A New Frontier in Exciton Transport: Transient Delocalization

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.

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.

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.

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.

Exciton dynamics from the mapping approach to surface hopping: comparison with Förster and Redfield theories

We compare the recently introduced multi-state mapping approach to surface hopping (MASH) with the Förster and Redfield theories of excitation energy transfer. Whereas Förster theory relies on weak coupling between chromophores, and Redfield theory assumes the electronic excitations to be weakly coupled to fast chromophore vibrations, MASH is free from any perturbative or Markovian approximations. We illustrate this with an example application to the rate of energy transfer in a Frenkel-exciton dimer, showing that MASH interpolates correctly between the opposing regimes in which the Förster and Redfield results are reliable. We then compare the three methods for a realistic model of the Fenna-Matthews-Olson complex with a structured vibrational spectral density and static disorder in the excitation energies. In this case there are no exact results for comparison so we use MASH to assess the validity of Förster and Redfield theories. We find that Förster theory is the more accurate of the two on the picosecond timescale, as has been shown previously for a simpler model of this particular light-harvesting complex. We also explore various ways to sample the initial electronic state in MASH and find that they all give very similar results for exciton dynamics.

Excitons in metal-halide perovskites from first-principles many-body perturbation theory

Metal-halide perovskites are a structurally, chemically, and electronically diverse class of semiconductors with applications ranging from photovoltaics to radiation detectors and sensors. Understanding neutral electron-hole excitations (excitons) is key for predicting and improving the efficiency of energy-conversion processes in these materials. First-principles calculations have played an important role in this context, allowing for a detailed insight into the formation of excitons in many different types of perovskites. Such calculations have demonstrated that excitons in some perovskites significantly deviate from canonical models due to the chemical and structural heterogeneity of these materials. In this Perspective, I provide an overview of calculations of excitons in metal-halide perovskites using Green's function-based many-body perturbation theory in the GW + Bethe-Salpeter equation approach, the prevalent method for calculating excitons in extended solids. This approach readily considers anisotropic electronic structures and dielectric screening present in many perovskites and important effects, such as spin-orbit coupling. I will show that despite this progress, the complex and diverse electronic structure of these materials and its intricate coupling to pronounced and anharmonic structural dynamics pose challenges that are currently not fully addressed within the GW + Bethe-Salpeter equation approach. I hope that this Perspective serves as an inspiration for further exploring the rich landscape of excitons in metal-halide perovskites and other complex semiconductors and for method development addressing unresolved challenges in the field.

Spin relaxation of electron and hole polarons in ambipolar conjugated polymers

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

A spectroscopic assessment of static and dynamic disorder in a film of a polythiophene with a planarized backbone

The optoelectronic performance of organic semiconductor devices is related to the static and dynamic disorder in the film. The disorder can be assessed by considering the linewidth of its optical spectra. We focus on identifying the effect of conjugation length distribution on the static energetic disorder. Hence, we disentangle the contributions of static and dynamic disorder to the absorption and emission spectra of poly(3-(2,5-dioctylphenyl)-thiophene) (PDOPT) by exploring how the linewidth and energy of the spectra evolve upon cooling the sample from 300 K to 5 K. PDOPT has sterically hindered side chains that arrange such as to cause a planarized polymer backbone. This makes it a suitable model for a quasi-one-dimensional molecular system. By modelling the conjugated segments as coupled oscillators we find that the linewidth contribution resulting from the variation of conjugation length decreases linearly with decreasing exciton energy and extrapolates to zero at the energy corresponding to an infinite chain. These results provide a new avenue to the design of low disorder and hence high mobility polymeric 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.

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.

Large Coherent States Formed from Disordered k-Regular Random Graphs

The present work is motivated by the need for robust, large-scale coherent states that can play possible roles as quantum resources. A challenge is that large, complex systems tend to be fragile. However, emergent phenomena in classical systems tend to become more robust with scale. Do these classical systems inspire ways to think about robust quantum networks? This question is studied by characterizing the complex quantum states produced by mapping interactions between a set of qubits from structure in graphs. We focus on maps based on k-regular random graphs where many edges were randomly deleted. We ask how many edge deletions can be tolerated. Surprisingly, it was found that the emergent coherent state characteristic of these graphs was robust to a substantial number of edge deletions. The analysis considers the possible role of the expander property of k-regular random graphs.

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.

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.

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.

Identification via Virtual Screening of Emissive Molecules with a Small Exciton-Vibration Coupling for High Color Purity and Potential Large Exciton Delocalization

A sequence of quantum chemical computations of increasing accuracy was used in this work to identify molecules with small exciton reorganization energy (exciton-vibration coupling), of interest for light emitting devices and coherent exciton transport, starting from a set of ∼4500 known molecules. We validated an approximate computational approach based on single-point calculations of the force in the excited state, which was shown to be very efficient in identifying the most promising candidates. We showed that a simple descriptor based on the bond order could be used to find molecules with potentially small exciton reorganization energies without performing excited state calculations. A small set of chemically diverse molecules with a small exciton reorganization energy was analyzed in greater detail to identify common features leading to this property. Many such molecules display an A-B-A structure where the bonding/antibonding patterns in the fragments A are similar in HOMO and LUMO. Another group of molecules with small reorganization energy displays instead HOMO and LUMO with a strong nonbonding character.

Surface hopping modeling of charge and energy transfer in active environments

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

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.

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.

Mapping the Energy Landscape from a Nanocrystal-Based Field Effect Transistor under Operation Using Nanobeam Photoemission Spectroscopy

As the field of nanocrystal-based optoelectronics matures, more advanced techniques must be developed in order to reveal the electronic structure of nanocrystals, particularly with device-relevant conditions. So far, most of the efforts have been focused on optical spectroscopy, and electrochemistry where an absolute energy reference is required. Device optimization requires probing not only the pristine material but also the material in its actual environment (i.e., surrounded by a transport layer and an electrode, in the presence of an applied electric field). Here, we explored the use of photoemission microscopy as a strategy for operando investigation of NC-based devices. We demonstrate that the method can be applied to a variety of materials and device geometries. Finally, we show that it provides direct access to the metal-semiconductor interface band bending as well as the distance over which the gate effect propagates in field-effect transistors.