Roles of inter- and intramolecular vibrations and band-hopping crossover in the charge transport in naphthalene crystal

Organic Charge Transfer Cocrystals as Additives for Dissipation of Contact Charges on Polymers

Common polymers can accumulate surface charges through contact, a phenomenon known since ancient times. This charge accumulation can have detrimental consequences in industry. It causes accidents and yields enormous economic losses. Many empirical methods have been developed to prevent the problems caused by charge accumulation. However, a general chemical approach is still missing in the literature since the charge accumulation and discharging mechanisms have not been completely clarified. The current practice to achieve charge mitigation is to increase materials conductivity by high doping of conductive additives. A recent study showed that using photoexcitation of some organic dyes, charge decay can be started remotely, and the minute amount of additive does not change the material's conductivity. Here, we show the contact charging and charge decay behavior of polydimethylsiloxane doped with a series of organic charge transfer cocrystals (CTC) of TCNQ acceptor and substituted pyrene donors (CTC-PDMS). The results show that the CTC-PDMS are antistatic, and the discharging propensity of the composites follows the calculated charge transfer degree of the complexes. On the other hand, the CTC-PDMS are still insulators, as shown by their high surface resistivities. Kelvin probe force microscopy images of the contact-charged and discharged samples show a quick potential decay in CTC domains upon illumination. Combined with the fast overall decay observed, the antistatic behavior in these insulators can be attributed to an electron transfer between the mechanoions in the polymer and the CTC frontier orbitals. We believe our results will help with the general understanding of the molecular mechanism of contact charging and discharging and help develop insulator antistatics.

Diagrammatic quantum Monte Carlo toward the calculation of transport properties in disordered semiconductors

A new diagrammatic quantum Monte Carlo approach is proposed to deal with the imaginary time propagator involving both dynamic disorder (i.e., electron–phonon interactions) and static disorder of local or nonlocal nature in a unified and numerically exact way. The establishment of the whole framework relies on a general reciprocal-space expression and a generalized Wick’s theorem for the static disorder. Since the numerical cost is independent of the system size, various physical quantities, such as the thermally averaged coherence, Matsubara one-particle Green’s function, and current autocorrelation function, can be efficiently evaluated in the thermodynamic limit (infinite in the system size). The validity and performance of the proposed approach are systematically examined in a broad parameter regime. This approach, combined with proper numerical analytic continuation methods and first-principles calculations, is expected to be a versatile tool toward the calculation of various transport properties, such as mobilities in realistic semiconductors involving multiple electronic energy bands, high-frequency optical and low-frequency acoustic phonons, different forms of dynamic and static disorders, and anisotropy.

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.

Design Rules to Maximize Charge-Carrier Mobility along Conjugated Polymer Chains

The emergence of polymeric materials displaying high charge-carrier mobility values despite poor interchain structural order has spawned a renewal of interest in the identification of structure-property relationships pertaining to the transport of charges along conjugated polymer chains and the subsequent design of optimized architectures. Here, we present the results of intrachain charge transport simulations obtained by applying a robust surface hopping algorithm to a phenomenological Hamiltonian parametrized against first-principles simulations. Conformational effects are shown to provide a clear signature in the temperature-dependent charge-carrier mobility that complies with recent experimental observations. We further contrast against molecular crystals the evolution with electronic bandwidth and electron-phonon interactions of the room-temperature mobility in polymers, showing that intrachain charge-carrier mobility values in excess of 100 cm²/(V s) can be achieved through a proper chemical engineering of the backbones.

Anharmonic Lattice Vibrations in Small-Molecule Organic Semiconductors

The intermolecular lattice vibrations in small-molecule organic semiconductors have a strong impact on their functional properties. Existing models treat the lattice vibrations within the harmonic approximation. In this work, polarization-orientation (PO) Raman measurements are used to monitor the temperature-evolution of the symmetry of lattice vibrations in anthracene and pentacene single crystals. Combined with first-principles calculations, it is shown that at 10 K, the lattice dynamics of the crystals are indeed harmonic. However, as the temperature is increased, specific lattice modes gradually lose their PO dependence and become more liquid-like. This finding is indicative of a dynamic symmetry breaking of the crystal structure and shows clear evidence of the strongly anharmonic nature of these vibrations. Pentacene also shows an apparent phase transition between 80 and 150 K, indicated by a change in the vibrational symmetry of one of the lattice modes. These findings lay the groundwork for accurate predictions of the electronic properties of high-mobility organic semiconductors at room temperature.

Unprecedented Enhancement of Thermoelectric Power Factor Induced by Pressure in Small-Molecule Organic Semiconductors

Establishing the relationship between pressure and heat-electricity interconversion in van der Waals bonded small-molecule organic semiconductors is critical not only in designing flexible thermoelectric materials, but also in developing organic electronics. Here, based on first-principles calculations and using naphthalene as a case study, an unprecedented elevation of p-type thermoelectric power factor induced by pressure is demonstrated; and the power factor increases by 267% from 159.5 µW m^-1 K^-2 under ambient conditions to 585.8 µW m^-1 K^-2 at 2.1 GPa. The underlying mechanism is attributed to the dramatic inhibition of lattice-vibration-caused electronic scattering. Furthermore, it is revealed that both restraining low-frequency intermolecular vibrational modes and increasing intermolecular electronic coupling are two essential factors that effectively suppress the electron-phonon scattering. From the standpoint of molecular design, these two conditions can be achieved by extending the π-conjugated backbones, introducing long alkyl sidechains to the π-cores, and substituting heteroatoms in the π-cores.

Subspace Surface Hopping with Size-Independent Dynamics

We present a subspace surface hopping strategy to deal with complex surface crossings in nonadiabatic dynamics. By focusing on only important adiabatic states, we make subspace crossing correction (SCC) in the framework of the standard fewest switches surface hopping (FSSH) and the global flux surface hopping (GFSH). The resulting SCC-FSSH and SCC-GFSH approaches show much better performance than the counterparts using all adiabatic states for surface hopping. As demonstrated in a series of Holstein models with up to over 1000 molecular sites, both SCC-FSSH and SCC-GFSH show excellent size independence with a large time step size of 1 fs. Especially, SCC-GFSH does not refer to nonadiabatic couplings at all and gives a more proper description of superexchange, and thus, it is promising for realistic applications with complex potential energy surfaces.

Crossing Classified and Corrected Fewest Switches Surface Hopping

In the traditional fewest switches surface hopping (FSSH), trivial crossings between uncoupled or weakly coupled states have highly peaked nonadiabatic couplings and thus are difficult to deal with in the preferred, adiabatic representation. Here, we classify surface crossings into four general types and propose a parameter-free crossing corrected FSSH (CC-FSSH) algorithm, which could treat multiple trivial crossings within a time interval. As examples, Holstein Hamiltonians with different parameters are adopted to mimic electron dynamics in tens to hundreds of molecules, which suffer from severe trivial crossing problems. Using existed surface hopping approaches as references, we show that CC-FSSH exhibits significantly fast time interval convergence and weak system size dependence. In all cases, a reliable description is achieved with a large time interval of 1 fs. With a simple formalism and the ability to describe complex surface crossings, CC-FSSH could potentially simulate general nonadiabatic dynamics in nanoscale materials with a high efficiency.

An efficient solution to the decoherence enhanced trivial crossing problem in surface hopping

We provide an in-depth investigation of the time interval convergence when both trivial crossing and decoherence corrections are applied to Tully's fewest switches surface hopping (FSSH) algorithm. Using one force-based and one energy-based decoherence strategies as examples, we show decoherence corrections intrinsically enhance the trivial crossing problem. We propose a restricted decoherence (RD) strategy and incorporate it into the self-consistent (SC) fewest switches surface hopping algorithm [L. Wang and O. V. Prezhdo, J. Phys. Chem. Lett. 5, 713 (2014)]. The resulting SC-FSSH-RD approach is applied to general Hamiltonians with different electronic couplings and electron-phonon couplings to mimic charge transport in tens to hundreds of molecules. In all cases, SC-FSSH-RD allows us to use a large time interval of 0.1 fs for convergence and the simulation time is reduced by over one order of magnitude. Both the band and hopping mechanisms of charge transport have been captured perfectly. SC-FSSH-RD makes surface hops in the adiabatic representation and can be implemented in both diabatic and locally diabatic representations for wave function propagation. SC-FSSH-RD can potentially describe general nonadiabatic dynamics of electrons and excitons in organics and other materials.

Dichotomy between the band and hopping transport in organic crystals: insights from experiments

The molecular understanding of charge-transport in organic crystals has often been tangled with identifying the true dynamical origin. While in two distinct cases where complete delocalization and localization of charge-carriers are associated with band-like and hopping-like transports, respectively, their possible coalescence poses some mystery. Moreover, the existing models are still controversial at ambient temperatures. Here, we review the issues in charge-transport theories of organic materials and then provide an overview of prominent transport models. We explored ∼60 organic crystals, the single-crystal hole/electron mobilities of which have been predicted by band-like and hopping-like transport models, separately. Our comparative results show that at room-temperature neither of the models are exclusively capable of accurately predicting mobilities in a very broad range. Hopping-like models well-predict experimental mobilities around μ ∼ 1 cm² V^-1 s^-1 but systematically diverge at high mobilities. Similarly, band-like models are good at μ > ∼50 cm² V^-1 s^-1 but systematically diverge at lower mobilities. These results suggest the development of a unique and robust room-temperature transport model incorporating a mixture of these two extreme cases, whose relative importance is associated with their predominant regions. We deduce that while band models are beneficial for rationally designing high mobility organic-semiconductors, hopping models are good to elucidate the charge-transport of most organic-semiconductors.

XRD- and infrared-probed anisotropic thermal expansion properties of an organic semiconducting single crystal

The anisotropic thermal expansion properties of an organic semiconducting single crystal constituted by 4-hydroxycyanobenzene (4HCB) have been probed by XRD in the range 120-300 K. The anisotropic thermal expansion coefficients for the three crystallographic axes and for the crystal volume have been determined. A careful analysis of the crystal structure revealed that the two different H-bonds stemming from the two independent, differently oriented 4HCB molecules composing the unit cell have different rearrangement patterns upon temperature variations, in terms of both bond length and bond angle. Linearly Polarized Mid InfraRed (LP-MIR) measurements carried out in the same temperature range, focused on the O-H bond spectral region, confirm this finding. The same LP-MIR measurements, on the basis of a semi-empirical relation and of geometrical considerations and assumptions, allowed calculation of the -CNH-O- hydrogen bond length along the a and b axes of the crystal. In turn, the so-calculated -CNH-O- bond lengths were used to derive the thermal expansion coefficients along the corresponding crystal axes, as well as the volumetric one, using just the LP-MIR data. Reasonable to good agreement with the same values obtained from XRD measurements was obtained. This proof-of-principle opens interesting perspectives about the possible development of a rapid, low cost and industry-friendly assessment of the thermal expansion properties of organic semiconducting single crystals (OSSCs) involving hydrogen bonds.

Mixed quantum-classical dynamics for charge transport in organics

Charge transport plays a crucial role in the working principle of most opto-electronic and energy devices. This is especially true for organic materials where the first theoretical models date back to the 1950s and have continuously evolved ever since. Most of these descriptions rely on perturbation theory to treat small interactions in the Hamiltonian. In particular, applying a perturbative treatment to the electron-phonon and electron-electron coupling results in the band and hopping models, respectively, the signature of which is conveyed by a characteristic temperature dependence of mobility. This perspective describes recent progress of studying charge transport in organics using mixed quantum-classical dynamics techniques, including mean field and surface hopping theories. The studies go beyond the perturbation treatments and represent the processes explicitly in the time-domain, as they occur in real life. The challenges, advantages, and disadvantages of both approaches are systematically discussed. Special focus is dedicated to the temperature dependence of mobility, the role of local and nonlocal electron-phonon couplings, as well as the interplay between electronic and electron-phonon interactions.

Negative isotope effect for charge transport in acenes and derivatives--a theoretical conclusion

The isotope effect (IE) on charge transport in polyacenes was proposed in 1970 to judge the transport mechanism. However, there had not been a definitive answer for more than 40 years as to whether such an IE is positive or negative, both theoretically and experimentally, because either theory was too approximate or the experimental estimate was too rough to make a judgment. Employing the quantum nuclear tunneling model for organic semiconductors, we investigate the IE on both hole and electron transport for acenes and their derivatives. We show that both (13)C-substitution and deuteration lead to a negative IE. By introducing phenyl, chlorine, or alkyl side-chains into acenes, the IE becomes more remarkable, especially for hole transport. The vibrational relaxation processes involving in-plane bending of ring or alkyl side-chain motions are found to be responsible for the IE.

Understanding the charge transport and polarities in organic donor-acceptor mixed-stack crystals: molecular insights from the super-exchange couplings

Charge transport and polarity in organic D-A mixed-stack crystals are examined in terms of super-exchange electronic couplings. When the super-exchange coupling is dominated by the interaction between donor HOMO and acceptor LUMO, ambipolar transport is achieved. Otherwise, involvement of other bridge orbitals can lead to unbalanced, even to unipolar transport in a special case that the HOMO-LUMO interaction vanishes.

Maximizing Singlet Fission by Intermolecular Packing

A novel nonadiabatic molecular dynamics scheme is applied to study the singlet fission (SF) process in pentacene dimers as a function of longitudinal and lateral displacements of the molecular backbones. Detailed two-dimensional mappings of both instantaneous and long-term triplet yields are obtained, characterizing the advantageous and unfavorable stacking arrangements, which can be achieved by chemical substitutions to the bare pentacene molecule. We show that the SF rate can be increased by more than an order of magnitude through tuning the intermolecular packing, most notably when going from cofacial to the slipped stacked arrangements encountered in some pentacene derivatives. The simulations indicate that the SF process is driven by thermal electron-phonon fluctuations at ambient and high temperatures, expected in solar cell applications. Although charge-transfer states are key to construct continuous channels for SF, a large charge-transfer character of the photoexcited state is found to be not essential for efficient SF. The reported time domain study mimics directly numerous laser experiments and provides novel guidelines for designing efficient photovoltaic systems exploiting the SF process with optimum intermolecular packing.

The effect of intermolecular interactions on the charge transport properties of thiazole/thiophene-based oligomers with trifluoromethylphenyl

A fundamental understanding of the relationship between intermolecular interactions and transport properties in organic semiconducting materials is significant for their potential applications as electronic device element. Carrier transport properties of thiazole/thiophene-based oligomers with trifluoromethylphenyl groups 1, 2, and 3, in which the type and strength of the intermolecular interactions are different, were investigated within the framework of band model. The results show that π-π stacking interactions are mainly responsible for the hole transport, while hydrogen bonding interactions have a great influence on the electron transport. The specific transport mechanism could be explained by analyzing the density of states (DOS) and Γ point wave functions.

From charge transport parameters to charge mobility in organic semiconductors through multiscale simulation

This review introduces the development and application of a multiscale approach to assess the charge mobility for organic semiconductors, which combines quantum chemistry, Kinetic Monte Carlo (KMC), and molecular dynamics (MD) simulations. This approach is especially applicable in describing a large class of organic semiconductors with intermolecular electronic coupling (V) much less than intramolecular charge reorganization energy (λ), a situation where the band description fails obviously. The charge transport is modeled as successive charge hopping from one molecule to another. We highlight the quantum nuclear tunneling effect in the charge transfer, beyond the semiclassical Marcus theory. Such an effect is essential for interpreting the "paradoxical" experimental finding that optical measurement indicated "local charge" while electrical measurement indicated "bandlike". Coupled MD and KMC simulations demonstrated that the dynamic disorder caused by intermolecular vibration has negligible effect on the carrier mobility. We further apply the approach for molecular design of n-type materials and for rationalization of experimental results. The charge reorganization energy is analyzed through decomposition into internal coordinates relaxation, so that chemical structure contributions to the intramolecular electron-phonon interaction are revealed and give helpful indication to reduce the charge reorganization energy.

Flexible Surface Hopping Approach to Model the Crossover from Hopping to Band-like Transport in Organic Crystals

Two distinct pictures are usually evoked when modeling charge transport in organic crystals, that is, band and hopping models, the signature of which is conveyed by a characteristic temperature dependence of mobility. Here, we present a novel flexible surface hopping approach compliant with general Hamiltonians that is able to grasp the crossover from hopping to band-like transport regimes. This approach is applied to solve a one-dimensional mixed quantum-classical model and to calculate the temperature dependence of charge mobility along with the degree of charge spatial localization. It is found that the roles of both local and nonlocal electron-phonon couplings strongly depend on the intrinsic charge localization strength.

First-principles prediction of charge mobility in carbon and organic nanomaterials

We summarize our recent progresses in developing first-principles methods for predicting the intrinsic charge mobility in carbon and organic nanomaterials, within the framework of Boltzmann transport theory and relaxation time approximation. The electron-phonon couplings are described by Bardeen and Shockley's deformation potential theory, namely delocalized electrons scattered by longitudinal acoustic phonons as modeled by uniform lattice dilation. We have applied such methodology to calculating the charge carrier mobilities of graphene and graphdiyne, both sheets and nanoribbons, as well as closely packed organic crystals. The intrinsic charge carrier mobilities for graphene sheet and naphthalene are calculated to be 3 × 10(5) and ∼60 cm(2) V(-1) s(-1) respectively at room temperature, in reasonable agreement with previous studies. We also present some new theoretical results for the recently discovered organic electronic materials, diacene-fused thienothiophenes, for which the charge carrier mobilities are predicted to be around 100 cm(2) V(-1) s(-1).

Interaction of charge carriers with lattice and molecular phonons in crystalline pentacene

The computational protocol we have developed for the calculation of local (Holstein) and non-local (Peierls) carrier-phonon coupling in molecular organic semiconductors is applied to both the low temperature and high temperature bulk crystalline phases of pentacene. The electronic structure is calculated by the semimpirical INDO/S (Intermediate Neglect of Differential Overlap with Spectroscopic parametrization) method. In the phonon description, the rigid molecule approximation is removed, allowing mixing of low-frequency intra-molecular modes with inter-molecular (lattice) phonons. A clear distinction remains between the low-frequency phonons, which essentially modulate the transfer integral from a molecule to another (Peierls coupling), and the high-frequency intra-molecular phonons, which modulate the on-site energy (Holstein coupling). The results of calculation agree well with the values extracted from experiment. The comparison with similar calculations made for rubrene allows us to discuss the implications for the current models of mobility.

Evaluation of charge mobility in organic materials: from localized to delocalized descriptions at a first-principles level

The carrier mobility for carbon electronic materials is an important parameter for optoelectronics. We report here some recently developed theoretical tools to predict the mobility without any free parameters. Carrier scatterings with phonons and traps are the key factors in evaluating the mobility. We consider three major scattering regimes: i) where the molecular internal vibration severely induces charge self-trapping and, thus, the hopping mechanism dominates; ii) where both intermolecular and intramolecular scatterings come to play roles, so the Holstein-Peierls polaron model is applied; and, iii) where charge is well delocalized with coherence length comparable with acoustic phonon wavelength, so that a deformation potential approach is more appropriate. We develop computational methods at the first-principles level for the three different cases that have extensive potential application in rationalizing material design.

Interaction of charge carriers with lattice vibrations in oligoacene crystals from naphthalene to pentacene

A key feature of organic π-conjugated materials is the strong connection between their electronic and geometric structures. In particular, it has been recently demonstrated that nonlocal electron-vibration (electron-phonon) interactions, which are related to the modulation of the electronic couplings (transfer integrals) between adjacent molecules by lattice vibrations, play an important role in the charge-transport properties of organic semiconductors. Here, we use density functional theory calculations and molecular mechanics simulations to estimate the strength of these nonlocal electron-vibration couplings in oligoacene crystals as a function of molecular size from naphthalene through pentacene. The effect of each optical vibrational mode on the electronic couplings is evaluated quantitatively. The results point to a very strong coupling to both intermolecular vibrational modes and intramolecular (including high-frequency) modes in all studied systems. Importantly, our results underline that the amount of relaxation energy associated with nonlocal electron-phonon coupling decreases as the size of the molecule increases. This work establishes an original relationship between chemical structure and nonlocal vibrational coupling in the description of charge transport in organic semiconductor crystals.

Multiscale study of charge mobility of organic semiconductor with dynamic disorders

The impact of dynamic disorder arising from the thermal fluctuations on the charge transport in organic semiconductors is studied by a multi-scale approach combining molecular dynamics, electronic structure calculations and kinetic Monte Carlo simulations for pentacene crystal of thin-film phase. It is found that for 1-D arrays, such fluctuations severely reduce charge mobility as temperature increases. However, when going from an 1-D array to an 2-D herringbone layer, for a wide range of temperatures, the charge transport property is found to be unaffected by such disorders from our multiscale computational study. And in some extreme cases, when the fluctuations of the hopping integral are even larger than their average values, the dynamic disorders can increase the charge mobility. In addition, we point out that the "band-like" behavior concluded by the experiment can be reproduced by quantum charge transfer involving nuclear vibration tunneling effects within a hopping model.

Bandlike motion and mobility saturation in organic molecular semiconductors

We analyze a model that accounts for the inherently large thermal lattice fluctuations associated with the weak van der Waals intermolecular bonding in crystalline organic semiconductors. In these materials the charge mobility generally exhibits a "metalliclike" power-law behavior, with no sign of thermally activated hopping characteristic of carrier self-localization, despite apparent mean free paths comparable to or lower than the intermolecular spacing. Our results show that such a puzzling transport regime can be understood from the simultaneous presence of band carriers and incoherent states that are dynamically localized by the thermal lattice disorder.

Charge carrier motion in disordered conjugated polymers: a multiscale Ab initio study

We developed an ab initio multiscale method for simulation of carrier transport in large disordered systems, based on direct calculation of electronic states and electron-phonon coupling constants. It enabled us to obtain the never seen before rich microscopic details of carrier motion in conjugated polymers, which led us to question several assumptions of phenomenological models, widely used in such systems. The macroscopic mobility of disordered poly(3-hexylthiophene) (P3HT) polymer, extracted from our simulation, is in agreement with experimental results from the literature.

Influence of intermolecular vibrations on the electronic coupling in organic semiconductors: the case of anthracene and perfluoropentacene

We have performed classical molecular dynamics simulations and quantum-chemical calculations on molecular crystals of anthracene and perfluoropentacene. Our goal is to characterize the amplitudes of the room-temperature molecular displacements and the corresponding thermal fluctuations in electronic transfer integrals, which constitute a key parameter for charge transport in organic semiconductors. Our calculations show that the thermal fluctuations lead to Gaussian-like distributions of the transfer integrals centered around the values obtained for the equilibrium crystal geometry. The calculated distributions have been plugged into Monte-Carlo simulations of hopping transport, which show that lattice vibrations impact charge transport properties to various degrees depending on the actual crystal structure.

Computational methods for design of organic materials with high charge mobility

Charge carrier mobility is at the center of organic electronic devices. The strong couplings between electrons and nuclear motions lead to complexities in theoretical description of charge transport, which pose a major challenge for the fundamental understanding and computational design of transport organic materials. This tutorial review describes recent progresses in developing computational tools to assess the carrier mobility in organic molecular semiconductors at the first-principles level. Some rational molecular design strategies for high mobility organic materials are outlined.