How to calculate charge mobility in molecular materials from surface hopping non-adiabatic molecular dynamics - beyond the hopping/band paradigm

Thermoelectric transport in molecular crystals driven by gradients of thermal electronic disorder

Thermoelectric materials convert a temperature gradient into a voltage. This phenomenon is relatively well understood for inorganic materials but much less so for organic semiconductors (OSs). These materials present a challenge because the strong thermal fluctuations of electronic coupling between the molecules result in partially delocalized charge carriers that cannot be treated with traditional theories for thermoelectricity. Here, we develop a quantum dynamical simulation approach revealing in atomistic detail how the charge carrier wave function moves along a temperature gradient in an organic molecular crystal. We find that the wave function propagates from hot to cold in agreement with the experiment, and we obtain a Seebeck coefficient in good agreement with experimental measurements that are also reported in this work. Detailed analysis reveals that gradients in thermal electronic disorder play an important role in determining the magnitude of the Seebeck coefficient, opening unexplored avenues for the design of OSs with improved Seebeck coefficients.

Charge transport in organic semiconductors from the mapping approach to surface hopping

We describe how to simulate charge diffusion in organic semiconductors using a recently introduced mixed quantum-classical method, the mapping approach to surface hopping. In contrast to standard fewest-switches surface hopping, this method propagates the classical degrees of freedom deterministically on the most populated adiabatic electronic state. This correctly preserves the equilibrium distribution of a quantum charge coupled to classical phonons, allowing one to time-average along trajectories to improve the statistical convergence of the calculation. We illustrate the method with an application to a standard model for the charge transport in the direction of maximum mobility in crystalline rubrene. Because of its consistency with the equilibrium distribution, the present method gives a time-dependent diffusion coefficient that plateaus correctly to a long-time limiting value. The resulting mobility is somewhat higher than that of the relaxation time approximation, which uses a phenomenological relaxation parameter to obtain a non-zero diffusion coefficient from a calculation with static phonon disorder. However, it is very similar to the mobility obtained from Ehrenfest dynamics, at least in the parameter regimes we have investigated here. This is somewhat surprising because Ehrenfest dynamics overheats the electronic subsystem and is, therefore, inconsistent with the equilibrium distribution.

Mori generalized master equations offer an efficient route to predict and interpret polaron transport

Predicting how a material's microscopic structure and dynamics determine its transport properties remains a fundamental challenge. To alleviate this task's often prohibitive computational expense, we propose a Mori-based generalized quantum master equation (GQME) to predict the frequency-resolved conductivity of small-polaron forming systems described by the dispersive Holstein model. Unlike previous GQME-based approaches to transport that scale with the system size and only give access to the DC conductivity, our method requires only one calculation and yields both the DC and AC mobilities. We further show how to easily augment our GQME with numerically accessible derivatives of the current to increase computational efficiency, collectively offering computational cost reductions of up to 90%, depending on the transport regime. Finally, we leverage our exact simulations to demonstrate the limited applicability of the celebrated and widely invoked Drude-Smith model in small-polaron forming systems. We instead introduce a cumulant-based analysis of experimentally accessible frequency data to infer the microscopic Hamiltonian parameters. This approach promises to provide valuable insights into material properties and facilitate guided design by linking macroscopic terahertz measurements to the microscopic details of small polaron-forming systems.

Exciton Transport in the Nonfullerene Acceptor O-IDTBR from Nonadiabatic Molecular Dynamics

Theory, computation, and experiment have given strong evidence that charge carriers in organic molecular crystals form partially delocalized quantum objects that diffuse very efficiently via a mechanism termed transient delocalization. It is currently unclear how prevalent this mechanism is for exciton transport. Here we carry out simulation of singlet Frenkel excitons (FE) in a molecular organic semiconductor that belongs to the class of nonfullerene acceptors, O-IDTBR, using the recently introduced FE surface hopping nonadiabatic molecular dynamics method. We find that FE are, on average, localized on a single molecule in the crystal due to sizable reorganization energy and moderate excitonic couplings. Yet, our simulations suggest that the diffusion mechanism is more complex than simple local hopping; in addition to hopping, we observe frequent transient delocalization events where the exciton wave function expands over 10 or more molecules for a short period of time in response to thermal excitations within the excitonic band, followed by de-excitation and contraction onto a single molecule. The transient delocalization events lead to an increase in the diffusion constant by a factor of 3-4, depending on the crystallographic direction as compared to the situation where only local hopping events are considered. Intriguingly, O-IDTBR appears to be a moderately anisotropic 3D "conductor" for excitons but a highly anisotropic 2D conductor for electrons. Taken together with previous simulation results, two trends seem to emerge for molecular organic crystals: excitons tend to be more localized and slower than charge carriers due to higher internal reorganization energy, while exciton transport tends to be more isotropic than charge transport due to the weaker distance dependence of excitonic versus electronic coupling.

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.

Stabilized coupled trajectory mixed quantum-classical algorithm with improved energy conservation: CTMQC-EDI

Coupled trajectory mixed quantum-classical (CTMQC) dynamics is a rigorous approach to trajectory-based non-adiabatic dynamics, which has recently seen an improvement to energy conservation via the introduction of the CTMQC-E algorithm. Despite this, the method's two key quantities distinguishing it from Ehrenfest dynamics, the modified Born-Oppenheimer momentum and the quantum momentum, require regularization procedures in certain circumstances. Such procedures in the latter can cause instabilities, leading to undesirable effects, such as energy drift and spurious population transfer, which is expected to become increasingly prevalent when the system gets larger as such events would happen more frequently. We propose a further modification to CTMQC-E, which includes a redefinition of the quantum momentum, CTMQC-EDI (double intercept), such that it has no formal divergences. We then show for Tully models I-III and the double arch model that the algorithm has greatly improved total energy conservation and negligible spurious population transfer at all times, in particular in regions of strong non-adiabatic coupling. CTMQC-EDI, therefore, shows promise as a numerically robust non-adiabatic dynamics technique that accounts for decoherence from first principles and that is scalable to large molecular systems and materials.

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.

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.

Learning Decoherence Time Formulas for Surface Hopping from Quantum Dynamics

Surface hopping simulations have achieved great success in many different fields, but their reliability has long been limited by the overcoherence problem. We here present a general machine learning assisted approach to identify optimal decoherence time formulas for surface hopping using exact quantum dynamics as references. In order to avoid computationally expensive force calculations, we use the nuclear kinetic energy and the adiabatic energy difference to iteratively generate the descriptor space. Through multilayer screening of the candidate descriptors and discrete optimization of the relevant parameters, we obtain new energy-based decoherence time formulas. As benchmarked in thousands of diverse multilevel systems and six standard scattering models, surface hopping with our new decoherence time formulas nearly reproduces the exact quantum dynamics while maintaining high efficiency. Thereby, our approach provides a promising avenue for systematically improving the accuracy of surface hopping simulations in complex systems from quantum dynamics data.

How Regiochemistry Influences Aggregation Behavior and Charge Transport in Conjugated Organosulfur Polymer Cathodes for Lithium-Sulfur Batteries

For lithium-sulfur (Li-S) batteries to become competitive, they require high stability and energy density. Organosulfur polymer-based cathodes have recently shown promising performance due to their ability to overcome common limitations of Li-S batteries, such as the insulating nature of sulfur. In this study, we use a multiscale modeling approach to explore the influence of the regiochemistry of a conjugated poly(4-(thiophene-3-yl)benzenethiol) (PTBT) polymer on its aggregation behavior and charge transport. Classical molecular dynamics simulations of the self-assembly of polymer chains with different regioregularity show that a head-to-tail/head-to-tail regularity can form a well-ordered crystalline phase of planar chains allowing for fast charge transport. Our X-ray diffraction measurements, in conjunction with our predicted crystal structure, confirm the presence of crystalline phases in the electropolymerized PTBT polymer. We quantitatively describe the charge transport in the crystalline phase in a band-like regime. Our results give detailed insights into the interplay between microstructural and electrical properties of conjugated polymer cathode materials, highlighting the effect of polymer chain regioregularity on its charge transport properties.

A mapping approach to surface hopping

We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the nuclei on the active adiabatic potential-energy surface, such as in FSSH. However, unlike in FSSH, transitions between active surfaces are deterministic and occur when the electronic mapping variables evolve between specified regions of the electronic phase space. This guarantees internal consistency between the active surface and the electronic degrees of freedom throughout the dynamics. MASH is rigorously derivable from exact quantum mechanics as a limit of the quantum-classical Liouville equation (QCLE), leading to a unique prescription for momentum rescaling and frustrated hops. Hence, a quantum-jump procedure can, in principle, be used to systematically converge the accuracy of the results to that of the QCLE. This jump procedure also provides a rigorous framework for deriving approximate decoherence corrections similar to those proposed for FSSH. We apply MASH to simulate the nonadiabatic dynamics in various model systems and show that it consistently produces more accurate results than FSSH at a comparable computational cost.

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.

Detailed Balance and Independent Electron Surface-Hopping Method: The Importance of Decoherence and Correct Calculation of Diabatic Populations

We benchmark and improve the independent electron surface-hopping (IESH) method developed by J. C. Tully's group for nonadiabatic simulations near metal surfaces. We have incorporated decoherence within the IESH method as well as implemented a scheme for the accurate calculation of diabatic populations. We benchmark the original IESH method with the above inclusions for a model system to calculate rate constants and long-time populations. The original IESH method fails to capture the detailed balance for some of the parameters, which is corrected with the inclusion of decoherence and accurate calculation of diabatic populations. Total rate constants are well captured both within the original IESH method as well as within our modified IESH.

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

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.

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

Organic semiconductors (OSs) are an exciting class of materials that have enabled disruptive technologies in this century including large-area electronics, flexible displays, and inexpensive solar cells. All of these technologies rely on the motion of electrical charges within the material and the diffusivity of these charges critically determines their performance. In this respect, it is remarkable that the nature of the charge transport in these materials has puzzled the community for so many years, even for apparently simple systems such as molecular single crystals: some experiments would better fit an interpretation in terms of a localized particle picture, akin to molecular or biological electron transfer, while others are in better agreement with a wave-like interpretation, more akin to band transport in metals.

Exciting recent progress in the theory and simulation of charge carrier transport in OSs has now led to a unified understanding of these disparate findings, and this Account will review one of these tools developed in our laboratory in some detail: direct charge carrier propagation by quantum-classical nonadiabatic molecular dynamics. One finds that even in defect-free crystals the charge carrier can either localize on a single molecule or substantially delocalize over a large number of molecules depending on the relative strength of electronic couplings between the molecules, reorganization, or charge trapping energy of the molecule and thermal fluctuations of electronic couplings and site energies, also known as electron–phonon couplings.

Our simulations predict that in molecular OSs exhibiting some of the highest measured charge mobilities to date, the charge carrier forms “flickering” polarons, objects that are delocalized over 10–20 molecules on average and that constantly change their shape and extension under the influence of thermal disorder. The flickering polarons propagate through the OS by short (≈10 fs long) bursts of the wave function that lead to an expansion of the polaron to about twice its size, resulting in spatial displacement, carrier diffusion, charge mobility, and electrical conductivity. Arguably best termed “transient delocalization”, this mechanistic scenario is very similar to the one assumed in transient localization theory and supports its assertions. We also review recent applications of our methodology to charge transport in disordered and nanocrystalline samples, which allows us to understand the influence of defects and grain boundaries on the charge propagation.

Unfortunately, the energetically favorable packing structures of typical OSs, whether molecular or polymeric, places fundamental constraints on charge mobilities/electronic conductivity compared to inorganic semiconductors, which limits their range of applications. In this Account, we review the design rules that could pave the way for new very high-mobility OS materials and we argue that 2D covalent organic frameworks are one of the most promising candidates to satisfy them.

We conclude that our nonadiabatic dynamics method is a powerful approach for predicting charge carrier transport in crystalline and disordered materials. We close with a brief outlook on extensions of the method to exciton transport, dissociation, and recombination. This will bring us a step closer to an understanding of the birth, survival, and annihiliation of charges at interfaces of optoelectronic devices.

De Novo Calculation of the Charge Carrier Mobility in Amorphous Small Molecule Organic Semiconductors

Organic semiconductors (OSC) are key components in applications such as organic photovoltaics, organic sensors, transistors and organic light emitting diodes (OLED). OSC devices, especially OLEDs, often consist of multiple layers comprising one or more species of organic molecules. The unique properties of each molecular species and their interaction determine charge transport in OSCs-a key factor for device performance. The small charge carrier mobility of OSCs compared to inorganic semiconductors remains a major limitation of OSC device performance. Virtual design can support experimental R&D towards accelerated R&D of OSC compounds with improved charge transport. Here we benchmark a de novo multiscale workflow to compute the charge carrier mobility solely on the basis of the molecular structure: We generate virtual models of OSC thin films with atomistic resolution, compute the electronic structure of molecules in the thin films using a quantum embedding procedure and simulate charge transport with kinetic Monte-Carlo protocol. We show that for 15 common amorphous OSC the computed zero-field and field-dependent mobility are in good agreement with experimental data, proving this approach to be an effective virtual design tool for OSC materials and devices.

Impact of Nanoscale Morphology on Charge Carrier Delocalization and Mobility in an Organic Semiconductor

A central challenge of organic semiconductor research is to make cheap, disordered materials that exhibit high electrical conductivity. Unfortunately, this endeavor is hampered by the poor fundamental understanding of the relationship between molecular packing structure and charge carrier mobility. Here a novel computational methodology is presented that fills this gap. Using a melt-quench procedure it is shown that amorphous pentacene spontaneously self-assembles to nanocrystalline structures that, at long quench times, form the characteristic herringbone layer of the single crystal. Quantum dynamical simulations of electron hole transport show a clear correlation between the crystallinity of the sample, the quantum delocalization, and the mobility of the charge carrier. Surprisingly, the long-held belief that charge carriers form relatively localized polarons in disordered OS is only valid for fully amorphous structures-for nanocrystalline and crystalline samples, significant charge carrier delocalization over several nanometers occurs that underpins their improved conductivities. The good agreement with experimentally available data makes the presented methodology a robust computational tool for the predictive engineering of disordered organic materials.

Mechanoelectric Response of Single-Crystal Rubrene from Ab Initio Molecular Dynamics

A robust understanding of the mechanoelectric response of organic semiconductors is crucial for the development of materials for flexible electronics. In particular, the prospect of using external mechanical strain to induce a controlled modulation in the charge mobility of the material is appealing. Here we develop an accurate computational protocol for the prediction of the mechanical strain dependence of charge mobility. Ab initio molecular dynamics simulations with a van der Waals density functional are carried out to quantify the off-diagonal electronic disorder in the system as a function of strain by the explicit calculation of the thermal distributions of electronic coupling matrix elements. The approach is applied to a representative molecular organic semiconductor, single-crystal rubrene. We find that charge mobility along the high-mobility direction a⃗ increases with compressive strain, as one might expect. However, the increase is larger when compressive strain is applied in the perpendicular direction than in the parallel direction with respect to a⃗, in agreement with experimental reports. We show that this seemingly counterintuitive result is a consequence of a significantly greater suppression of electronic coupling fluctuations in the range of 50-150 cm^-1, when strain is applied in the perpendicular direction. Thus our study highlights the importance of considering off-diagonal electron-phonon coupling in understanding the mechanoelectric response of organic semiconducting crystals. The computational approach developed here is well suited for the accurate prediction of strain-charge mobility relations and should provide a useful tool for the emerging field of molecular strain engineering.

Crystal Symmetry and Static Electron Correlation Greatly Accelerate Nonradiative Dynamics in Lead Halide Perovskites

Using a recently developed many-body nonadiabatic molecular dynamics (NA-MD) framework for large condensed matter systems, we study the phonon-driven nonradiative relaxation of excess electronic excitation energy in cubic and tetragonal phases of the lead halide perovskite CsPbI₃. We find that the many-body treatment of the electronic excited states significantly changes the structure of the excited states' coupling, promotes a stronger nonadiabatic coupling of states, and ultimately accelerates the relaxation dynamics relative to the single-particle description of excited states. The acceleration of the nonadiabatic dynamics correlates with the degree of configurational mixing, which is controlled by the crystal symmetry. The higher-symmetry cubic phase of CsPbI₃ exhibits stronger configuration mixing than does the tetragonal phase and subsequently yields faster nonradiative dynamics. Overall, using a many-body treatment of excited states and accounting for decoherence dynamics are important for closing the gap between the computationally derived and experimentally measured nonradiative excitation energy relaxation rates.

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

When nonadiabatic dynamics are described on the basis of trajectories, severe trajectory branching occurs when the nuclear wave packets on some potential energy surfaces are reflected while those on the remaining surfaces are not. As a result, the traditional Ehrenfest mean field (EMF) approximation breaks down. In this study, two versions of the branching corrected mean field (BCMF) method are proposed. Namely, when trajectory branching is identified, BCMF stochastically selects either the reflected or the nonreflected group to build the new mean field trajectory or splits the mean field trajectory into two new trajectories with the corresponding weights. As benchmarked in six standard model systems and an extensive model base with two hundred diverse scattering models, BCMF significantly improves the accuracy while retaining the high efficiency of the traditional EMF. In fact, BCMF closely reproduces the exact quantum dynamics in all investigated systems, thus highlighting the essential role of branching correction in nonadiabatic dynamics simulations of general systems.

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.

Ultrathin porphyrin and tetra-indole covalent organic frameworks for organic electronics applications

The electronic and charge transport properties of porphyrin and tetra-indole porphyrinoid single layer covalent organic frameworks (COFs) are investigated by means of density functional theory calculations. Ultrathin diacetylene-linked COFs based on oxidized tetra-indole cores are narrow gap 2D semiconductors, featuring a pronounced anisotropic electronic band structure due to the combination of dispersive and flat band characteristics, while registering high room temperature charge carrier mobilities. The capability of bandgap and charge carrier localization tuning via the careful selection of fourfold porphyrin and porphyrinoid cores and twofold articulated linkers is demonstrated, with the majority of systems exhibiting electronic gap values between 1.75 eV and 2.3 eV. Tetra-indoles are also capable of forming stable monolayers via non-articulated core fusing, resulting in 2D morphologies with extended π-conjugation and semi-metallic behavior.

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.