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

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.

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.

Nonadiabatic Dynamics with Exact Factorization: Implementation and Assessment

In this work, we report our implementation of several independent-trajectory mixed-quantum-classical (ITMQC) nonadiabatic dynamics methods based on exact factorization (XF) in the Libra package for nonadiabatic and excited-state dynamics. Namely, the exact factorization surface hopping (SHXF), mixed quantum-classical dynamics (MQCXF), and mean-field (MFXF) are introduced. Performance of these methods is compared to that of several traditional surface hopping schemes, such as the fewest-switches surface hopping (FSSH), branching-corrected surface hopping (BCSH), and the simplified decay of mixing (SDM), as well as conventional Ehrenfest (mean-field, MF) method. Based on a comprehensive set of 1D model Hamiltonians, we find the ranking SHXF ≈ MQCXF > BCSH > SDM > FSSH ≫ MF, with the BCSH sometimes outperforming the XF methods in terms of describing coherences. Although the MFXF method can yield reasonable populations and coherences for some cases, it does not conserve the total energy and is therefore not recommended. We also find that the branching correction for auxiliary trajectories is important for the XF methods to yield accurate populations and coherences. However, the branching correction can worsen the quality of the energy conservation in the MQCXF. Finally, we find that using the time-dependent Gaussian width approximation used in the XF methods for computing decoherence correction can improve the quality of energy conservation in the MQCXF dynamics. The parameter-free scheme of Subotnik for computing the Gaussian widths is found to deliver the best performance in situations where such widths are not known a priori.

Exciton annihilation and diffusion length in disordered multichromophoric nanoparticles

Efficient exciton transport is the essential property of natural and synthetic light-harvesting (LH) devices. Here we investigate exciton transport properties in LH organic polymer nanoparticles (ONPs) of 40 nm diameter. The ONPs are loaded with a rhodamine B dye derivative and bulky counterion, enabling dye loadings as high as 0.3 M, while preserving fluorescence quantum yields larger than 30%. We use time-resolved fluorescence spectroscopy to monitor exciton-exciton annihilation (EEA) kinetics within the ONPs dispersed in water. We demonstrate that unlike the common practice for photoluminescence investigations of EEA, the non-uniform intensity profile of the excitation light pulse must be taken into account to analyse reliably intensity-dependent population dynamics. Alternatively, a simple confocal detection scheme is demonstrated, which enables (i) retrieving the correct value for the bimolecular EEA rate which would otherwise be underestimated by a typical factor of three, and (ii) revealing minor EEA by-products otherwise unnoticed. Considering the ONPs as homogeneous rigid solutions of weakly interacting dyes, we postulate an incoherent exciton hoping mechanism to infer a diffusion constant exceeding 0.003 cm2 s-1 and a diffusion length as large as 70 nm. This work demonstrates the success of the present ONP design strategy at engineering efficient exciton transport in disordered multichromophoric systems.

Impact of Local and Nonlocal Vibronic Coupling on the Absorption and Emission Spectra of J- and H-Dimers

The impact of exciton-vibrational (EV) coupling involving low-energy ("slow") intermolecular vibrations and higher-energy ("fast") intramolecular vibrations on the absorption and emission spectra of H- and J-dimers is studied theoretically for a pair of chromophores with excitonic coupling dominated by transition dipole-dipole coupling, JC. Exact quantum-mechanical solutions based on a Frenkel-Holstein-Peierls Hamiltonian reveal a fascinating interplay between the two coupling sources in determining the spectral line widths, Stoke shifts and radiative decay rates. It is shown that the ratio rules derived from the vibronic progression of the fast mode in molecular dimers remain valid under the influence of slow-mode EV coupling under most conditions. However, a highly unusual aggregate behavior occurs when the product of local and nonlocal couplings, |gLgNL|, exceeds 2ℏωs|JC|, where ℏωs is the energy of the slow mode. In this regime and when gL and gNL are in-phase, an H-dimer (JC > 0) becomes strongly emissive and can even be super-radiant, while a J-dimer (JC < 0) with out-of-phase gL and gNL values becomes subradiant. Such behaviors are in marked contrast to the predictions of Kasha theory and demonstrate the richness of the photophysical behavior resulting from EV coupling involving inter- and intramolecular vibrations.

Theory of acoustic polarons in the two-dimensional SSH model applied to the layered superatomic semiconductor Re6Se8Cl2

Layered superatomic semiconductors, whose building blocks are atomically precise molecular clusters, exhibit interesting electronic and vibrational properties. In recent work [Tulyagankhodjaev et al., Science 382, 438 (2023)], transient reflection microscopy revealed quasi-ballistic exciton dynamics in Re6Se8Cl2, which was attributed to the formation of polarons due to coupling with acoustic phonons. Here, we characterize the electronic, excitonic, and phononic properties with periodic density functional theory. We further parameterize a polaron Hamiltonian with nonlocal (Su-Schrieffer-Heeger) coupling to an acoustic phonon to study the polaron ground state binding energy and dispersion relation with variational wavefunctions. We calculate a polaron binding energy of about 10 meV at room temperature, and the maximum group velocity of our polaron dispersion relation is 1.5 km/s, which is similar to the experimentally observed exciton transport velocity.

Decoupling excitons from high-frequency vibrations in organic molecules

The coupling of excitons in π-conjugated molecules to high-frequency vibrational modes, particularly carbon-carbon stretch modes (1,000-1,600 cm-1) has been thought to be unavoidable1,2. These high-frequency modes accelerate non-radiative losses and limit the performance of light-emitting diodes, fluorescent biomarkers and photovoltaic devices. Here, by combining broadband impulsive vibrational spectroscopy, first-principles modelling and synthetic chemistry, we explore exciton-vibration coupling in a range of π-conjugated molecules. We uncover two design rules that decouple excitons from high-frequency vibrations. First, when the exciton wavefunction has a substantial charge-transfer character with spatially disjoint electron and hole densities, we find that high-frequency modes can be localized to either the donor or acceptor moiety, so that they do not significantly perturb the exciton energy or its spatial distribution. Second, it is possible to select materials such that the participating molecular orbitals have a symmetry-imposed non-bonding character and are, thus, decoupled from the high-frequency vibrational modes that modulate the π-bond order. We exemplify both these design rules by creating a series of spin radical systems that have very efficient near-infrared emission (680-800 nm) from charge-transfer excitons. We show that these systems have substantial coupling to vibrational modes only below 250 cm-1, frequencies that are too low to allow fast non-radiative decay. This enables non-radiative decay rates to be suppressed by nearly two orders of magnitude in comparison to π-conjugated molecules with similar bandgaps. Our results show that losses due to coupling to high-frequency modes need not be a fundamental property of these systems.

MesoHOPS: Size-invariant scaling calculations of multi-excitation open quantum systems

The photoexcitation dynamics of molecular materials on the 10-100 nm length scale depend on complex interactions between electronic and vibrational degrees of freedom, rendering exact calculations difficult or intractable. The adaptive Hierarchy of Pure States (adHOPS) is a formally exact method that leverages the locality imposed by interactions between thermal environments and electronic excitations to achieve size-invariant scaling calculations for single-excitation processes in systems described by a Frenkel-Holstein Hamiltonian. Here, we extend adHOPS to account for arbitrary couplings between thermal environments and vertical excitation energies, enabling formally exact, size-invariant calculations that involve multiple excitations or states with shared thermal environments. In addition, we introduce a low-temperature correction and an effective integration of the noise to reduce the computational expense of including ultrafast vibrational relaxation in Hierarchy of Pure States (HOPS) simulations. We present these advances in the latest version of the open-source MesoHOPS library and use MesoHOPS to characterize charge separation at a one-dimensional organic heterojunction when both the electron and hole are mobile.

Impact of Photoluminescence Imaging Methodology on Transport Parameters in Semiconductors

Triplet-triplet annihilation-induced delayed emission provides a pathway for investigating triplets via emission spectroscopy. This bimolecular annihilation depends directly on the transport properties of triplet excitons in disordered organic semiconductors. Photoluminescence (PL) imaging is a direct method for studying exciton and charge-carrier diffusivity. However, most of these studies neglect dispersive transport. Early time scale measurements using this technique can lead to an overestimation of the diffusion coefficient (DT) or diffusion length (Ld). In this study, we investigated the time-dependent triplet DT using PL imaging. We observed an overestimation of Ld in classical delayed PL imaging, often 1 order of magnitude higher than the actual Ld value. We compared various thicknesses of polymeric thin films to study the dispersive nature of triplet excitons. Transient analysis of delayed PL imaging and steady state imaging reveals the importance of considering the time-dependent nature of DT for the triplet excitons in disordered electronic materials.

Coherent Transient Localization Mechanism of Interchain Exciton Transport in Regioregular P3HT: A Quantum-Dynamical Study

Transient localization has been proposed as a transport mechanism in organic materials, for both charge carriers and excitons. Here, we characterize a quantum coherent transient localization mechanism using full quantum simulations of an H-aggregated model system representative of regioregular poly(3-hexylthiophene) (rrP3HT). A Frenkel-Holstein Hamiltonian parametrized from first principles is considered, including local high-frequency modes and anharmonic, site-correlated interchain modes. Quantum-dynamical calculations are carried out using the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method for a 13-site system with 195 vibrational modes, under periodic boundary conditions. It is shown that temporary localization of exciton polarons alternates with resonant transfer driven by interchain modes. While the transport process is mainly determined by exciton-polarons at the low-energy band edge, persistent coupling with the excitonic manifold is observed, giving rise to a nonadiabatic excitonic flux. This elementary transport mechanism remains preserved for limited static disorder and gives way to Anderson localization when the static disorder becomes dominant.

Vibrational Coupling Infrared Nanocrystallography

Coupling between molecular vibrations leads to collective vibrational states with spectral features sensitive to local molecular order. This provides spectroscopic access to the low-frequency intermolecular energy landscape. In its nanospectroscopic implementation, this technique of vibrational coupling nanocrystallography (VCNC) offers information on molecular disorder and domain formation with nanometer spatial resolution. However, deriving local molecular order relies on prior knowledge of the transition dipole magnitude and crystal structure of the underlying ordered phase. Here we develop a quantitative model for VCNC by relating nano-FTIR collective vibrational spectra to the molecular crystal structure from X-ray crystallography. We experimentally validate our approach at the example of a metal organic porphyrin complex with a carbonyl ligand as the probe vibration. This framework establishes VCNC as a powerful tool for measuring low-energy molecular interactions, wave function delocalization, nanoscale disorder, and domain formation in a wide range of molecular systems.

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.

Role of Charge-Carrier Dynamics Toward the Fabrication of Efficient Air-Processed Organic Solar Cells

Over the past couple of decades, immense research has been carried out to understand the photo-physics of an organic solar cell (OSC) that is important to enhance its efficiency and stability. Since OSCs undergoes complex photophysical phenomenon, studying these factors has led to designing new materials and implementing new strategies to improve efficiency in OSCs. In this regard, the invention of the non-fullerene acceptorshas greatly revolutionized the understanding of the fundamental processes occurring in OSCs. However, such vital fundamental research from device physics perspectives is carried out on glovebox (GB) processed OSCs and there is a scarcity of research on air-processed (AP) OSCs. This review will focus on charge carrier dynamics such as exciton diffusion, exciton dissociation, charge-transfer states, significance of highest occupied molecular orbital-offsets, and hole-transfer efficiencies of GB-OSCs and compare them with the available data from the AP-OSCs. Finally, key requirements for the fabrication of efficient AP-OSCs will be presented from a charge-carrier dynamics perspective. The key aspects from the charge-carrier dynamics view to fabricate efficient OSCs either from GB or air are provided.

Third-Order Nonlinear Optical Properties of Aqueous Silver Sulfide Quantum Dots

Wide spectral wavelength range (500-1600 nm) measurements of nonlinear optical properties of silver sulfide (Ag2S, with 2- or 3-mercaptopropionic acid, 2 or 3MPA ligands) quantum dots (QDs) in aqueous colloidal solutions were performed using the Z-scan technique with tunable ∼55 fs laser pulses at 1 kHz. We have identified regions of the occurrence of various NLO effects including two-photon absorption, nonlinear refraction, as well as saturation of one-photon absorption. At the same time, we evaluated the relationship between the properties of the QDs and the variation of the material that covers their surface. The peak two-photon absorption cross section (σ2) values were determined to be 632 ± 271 GM (at 850 nm) for Ag2S-2MPA QDs and 772 ± 100 GM (at 875 nm) for Ag2S-3MPA QDs. The physicochemical factors influencing the three-dimensional self-organization of Ag2S QDs in water as well as their impact on spectroscopic properties were also investigated.

The Exciton Model for Molecular Materials: Past, Present and Future?

In assemblies of identical molecules or chromophores, electronic excitations can be described as excitons, bound electron-hole pairs that can move from site to site as a pair in a coherent manner. The understanding of excitons is crucial when trying to engineer favorable photophysical properties through structuring organic molecular matter. In recent decades, limitations of the concept of an exciton have become clear. The exciton can hybridize with phonon and photons. To clarify these issues, the exciton is discussed within the broader context of the gauge properties of the electromagnetic force.

Ultrafast many-body bright-dark exciton transition in anatase TiO2

The momentum-forbidden dark excitons can have a pivotal role in quantum information processing, Bose-Einstein condensation, and light-energy harvesting. Anatase TiO2 with an indirect band gap is a prototypical platform to study bright to momentum-forbidden dark exciton transition. Here, we examine, by GW plus the real-time Bethe-Salpeter equation combined with the nonadiabatic molecular dynamics (GW + rtBSE-NAMD), the many-body transition that occurs within 100 fs from the optically excited bright to the strongly bound momentum-forbidden dark excitons in anatase TiO2. Comparing with the single-particle picture in which the exciton transition is considered to occur through electron-phonon scattering, within the GW + rtBSE-NAMD framework, the many-body electron-hole Coulomb interaction activates additional exciton relaxation channels to notably accelerate the exciton transition in competition with other radiative and nonradiative processes. The existence of dark excitons and ultrafast bright-dark exciton transitions sheds insights into applications of anatase TiO2 in optoelectronic devices and light-energy harvesting as well as the formation process of dark excitons in semiconductors.

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

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

Transiently delocalized states enhance hole mobility in organic molecular semiconductors

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

Exploring plasmonic effect on exciton transport: A theoretical insight from macroscopic quantum electrodynamics

Exciton transport in extended molecular systems and how to manipulate such transport in a complex environment are essential to many energy and optical-related applications. We investigate the mechanism of plasmon-coupled exciton transport by using the Pauli master equation approach, combined with kinetic rates derived from macroscopic quantum electrodynamics. Through our theoretical framework, we demonstrate that the presence of a silver nanorod induces significant frequency dependence in the ability of transporting exciton through a molecule chain, indicated by the exciton diffusion coefficient, due to the dispersive nature of the silver dielectric response. Compared with the same system in vacuum, great enhancement (up to a factor of 103) in the diffusion coefficient can be achieved by coupling the resonance energy transfer process to localized surface plasmon polariton modes of the nanorod. Furthermore, our analysis reveals that the diffusion coefficients with the nearest-neighbor coupling approximation are ∼10 times smaller than the results obtained beyond this approximation, emphasizing the significance of long-range coupling in exciton transport influenced by plasmonic nanostructures. This study not only paves the way for exploring practical approaches to study plasmon-coupled exciton transport but also provides crucial insights for the design of innovative plasmon-assisted photovoltaic applications.

Multi-scale molecular dynamics simulations of enhanced energy transfer in organic molecules under strong coupling

Exciton transport can be enhanced in the strong coupling regime where excitons hybridize with confined light modes to form polaritons. Because polaritons have group velocity, their propagation should be ballistic and long-ranged. However, experiments indicate that organic polaritons propagate in a diffusive manner and more slowly than their group velocity. Here, we resolve this controversy by means of molecular dynamics simulations of Rhodamine molecules in a Fabry-Pérot cavity. Our results suggest that polariton propagation is limited by the cavity lifetime and appears diffusive due to reversible population transfers between polaritonic states that propagate ballistically at their group velocity, and dark states that are stationary. Furthermore, because long-lived dark states transiently trap the excitation, propagation is observed on timescales beyond the intrinsic polariton lifetime. These insights not only help to better understand and interpret experimental observations, but also pave the way towards rational design of molecule-cavity systems for coherent exciton transport.

Tailored Energy Funneling in Photocatalytic π-Conjugated Polymer Nanofibers for High-Performance Hydrogen Production

The creation of artificial high-performance photosynthetic assemblies with a tailorable antenna system to deliver absorbed solar energy to a photosynthetic reaction center, thereby mimicking biological photosynthesis, remains a major challenge. We report the construction of recyclable, high-performance photosynthetic nanofibers with a crystalline π-conjugated polyfluorene core as an antenna system that funnels absorbed solar energy to spatially defined sensitized Co(II) porphyrin photocatalysts for the hydrogen evolution reaction. Highly effective energy funneling was achieved by tuning the dimensions of the nanofibers to exploit the very long exciton diffusion lengths (>200 nm) associated with the highly crystalline polyfluorene core formed using the living crystallization-driven self-assembly seeded growth method. This enabled efficient solar light-driven hydrogen production from water with a turnover number of over 450 for 8 h of irradiation, an H2 production rate of ca. 65 mmol h-1 g-1, and an overall quantum yield of 0.4% in the wavelength region (<405 nm) beyond the absorption of the molecular photocatalyst. The strategy of using a tailored antenna system based on π-conjugated polymers and maximizing exciton transport to a reaction center reported in this work opens up future opportunities for potential applications in other fields such as solar overall water splitting, CO2 reduction, and photocatalytic small molecule synthesis.

Tailoring Interlayer Charge Transfer Dynamics in 2D Perovskites with Electroactive Spacer Molecules

The family of hybrid organic-inorganic lead-halide perovskites are the subject of intense interest for optoelectronic applications, from light-emitting diodes to photovoltaics to X-ray detectors. Due to the inert nature of most organic molecules, the inorganic sublattice generally dominates the electronic structure and therefore the optoelectronic properties of perovskites. Here, we use optically and electronically active carbazole-based Cz-Ci molecules, where Ci indicates an alkylammonium chain and i indicates the number of CH2 units in the chain, varying from 3 to 5, as cations in the two-dimensional (2D) perovskite structure. By investigating the photophysics and charge transport characteristics of (Cz-Ci)2PbI4, we demonstrate a tunable electronic coupling between the inorganic lead-halide and organic layers. The strongest interlayer electronic coupling was found for (Cz-C3)2PbI4, where photothermal deflection spectroscopy results remarkably reveal an organic-inorganic charge transfer state. Ultrafast transient absorption spectroscopy measurements demonstrate ultrafast hole transfer from the photoexcited lead-halide layer to the Cz-Ci molecules, the efficiency of which increases by varying the chain length from i = 5 to i = 3. The charge transfer results in long-lived carriers (10-100 ns) and quenched emission, in stark contrast to the fast (sub-ns) and efficient radiative decay of bound excitons in the more conventional 2D perovskite (PEA)2PbI4, in which phenylethylammonium (PEA) acts as an inert spacer. Electrical charge transport measurements further support enhanced interlayer coupling, showing increased out-of-plane carrier mobility from i = 5 to i = 3. This study paves the way for the rational design of 2D perovskites with combined inorganic-organic electronic properties through the wide range of functionalities available in the world of organics.

Directed exciton transport highways in organic semiconductors

Exciton bandwidths and exciton transport are difficult to control by material design. We showcase the intriguing excitonic properties in an organic semiconductor material with specifically tailored functional groups, in which extremely broad exciton bands in the near-infrared-visible part of the electromagnetic spectrum are observed by electron energy loss spectroscopy and theoretically explained by a close contact between tightly packing molecules and by their strong interactions. This is induced by the donor-acceptor type molecular structure and its resulting crystal packing, which induces a remarkable anisotropy that should lead to a strongly directed transport of excitons. The observations and detailed understanding of the results yield blueprints for the design of molecular structures in which similar molecular features might be used to further explore the tunability of excitonic bands and pave a way for organic materials with strongly enhanced transport and built-in control of the propagation direction.

Long-Range Charge Separation Enabled by Intramoiety Delocalized Excitations in Copolymer Donors in Organic Photovoltaic Blends

For over two decades, most high-performance organic photovoltaics (OPVs) have been made with donor:acceptor bulk heterojunctions with domain sizes limited by exciton diffusion, where charge separation mostly takes place through the dissociation of the interfacial charge-transfer (xCT) excitons. Recently, nonfullerene acceptor (NFA)-based OPVs have shown excellent compatibility to device structures with large domains in active layers. However, it remains elusive how the excitations that are distant from the interfaces are converted into free charges. Here, we report the identification of a new charge separation channel in model copolymer/NFA blends mediated by intra-moiety delocalized excitations in both planar heterojunctions and donor-enriched bulk heterojunctions. The delocalized excitations induced by interchromophore electronic interactions in copolymer donors mediate the long-range charge separation and dissociate into free charges without forming the bound xCT states first, releasing the constraints associated with the short exciton diffusion length in organic materials. The long-range charge separation mechanism uncovered in this work, in cooperation with the short-range xCT-mediated pathway, holds the potential to further optimize OPVs with diverse device structures.

Accumulation and ordering of P3HT oligomers at the liquid-vapor interface with implications for thin-film morphology

The morphology of semiconducting polymer thin films is known to have a profound effect on their opto-electronic properties. Although considerable efforts have been made to control and understand the processes which influence the structures of these systems, it remains largely unclear what physical factors determine the arrangement of polymer chains in spin-cast films. Here, we investigate the role that the liquid-vapor interfaces in chlorobenzene solutions of poly(3-hexylthiophene) [P3HT] play in the conformational geometries adopted by the polymers. Using all-atom molecular dynamics (MD), and supported by toy-model simulations, we demonstrate that, with increasing concentration, P3HT oligomers in solution exhibit a strong propensity for the liquid-vapor interface. Due to the differential solubility of the backbone and side chains of the oligomers, in the vicinity of this interface, hexyl chains and the thiophene rings, have a clear orientational preference with respect to the liquid surface. At high concentrations, we additionally establish a substantial degree of inter-oligomer alignment and thiophene ring stacking near the interface. Our results broadly concur with the limited existing experimental evidence and we suggest that the interfacial structure can act as a template for film structure. We argue that the differences in solvent affinity of the side chain and backbone moieties are the driving force for the anisotropic orientations of the polymers near the interface. This finer grained description contrasts with the usual monolithic characterization of polymer units. Since this phenomenon can be controlled by concurrent chemical design and the choice of solvents, this work establishes a fabrication principle which may be useful to develop more highly functional polymer films.

Exciton annihilation in molecular aggregates suppressed through qu antum interference

Exciton-exciton annihilation (EEA), an important loss channel in optoelectronic devices and photosynthetic complexes, has conventionally been assumed to be an incoherent, diffusion-limited process. Here we challenge this assumption by experimentally demonstrating the ability to control EEA in molecular aggregates using the quantum phase relationships of excitons. We employed time-resolved photoluminescence microscopy to independently determine exciton diffusion constants and annihilation rates in two substituted perylene diimide aggregates featuring contrasting excitonic phase envelopes. Low-temperature EEA rates were found to differ by more than two orders of magnitude for the two compounds, despite comparable diffusion constants. Simulated rates based on a microscopic theory, in excellent agreement with experiments, rationalize this EEA behaviour based on quantum interference arising from the presence or absence of spatial phase oscillations of delocalized excitons. These results offer an approach for designing molecular materials using quantum interference where low annihilation can coexist with high exciton concentrations and mobilities.

High-resolution cryo-electron microscopy structure of block copolymer nanofibres with a crystalline core

Seeded growth of crystallizable block copolymers and π-stacking molecular amphiphiles in solution using living crystallization-driven self-assembly is an emerging route to fabricate uniform one-dimensional and two-dimensional core-shell micellar nanoparticles of controlled size with a range of potential applications. Although experimental evidence indicates that the crystalline core of these nanomaterials is highly ordered, a direct observation of their crystal lattice has not been successful. Here we report the high-resolution cryo-transmission electron microscopy studies of vitrified solutions of nanofibres made from a crystalline core of poly(ferrocenyldimethylsilane) (PFS) and a corona of polysiloxane grafted with 4-vinylpyridine groups. These studies show that poly(ferrocenyldimethylsilane) chains pack in an 8-nm-diameter core lattice with two-dimensional pseudo-hexagonal symmetry that is coated by a 27 nm 4-vinylpyridine corona with a 3.5 nm distance between each 4-vinylpyridine strand. We combine this structural information with a molecular modelling analysis to propose a detailed molecular model for solvated poly(ferrocenyldimethylsilane)-b-4-vinylpyridine nanofibres.

Mapping nanocrystalline disorder within an amorphous metal-organic framework

Intentionally disordered metal-organic frameworks (MOFs) display rich functional behaviour. However, the characterisation of their atomic structures remains incredibly challenging. X-ray pair distribution function techniques have been pivotal in determining their average local structure but are largely insensitive to spatial variations in the structure. Fe-BTC (BTC = 1,3,5-benzenetricarboxylate) is a nanocomposite MOF, known for its catalytic properties, comprising crystalline nanoparticles and an amorphous matrix. Here, we use scanning electron diffraction to first map the crystalline and amorphous components to evaluate domain size and then to carry out electron pair distribution function analysis to probe the spatially separated atomic structure of the amorphous matrix. Further Bragg scattering analysis reveals systematic orientational disorder within Fe-BTC's nanocrystallites, showing over 10° of continuous lattice rotation across single particles. Finally, we identify candidate unit cells for the crystalline component. These independent structural analyses quantify disorder in Fe-BTC at the critical length scale for engineering composite MOF materials.

Highly Ordered Supramolecular Materials of Phase-Separated Block Molecules for Long-Range Exciton Transport

Efficient energy transport over long distances is essential for optoelectronic and light-harvesting devices. Although self-assembled nanofibers of organic molecules are shown to exhibit long exciton diffusion lengths, alignment of these nanofibers into films with large, organized domains with similar properties remains a challenge. Here, it is shown how the functionalization of C₃ -symmetric carbonyl-bridged triarylamine trisamide (CBT) with oligodimethylsiloxane (oDMS) side chains of discrete length leads to fully covered surfaces with aligned domains up to 125 × 70 µm² in which long-range exciton transport takes place. The nanoscale morphology within the domains consists of highly ordered nanofibers with discrete intercolumnar spacings within a soft amorphous oDMS matrix. The oDMS prevents bundling of the CBT fibers, reducing the number of defects within the CBT columns. As a result, the columns have a high degree of coherence, leading to exciton diffusion lengths of a few hundred nanometers with exciton diffusivities (≈0.05 cm² s^-1 ) that are comparable to those of a crystalline tetracene. These findings represent the next step toward fully covered surfaces of highly aligned nanofibers through functionalization with oDMS.

Mechanism of Delocalization-Enhanced Exciton Transport in Disordered Organic Semiconductors

Large exciton diffusion lengths generally improve the performance of organic semiconductor devices, because they enable energy to be transported farther during the exciton lifetime. However, the physics of exciton motion in disordered organic materials is not fully understood, and modeling the transport of quantum-mechanically delocalized excitons in disordered organic semiconductors is a computational challenge. Here, we describe delocalized kinetic Monte Carlo (dKMC), the first model of three-dimensional exciton transport in organic semiconductors that includes delocalization, disorder, and polaron formation. We find that delocalization can dramatically increase exciton transport; for example, delocalization across less than two molecules in each direction can increase the exciton diffusion coefficient by over an order of magnitude. The mechanism for the enhancement is 2-fold: delocalization enables excitons to hop both more frequently and further in each hop. We also quantify the effect of transient delocalization (short-lived periods where excitons become highly delocalized) and show that it depends strongly upon the disorder and transition dipole moments.

Harvesting Triplet Excitons in High Mobility Emissive Organic Semiconductor for Efficiency Enhancement of Light-Emitting Transistors

Organic light-emitting transistors (OLETs), a kind of highly integrated and minimized optoelectronic device, demonstrate great potential applications in various fields. The construction of high-performance OLETs requires the integration of high charge carrier mobility, strong emission, and high triplet exciton utilization efficiency in the active layer. However, it remains a significant long-term challenge, especially for single component active layer OLETs. Herein, the successful harvesting of triplet excitons in a high mobility emissive molecule, 2,6-diphenylanthracene (DPA), through the triplet-triplet annihilation process is demonstrated. By incorporating a highly emissive guest into the DPA host system, an obvious increase in photoluminescence efficiency along with exciton utilization efficiency results in an obvious enhancement of external quantum efficiency of 7.2 times for OLETs compared to the non-doped devices. Moreover, well-tunable multi-color electroluminescence, especially white emission with Commission Internationale del'Eclairage  of (0.31, 0.35), from OLETs is also achieved by modulating the doping concentration with a controlled energy transfer process. This work opens a new avenue for integrating strong emission and efficient exciton utilization in high-mobility organic semiconductors for high-performance OLETs and advancing their related functional device applications.

Phonon-Induced Localization of Excitons in Molecular Crystals from First Principles

The spatial extent of excitons in molecular systems underpins their photophysics and utility for optoelectronic applications. Phonons are reported to lead to both exciton localization and delocalization. However, a microscopic understanding of phonon-induced (de)localization is lacking, in particular, how localized states form, the role of specific vibrations, and the relative importance of quantum and thermal nuclear fluctuations. Here, we present a first-principles study of these phenomena in solid pentacene, a prototypical molecular crystal, capturing the formation of bound excitons, exciton-phonon coupling to all orders, and phonon anharmonicity, using density functional theory, the ab initio GW-Bethe-Salpeter equation approach, finite-difference, and path integral techniques. We find that for pentacene zero-point nuclear motion causes uniformly strong localization, with thermal motion providing additional localization only for Wannier-Mott-like excitons. Anharmonic effects drive temperature-dependent localization, and, while such effects prevent the emergence of highly delocalized excitons, we explore the conditions under which these might be realized.

Direct observation of ultrafast singlet exciton fission in three dimensions

We present quantitative ultrafast interferometric pump-probe microscopy capable of tracking of photoexcitations with sub-10 nm spatial precision in three dimensions with 15 fs temporal resolution, through retrieval of the full transient photoinduced complex refractive index. We use this methodology to study the spatiotemporal dynamics of the quantum coherent photophysical process of ultrafast singlet exciton fission. Measurements on microcrystalline pentacene films grown on glass (SiO₂) and boron nitride (hBN) reveal a 25 nm, 70 fs expansion of the joint-density-of-states along the crystal a,c-axes accompanied by a 6 nm, 115 fs change in the exciton density along the crystal b-axis. We propose that photogenerated singlet excitons expand along the direction of maximal orbital π-overlap in the crystal a,c-plane to form correlated triplet pairs, which subsequently electronically decouples into free triplets along the crystal b-axis due to molecular sliding motion of neighbouring pentacene molecules. Our methodology lays the foundation for the study of three dimensional transport on ultrafast timescales.

Collective Mid-Infrared Vibrations in Surface-Enhanced Raman Scattering

Surface-enhanced Raman scattering (SERS) is typically assumed to occur at individual molecules neglecting intermolecular vibrational coupling. Here, we show instead how collective vibrations from infrared (IR) coupled dipoles are seen in SERS from molecular monolayers. Mixing IR-active molecules with IR-inactive spacer molecules controls the intermolecular separation. Intermolecular coupling leads to vibrational frequency upshifts up to 8 cm^-1, tuning with the mixing fraction and IR dipole strength, in excellent agreement with microscopic models and density functional theory. These cooperative frequency shifts can be used as a ruler to measure intermolecular distance and disorder with angstrom resolution. We demonstrate this for photochemical reactions of 4-nitrothiophenol, which depletes the number of neighboring IR-active molecules and breaks the collective vibration, enabling direct tracking of the reaction. Collective molecular vibrations reshape SERS spectra and need to be considered in the analysis of vibrational spectra throughout analytical chemistry and sensing.

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.

Quantum dynamical study of inter-chain exciton transport in a regioregular P3HT model system at finite temperature: HJ vs. H-aggregate models

We report on quantum dynamical simulations of inter-chain exciton transport in a model of regioregular poly(3-hexylthiophene), rr-P3HT, at finite temperature, using the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method for a system of up to 63 electronic states and 180 vibrational modes. A Frenkel Hamiltonian of HJ aggregate type is used, along with a reduced H-aggregate representation; electron-phonon coupling includes local high-frequency modes as well as anharmonic intermolecular modes. The latter are operative in mediating inter-chain transport, by a mechanism of transient localization type. Strikingly, this mechanism is found to be of quantum coherent character and involves non-adiabatic effects. Using periodic boundary conditions, a normal diffusion regime is identified from the exciton mean-squared displacement, apart from early-time transients. Diffusion coefficients are found to be of the order of 3 x 10-3 cm2/s, showing a non-monotonous increase with temperature.

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.

On the interface reactions and stability of nonfullerene organic solar cells

Long-term stability is critical for organic solar cells (OSCs) for practical applications. Several factors affect the stability of OSCs, including materials stability, morphology stability of bulk-heterojunctions and interface stability. In this perspective, we focus on interface stability due to interfacial reactions between the emerging acceptor-donor-acceptor (A-D-A) type nonfullerene active layers and interfacial layers. The description covers the initial phenomena of interfacial instability, mechanism of interfacial reactions, and strategies adopted to suppress interfacial reactions between the nonfullerene active layers and interfacial layers. Methods to test and analyze the chemical instability of nonfullerene acceptors are also included. The C[double bond, length as m-dash]C vinyl linker between the donor moiety and acceptor moiety is chemically or photochemically reactive and is a weak point for interface stability. The interface stability of OSCs could be enhanced by reducing the reactivity of the C[double bond, length as m-dash]C vinyl linker or removing it directly, modifying the surface of interfacial layers, and developing other novel interfacial materials.

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.

Dynamics of Excitons in Conjugated Molecules and Organic Semiconductor Systems

The exciton, an excited electron-hole pair bound by Coulomb attraction, plays a key role in photophysics of organic molecules and drives practically important phenomena such as photoinduced mechanical motions of a molecule, photochemical conversions, energy transfer, generation of free charge carriers, etc. Its behavior in extended π-conjugated molecules and disordered organic films is very different and very rich compared with exciton behavior in inorganic semiconductor crystals. Due to the high degree of variability of organic systems themselves, the exciton not only exerts changes on molecules that carry it but undergoes its own changes during all phases of its lifetime, that is, birth, conversion and transport, and decay. The goal of this review is to give a systematic and comprehensive view on exciton behavior in π-conjugated molecules and molecular assemblies at all phases of exciton evolution with emphasis on rates typical for this dynamic picture and various consequences of the above dynamics. To uncover the rich variety of exciton behavior, details of exciton formation, exciton transport, exciton energy conversion, direct and reverse intersystem crossing, and radiative and nonradiative decay are considered in different systems, where these processes lead to or are influenced by static and dynamic disorder, charge distribution symmetry breaking, photoinduced reactions, electron and proton transfer, structural rearrangements, exciton coupling with vibrations and intermediate particles, and exciton dissociation and annihilation as well.

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.

Intrachain Exciton Motion Can Compete with Interchain Hopping in Conjugated Polymer Films with a Strong J-Aggregate Property

Understanding exciton diffusion properties in organic semiconductor films is crucial for organic solar cells because excitons need to diffuse to an electron donor/acceptor interface to dissociate into charges. We previously found that singlet excitons generated in the thin films of a novel naphthobisoxadiazole-based low-bandgap polymer PNOz4T exhibit two-dimensional exciton diffusion characteristics along the backbone and π-stacking directions owing to the HJ-aggregate property of PNOz4T. However, the diffusion constants along these directions could not be determined owing to the difficulty of data analysis. Herein, we present a detailed analysis based on a simulated annealing metaheuristic. We found that intrachain exciton motion can be faster than interchain hopping. On the basis of temperature dependence measurements, we found that exciton diffusion is more favorable at lower temperatures because the coherent component partly contributes to exciton motion.

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

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

Fluorescent supramolecular polymers of barbiturate dyes with thiophene-cored twisted π-systems

Because supramolecular polymerization of emissive π-conjugated molecules depends strongly on π-π stacking interaction, the formation of well-defined one-dimensional nanostructures often results in a decrease or only a small increase of emission efficiency. This is also true for our barbiturate-based supramolecular polymers wherein hydrogen-bonded rosettes of barbiturates stack quasi-one-dimensionally through π-π stacking interaction. Herein we report supramolecular polymerization-induced emission of two regioisomeric 2,3-diphenylthiophene derivatives functionalized with barbituric acid and tri(dodecyloxy)benzyl wedge units. In CHCl3, both compounds are molecularly dissolved and accordingly poorly emissive due to a torsion-induced non-radiative decay. In methylcyclohexane-rich conditions, these barbiturates self-assemble to form crystalline nanofibers and exhibit strongly enhanced emission through supramolecular polymerization driven by hydrogen-bonding. Our structural analysis suggests that the barbiturates form a tape-like hydrogen-bonding motif, which is rationalized by considering that the twisted geometries of 2,3-diphenylthiophene cores prevend the competing rosettes from stacking into columnar supramolecular polymers. We also found that a small difference in the molecular polarity originating from the substitutional position of the thiophene core influences interchain association of the supramolecular polymers, affording different luminescent soft materials, gel and nanosheet.

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

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

Exploring the "Living" Growth of Block Copolymer Nanofibers from Surface-Confined Seeds by In Situ Solution-Phase Atomic Force Microscopy

Living crystallization-driven self-assembly of polymeric and molecular amphiphiles is of growing interest as a seeded growth route to uniform 1D, 2D, and more complex micellar nanoparticles with controlled dimensions and a range of potential applications. Although most studies have been performed using colloidally stable seeds in bulk solution, growth of block copolymer (BCP) nanofibers from seeds confined to a surface is attracting increased attention. Herein, we have used atomic force microscopy (AFM) to undertake detailed studies of the growth of BCP nanofibers from immobilized seeds located on a Si surface. Through initial ex situ AFM studies and in situ AFM video analysis in solution, we determined that growth occurred in four stages, whereby an initial surface-bound growth regime transitions to surface-limited growth. As the nanofiber length increases, surface influence is diminished as the newly grown micelle segment is no longer bound to the Si substrate. Finally, a surface-independent regime occurs where nanofiber growth continues into bulk solution. In addition to the anticipated nanofiber elongation, our studies revealed occasional examples of AFM tip-induced core fragmentation. In these cases, the termini of the newly formed fragments were also active to further growth. Furthermore, unidirectional growth was detected in cases where the seed was oriented at a significant angle with respect to the surface, thereby restricting unimer access to one terminus.