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

ConspectusOrganic 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

Nanosecond solvation dynamics of the hematite/liquid water interface at hybrid DFT accuracy using committee neural network potentials

Metal oxide/water interfaces play an important role in biology, catalysis, energy storage and photocatalytic water splitting. The atomistic structure at these interfaces is often difficult to characterize by experimental techniques, whilst results from ab initio molecular dynamics simulations tend to be uncertain due to the limited length and time scales accessible. In this work, we train a committee neural network potential to simulate the hematite/water interface at the hybrid DFT level of theory to reach the nanosecond timescale and systems containing more than 3000 atoms. The NNP enables us to converge dynamical properties, not possible with brute-force ab initio molecular dynamics. Our simulations uncover a rich solvation dynamics at the hematite/water interface spanning three different time scales: picosecond H-bond dynamics between surface hydroxyls and the first water layer, in-plane/out-of-plane tilt motion of surface hydroxyls on the 10 ps time scale, and diffusion of water molecules from the oxide surface characterized by a mean residence lifetime of about 60 ps. Calculation of vibrational spectra confirm that H-bonds between surface hydroxyls and first layer water molecules are stronger than H-bonds in bulk water. Our study showcases how state of the art machine learning approaches can routinely be utilized to explore the structural dynamics at transition metal oxide interfaces with complex electronic structure. It foreshadows that c-NNPs are a promising tool to tackle the sampling problem in ab initio electrochemistry with explicit solvent molecules

Ultrafast Electronic Coupling Estimators: Neural Networks versus Physics-Based Approaches

Fast and accurate estimation of electronic coupling matrix elements between molecules is essential for the simulation of charge transfer phenomena in chemistry, materials science, and biology. Here we investigate neural-network-based coupling estimators combined with different protocols for sampling reference data (random, farthest point, and query by committee) and compare their performance to the physics-based analytic overlap method (AOM), introduced previously. We find that neural network approaches can give smaller errors than AOM, in particular smaller maximum errors, while they require an order of magnitude more reference data than AOM, typically one hundred to several hundred training points, down from several thousand required in previous ML works. A Δ-ML approach taking AOM as a baseline is found to give the best overall performance at a relatively small computational overhead of about a factor of 2. Highly flexible π-conjugated organic molecules like non-fullerene acceptors are found to be a particularly challenging case for ML because of the varying (de)localization of the frontier orbitals for different intramolecular geometries sampled along molecular dynamics trajectories. Here the local symmetry functions used in ML are insufficient, and long-range descriptors are expected to give improved performance

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

Constrained density functional theory (CDFT) is a powerful tool for the prediction of electron transfer parameters in condensed phase simulations at a reasonable computational cost. In this work we present an extension to CDFT in the popular mixed Gaussian/plane wave electronic structure package CP2K, implementing the additional force terms arising from a constraint based on Hirshfeld charge partitioning. This improves upon the existing Becke partitioning scheme, which is prone to give unphysical atomic charges. We verify this implementation for a variety of systems: electron transfer in (H_{2}O)_{2}^{+} in a vacuum, electron tunnelling between oxygen vacancy centers in solid MgO, and electron self-exchange in aqueous Ru^{2+}-Ru^{3+}. We find good agreement with previous plane-wave CDFT results for the same systems, but at a significantly lower computational cost, and we discuss the general reliability of condensed phase CDFT calculations

Multi-heme Cytochromes in Shewanella oneidensis MR-1:Structures, functions and opportunities

Multi-heme cytochromes are employed by a range of microorganisms to transport electrons over distances of up to tens of nanometers. Perhaps the most spectacular utilization of these proteins is in the reduction of extracellular solid substrates, including electrodes and insoluble mineral oxides of Fe(III) and Mn(III/IV), by species of Shewanella and Geobacter. However, multi-heme cytochromes are found in numerous and phylogenetically diverse prokaryotes where they participate in electron transfer and redox catalysis that contributes to biogeochemical cycling of N, S and Fe on the global scale. These properties of multi-heme cytochromes have attracted much interest and contributed to advances in bioenergy applications and bioremediation of contaminated soils. Looking forward there are opportunities to engage multi-heme cytochromes for biological photovoltaic cells, microbial electrosynthesis and developing bespoke molecular devices. As a consequence it is timely to review our present understanding of these proteins and we do this here with a focus on the multitude of functionally diverse multi-heme cytochromes in Shewanella oneidensis MR-1. We draw on findings from experimental and computational approaches which ideally complement each other in the study of these systems: computational methods can interpret experimentally determined properties in terms of molecular structure to cast light on the relation between structure and function. We show how this synergy has contributed to our understanding of multi-heme cytochromes and can be expected to continue to do so for greater insight into natural processes and their informed exploitation in biotechnologies

HAB79: A new molecular dataset for benchmarking DFT and DFTB electronic couplings against high-level ab initio calculations

A new molecular dataset called HAB79 is introduced to provide ab initio reference values for electronic couplings (transfer integrals) and to benchmark density functional theory (DFT) and density functional tight-binding (DFTB) calculations. The HAB79 dataset is composed of 79 planar heterocyclic polyaromatic hydrocarbon molecules frequently encountered in organic (opto)electronics, arranged to 921 structurally diverse dimer configurations. We show that CASSCF/NEVPT2 with a minimal active space provides a robust reference method that can be applied to the relatively large molecules of the dataset. Electronic couplings are largest for cofacial dimers, in particular, sulfur-containing polyaromatic hydrocarbons, with values in excess of 0.5 eV, followed by parallel displaced cofacial dimers. V-shaped dimer motifs, often encountered in the herringbone layers of organic crystals, exhibit medium-sized couplings, whereas T-shaped dimers have the lowest couplings. DFT values obtained from the projector operator-based diabatization (POD) method are initially benchmarked against the smaller databases HAB11 (HAB7-) and found to systematically improve when climbing Jacob’s ladder, giving mean relative unsigned errors (MRUEs) of 27.7% (26.3%) for the generalized gradient approximation (GGA) functional BLYP, 20.7% (15.8%) for hybrid functional B3LYP, and 5.2% (7.5%) for the long-range corrected hybrid functional omega-B97X. Cost-effective POD in combination with a GGA functional and very efficient DFTB calculations on the dimers of the HAB79 database give a good linear correlation with the CASSCF/NEVPT2 reference data, which, after scaling with a multiplicative constant, gives reasonably small MRUEs of 17.9% and 40.1%, respectively, bearing in mind that couplings in HAB79 vary over 4 orders of magnitude. The ab initio reference data reported here are expected to be useful for benchmarking other DFT or semi-empirical approaches for electronic coupling calculations

Exciton transport in molecular organic semiconductors boosted by transient quantum delocalization

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

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

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

Combining experimental and theoretical methods to learn about the reactivity of gas-processing metalloenzymes

International audienceAfter enzymes were first discovered in the late XIX century, and for the first seventy years of enzymology, kinetic experiments were the only source of information about enzyme mechanisms. Over the following fifty years, these studies were taken over by approaches that give information at the molecular level, such as crystallography, spectroscopy and theoretical chemistry (as emphasized by the Nobel Prize in Chemistry awarded last year to M. Karplus, M. Levitt and A. Warshel). In this review, we thoroughly discuss the interplay between the information obtained from theoretical and experimental methods, by focussing on enzymes that process small molecules such as H 2 or CO 2 (hydrogenases, CO-dehydrogenase and carbonic anhydrase), and that are therefore relevant in the context of energy and environment. We argue that combining theoretical chemistry (DFT, MD, QM/MM) and detailed investigations that make use of modern kinetic methods, such as protein film voltammetry, is an innovative way of learning about individual steps and/or complex reactions that are part of the catalytic cycles. We illustrate this with recent results from our labs and others, including studies of gas transport along substrate channels, long range proton transfer, and mechanisms of catalysis, inhibition or inactivation. Broader context Some reactions which are very important in the context of energy and environment, such as the conversion between CO and CO2 , or H+ and H2 , are catalyzed in living organisms by large and complex enzymes that use inorganic active sites to transform substrates, chains of redox centers to transfer electrons, ionizable amino acids to transfer protons, and networks of hydrophobic cavities to guide the diffusion of substrates and products within the protein. This highly sophisticated biological plumbing and wiring makes turnover frequencies of thousands of substrate molecules per second possible. Understanding the molecular details of catalysis is still a challenge. We explain in this review how a great deal of information can be obtained using an interdisciplinary approach that combines state-of-the art kinetics and computational chemistry. This differs from—and complements—the more traditional strategies that consist in trying to see the catalytic intermediates using methods that rely on the interaction between light and matter, such as X-ray diffraction and spectroscopic techniques