Charge Transport in Molecular Materials: An Assessment of Computational Methods

Theoretical insights on acceptor-donor dyads for organic photovoltaics

The field of organic photovoltaics has witnessed a steady growth in the last few decades and a recent renewal with the blossoming of single-material organic solar cells (SMOSCs). However, due to the intrinsic complexity of these devices (both in terms of their size and of the condensed phases involved), computational approaches to accurately predict their geometrical and electronic structure and to link their microscopic properties to the observed macroscopic behaviour are still lacking. In this work, we have focused on the rationalization of transport dynamics and we have set up a computational approach that makes a combined use of classical simulations and Density Functional Theory with the aim of disclosing the most relevant electronic and structural features of dyads used for SMOSC applications. As a prototype dyad, we have considered a molecule that consists in a dithiafulvalene-functionalized diketopyrrolopyrrole (DPP), acting as an electron donor, covalently linked to a fulleropyrrolidine (Ful), the electron acceptor. Our results, beside a quantitative agreement with experiments, show that the overall observed mobilities result from the competing packing mechanisms of the constituting units within the dyad both in the case of crystalline and amorphous phases. As a consequence, not all stable polymorphs have the same efficiency in transporting holes or electrons which often results in a highly directional carrier transport that is not, in general, a desirable feature for polycrystalline thin-films. The present work, linking microscopic packing to observed transport, thus opens the route for the in silico design of new dyads with enhanced and controlled structural and electronic features.

Artificial neural networks for predicting charge transfer coupling

Quantum chemistry calculations have been very useful in providing many key detailed properties and enhancing our understanding of molecular systems. However, such calculation, especially with ab initio models, can be time-consuming. For example, in the prediction of charge-transfer properties, it is often necessary to work with an ensemble of different thermally populated structures. A possible alternative to such calculations is to use a machine-learning based approach. In this work, we show that the general prediction of electronic coupling, a property that is very sensitive to intermolecular degrees of freedom, can be obtained with artificial neural networks, with improved performance as compared to the popular kernel ridge regression method. We propose strategies for optimizing the learning rate and batch size, improving model performance, and further evaluating models to ensure that the physical signatures of charge-transfer coupling are well reproduced. We also address the effect of feature representation as well as statistical insights obtained from the loss function and the data structure. Our results pave the way for designing a general strategy for training such neural-network models for accurate prediction.

Strategies for Controlling Through-Space Charge Transport in Metal-Organic Frameworks via Structural Modifications

In recent years, charge transport in metal-organic frameworks (MOFs) has shifted into the focus of scientific research. In this context, systems with efficient through-space charge transport pathways resulting from π-stacked conjugated linkers are of particular interest. In the current manuscript, we use density functional theory-based simulations to provide a detailed understanding of such MOFs, which, in the present case, are derived from the prototypical Zn2(TTFTB) system (with TTFTB4- corresponding to tetrathiafulvalene tetrabenzoate). In particular, we show that factors such as the relative arrangement of neighboring linkers and the details of the structural conformations of the individual building blocks have a profound impact on bandwidths and charge transfer. Considering the helical stacking of individual tetrathiafulvalene (TTF) molecules around a screw axis as the dominant symmetry element in Zn2(TTFTB)-derived materials, the focus, here, is primarily on the impact of the relative rotation of neighboring molecules. Not unexpectedly, changing the stacking distance in the helix also plays a distinct role, especially for structures which display large electronic couplings to start with. The presented results provide guidelines for achieving structures with improved electronic couplings. It is, however, also shown that structural defects (especially missing linkers) provide major obstacles to charge transport in the studied, essentially one-dimensional systems. This suggests that especially the sample quality is a decisive factor for ensuring efficient through-space charge transport in MOFs comprising stacked π-systems.

The role of ligands in electron transport in nanocrystal solids

We investigate theoretically the transport of electrons and holes in crystalline solids consisting of three-dimensional arrays of semiconductor nanocrystals passivated by two types of organic ligands-linear chain carboxylates and functionalized aromatic cinnamates. We focus on a critical quantity in transport: the quantum-mechanical overlap of the strongly confined electron and hole wavefunctions on neighboring nanocrystals. Using results from density-functional-theory (DFT) calculations, we construct a one-dimensional model system whose analytic wavefunctions reproduce the full DFT numerical overlap values. By investigating the analytic behavior of this model, we reveal several important features of electron transport. The most significant is that the wavefunction overlap decays exponentially with ligand length, with a characteristic decay length that depends primarily on properties of the ligand and is almost independent of the size and type of nanocrystal. Functionalization of the ligands can also affect the overlap by changing the height of the tunneling barrier. The physically transparent analytic expressions we obtain for the wavefunction overlap and its decay length should be useful for future efforts to control transport in nanocrystal solids.

Toward a First-Principles Evaluation of Transport Mechanisms in Molecular Wires

Understanding charge transport through molecular wires is important for nanoscale electronics and biochemistry. Our goal is to establish a simple first-principles protocol for predicting the charge transport mechanism in such wires, in particular the crossover from coherent tunneling for short wires to incoherent hopping for longer wires. This protocol is based on a combination of density functional theory with a polarizable continuum model introduced by Kaupp et al. for mixed-valence molecules, which we had previously found to work well for length-dependent charge delocalization in such systems. We combine this protocol with a new charge delocalization measure tailored for molecular wires, and we show that it can predict the tunneling-to-hopping transition length with a maximum error of one subunit in five sets of molecular wires studied experimentally in molecular junctions at room temperature. This suggests that the protocol is also well suited for estimating the extent of hopping sites as relevant, for example, for the intermediate tunneling-hopping regime in DNA.

Backbone charge transport in double-stranded DNA

Understanding charge transport in DNA molecules is a long-standing problem of fundamental importance across disciplines^1,2. It is also of great technological interest due to DNA's ability to form versatile and complex programmable structures. Charge transport in DNA-based junctions has been reported using a wide variety of set-ups^2-4, but experiments so far have yielded seemingly contradictory results that range from insulating^5-8 or semiconducting^9,10 to metallic-like behaviour¹¹. As a result, the intrinsic charge transport mechanism in molecular junction set-ups is not well understood, which is mainly due to the lack of techniques to form reproducible and stable contacts with individual long DNA molecules. Here we report charge-transport measurements through single 30-nm-long double-stranded DNA (dsDNA) molecules with an experimental set-up that enables us to address individual molecules repeatedly and to measure the current-voltage characteristics from 5 K up to room temperature. Strikingly, we observed very high currents of tens of nanoamperes, which flowed through both homogeneous and non-homogeneous base-pair sequences. The currents are fairly temperature independent in the range 5-60 K and show a power-law decrease with temperature above 60 K, which is reminiscent of charge transport in organic crystals. Moreover, we show that the presence of even a single discontinuity ('nick') in both strands that compose the dsDNA leads to complete suppression of the current, which suggests that the backbones mediate the long-distance conduction in dsDNA, contrary to the common wisdom in DNA electronics^2-4.

Correlation between structural and optical characteristics of conjugated copolymers differing by a Si bridge atom

In this study, we investigate two copolymers as electron donors in photovoltaic devices, PFO-DBT (poly[2,7-(9,9-dioctylfluorene)-alt-4,7-bis(thiophen-2-yl)benzo-2,1,3-thiadiazole]) and its analogue with Si, PSiF-DBT (poly[2,7-(9,9-dioctyl-dibenzosilole)-alt-4,7-bis(thiophen-2-yl)benzo-2,1,3-thiadiazole]). The results discussed here are related to the influence of heavy atoms on the electrical and morphological properties of the devices. Charge transfer dynamics in the polymeric films were evaluated using the core-hole clock method. Besides that, using density functional theory (DFT) and time-dependent DFT (TD-DFT) methods, we investigate the electronic structure and charge transfer properties of the two systems. The charge transfer rates were estimated in the framework of the semiclassical Marcus/Hush theory. We found that the better stacking between the polymer chains for PSiF-DBT provides higher solar absorption capacity in regions of higher wavelengths and faster hole transfer rates. We also obtain a faster electron transfer rate at the PSiF-DBT/C₆₀ interface compared to the PFO-DBT/C₆₀ interface that is mainly related to the difference in the driving force between the two systems. These features help to explain why the organic photovoltaic devices using PSiF-DBT as the active layer exhibited a higher performance compared to devices using PFO-DBT. Here, we show that our results are able to provide important insights about the parameters that can influence the photovoltaic performance of the devices.

A "backtracking" correction for the fewest switches surface hopping algorithm

We propose a "backtracking" mechanism within Tully's fewest switches surface hopping (FSSH) algorithm, whereby whenever one detects consecutive (double) hops during a short period of time, one simply rewinds the dynamics backward in time. In doing so, one reduces the number of hopping events and comes closer to a truly fewest switches surface hopping approach with independent trajectories. With this algorithmic change, we demonstrate that surface hopping can be reasonably accurate for nuclear dynamics in a multidimensional configuration space with a complex-valued (i.e., not real-valued) electronic Hamiltonian; without this adjustment, surface hopping often fails. The added computational cost is marginal. Future research will be needed to assess whether or not this backtracking correction can improve the accuracy of a typical FSSH calculation with a real-valued electronic Hamiltonian (that ignores spin).

Applying Marcus theory to describe the carrier transports in organic semiconductors: Limitations and beyond

Marcus theory has been successfully applied to molecular design for organic semiconductors with the aid of quantum chemistry calculations for the molecular parameters: the intermolecular electronic coupling V and the intramolecular charge reorganization energy λ. The assumption behind this is the localized nature of the electronic state for representing the charge carriers, being holes or electrons. As far as the quantitative description of carrier mobility is concerned, the direct application of Marcus semiclassical theory usually led to underestimation of the experimental data. A number of effects going beyond such a semiclassical description will be introduced here, including the quantum nuclear effect, dynamic disorder, and delocalization effects. The recently developed quantum dynamics simulation at the time-dependent density matrix renormalization group theory is briefly discussed. The latter was shown to be a quickly emerging efficient quantum dynamics method for the complex system.

Computational modeling of charge hopping dynamics along a disordered one-dimensional wire with energy gradients in quantum environments

This computational study investigates the effects of energy gradients on charge hopping dynamics along a one-dimensional chain of discrete sites coupled to quantum bath, which is modeled at the level of Pauli master equation (PME). This study also assesses the performance of different approximations for the hopping rates. Three different methods for solving the PME, a fourth order Runge-Kutta method, numerical diagonalization of the rate matrix followed by analytic propagation, and kinetic Monte Carlo simulation method, are tested and confirmed to produce virtually identical values of time dependent mean square displacement, diffusion constant, and mobility. Five different rate expressions, exact numerical evaluation of Fermi's Golden Rule (FGR) rate, stationary phase interpolation (SPI) approximation, semiclassical approximation, classical Marcus rate, and Miller-Abrahams rate, are tested to help understand the effects of approximations in representing quantum environments in the presence of energy gradients. The results based on direct numerical evaluation of FGR rate exhibit transition from diffusive to non-diffusive behavior with the increase in the gradient and show that the charge transport in the quantum bath is more sensitive to the magnitude of the gradient and the disorder than in the classical bath. Among all the four approximations for the hopping rates, the SPI approximation is confirmed to work best overall. A comparison of two different methods to calculate the mobility identifies drift motion of the population distribution as the major source of non-diffusive behavior and provides more reliable information on the contribution of quantum bath.

Finite-Temperature TD-DMRG for the Carrier Mobility of Organic Semiconductors

A large number of nonadiabatic dynamical studies have been applied to reveal the nature of carrier transport in organic semiconductors with different approximations. We present here a "nearly exact" graphical-process-unit-based finite-temperature time-dependent density matrix renormalization group (TD-DMRG) method to evaluate the carrier mobility in organic semiconductors, as described by the electron-phonon model, in particular, in rubrene crystal, one of the prototypical organic semiconductors, with parameters derived from first-principles. We find that (i) TD-DMRG is a general and robust method that can bridge the gap between hopping and band pictures, covering a wide range of electronic coupling strengths and (ii) with realistic parameters, TD-DMRG is able to account for the experimentally observed "band-like" transport behavior (∂μ/∂T < 0) in rubrene. We further study the long-standing puzzle of the isotope effect for charge transport and unambiguously demonstrate that the negative isotope effect (∂μ/∂m < 0 where m is the atomic mass) should be universal.

Uniform potential difference scheme to evaluate effective electronic couplings for superexchange electron transfer in donor-bridge-acceptor systems

This article proposes an ab initio quantum chemical method to evaluate the effective electronic coupling that determines the rate of superexchange electron transfer in donor-bridge-acceptor (D-B-A) systems. The method utilizes the fragment charge difference to define electronic diabatic states and to apply an electrostatic potential in a form of a uniform potential difference that mimics solvation effects on the relative energies of the electronic states. The two-state generalized Mulliken-Hush method is used to obtain the effective electronic coupling as the nondiagonal element of the effective Hamiltonian that is derived based on the Green's function approach and the quasi-degenerate perturbation theory. A theoretical basis is provided for the dependence of the calculated effective electronic coupling on the applied potential and for how to find the optimal potential to give the desired effective electronic coupling that coincides with the result of the minimum energy splitting method. The method is applied to typical D-B-A molecules and gives the effective electronic couplings in reasonable agreement with the experimental estimates.

PyCDFT: A Python package for constrained density functional theory

We present PyCDFT, a Python package to compute diabatic states using constrained density functional theory (CDFT). PyCDFT provides an object-oriented, customizable implementation of CDFT, and allows for both single-point self-consistent-field calculations and geometry optimizations. PyCDFT is designed to interface with existing density functional theory (DFT) codes to perform CDFT calculations where constraint potentials are added to the Kohn-Sham Hamiltonian. Here, we demonstrate the use of PyCDFT by performing calculations with a massively parallel first-principles molecular dynamics code, Qbox, and we benchmark its accuracy by computing the electronic coupling between diabatic states for a set of organic molecules. We show that PyCDFT yields results in agreement with existing implementations and is a robust and flexible package for performing CDFT calculations. The program is available at https://dx.doi.org/10.5281/zenodo.3821097.

FB-REDA: fragment-based decomposition analysis of the reorganization energy for organic semiconductors

We present a fragment-based decomposition analysis tool (FB-REDA) for the reorganisation energy (λ). This tool delivers insights on how to rationally design low-λ organic semiconductors. The contribution of the fragment vibrational modes to the reorganization energy is exploited to identity the individual contributions of the molecular building blocks. The usefulness of the approach is demonstrated by offering three strategies to reduce the reorganization energy of a promising dopant-free hole transport material (TPA1PM, λ = 213 meV). A reduction of nearly 50% (TPD3PM, λ = 108 meV) is achieved. The proposed design principles are likely transferable to other organic semiconductors exploiting common molecular building blocks.

Acceleration scheme for particle transport in kinetic Monte Carlo methods

Kinetic Monte Carlo (kMC) simulations are frequently used to study (electro-)chemical processes within science and engineering. kMC methods provide insight into the interplay of stochastic processes and can link atomistic material properties with macroscopic characteristics. Significant problems concerning the computational demand arise if processes with large time disparities are competing. Acceleration algorithms are required to make slow processes accessible. Especially, the accelerated superbasin kMC (AS-kMC) scheme has been frequently applied within chemical reaction networks. For larger systems, the computational overhead of the AS-kMC is significant as the computation of the superbasins is done during runtime and comes with the need for large databases. Here, we propose a novel acceleration scheme for diffusion and transport processes within kMC simulations. Critical superbasins are detected during the system initialization. Scaling factors for the critical rates within the superbasins, as well as a lower bound for the number of sightings, are derived. Our algorithm exceeds the AS-kMC in the required simulation time, which we demonstrate with a 1D-chain example. In addition, we apply the acceleration scheme to study the time-of-flight (TOF) of charge carriers within organic semiconductors. In this material class, time disparities arise due to a significant spread of transition rates. The acceleration scheme allows a significant acceleration up to a factor of 65 while keeping the error of the TOF values negligible. The computational overhead is negligible, as all superbasins only need to be computed once.

Polaron Diffusion in Pentathienoacene Crystals

Molecular crystals have been used as prototypes for studying the energetic and dynamic properties of charge carriers in organic electronics. The growing interest in oligoacenes and fused-ring oligothiophenes in the last two decades is due, in particular, to the success achieved in conceiving pentacene-based organic photovoltaic devices. In the present work, a one-dimensional Holstein-Peierls model is designed to study the temperature-dependent polaron transport in pentathienoacene (PTA) lattices. The tight-binding Hamiltonian employed here takes into account intra and intermolecular electron-lattice interactions. Results reveal that polarons in PTAs can be stable structures even at high temperatures, about 400 K. During the dynamical process, these charge carriers present a typical 1D random walk diffusive motion with a low activation energy of 13 meV and a room temperature diffusivity constant of 1.07 × 10⁻³ cm² s⁻¹. Importantly, these critical values for the polaron diffusion and activation energy are related to the choice of model parameters, which are adopted to describe pristine lattices.

Reduced Common Molecular Orbital Basis for Nonorthogonal Configuration Interaction

Electron and charge transfers are part of many vital processes in nature and technology. Ab initio descriptions of these processes provide useful insights that can be utilized for applications. A combination of the embedded cluster material model and nonorthogonal configuration interaction (NOCI), in which the cluster wave functions are expanded in many-electron basis functions (MEBFs) consisting of spin-adapted, antisymmetrized products of multiconfigurational wave functions of fragments (which are usually molecules) in the cluster, appears to provide a compromise between accuracy and calculation time. Additional advantages of this NOCI-Fragments approach are the chemically convenient interpretation of the wave function in terms of molecular states, and the direct accessibility of electronic coupling between diabatic states to describe energy and electron transfer processes. Bottlenecks in this method are the large number of two-electron integrals that have to be handled for the calculation of an electronic coupling matrix element and the enormous number of matrix elements over determinant pairs that have to be evaluated for the calculation of one matrix element between the MEBFs. We show here how we created a reduced common molecular orbital basis that is utilized to significantly reduce the number of two-electron integrals that need to be handled. The results obtained with this basis do not show any loss of accuracy in relevant quantities like electronic couplings and vertical excitation energies. We also show a significant reduction in computation time without loss in accuracy when matrix elements over determinant pairs with small weights are neglected in the NOCI. These improvements in the methodology render NOCI-Fragments to be also applicable to treat clusters of larger molecular systems with larger atomic basis sets and larger active spaces, as the computation time becomes dependent on the number of occupied orbitals and less dependent on the size of the active space.

Evolutionary chemical space exploration for functional materials: computational organic semiconductor discovery

Computational methods, including crystal structure and property prediction, have the potential to accelerate the materials discovery process by enabling structure prediction and screening of possible molecular building blocks prior to their synthesis. However, the discovery of new functional molecular materials is still limited by the need to identify promising molecules from a vast chemical space. We describe an evolutionary method which explores a user specified region of chemical space to identify promising molecules, which are subsequently evaluated using crystal structure prediction. We demonstrate the methods for the exploration of aza-substituted pentacenes with the aim of finding small molecule organic semiconductors with high charge carrier mobilities, where the space of possible substitution patterns is too large to exhaustively search using a high throughput approach. The method efficiently explores this large space, typically requiring calculations on only ∼1% of molecules during a search. The results reveal two promising structural motifs: aza-substituted naphtho[1,2-a]anthracenes with reorganisation energies as low as pentacene and a series of pyridazine-based molecules having both low reorganisation energies and high electron affinities.

Mobile Small Polarons Qualitatively Explain Conductivity in Lithium Titanium Oxide Battery Electrodes

Lithium titanium oxide Li₄Ti₅O₁₂ is an intriguing anode material promising particularly long-life batteries, due to its remarkable phase stability during (dis)charging of the cell. However, its usage is limited by its low intrinsic electronic conductivity. Introducing oxygen vacancies can be one method for overcoming this drawback, possibly by altering the charge carrier transport mechanism. We use Hubbard corrected density functional theory to show that polaronic states in combination with a possible hopping mechanism can play a crucial role in the experimentally observed increase in electronic conductivity. To gauge polaronic charge mobility, we compute the relative stabilities of different localization patterns and estimate polaron hopping barrier heights.

Performance of Mixed Quantum-Classical Approaches on Modeling the Crossover from Hopping to Bandlike Charge Transport in Organic Semiconductors

In the present study, several mixed quantum-classical (MQC) methods are applied to on-the-fly nonadiabatic molecular dynamics simulations of hole transport in molecular organic semiconductors (OSCs). The tested MQC methods contain the mean-field Ehrenfest (MFE), trajectory surface hopping (TSH) approaches based on Tully's fewest switches surface hopping (FSSH) and the global flux surface hopping (GFSH), the latter in the diabatic/adiabatic representation, and a Landau-Zener type trajectory surface hopping (LZSH). We also tested several correction schemes which were proposed to identify trivial crossings and to remove unphysical long-range charge transfers due to decoherence corrections. In addition, several cost-effective approaches for the nuclear velocity adjustment after an energy-allowed/energy-forbidden hop are investigated with respect to detailed balance and internal consistency conditions. To model a broad spectrum of OSCs with different charge transport characteristics, we derived from the anthracene structural model the construction of two additional models by uniformly scaling down the electronic couplings by the factors of 0.1 and 0.5. Anthracene shows a bandlike charge transport mechanism, characterized by slightly delocalized charge carriers 'diffusing' through the crystal. For smaller couplings, the mechanism changes to a hopping type, characteristically differing in the charge delocalization and temperature dependence. The MFE and corrected adiabatic TSH approaches are able to quantitatively reproduce the expected behavior, while the diabatic LZSH method fails for large couplings, as do approaches which are based on the hopping of localized charge between neighboring sites. Moreover, we find that while the hole mobility of the anthracene crystal simulated using the celebrated Marcus theory is in good agreement with the experimental value, its agreement has to be regarded as an accident due to the overestimation of the prefactor in the Marcus rate equation.

Evaluating Computational Shortcuts in Supercell-Based Phonon Calculations of Molecular Crystals: The Instructive Case of Naphthalene

Phonons crucially impact a variety of properties of organic semiconductor materials. For instance, charge- and heat transport depend on low-frequency phonons, while for other properties, such as the free energy, especially high-frequency phonons count. For all these quantities one needs to know the entire phonon band structure, whose simulation becomes exceedingly expensive for more complex systems when using methods like dispersion-corrected density functional theory (DFT). Therefore, in the present contribution we evaluate the performance of more approximate methodologies, including density functional tight binding (DFTB) and a pool of force fields (FF) of varying complexity and sophistication. Beyond merely comparing phonon band structures, we also critically evaluate to what extent derived quantities, like temperature-dependent heat capacities, mean squared thermal displacements, and temperature-dependent free energies are impacted by shortcomings in the description of the phonon bands. As a benchmark system, we choose (deuterated) naphthalene, as the only organic semiconductor material for which to date experimental phonon band structures are available in the literature. Overall, the best performance among the approximate methodologies is observed for a system-specifically parametrized second-generation force field. Interestingly, in the low-frequency regime also force fields with a rather simplistic model for the bonding interactions (like the General Amber Force Field) perform rather well. As far as the tested DFTB parametrization is concerned, we obtain a significant underestimation of the unit-cell volume resulting in a pronounced overestimation of the phonon energies in the low-frequency region. This cannot be mended by relying on the DFT-calculated unit cell, since with this unit cell the DFTB phonon frequencies significantly underestimate the experiments.

Molecular Semiconductors for Logic Operations: Dead-End or Bright Future?

The field of organic electronics has been prolific in the last couple of years, leading to the design and synthesis of several molecular semiconductors presenting a mobility in excess of 10 cm² V^-1 s^-1 . However, it is also started to recently falter, as a result of doubtful mobility extractions and reduced industrial interest. This critical review addresses the community of chemists and materials scientists to share with it a critical analysis of the best performing molecular semiconductors and of the inherent charge transport physics that takes place in them. The goal is to inspire chemists and materials scientists and to give them hope that the field of molecular semiconductors for logic operations is not engaged into a dead end. To the contrary, it offers plenty of research opportunities in materials chemistry.

Decoupling from a Thermal Bath via Molecular Polariton Formation

The coupling between an electronic system and an environmental bath plays a decisive role in the excited state dynamics of artificial/natural molecular condensed phases. Although it is generally difficult to control the coupling between the system and the thermal bath in condensed matter, a strong light-matter coupling can control system-bath coupling properties using the polaron decoupling effect, in which a coherent interaction between excitons and photons reduces the reorganization energy. Here we demonstrate that this polaron decoupling strongly reduces the fluctuations in electronic energy in tetraphenyldibenzoperiflanthene thin films embedded in an optical microcavity. Using two-dimensional electronic spectroscopy, the frequency-fluctuation correlation function of the lower polariton state was revealed, showing that the dynamic inhomogeneity due to bath coupling inside the microcavity almost vanishes completely. This was attributed to a significant delocalization of the lower polariton state over 10⁵ molecules in the cavity, reducing the effective coupling strength of the bath modes.

Hole hopping in dimers of N,N' di(1-naphthyl)-N,N'-diphenyl-4,4'-diamine (α-NPD): a theoretical study

Hole-hopping parameters for Marcus-like charge transport, Marcus hole hopping rates, and hole mobilities are calculated for a series of model dimers of a typical hole-transporting material α-NPD using multireference quantum chemistry. The parameters are extracted from the two-state energy profiles built for charge hopping between two states with a hole localized on each of the monomers. The dependence of the hopping integral on the intermolecular arrangement in the dimer is studied. It is shown that at short intermolecular distances strong orbital interactions between molecules cause a drastic increase in the hopping integral and, therefore, in the hopping rate.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

Strong dependence of the vertical charge carrier mobility on the π-π stacking distance in molecule/graphene heterojunctions

Due to mechanical flexibility and low cost, heterojunctions consisting of graphene and small organic molecules are regarded as promising candidate materials for vertical organic field-effect transistors (VOFETs), where the charge carrier mobility perpendicular to the graphene plane is crucial to their performance. Herein, through density functional simulations, we find that the vertical charge carrier mobility of the heterojunctions can be greatly adjusted by tuning their π-π stacking distances. For the 6,13-dichloropentacene (DCP)/graphene heterojunctions, with the distance between the first DCP layer and graphene decreasing to below 2.4 Å, the vertical electron mobility between DCP layers is improved dramatically while the vertical hole mobility is greatly reduced. The strong dependence of vertical charge carrier mobility on the distance between the first molecular layer and substrate for smaller values than the typical π-π stacking distance (3.3-3.8 Å) was also observed in the perylenetetracarboxylic dianhydride (PTCDA)/graphene and DCP/hexagonal-BN heterojunctions, where the tendency is very different to that of the DCP/graphene heterojunction. Our simulation results enabled us to develop a new strategy to tune the vertical charge transport properties in molecule/graphene heterojunctions, which provides insights into developing efficient VOFETs.

Reorganization energies and spectral densities for electron transfer problems in charge transport materials

Various contributions to the outer reorganization energy of an electron transfer system and their theoretical and computational aspects have been discussed.

Symmetry controlled photo-selection and charge separation in butadiyne-bridged donor–bridge–acceptor compounds

Electron transfer (ET) in donor–bridge–acceptor (DBA) compounds featuring alkyne bridges depends strongly on the torsion angle between the donor and acceptor.

Nonadiabatic dynamics with quantum nuclei: simulating charge transfer with ring polymer surface hopping

Exploring effects of quantizing nuclei in non-adiabatic dynamics for simulating charge transfer in a dimer of “ethylene-like-molecules” at different temperatures.

Unexpectedly Large Couplings Between Orthogonal Units in Anthraquinone Polymers

The unusual electronic properties of directly linked 1,4-polyanthraquinones (14PAQs) are investigated. The dihedral angle between the molecular planes of anthraquinones (AQs) is found to be close to 90°. Contrary to the prevailing notion that the interaction between orthogonal units is negligible due to broken π-electron conjugation, the coupling between neighboring AQ units does not have a minimum at 90° and is much larger than that expected. The unexpectedly large electronic coupling between orthogonal AQ units is explained by the interaction between the lone pairs of the carbonyl oxygen and the π system of the neighboring unit, which allows favorable overlap between frontier molecular orbitals at the orthogonal geometry. It is shown that this effect, which is described computationally for the first time, can be strengthened by adding more quinone units. The effect of thermal fluctuations on the couplings is assessed through ab initio molecular dynamics simulations. The distributions of the couplings reveal that electron transport is resilient to dynamic disorder in all systems considered, whereas the hole couplings are much more sensitive to disorder. Lone pair-π interactions are described, as a previously largely overlooked conjugation mechanism, for incorporation into a new class of disorder-resilient semiconducting redox polymers.

Electron transfer in extended systems: characterization by periodic density functional theory including the electronic coupling

We describe a new computer implementation of electron transfer (ET) theory in extended systems treated by periodic density functional theory (DFT), including the calculation of the electronic coupling transition element V_AB. In particular, the development opens up the full characterization of electron transfer in the solid state. The approach is valid for any single-determinant wavefunction with localized character representing the electronic structure of the system, from Hartree-Fock (HF) theory, to density functional theory (DFT), hybrid DFT theory, DFT+U theory, and constrained DFT (cDFT) theory. The implementation in CP2K reuses the high-performance functions of the code. The computational cost is equivalent to only one iteration of an HF calculation. We present test calculations for electron transfer in a number of systems, including a 1D-model of ferric oxide, hematite Fe₂O₃, rutile TiO₂, and finally bismuth vanadate BiVO₄.

Machine Learning for Predicting Electron Transfer Coupling

Electron transfer coupling is a critical factor in determining electron transfer rates. This coupling strength can be sensitive to details in molecular geometries, especially intermolecular configurations. Thus, studying charge transporting behavior with a full first-principle approach demands a large amount of computation resources in quantum chemistry (QC) calculation. To address this issue, we developed a machine learning (ML) approach to evaluate electronic coupling. A prototypical ML model for an ethylene system was built by kernel ridge regression with Coulomb matrix representation. Since the performance of the ML models highly dependent on their building strategies, we systematically investigated the generality of the ML models, the choice of features and target labels. The best ML model trained with 40 000 samples achieved a mean absolute error of 3.5 meV and greater than 98% accuracy in predicting phases. The distance and orientation dependence of electronic coupling was successfully captured. Bypassing QC calculation, the ML model saved 10-10⁴ times the computation cost. With the help of ML, reliable charge transport models and mechanisms can be further developed.

Ergodicity-Breaking in Thermal Biological Electron Transfer? Cytochrome C Revisited

It was recently suggested that certain redox proteins operate in an ergodicity-breaking regime to facilitate biological electron transfer (ET). A signature for this is a large variance reorganization free energy (several electronvolts) but a significantly smaller Stokes reorganization free energy due to incomplete protein relaxation on the time scale of the ET event. Here we investigate whether this picture holds for oxidation of cytochrome c in aqueous solution, at various levels of theory including classical molecular dynamics with two additive and one electronically polarizable force field, and QM/MM calculations with the QM region treated by full electrostatic DFT embedding and by the perturbed matrix method. Sampling the protein and energy gap dynamics over more than 250 ns, we find no evidence for ergodicity-breaking effects. In particular, the inclusion of electronic polarizability of the heme group at QM/MM levels did not induce nonergodic effects, contrary to previous reports by Matyushov et al. The well-known problem of overestimation of reorganization free energies with additive force fields is cured when the protein and solvent are treated as electronically polarizable. Ergodicity-breaking effects may occur in other redox proteins, and our results suggest that long simulations, ideally on the ET time scale, with electronically polarizable force fields are required to obtain strong numerical evidence for them.

Quantum localization and delocalization of charge carriers in organic semiconducting crystals

Charge carrier transport in organic semiconductors is at the heart of many revolutionary technologies ranging from organic transistors, light-emitting diodes, flexible displays and photovoltaic cells. Yet, the nature of charge carriers and their transport mechanism in these materials is still unclear. Here we show that by solving the time-dependent electronic Schrödinger equation coupled to nuclear motion for eight organic molecular crystals, the excess charge carrier forms a polaron delocalized over up to 10-20 molecules in the most conductive crystals. The polaron propagates through the crystal by diffusive jumps over several lattice spacings at a time during which it expands more than twice its size. Computed values for polaron size and charge mobility are in excellent agreement with experimental estimates and correlate very well with the recently proposed transient localization theory.

Toward First-Principles-Level Polarization Energies in Force Fields: A Gaussian Basis for the Atom-Condensed Kohn-Sham Method

The last 20 years of force field development have shown that even well parametrized classical models need to at least approximate the dielectric response of molecular systems-based, e.g., on atomic polarizabilities-in order to correctly render their structural and dynamic properties. Yet, despite great advances most approaches tend to be based on ad hoc assumptions and often insufficiently capture the dielectric response of the system to external perturbations, such as, e.g., charge carriers in semiconducting materials. A possible remedy was recently introduced with the atom-condensed Kohn-Sham density-functional theory approximated to second order (ACKS2), which is fully derived from first principles. Unfortunately, specifically its reliance on first-principles derived parameters so far precluded the widespread adoption of ACKS2. Opening up ACKS2 for general use, we here present a reformulation of the method in terms of Gaussian basis functions, which allows us to determine many of the ACKS2 parameters analytically. Two sets of parameters depending on exchange-correlation interactions are still calculated numerically, but we show that they could be straightforwardly parametrized owing to the smoothness of the new basis. Our approach exhibits three crucial benefits for future applications in force fields: i) efficiency, ii) accuracy, and iii) transferability. We numerically validate our Gaussian augmented ACKS2 model for a set of small hydrocarbons which shows a very good agreement with density-functional theory reference calculations. To further demonstrate the method's accuracy and transferability for realistic systems, we calculate polarization responses and energies of anthracene and tetracene, two major building blocks in organic semiconductors.

Toward Efficient GW Calculations Using Numerical Atomic Orbitals: Benchmarking and Application to Molecular Dynamics Simulations

The use of atomic orbitals in Hedin's GW approximation provides, in principle, an inexpensive alternative to plane-wave basis sets, especially when modeling large molecules. However, benchmarking of the algorithms and basis sets is essential for a careful balance between cost and accuracy. In this paper, we present an implementation of the GW approximation using numerical atomic orbitals and a pseudopotential treatment of core electrons. The combination of a contour deformation technique with a one-shot extraction of quasiparticle energies provides an efficient scheme for many applications. The performance of the implementation with respect to the basis set convergence and the effect of the use of pseudopotentials has been tested for the 117 closed-shell molecules from the G2/97 test set and 24 larger acceptor molecules from another recently proposed test set. Moreover, to demonstrate the potential of our method, we compute the thermally averaged GW density of states of a large photochromic compound by sampling ab initio molecular dynamics trajectories at different temperatures. The computed thermal line widths indicate approximately twice as large electron-phonon couplings with GW than with standard DFT-GGA calculations. This is further confirmed using frozen-phonon calculations.