Understanding Carrier Transport in Organic Semiconductors: Computation of Charge Mobility Considering Quantum Nuclear Tunneling and Delocalization Effects

Interlayer Charge Transport in 2D Lead Halide Perovskites from First Principles

We report on the implementation of a versatile projection-operator diabatization approach to calculate electronic coupling integrals in layered periodic systems. The approach is applied to model charge transport across the saturated organic spacers in two-dimensional (2D) lead halide perovskites. The calculations yield out-of-plane charge transfer rates that decay exponentially with the increasing length of the alkyl chain, range from a few nanoseconds to milliseconds, and are supportive of a hopping mechanism. Most importantly, we show that the charge carriers strongly couple to distortions of the Pb-I framework and that accounting for the associated nonlocal dynamic disorder increases the thermally averaged interlayer rates by a few orders of magnitude compared to the frozen-ion 0 K-optimized structure. Our formalism provides the first comprehensive insight into the role of the organic spacer cation on vertical transport in 2D lead halide perovskites and can be readily extended to functional π-conjugated spacers, where we expect the improved energy alignment with the inorganic layout to speed up the charge transfer between the semiconducting layers.

Charge carrier dynamics in conducting polymer PEDOT using ab initio molecular dynamics simulations

As conducting polymers become increasingly important in electronic devices, understanding their charge transport is essential for material and device development. Various semi-empirical approaches have been used to describe temporal charge carrier dynamics in these materials, but there have yet to be any theoretical approaches utilizing ab initio molecular dynamics. In this work, we develop a computational technique based on ab initio Car-Parrinello molecular dynamics to trace charge carrier temporal motion in archetypical conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT). Particularly, we analyze charge dynamics in a single PEDOT chain and in two coupled chains with different degrees of coupling and study the effect of temperature. In our model we first initiate a positively charged polaron (compensated by a negative counterion) at one end of the chain, and subsequently displace the counterion to the other end of the chain and trace polaron dynamics in the system by monitoring bond length alternation in the PEDOT backbone and charge density distribution. We find that at low temperature (T = 1 K) the polaron distortion gradually disappears from its initial location and reappears near the new position of the counterion. At the room temperature (T = 300 K), we find that the distortions induced by polaron, and atomic vibrations are of the same magnitude, which makes tracking the polaron distortion challenging because it is hidden behind the temperature-induced vibrations. The novel approach developed in this work can be used to study polaron mobility along and between the chains, investigate charge transport in highly doped polymers, and explore other flexible polymers, including n-doped ones.

Theoretical insight on the charge transport properties: The formation of "head-to-tail" and "head-to-head" stacking of asymmetric aryl anthracene derivatives

Organic semiconductors (OSCs) are widely used in flexible display, renewable energy, and biosensors, owing to their unique solid-state physical and optoelectronic properties. Among the abundant crystal library of OSCs, asymmetric aryl anthracene derivatives have irreplaceable advantages due to the interplay between their distinct π-conjugated geometry and molecular stacking as well as efficient light emission and charge transport properties that can be simultaneously utilized. However, the poor crystal stacking patterns of most asymmetric molecules limit their utility as excellent OSCs. Thus, it is crucial to clarify the structural features that enable the extremely ordered stacking and favorable electronic structure of asymmetric anthracene derivatives to become high-performance OSCs. This contribution investigates the charge transport properties of a series of asymmetric aryl anthracene derivatives to reveal the modulation factors of the molecular stacking modes and to explore the structural factors, which are beneficial to charge transport. The analysis demonstrated that the vinyl-linker facilitated the injection of hole carriers, and the alkynyl-linker effectively reduces the reorganization energy. Importantly, the linear polarizability and permanent dipole moment of a single molecule play a vital regulation to molecular stacking modes and the transfer integral of the dimer. The "head-to-head stacking" motif shows a compact stacking pattern and the maximum 2D anisotropic mobility more than 10 cm2 V-1 s-1. These findings sharpen our understanding of the charge transport properties in asymmetric organic semiconductors and are essential for developing a diverse range of high-performance OSC materials.

Efficiently predicting directional carrier mobilities in organic materials with the Boltzmann transport equation

Describing charge carrier anisotropy in crystalline organic semiconductors with ab initio methods is challenging because of the weak intermolecular interactions that lead to both localized and delocalized charge transport mechanisms. Small polaron hopping models (localized) are generally used to describe materials with small charge carrier mobilities, while periodic band models (delocalized) are used to describe materials with high charge carrier mobilities. Here, we prove the advantage of applying the constant relaxation time approximation of the Boltzmann transport equation (BTE) to efficiently predict the anisotropic hole mobilities of several unsubstituted (anthracene, tetracene, pentacene, and hexacene) and substituted (2,6-diphenylanthracene, rubrene, and TIPS-pentacene) high-mobility n-acene single crystals. Several density functionals are used to optimize the crystals, and the composite density functional PBEsol0-3c/sol-def2-mSVP predicts the most experimentally similar geometries, adequate indirect bandgaps, and the theoretically consistent n-acene charge transport mobility trend. Similarities between BTE and Marcus mobilities are presented for each crystal. BTE and Marcus charge carrier mobilities computed at the same geometry result in similar mobility trends, differing mostly in materials with more substitutions or structurally complex substituents. By using a reduced number of calculations, BTE is able to predict anisotropic carrier mobilities efficiently and effectively for a range of high-mobility organic semiconductors.

Quantitative Hole Mobility Simulation and Validation in Substituted Acenes

Knowledge of the full phonon spectrum is essential to accurately calculate the dynamic disorder (σ) and hole mobility (μ_h) in organic semiconductors (OSCs). However, most vibrational spectroscopy techniques under-measure the phonons, thus limiting the phonon validation. Here, we measure and model the full phonon spectrum using multiple spectroscopic techniques and predict μ_h using σ from only the Γ-point and the full Brillouin zone (FBZ). We find that only inelastic neutron scattering (INS) provides validation of all phonon modes, and that σ in a set of small molecule semiconductors can be miscalculated by up to 28% when comparing Γ-point against FBZ calculations. A subsequent mode analysis shows that many modes contribute to σ and that no single mode dominates. Our results demonstrate the importance of a thoroughly validated phonon calculation, and a need to develop design rules considering the full spectrum of phonon modes.

Energetics of the charge generation in organic donor-acceptor interfaces

Non-fullerene acceptor materials have posed new paradigms for the design of organic solar cells , whereby efficient carrier generation is obtained with small driving forces, in order to maximize the open-circuit voltage (V_OC). In this paper, we use a coarse-grained mixed quantum-classical method, which combines Ehrenfest and Redfield theories, to shed light on the charge generation process in small energy offset interfaces. We have investigated the influence of the energetic driving force as well as the vibronic effects on the charge generation and photovoltaic energy conversion. By analyzing the effects of the Holstein and Peierls vibrational couplings, we find that vibrational couplings produce an overall effect of improving the charge generation. However, the two vibronic mechanisms play different roles: the Holstein relaxation mechanism decreases the charge generation, whereas the Peierls mechanism always assists the charge generation. Moreover, by examining the electron-hole binding energy as a function of time, we evince two distinct regimes for the charge separation: the temperature independent excitonic spread on a sub-100 fs timescale and the complete dissociation of the charge-transfer state that occurs on the timescale of tens to hundreds of picoseconds, depending on the temperature. The quantum dynamics of the system exhibits the three regimes of the Marcus electron transfer kinetics as the energy offset of the interface is varied.

Accurate Analysis of Anisotropic Carrier Mobility and Structure-property Relationships in Organic BOXD Crystalline Materials

Charge mobility is an essential factor of organic crystalline materials. Although many investigators have made important progress, the exact relationship between the crystal structure and carrier mobility remains to be clarified. Fortunately, a series of bis-1,3,4-oxadiazole derivatives have been successfully prepared and reported. They have similar main molecular fragments but different crystal packing modes, which provide an ideal research objective for studying the effect of molecular packing on charge mobility in organic photoelectric conversion systems. In this work, the charge mobilities of these molecules are systematically evaluated from the perspective of first-principles calculation, and the effect of a molecular overlap on orbital overlap integral and final charge carrier mobility is fully discussed. It can be seen that the small intermolecular distance (less than 6 Å) is the decisive factor to achieve high electron mobility in π stacking, and better mobility can be obtained by increasing the hole migration distance appropriately. A larger dihedral angle of anisotropy is an important point limiting the charge mobility in the herringbone arrangement. It is hoped that the correlation results between the crystal structure and mobility can assist the experimental study and provide an effective way to improve the photoelectric conversion efficiency of the organic semiconductor devices and multiple basis for multiscale material system characterization and material information.

Theoretical investigations on the charge transport properties of anthracene derivatives with aryl substituents at the 2,6-position-thermally stable "herringbone" stacking motifs

High-performance organic semiconductor materials based on the small aromatic anthracene-core and its derivatives develop comparatively slowly due to the lack of a profound understanding of the influence of chemical modifications on their charge-transfer properties. Herein, the electronic properties and the charge transport characteristics of several typical anthracene-based derivatives with aryl groups substituted at the 2,6-site are systematically investigated by multi-scale simulation methods including Molecular Dynamics (MD) simulation and the full quantum nuclear tunneling model in the framework of density functional theory (DFT). To elucidate the origin of different charge transport properties of these anthracene-based materials, analysis of the molecular stacking and noncovalent intermolecular interaction caused by different substituents was carried out. The results indicate that the electron and hole injection capabilities and the air oxidation stability of the anthracene derivatives are greatly improved when the size of the aryl substituent increases. In addition, the incorporation of 2,6-site aryl substituents can inhibit the stretching vibration of the anthracene-core during charge transport, and allow molecular packing along the long axis (a-axis of DPA and BDBFAnt, and c-axis of dNaAnt) with almost no slippage, and the main transport channels remain unchanged, exhibiting more isotropic 2D transport properties. It should be emphasized that the edge-to-face dimers with smallest dihedral angles are closest to the thermally stable dimer model, with relatively larger π-orbital distributions in transmission channels (dimer 1, 2) and the largest spatial overlap, resulting in the largest hole transfer integral in DPA (Vh1/h2 = 57 meV). Although the analysis of the thermal disorder effect shows a phonon scattering effect, the maximum hole mobility of the DPA molecule is still as high as 1.5 cm2 V-1 s-1.

Hopping Conductance in Molecular Wires Exhibits a Large Heavy-Atom Kinetic Isotope Effect

We report a large kinetic isotope effect (KIE) for intramolecular charge transport in π-conjugated oligophenyleneimine (OPI) molecules connected to Au electrodes. ¹³C and ¹⁵N substitution on the imine bonds produces a conductance KIE of ∼2.7 per labeled atom in long OPI wires >4 nm in length, far larger than typical heavy-atom KIEs for chemical reactions. In contrast, isotopic labeling in shorter OPI wires <4 nm does not produce a conductance KIE, consistent with a direct tunneling mechanism. Temperature-dependent measurements reveal that conductance for a long ¹⁵N-substituted OPI wire is activated, and we propose that the exceptionally large conductance KIEs imply a thermally assisted, through-barrier polaron tunneling mechanism. In general, observation of large conductance KIEs opens up considerable opportunities for understanding microscopic conduction mechanisms in π-conjugated molecules.

Influences of dynamic and static disorder on the carrier mobility of BTBT-C12 derivatives: a multiscale computational study

The role of dynamic and static disorder has been widely discussed for carrier transport in organic semiconductors. In this work, we apply a multiscale approach by combining molecular dynamics simulations, quantum mechanics calculations and kinetic Monte-Carlo simulations to study the influence of dynamic and static disorder on the hole mobility of four didodecyl[1]benzothieno[3,2-b]benzothiophene (BTBT-C12) isomers. It is found that the dynamic disorder of transfer integral tends to decrease the mobility for quasi-1D (quasi one-dimensional) BTBT1 and BTBT4 isomers and increase the mobility for 2D (two-dimensional) BTBT2 and BTBT3 isomers, while the dynamic disorder of site energy tends to decrease mobility for all the four isomers; however, the reduction in 2D molecules is much less than that in quasi-1D molecules. Results show that trap defects could reduce the mobility for both the quasi-1D and 2D molecular structures significantly, even to several orders of magnitude. In addition, our work also reveals that there might exist two kinds of oxidation defects of the scatter type for the concerned isomers, which thus leads to greater reduction in mobility for the quasi-1D molecular structures than the 2D molecular structures. The study shows that the 2D molecular structures are favored over the quasi-1D or 1D molecular structure, and it is expected that these results could be used to shed light on device design in organic electronics.

Computational screen-out strategy for electrically pumped organic laser materials

Electrically pumped organic lasing is one of the most challenging issues in organic optoelectronics. We present a systematic theoretical investigation to screen out electrical pumping lasing molecules over a wide range of organic materials. With the electronic structure information obtained from time-dependent density functional theory, we calculate multiple photophysical parameters of a set of optical pumping organic laser molecules in our self-developed molecular material property prediction package (MOMAP) to judge whether the electrically pumped lasing conditions can be satisfied, namely, to avoid reabsorption from excitons and/or polarons, and the accumulation of triplet excitons. In addition, a large oscillator strength of S₁ and weak intermolecular π–π interaction are preferred. With these criteria, we are able to conclude that BP3T, BSBCz, and CzPVSBF compounds are promising candidates for electrically pumped lasing, and the proposed computational strategy could serve as a general protocol for molecular design of organic lasing materials.

Though the goal of current organic solid-state laser research remains the realization of electrically pumped lasing, identifying organic semiconductors with ideal properties remains a challenge. Here, the authors report a computational strategy for screening electrical pumping lasing molecules.

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.

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

It was recently suggested that cytochrome c operates in an ergodicity-breaking regime characterized by unusually large energy gap thermal fluctuations and associated reorganization free energies for heme oxidation of up to 3.0 eV. The large fluctuations were reported to lower activation free energy for oxidation of the heme cofactor by almost a factor of 2 compared to the case where ergodicity is maintained. Our group has recently investigated this claim computationally at several levels of theory and found no evidence for such large energy gap fluctuations. Here we address the points of our earlier work that have raised criticism and we also extend our previous investigation by considering a simple linear polarizability model for cytochrome c oxidation. We find very consistent results among all our computational approaches, ranging from classical molecular dynamics, to the linear polarizability model to QM(PMM)/MM to full QM(DFT)/MM electrostatic emdedding. None of them support the notion of very large energy gap fluctuations or ergodicity breaking. The deviation between our simulations and the ones reported in [ J. Phys. Chem. B 2017, 121, 4958] is traced back to rather large electric fields at the Fe site of the heme c cofactor in that study, not seen in our simulations, neither with the AMBER nor with the CHARMM force field. While ergodicity breaking effects may well occur in other biological ET, our numerical evidence suggests that this is not the case for cytochrome c.

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.

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.

Charge and energy transfer in large molecular assemblies: Quantum state diffusion with an adaptive basis

We show that the stochastic, wave-function based quantum state diffusion approach in combination with an adaptive basis is well suited to numerically treat the motion of an excitation in large molecular aggregates in the complicated regime where the transfer-time between molecules is comparable to the decoherence caused by environmental degrees of freedom.