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.

Aggregation of Charge Acceptors on Nanocrystal Surfaces Alters Rates of Photoinduced Electron Transfer.

Semiconductor nanocrystals (NCs) interfaced with molecular ligands that function as charge and energy acceptors are an emerging platform for the design of light-harvesting, photon-upconverting, and photocatalytic materials. However, NC systems explored for these applications often feature high concentrations of bound acceptor ligands, which can lead to ligand-ligand interactions that may alter each system's ability to undergo charge and energy transfer. Here, we demonstrate that aggregation of acceptor ligands impacts the rate of photoinduced NC-to-ligand charge transfer between lead(II) sulfide (PbS) NCs and perylenediimide (PDI) electron acceptors. As the concentration of PDI acceptors is increased, we find the average electron transfer rate from PbS to PDI ligands decreases by nearly an order of magnitude. The electron transfer rate slowdown with increasing PDI concentration correlates strongly with the appearance of PDI aggregates in steady-state absorption spectra. Electronic structure calculations and molecular dynamics (MD) simulations suggest PDI aggregation slows the rate of electron transfer by reducing orbital overlap between PbS charge donors and PDI charge acceptors. While we find aggregation slows electron transfer in this system, the computational models we employ predict ligand aggregation could also be used to speed electron transfer by producing delocalized states that exhibit improved NC-molecule electronic coupling and energy alignment with NC conduction band states. Our results demonstrate that ligand aggregation can alter rates of photoinduced electron transfer between NCs and organic acceptor ligands and should be considered when designing hybrid NC:molecule systems for charge separation.

Charge-State Dependent Vibrational Relaxation in a Single-Molecule Junction.

The outcome of an electron-transfer process is determined by the quantum-mechanical interplay between electronic and vibrational degrees of freedom. Nonequilibrium vibrational dynamics are known to direct electron-transfer mechanisms in molecular systems; however, the structural features of a molecule that lead to certain modes being pushed out of equilibrium are not well understood. Herein, we report on electron transport through a porphyrin dimer molecule, weakly coupled to graphene electrodes, that displays sequential tunneling within the Coulomb-blockade regime. The sequential transport is initiated by current-induced phonon absorption and proceeds by rapid sequential transport via a nonequilibrium vibrational distribution of low-energy modes, likely related to torsional molecular motions. We demonstrate that this is an experimental signature of slow vibrational dissipation, and obtain a lower bound for the vibrational relaxation time of 8 ns, a value dependent on the molecular charge state.

Light-Triggered Switching of Quantum Dot Photoluminescence through Excited-State Electron Transfer to Surface-Bound Photochromic Molecules.

This paper describes reversible "on-off" switching of the photoluminescence (PL) intensity of CdSe quantum dots (QDs), mediated by photochromic furylfulgide carboxylate (FFC) molecules chemisorbed to the surfaces of the QDs. Repeated cycles of UV and visible illumination switch the FFC between "closed" and "open" isomers. Reversible switching of the QDs' PL intensity by >80% is enabled by different rates and yields of PL-quenching photoinduced electron transfer (PET) from the QDs to the respective isomers. This difference is consistent with cyclic voltammetry measurements and density functional calculations of the isomers' frontier orbital energies. This work demonstrates fatigue-resistant modulation of the PL of a QD-molecule complex through remote control of PET. Such control potentially enables applications, such as all-optical memory, sensing, and imaging, that benefit from a fast, tunable, and reversible response to light stimuli.

On the theory of charge transport and entropic effects in solvated molecular junctions.

Experimental studies on single-molecule junctions are typically in need of a simple theoretical approach that can reproduce or be fitted to experimentally measured transport data. In this context, the single-level variant of the Landauer approach is most commonly used, but methods based on Marcus theory are also gaining popularity. Recently, a generalized theory unifying these two approaches has also been developed. In the present work, we extend this theory so that it includes entropic effects (which can be important when polar solvents are involved but are likely minor for solid-state systems). We investigate the temperature-dependence of the electric current and compare it to the behavior predicted by the Landauer and the conventional Marcus theory. We argue that this generalized theory provides a simple yet effective framework for understanding charge transport through molecular junctions. Furthermore, we explore the role of the entropic effects in different transport regimes and suggest experimental criteria for detecting them in solvated molecular junctions. Finally, in order to account for nuclear tunneling effects, we also demonstrate how lifetime broadening can be introduced into the Marcus-Levich-Dogonadze-Jortner-type description of electron transport.

Photoisomerization-coupled electron transfer.

Photochromic molecular structures constitute a unique platform for constructing molecular switches, sensors, and memory devices. One of their most promising applications is as light-switchable electron acceptor or donor units. Here, we investigate a previously unexplored process that we postulate may occur in such systems: an ultrafast electron transfer triggered by a simultaneous photoisomerization of the donor or the acceptor moiety. We propose a theoretical model for this phenomenon and, with the aid of density functional theory calculations, apply it to the case of a dihydropyrene-type photochromic molecular donor. By considering the wavepacket dynamics and the photoisomerization yield, we show that the two processes involved, electron transfer and photoisomerization, are in general inseparable and need to be treated in a unified manner. We finish by discussing how the efficiency of photoisomerization-coupled electron transfer can be controlled experimentally.

Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions. II. A self-consistent Born approach.

Marcus and Landauer-Büttiker approaches to charge transport through molecular junctions describe two contrasting mechanisms of electronic conduction. In previous work, we have shown how these charge transport theories can be unified in the single-level case by incorporating lifetime broadening into the second-order quantum master equation. Here, we extend our previous treatment by incorporating lifetime broadening in the spirit of the self-consistent Born approximation. By comparing both theories to numerically converged hierarchical-equations-of-motion results, we demonstrate that our novel self-consistent approach rectifies shortcomings of our earlier framework, which are present especially in the case of relatively strong electron-vibrational coupling. We also discuss circumstances under which the theory developed here simplifies to the generalized theory developed in our earlier work. Finally, by considering the high-temperature limit of our new self-consistent treatment, we show how lifetime broadening can also be self-consistently incorporated into Marcus theory. Overall, we demonstrate that the self-consistent approach constitutes a more accurate description of molecular conduction while retaining most of the conceptual simplicity of our earlier framework.

Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions: A unified framework.

Charge transport through molecular junctions is often described either as a purely coherent or a purely classical phenomenon, and described using the Landauer-Büttiker formalism or Marcus theory (MT), respectively. Using a generalised quantum master equation, we here derive an expression for current through a molecular junction modelled as a single electronic level coupled with a collection of thermalised vibrational modes. We demonstrate that the aforementioned theoretical approaches can be viewed as two limiting cases of this more general expression and present a series of approximations of this result valid at higher temperatures. We find that MT is often insufficient in describing the molecular charge transport characteristics and gives rise to a number of artefacts, especially at lower temperatures. Alternative expressions, retaining its mathematical simplicity, but rectifying those shortcomings, are suggested. In particular, we show how lifetime broadening can be consistently incorporated into MT, and we derive a low-temperature correction to the semi-classical Marcus hopping rates. Our results are applied to examples building on phenomenological as well as microscopically motivated electron-vibrational coupling. We expect them to be particularly useful in experimental studies of charge transport through single-molecule junctions as well as self-assembled monolayers.

Environment-assisted quantum transport through single-molecule junctions.

Single-molecule electronics has been envisioned as the ultimate goal in the miniaturisation of electronic circuits. While the aim of incorporating single-molecule junctions into modern technology still proves elusive, recent developments in this field have begun to enable experimental investigation of fundamental concepts within the area of chemical physics. One such phenomenon is the concept of environment-assisted quantum transport which has emerged from the investigation of exciton transport in photosynthetic complexes. Here, we study charge transport through a two-site molecular junction coupled to a vibrational environment. We demonstrate that vibrational interactions can significantly enhance the current through specific molecular orbitals. Our study offers a clear pathway towards finding and identifying environment-assisted transport phenomena in charge transport settings.

A Bond-Based Machine Learning Model for Molecular Polarizabilities and A Priori Raman Spectra.

The use of machine learning (ML) algorithms in molecular simulations has become commonplace in recent years. There now exists, for instance, a multitude of ML force field algorithms that have enabled simulations approaching ab initio level accuracy at time scales and system sizes that significantly exceed what is otherwise possible with traditional methods. Far fewer algorithms exist for predicting rotationally equivariant, tensorial properties such as the electric polarizability. Here, we introduce a kernel ridge regression algorithm for machine learning of the polarizability tensor. This algorithm is based on the bond polarizability model and allows prediction of the tensor components at the cost similar to that of scalar quantities. We subsequently show the utility of this algorithm by simulating gas phase Raman spectra of biphenyl and malonaldehyde using classical molecular dynamics simulations of these systems performed with the recently developed MACE-OFF23 potential. The calculated spectra are shown to agree very well with the experiments and thus confirm the expediency of our algorithm as well as the accuracy of the used force field. More generally, this work demonstrates the potential of physics-informed approaches to yield simple yet effective machine learning algorithms for molecular properties.

Exploring Configurations of Nanocrystal Ligands Using Machine-Learned Force Fields.

Semiconducting nanocrystals passivated with organic ligands have emerged as a powerful platform for light harvesting, light-driven chemical reactions, and sensing. Due to their complexity and size, little structural information is available from experiments, making these systems challenging to model computationally. Here, we develop a machine-learned force field trained on DFT data and use it to investigate the surface chemistry of a PbS nanocrystal interfaced with acetate ligands. In doing so, we go beyond considering individual local minimum energy geometries and, importantly, circumvent a precarious issue associated with the assumption of a single assigned atomic partial charge for each element in a nanocrystal, independent of its structural position. We demonstrate that the carboxylate ligands passivate the metal-rich surfaces by adopting a very wide range of "tilted-bridge" and "bridge" geometries and investigate the corresponding ligand IR spectrum. This work illustrates the potential of machine-learned force fields to transform computational modeling of these materials.

Structural Disorder at the Edges of Rubrene Crystals Enhances Singlet Fission.

Materials that undergo singlet fission are of interest for their use in light-harvesting, photocatalysis, and quantum information science, but their ability to undergo fission can be sensitive to local variations in molecular packing. Herein we employ transient absorption microscopy, molecular dynamics simulations, and electronic structure calculations to interrogate how structures found at the edges of orthorhombic rubrene crystals impact singlet fission. Within a micrometer-scale spatial region at the edges of rubrene crystals, we find that the rate of singlet fission increases nearly 4-fold. This observation is consistent with formation of a region at crystal edges with reduced order that accelerates singlet fission by disrupting the symmetry found in rubrene's orthorhombic crystal structure. Our work demonstrates that structural distortions of singlet fission materials can be used to control fission in time and in space, potentially offering a means of controlling this process in light harvesting and quantum information applications.

Complete mapping of the thermoelectric properties of a single molecule.

Theoretical studies suggest that mastering the thermocurrent through single molecules can lead to thermoelectric energy harvesters with unprecedentedly high efficiencies.1-6 This can be achieved by engineering molecule length,7 optimizing the tunnel coupling strength of molecules via chemical anchor groups8 or by creating localized states in the backbone with resulting quantum interference features.4 Empirical verification of these predictions, however, faces considerable experimental challenges and is still awaited. Here we use a novel measurement protocol that simultaneously probes the conductance and thermocurrent flow as a function of bias voltage and gate voltage. We find that the resulting thermocurrent is strongly asymmetric with respect to the gate voltage, with evidence of molecular excited states in the thermocurrent Coulomb diamond maps. These features can be reproduced by a rate-equation model only if it accounts for both the vibrational coupling and the electronic degeneracies, thus giving direct insight into the interplay of electronic and vibrational degrees of freedom, and the role of spin entropy in single molecules. Overall these results show that thermocurrent measurements can be used as a spectroscopic tool to access molecule-specific quantum transport phenomena.

Charge transport through extended molecular wires with strongly correlated electrons.

Electron-electron interactions are at the heart of chemistry and understanding how to control them is crucial for the development of molecular-scale electronic devices. Here, we investigate single-electron tunneling through a redox-active edge-fused porphyrin trimer and demonstrate that its transport behavior is well described by the Hubbard dimer model, providing insights into the role of electron-electron interactions in charge transport. In particular, we empirically determine the molecule's on-site and inter-site electron-electron repulsion energies, which are in good agreement with density functional calculations, and establish the molecular electronic structure within various oxidation states. The gate-dependent rectification behavior confirms the selection rules and state degeneracies deduced from the Hubbard model. We demonstrate that current flow through the molecule is governed by a non-trivial set of vibrationally coupled electronic transitions between various many-body ground and excited states, and experimentally confirm the importance of electron-electron interactions in single-molecule devices.

Understanding resonant charge transport through weakly coupled single-molecule junctions.

Off-resonant charge transport through molecular junctions has been extensively studied since the advent of single-molecule electronics and is now well understood within the framework of the non-interacting Landauer approach. Conversely, gaining a qualitative and quantitative understanding of the resonant transport regime has proven more elusive. Here, we study resonant charge transport through graphene-based zinc-porphyrin junctions. We experimentally demonstrate an inadequacy of non-interacting Landauer theory as well as the conventional single-mode Franck-Condon model. Instead, we model overall charge transport as a sequence of non-adiabatic electron transfers, with rates depending on both outer and inner-sphere vibrational interactions. We show that the transport properties of our molecular junctions are determined by a combination of electron-electron and electron-vibrational coupling, and are sensitive to interactions with the wider local environment. Furthermore, we assess the importance of nuclear tunnelling and examine the suitability of semi-classical Marcus theory as a description of charge transport in molecular devices.

Charge-state assignment of nanoscale single-electron transistors from their current-voltage characteristics.

The electronic and magnetic properties of single-molecule transistors depend critically on the molecular charge state. Charge transport in single-molecule transistors is characterized by Coulomb-blocked regions in which the charge state of the molecule is fixed and current is suppressed, separated by high-conductance, sequential-tunneling regions. It is often difficult to assign the charge state of the molecular species in each Coulomb-blocked region due to variability in the work-function of the electrodes. In this work, we provide a simple and fast method to assign the charge state of the molecular species in the Coulomb-blocked regions based on signatures of electron-phonon coupling together with the Pauli-exclusion principle, simply by observing the asymmetry in the current in high-conductance regions of the stability diagram. We demonstrate that charge-state assignments determined in this way are consistent with those obtained from measurements of Zeeman splittings. Our method is applicable at 77 K, in contrast to magnetic-field-dependent measurements, which generally require low temperatures (below 4 K). Due to the ubiquity of electron-phonon coupling in molecular junctions, we expect this method to be widely applicable to single-electron transistors based on single molecules and graphene quantum dots. The correct assignment of charge states allows researchers to better understand the fundamental charge-transport properties of single-molecule transistors.

Spiro-Conjugated Molecular Junctions: Between Jahn-Teller Distortion and Destructive Quantum Interference.

The quest for molecular structures exhibiting strong quantum interference effects in the transport setting has long been on the forefront of chemical research. We establish theoretically that the unusual geometry of spiro-conjugated systems gives rise to complete destructive interference in the resonant-transport regime. This results in a current blockade of the type not present in meta-connected benzene or similar molecular structures. We further show that these systems can undergo a transport-driven Jahn-Teller distortion, which can lift the aforementioned destructive-interference effects. The overall transport characteristics are determined by the interplay between the two phenomena. Spiro-conjugated systems may therefore serve as a novel platform for investigations of quantum interference and vibronic effects in the charge-transport setting. The potential to control quantum interference in these systems can also turn them into attractive components in designing functional molecular circuits.

Distinguishing Lead and Molecule States in Graphene-Based Single-Electron Transistors.

Graphene provides a two-dimensional platform for contacting individual molecules, which enables transport spectroscopy of molecular orbital, spin, and vibrational states. Here we report single-electron tunneling through a molecule that has been anchored to two graphene leads. Quantum interference within the graphene leads gives rise to an energy-dependent transmission and fluctuations in the sequential tunnel-rates. The lead states are electrostatically tuned by a global back-gate, resulting in a distinct pattern of varying intensity in the measured conductance maps. This pattern could potentially obscure transport features that are intrinsic to the molecule under investigation. Using ensemble averaged magneto-conductance measurements, lead and molecule states are disentangled, enabling spectroscopic investigation of the single molecule.