs, ECG enables the first calculations of the morphology dependence of the electronic structure of charge carriers across LC phases at the ∼20 nm length scale, with robust statistical sampling. Kinetic Monte Carlo (kMC) simulations reveal a strong morphology dependence on zero-field charge mobility among different LC phases as well as the presence of two-molecule charge carriers that act as traps and hinder charge transport. We leverage these results to further evaluate the feasibility of developing mesoscopic, field-based ECG models in future works. The fully CG approach to electronic property predictions in LC semiconductors opens a new computational direction for designing electronic processes in soft materials at their characteristic length scales.

Excitons at the interface of 2D TMDs and molecular semiconductors

Van der Waals heterostructures (vdWHs) of vertically stacked two-dimensional (2D) atomic crystals have been used to elicit intriguing phenomena stemming from strong electronic correlations, magnetic textures, and interlayer excitons spawned at the heterointerface. However, vdWHs comprised of heterointerfaces between these 2D atomic crystal lattices and molecular assemblies are emerging as equally intriguing platforms supporting properties to be harnessed for photovoltaic energy conversion, photodetection, spin-selective charge injection, and quantum emission. In this perspective, we summarize recent research examining exciton dynamics in heterostructures between semiconducting 2D transition metal dichalcogenides and molecular organic semiconductors. We discuss methods for assembly of these heterostructures, the nature of interlayer or charge-transfer excitons at transition-metal dichalcogenide (TMD)-molecule interfaces, explicit exciton transfer between organics and TMDs, and other interfacial phenomena driven by the merger of these two material classes. We also suggest key new research directions extending the remit of these 2D atomic-molecular lattice heterointerfaces into the domains of condensed matter physics, quantum sensing, and energy conversion.

Surface Hopping with Reliable Wave Function by Introducing Auxiliary Wave Packets to Trajectory Branching

It is well-known that the widely utilized fewest switches surface hopping method suffers from the severe overcoherence problem, and thus adiabatic populations calculated by wave functions are generally inferior to those based on active states. More importantly, to achieve a complete description of nonadiabatic dynamics, the density matrix is essential. In this paper, we present an auxiliary branching corrected surface hopping (A-BCSH) method that introduces auxiliary wave packets (WPs) on the adiabatic potential energy surfaces for trajectory branching. Both rapid and gradual separation of WP components on different surfaces are characterized, and thus the correct decoherence time along each trajectory is captured. As demonstrated in the three standard Tully models, A-BCSH exhibits excellent internal consistency. Namely, close adiabatic populations are obtained based on both wave functions and active states. In particular, A-BCSH successfully obtains a reliable time-dependent spatial distribution of the density matrix, which relies only on electronic wave functions. Due to its high performance, our A-BCSH method provides a new and highly promising perspective on further development of more consistent surface hopping with reliable wave function.

Calculation of Charge Transport Phenomena and Mobility Analysis in the Insulating Oil Using First Principle and Marcus Theory

Oil-paper insulation is widely used as a reliable composite insulation system in power transformers. The dielectric property of oil insulation plays an important role in the reliable operation of power equipment. To recognize the charge transfer process in composite insulation, the mobility of the charge in aged insulating oil is studied. However, few studies have been conducted on the microscopic mechanism of charge transport phenomena at the molecular level. In this research, we have studied the molecular electronic structure and the distribution of holes and electrons in the insulating oil by first-principles calculation. By combining with Marcus theory, the corresponding electron coupling energy, reorganization energy, and free energy are obtained. The corresponding charge hopping model is chosen by the parameter relation, and the hopping rate is calculated. At last, the mobility of holes and electrons in insulating oil within the insulation is simulated by the Monte Carlo method. Other possible charge migration methods are also studied and discussed for the comparison. It is observed that the transfer integral of electrons is 2 orders of magnitude larger than that of holes, which is mostly due to the localization of lowest unoccupied molecular orbitals (LUMO). The hole and charge transfers accord with Marcus hopping, the adiabatic charge transfer model, and the charge hopping rate is obtained. The actual free energy action under an external electric field is obtained by calculating polarizability and permittivity. Monte Carlo simulation is used to obtain the charge transfer image and mobility under an actual electric field. Possible types of traps and mobility of ions and clusters in the insulating oil are also studied.

Intuitive and Efficient Approach to Determine the Band Structure of Covalent Organic Frameworks from Their Chemical Constituents

The optical, electronic, and (photo) catalytic properties of covalent organic frameworks (COFs) are largely determined by their electronic structure and, specifically, by their Frontier conduction and valence bands (VBs). In this work, we establish a transparent relationship between the periodic electronic structure of the COFs and the orbital characteristics of their individual molecular building units, a relationship that is challenging to unravel through conventional solid-state calculations. As a demonstration, we applied our method to five COFs with distinct framework topologies. Our approach successfully predicts their first-principles conduction and VBs by expressing them as a linear combination of the Frontier molecular orbitals localized on the COF fragments. We demonstrate that our method allows for the rapid exploration of the impact of chemical modifications on the band structures of COFs, making it highly suitable for further application in the quest to discover new functional materials.

Anomalous Transport of Small Polarons Arises from Transient Lattice Relaxation or Immovable Boundaries

Elucidating transport mechanisms is crucial for advancing material design, yet state-of-the-art theory is restricted to exact simulations of small lattices with severe finite-size effects or approximate ones that assume the nature of transport. We leverage algorithmic advances to tame finite-size effects and exactly simulate small polaron formation and transport in the Holstein model. We further analyze the applicability of the ubiquitously used equilibrium-based Green-Kubo relations and nonequilibrium methods to predict charge mobility. We find that these methods can converge to different values and track this disparity to finite-size dependence and the sensitivity of Green-Kubo relations to the system's topology. Contrary to standard perturbative calculations, our results demonstrate that small polarons exhibit anomalous transport that manifests transiently due to nonequilibrium lattice relaxation or permanently as a signature of immovable boundaries. These findings can offer new interpretations of transport experiments on polymers and transition metal oxides.

Tryptophan to Tryptophan Hole Hopping in an Azurin Construct

Electron transfer (ET) between neutral and cationic tryptophan residues in the azurin construct [ReI(H126)(CO)3(dmp)](W124)(W122)CuI (dmp = 4,7-Me2-1,10-phenanthroline) was investigated by Born-Oppenheimer quantum-mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) simulations. We focused on W124•+ ← W122 ET, which is the middle step of the photochemical hole-hopping process *ReII(CO)3(dmp•-) ← W124 ← W122 ← CuI, where sequential hopping amounts to nearly 10,000-fold acceleration over single-step tunneling (ACS Cent. Sci. 2019, 5, 192-200). In accordance with experiments, UKS-DFT QM/MM/MD simulations identified forward and reverse steps of W124•+ ↔ W122 ET equilibrium, as well as back ET ReI(CO)3(dmp•-) → W124•+ that restores *ReII(CO)3(dmp•-). Strong electronic coupling between the two indoles (≥40 meV in the crossing region) makes the productive W124•+ ← W122 ET adiabatic. Energies of the two redox states are driven to degeneracy by fluctuations of the electrostatic potential at the two indoles, mainly caused by water solvation, with contributions from the protein dynamics in the W122 vicinity. ET probability depends on the orientation of Re(CO)3(dmp) relative to W124 and its rotation diminishes the hopping yield. Comparison with hole hopping in natural systems reveals structural and dynamics factors that are important for designing efficient hole-hopping processes.

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.

Benchmark Data Set of Crystalline Organic Semiconductors

This work reports a Benchmark Data set of Crystalline Organic Semiconductors to test calculations of the structural and electronic properties of these materials in the solid state. The data set contains 67 crystals consisting of mostly rigid molecules with a single dominant conformer, covering the majority of known structural types. The experimental crystal structure is available for the entire data set, whereas zero-temperature unit cell volume can be reliably estimated for a subset of 28 crystals. Using this subset, we benchmark r2SCAN-D3 and PBE-D3 density functionals. Then, for the entire data set, we benchmark approximate density functional theory (DFT) methods, including GFN1-xTB and DFTB3(3ob-3-1), with various dispersion corrections against r2SCAN-D3. Our results show that r2SCAN-D3 geometries are accurate within a few percent, which is comparable to the statistical uncertainty of experimental data at a fixed temperature, but the unit cell volume is systematically underestimated by 2% on average. The several times faster PBE-D3 provides an unbiased estimate of the volume for all systems except for molecules with highly polar bonds, for which the volume is substantially overestimated in correlation with the underestimation of atomic charges. Considered approximate DFT methods are orders of magnitude faster and provide qualitatively correct but overcompressed crystal structures unless the dispersion corrections are fitted by unit cell volume.

Electron transport through supercrystals of atomically precise gold nanoclusters: a thermal bi-stability effect

Nanoparticles (NPs) may behave like atoms or molecules in the self-assembly into artificial solids with stimuli-responsive properties. However, the functionality engineering of nanoparticle-assembled solids is still far behind the aesthetic approaches for molecules, with a major problem arising from the lack of atomic-precision in the NPs, which leads to incoherence in superlattices. Here we exploit coherent superlattices (or supercrystals) that are assembled from atomically precise Au103S2(SR)41 NPs (core dia. = 1.6 nm, SR = thiolate) for controlling the charge transport properties with atomic-level structural insights. The resolved interparticle ligand packing in Au103S2(SR)41-assembled solids reveals the mechanism behind the thermally-induced sharp transition in charge transport through the macroscopic crystal. Specifically, the response to temperature induces the conformational change to the R groups of surface ligands, as revealed by variable temperature X-ray crystallography with atomic resolution. Overall, this approach leads to an atomic-level correlation between the interparticle structure and a bi-stability functionality of self-assembled supercrystals, and the strategy may enable control over such materials with other novel functionalities.

What is Missing in the Mean Field Description of Spatial Distribution of Population? Important Role of Auxiliary Wave Packets in Trajectory Branching

When the traditional Ehrenfest mean field approach is employed to simulate nonadiabatic dynamics, an effective wave packet (WP) on the average potential energy surface (PES) is utilized to describe the nuclear motion. In the fully quantum picture, however, the WP components on different adiabatic PESs gradually separate in space because they evolve under different velocities and forces. Due to trajectory branching of the WP components, proper decoherence needs to be taken into account, and the spatial distribution of population cannot be described by a single effective WP. Here, we propose an auxiliary branching corrected mean field (A-BCMF) method, where trajectories of auxiliary WPs on adiabatic PESs are introduced. As benchmarked in the three standard Tully models, A-BCMF not only gives correct channel populations but also captures an accurate time-dependent spatial distribution of population. Thereby, we reveal the important role of auxiliary WPs in solving intrinsic problems of the widely used mean field description of nonadiabatic dynamics.

Designing Benzodithiophene-Based Small Molecule Donors for Organic Solar Cells by Regulation of Halogenation Effects

The donors are key components of organic solar cells (OSCs) and play crucial roles in their photovoltaic performance. Herein, we designed two new donors (BTR-γ-Cl and BTR-γ-F) by finely optimizing small molecule donors (BTR-Cl and BTR-F) with a high performance. The optoelectronic properties of the four donors and their interfacial properties with the well-known acceptor Y6 were studied by density functional theory and time-dependent density functional theory. Our calculations show that the studied four donors have large hole mobility and strong interactions with Y6, where the BTR-γ-Cl/Y6 has the largest binding energy. Importantly, the proportion of charge transfer (CT) states increases at the BTR-γ-Cl/Y6 (50%) and BTR-γ-F/Y6 (45%) interfaces. The newly designed donors are more likely to achieve CT states through intermolecular electric field (IEF) and hot exciton mechanisms than the parent molecules; meanwhile, donors containing Cl atoms are more inclined to produce CT states through the direct excitation mechanism than those containing F atoms. Our results not only provided two promising donors but also shed light on the halogenation effects on donors in OSCs, which might be important to design efficient photovoltaic materials.

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.

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.

Competing quantum effects in heavy-atom tunnelling through conical intersections

Thermally activated chemical reactions are typically understood in terms of overcoming potential-energy barriers. However, standard rate theories break down in the presence of a conical intersection (CI) because these processes are inherently nonadiabatic, invalidating the Born-Oppenheimer approximation. Moreover, CIs give rise to intricate nuclear quantum effects such as tunnelling and the geometric phase, which are neglected by standard trajectory-based simulations and remain largely unexplored in complex molecular systems. We present new semiclassical transition-state theories based on an extension of golden-rule instanton theory to describe nonadiabatic tunnelling through CIs and thus provide an intuitive picture for the reaction mechanism. We apply the method in conjunction with first-principles electronic-structure calculations to the electron transfer in the bis(methylene)-adamantyl cation. Our study reveals a strong competition between heavy-atom tunnelling and geometric-phase effects.

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

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

Physics-inspired machine learning of localized intensive properties

Machine learning (ML) has been widely applied to chemical property prediction, most prominently for the energies and forces in molecules and materials. The strong interest in predicting energies in particular has led to a 'local energy'-based paradigm for modern atomistic ML models, which ensures size-extensivity and a linear scaling of computational cost with system size. However, many electronic properties (such as excitation energies or ionization energies) do not necessarily scale linearly with system size and may even be spatially localized. Using size-extensive models in these cases can lead to large errors. In this work, we explore different strategies for learning intensive and localized properties, using HOMO energies in organic molecules as a representative test case. In particular, we analyze the pooling functions that atomistic neural networks use to predict molecular properties, and suggest an orbital weighted average (OWA) approach that enables the accurate prediction of orbital energies and locations.

Models of Polaron Transport in Inorganic and Hybrid Organic-Inorganic Titanium Oxides

Polarons are a type of localized excess charge in materials and often form in transition metal oxides. The large effective mass and confined nature of polarons make them of fundamental interest for photochemical and electrochemical reactions. The most studied polaronic system is rutile TiO₂ where electron addition results in small polaron formation through the reduction of Ti(IV) d⁰ to Ti(III) d¹ centers. Using this model system, we perform a systematic analysis of the potential energy surface based on semiclassical Marcus theory parametrized from the first-principles potential energy landscape. We show that F-doped TiO₂ only binds polaron weakly with effective dielectric screening after the second nearest neighbor. To tailor the polaron transport, we compare TiO₂ to two metal-organic frameworks (MOFs): MIL-125 and ACM-1. The choice of MOF ligands and connectivity of the TiO₆ octahedra largely vary the shape of the diabatic potential energy surface and the polaron mobility. Our models are applicable to other polaronic materials.

How Regiochemistry Influences Aggregation Behavior and Charge Transport in Conjugated Organosulfur Polymer Cathodes for Lithium-Sulfur Batteries

For lithium-sulfur (Li-S) batteries to become competitive, they require high stability and energy density. Organosulfur polymer-based cathodes have recently shown promising performance due to their ability to overcome common limitations of Li-S batteries, such as the insulating nature of sulfur. In this study, we use a multiscale modeling approach to explore the influence of the regiochemistry of a conjugated poly(4-(thiophene-3-yl)benzenethiol) (PTBT) polymer on its aggregation behavior and charge transport. Classical molecular dynamics simulations of the self-assembly of polymer chains with different regioregularity show that a head-to-tail/head-to-tail regularity can form a well-ordered crystalline phase of planar chains allowing for fast charge transport. Our X-ray diffraction measurements, in conjunction with our predicted crystal structure, confirm the presence of crystalline phases in the electropolymerized PTBT polymer. We quantitatively describe the charge transport in the crystalline phase in a band-like regime. Our results give detailed insights into the interplay between microstructural and electrical properties of conjugated polymer cathode materials, highlighting the effect of polymer chain regioregularity on its charge transport properties.

Reorganization Energy Predictions with Graph Neural Networks Informed by Low-Cost Conformers

A critical bottleneck for the design of high-conductivity organic materials is finding molecules with low reorganization energy. To enable high-throughput virtual screening campaigns for many types of organic electronic materials, a fast reorganization energy prediction method compared to density functional theory is needed. However, the development of low-cost machine-learning-based models for calculating the reorganization energy has proven to be challenging. In this paper, we combine a 3D graph-based neural network (GNN) recently benchmarked for drug design applications, ChIRo, with low-cost conformational features for reorganization energy predictions. By comparing the performance of ChIRo to another 3D GNN, SchNet, we find evidence that the bond-invariant property of ChIRo enables the model to learn from low-cost conformational features more efficiently. Through an ablation study with a 2D GNN, we find that using low-cost conformational features on top of 2D features informs the model for making more accurate predictions. Our results demonstrate the feasibility of reorganization energy predictions on the benchmark QM9 data set without needing DFT-optimized geometries and demonstrate the types of features needed for robust models that work on diverse chemical spaces. Furthermore, we show that ChIRo informed with low-cost conformational features achieves comparable performance with the previously reported structure-based model on π-conjugated hydrocarbon molecules. We expect this class of methods can be applied to the high-throughput screening of high-conductivity organic electronics candidates.

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.

The hierarchy of Davydov's Ansätze: From guesswork to numerically "exact" many-body wave functions

This Perspective presents an overview of the development of the hierarchy of Davydov's Ansätze and a few of their applications in many-body problems in computational chemical physics. Davydov's solitons originated in the investigation of vibrational energy transport in proteins in the 1970s. Momentum-space projection of these solitary waves turned up to be accurate variational ground-state wave functions for the extended Holstein molecular crystal model, lending unambiguous evidence to the absence of formal quantum phase transitions in Holstein systems. The multiple Davydov Ansätze have been proposed, with increasing Ansatz multiplicity, as incremental improvements of their single-Ansatz parents. For a given Hamiltonian, the time-dependent variational formalism is utilized to extract accurate dynamic and spectroscopic properties using Davydov's Ansätze as its trial states. A quantity proven to disappear for large multiplicities, the Ansatz relative deviation is introduced to quantify how closely the Schrödinger equation is obeyed. Three finite-temperature extensions to the time-dependent variation scheme are elaborated, i.e., the Monte Carlo importance sampling, the method of thermofield dynamics, and the method of displaced number states. To demonstrate the versatility of the methodology, this Perspective provides applications of Davydov's Ansätze to the generalized Holstein Hamiltonian, variants of the spin-boson model, and systems of cavity-assisted singlet fission, where accurate dynamic and spectroscopic properties of the many-body systems are given by the Davydov trial states.

Giant Tunability of Charge Transport in 2D Inorganic Molecular Crystals by Pressure Engineering

The unique intermolecular van der Waals force in emerging two-dimensional inorganic molecular crystals (2DIMCs) endows them with highly tunable structures and properties upon applying external stimuli. Using high pressure to modulate the intermolecular bonding, here we reveal the highly tunable charge transport behavior in 2DIMCs for the first time, from an insulator to a semiconductor. As pressure increases, 2D α-Sb₂ O₃ molecular crystal undergoes three isostructural transitions, and the intermolecular bonding enhances gradually, which results in a considerably decreased band gap by 25 % and a greatly enhanced charge transport. Impressively, the in situ resistivity measurement of the α-Sb₂ O₃ flake shows a sharp drop by 5 orders of magnitude in 0-3.2 GPa. This work sheds new light on the manipulation of charge transport in 2DIMCs and is of great significance for promoting the fundamental understanding and potential applications of 2DIMCs in advanced modern technologies.

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.

Wearable in-sensor reservoir computing using optoelectronic polymers with through-space charge-transport characteristics for multi-task learning

In-sensor multi-task learning is not only the key merit of biological visions but also a primary goal of artificial-general-intelligence. However, traditional silicon-vision-chips suffer from large time/energy overheads. Further, training conventional deep-learning models is neither scalable nor affordable on edge-devices. Here, a material-algorithm co-design is proposed to emulate human retina and the affordable learning paradigm. Relying on a bottle-brush-shaped semiconducting p-NDI with efficient exciton-dissociations and through-space charge-transport characteristics, a wearable transistor-based dynamic in-sensor Reservoir-Computing system manifesting excellent separability, fading memory, and echo state property on different tasks is developed. Paired with a 'readout function' on memristive organic diodes, the RC recognizes handwritten letters and numbers, and classifies diverse costumes with accuracies of 98.04%, 88.18%, and 91.76%, respectively (higher than all reported organic semiconductors). In addition to 2D images, the spatiotemporal dynamics of RC naturally extract features of event-based videos, classifying 3 types of hand gestures at an accuracy of 98.62%. Further, the computing cost is significantly lower than that of the conventional artificial-neural-networks. This work provides a promising material-algorithm co-design for affordable and highly efficient photonic neuromorphic systems.

The impacts of dopants on the small polaron mobility and conductivity in hematite - the role of disorder

Hematite (α-Fe₂O₃) is a promising transition metal oxide for various energy conversion and storage applications due to its advantages of low cost, high abundance, and good chemical stability. However, its low carrier mobility and electrical conductivity have hindered the wide application of hematite-based devices. Fundamentally, this is mainly caused by the formation of small polarons, which show conduction through thermally activated hopping. Atomic doping is one of the most promising approaches for improving the electrical conductivity in hematite. However, its impact on the carrier mobility and electrical conductivity of hematite at the atomic level remains to be illusive. In this work, through a kinetic Monte-Carlo sampling approach for diffusion coefficients combined with carrier concentrations computed under charge neutrality conditions, we obtained the electrical conductivity of the doped hematite. We considered the contributions from individual Fe-O layers, given that the in-plane carrier transport dominates. We then studied how different dopants impact the carrier mobility in hematite using Sn, Ti, and Nb as prototypical examples. We found that the carrier mobility change is closely correlated with the local distortion of Fe-Fe pairs, i.e. the more stretched the Fe-Fe pairs are compared to the pristine systems, the lower the carrier mobility will be. Therefore, elements which limit the distortion of Fe-Fe pair distances from pristine are more desired for higher carrier mobility in hematite. The calculated local structure and pair distribution functions of the doped systems have remarkable agreement with the experimental EXAFS measurements on hematite nanowires, which further validates our first-principles predictions. Our work revealed how dopants impact the carrier mobility and electrical conductivity of hematite and provided practical guidelines to experimentalists on the choice of dopants for the optimal electrical conductivity of hematite and the performance of hematite-based devices.

Electrochemical Properties and Local Structure of the TEMPO/TEMPO+ Redox Pair in Ionic Liquids

Redox-active organic species play an important role in catalysis, energy storage, and biotechnology. One of the representatives is the 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) radical, used as a mediator in organic synthesis and considered a safe alternative to heavy metals. In order to develop a TEMPO-based system with well-controlled electrochemical and catalytic properties, a reaction medium should be carefully chosen. Being highly conductive, stable, and low flammability fluids, ionic liquids (ILs) seem to be promising solvents with easily adjustable physical and solvation properties. In this work, we give an insight into the local structure of ILs around TEMPO and its oxidized form, TEMPO⁺, underlining striking differences in the solvation of these two species. The analysis is coupled with a study of thermodynamics and kinetics of oxidation in the frame of Marcus theory. Our systematic investigation includes imidazolium, pyrrolydinium, and phosphonium families combined with anions of different size, polarity, and flexibility, opting to provide a clear and comprehensive picture of the impact of the nature of IL ions on the behavior of radical/cation redox pairs. The obtained results will help to explain experimentally observed effects and to rationalize the design of TEMPO/IL systems.

A Green's Function Approach for Determining Surface Induced Broadening and Shifting of Molecular Energy Levels

Upon adsorption of a molecule onto a surface, the molecular energy levels (MELs) broaden and change their alignment. This phenomenon directly affects electron transfer across the interface and is, therefore, a fundamental observable that influences electrochemical device performance. Here, we propose a rigorous parameter-free framework, built upon the theoretical construct of Green's functions, for studying the interface between a molecule and a bulk surface and its effect on MELs. The method extends beyond the usual wide-band limit approximation, and its generality allows its use with any level of electronic structure theory. We demonstrate its ability to predict the broadening and shifting of MELs as a function of intramolecular coupling, molecule/surface coupling, and the surface density of states for a molecule with two MELs adsorbed on a one-dimensional model metal surface. The new approach could help provide guidelines for the design and experimental characterization of electrochemical devices with optimal electron transport.

Molecular Design of A-D-A Electron Acceptors Towards Low Energy Loss for Organic Solar Cells

Low energy loss is a prerequisite for organic solar cells to achieve high photovoltaic efficiency. Electron-vibration coupling (i. e., intramolecular reorganization energy) plays a crucial role in the photoelectrical conversion and energy loss processes. In this Concept article, we summarize our recent theoretical advances on revealing the energy loss mechanisms at the molecular level of A-D-A electron acceptors. We underline the importance of electron-vibration couplings on reducing the energy loss and describe the effective molecular design strategies towards low energy loss through decreasing the electron-vibration couplings.

Plenty of Room on the Top: Pathways and Spectroscopic Signatures of Singlet Fission from Upper Singlet States

We investigate dynamic signatures of the singlet fission (SF) process triggered by the excitation of a molecular system to an upper singlet state S_N (N > 1) and develop a computational methodology for the simulation of nonlinear spectroscopic signals revealing the S_N → TT₁ SF in real time. We demonstrate that SF can proceed directly from the upper state S_N, bypassing the lowest excited state, S₁. We determine the main S_N → TT₁ reaction pathways and show by computer simulation and spectroscopic measurements that the S_N-initiated SF can be faster and more efficient than the traditionally studied S₁ → TT₁ SF. We claim that the S_N → TT₁ SF offers novel promising opportunities for engineering SF systems and enhancing SF yields.

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

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

Even a little delocalization produces large kinetic enhancements of charge-separation efficiency in organic photovoltaics

In organic photovoltaics, charges can separate efficiently even if their Coulomb attraction is an order of magnitude greater than the available thermal energy. Delocalization has been suggested to explain this fact, because it could increase the initial separation of charges in the charge-transfer (CT) state, reducing their attraction. However, understanding the mechanism requires a kinetic model of delocalized charge separation, which has proven difficult because it involves tracking the correlated quantum-mechanical motion of the electron and the hole in large simulation boxes required for disordered materials. Here, we report the first three-dimensional simulations of charge-separation dynamics in the presence of disorder, delocalization, and polaron formation, finding that even slight delocalization, across less than two molecules, can substantially enhance the charge-separation efficiency, even starting with thermalized CT states. Delocalization does not enhance efficiency by reducing the Coulomb attraction; instead, the enhancement is a kinetic effect produced by the increased overlap of electronic states.

Conduction band structure of high-mobility organic semiconductors and partially dressed polaron formation

The energy band structure provides crucial information on charge transport behaviour in organic semiconductors, such as effective mass, transfer integrals and electron-phonon coupling. Despite the discovery of the valence (the highest occupied molecular orbital (HOMO)) band structure in the 1990s, the conduction band (the lowest unoccupied molecular orbital (LUMO)) has not been experimentally observed. Here we employ angle-resolved low-energy inverse photoelectron spectroscopy to reveal the LUMO band structure of pentacene, a prototypical high-mobility organic semiconductor. The derived transfer integrals and bandwidths from the LUMO are substantially smaller than those predicted by density functional theory calculations. To reproduce this bandwidth reduction, we propose an improved (partially dressed) polaron model that accounts for the electron-intramolecular vibrational interaction with frequency-dependent coupling constants based on Debye relaxation. This model quantitatively reproduces not only the transfer integrals, but also the temperature-dependent HOMO and LUMO bandwidths, and the hole and electron mobilities. The present results demonstrate that electron mobility in high-mobility organic semiconductors is indeed limited by polaron formation.

Combining Theory and Experiments To Study the Influence of Gas Sorption on the Conductivity Properties of Metal-Organic Frameworks

With a view on adding to their use in trace gas sensing, we perform a combined experimental and theoretical study of the change of the conductivity of a metal organic framework (iron (1,2,3)-triazolate, Fe(ta)2) with the uptake of chemically inert gases. To align our first-principles calculations with experimental measurements, we perform an ensemble average over different microscopic arrangements of the gas molecules in the pores of the metal-organic framework (MOF). Up to the experimentally reachable limit of gas uptake, we find a good agreement between both approaches. Thus, we can employ theory to further interpret our experimental results in terms of changes to the parameters of the Bardeen-Shockley band theory, electron-phonon coupling (in the form of the deformation potential), bulk modulus, and carrier effective mass. We find the first of these to be most strongly influenced through the gas uptake. Furthermore, we find the changes to the deformation potential to strongly depend on the individual microscopic arrangements of molecules in the pores of the MOF. This hints at a possible synthetic engineering of the material, e.g., by closing off certain pores, for a stronger, more interpretable electric response upon gas sorption.

Modeling of Electron Hole Transport within a Small Ribosomal Subunit

Abstract—

Synchronized operation of various parts of the ribosome during protein synthesis implies the presence of a coordinating pathway, however, this is still unknown. We have recently suggested that such a pathway can be based on charge transport along the transfer and ribosomal RNA molecules and localization of the charges in functionally important areas of the ribosome. In the current study, using density functional theory calculations, we show that charge carriers (electron holes) can efficiently migrate within the central element of the small ribosomal subunit—the h44 helix. Monte-Carlo modeling revealed that electron holes tend to localize in the functionally important areas of the h44 helix, near the decoding center and intersubunit bridges. On the basis of the results obtained, we suggest that charge transport and localization within the h44 helix could coordinate intersubunit ratcheting with other processes occurring during protein synthesis.

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.

Feasibility of p-Doped Molecular Crystals as Transparent Conductive Electrodes via Virtual Screening

Transparent conducting materials are an essential component of optoelectronic devices. It is proven difficult, however, to develop high-performance materials that combine the often-incompatible properties of transparency and conductivity, especially for p-type-doped materials. In this work, we have employed a large set of molecular semiconductors extracted from the Cambridge Structural Database to evaluate the likelihood of transparent conducting material technology based on p-type-doped molecular crystals. Candidates are identified imposing the condition of high highest occupied molecular orbital (HOMO) energy level (for the material to be easily dopable), high charge carrier mobility (for the material to display large conductivity when doped), and a high threshold for energy absorption (for the material to absorb radiation only in the ultraviolet). The latest condition is found to be the most stringent criterion in a virtual screening protocol on a database composed of structures with sufficiently wide two-dimensional (2D) electronic bands. Calculation of excited-state energy is shown to be essential as the HOMO-lowest unoccupied molecular orbital (LUMO) gap cannot be reliably used to predict the transparency of this material class. Molecular semiconductors with desirable mobility are transparent because they display either forbidden electronic transition(s) to the lower excited states or small exchange energy between the frontier orbitals. Both features are difficult to design but can be found in a good number of compounds through virtual screening.

Reorganization Free Energy of Copper Proteins in Solution, in Vacuum, and on Metal Surfaces

Metalloproteins, known to efficiently transfer electronic charge in biological systems, recently found their utilization in nanobiotechnological devices where the protein is placed into direct contact with metal surfaces. The feasibility of oxidation/reduction of the protein redox sites is affected by the reorganization free energies, one of the key parameters determining the transfer rates. While their values have been measured and computed for proteins in their native environments, i.e., in aqueous solution, the reorganization free energies of dry proteins or proteins adsorbed to metal surfaces remain unknown. Here, we investigate the redox properties of blue copper protein azurin, a prototypical redox-active metalloprotein previously probed by various experimental techniques both in solution and on metal/vacuum interfaces. We used a hybrid QM/MM computational technique based on DFT to explore protein dynamics, flexibility, and corresponding reorganization free energies in aqueous solution, vacuum, and on vacuum gold interfaces. Somewhat surprisingly, the reorganization free energy only slightly decreases when azurin is dried because the loss of the hydration shell leads to larger flexibility of the protein near its redox site. At the vacuum gold surfaces, the energetics of the structure relaxation depends on the adsorption geometry, however, significant reduction of the reorganization free energy was not observed. These findings have important consequences for the charge transport mechanism in vacuum devices, showing that the free energy barriers for protein oxidation remain significant even under ultra-high vacuum conditions.

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.