Effects of pressure and temperature on the carrier transports in organic crystal: a first-principles study

By employing density-functional theory coupled with Holstein-Peierls model, we investigate the pressure and temperature dependence of the hole and electron mobilities in naphthalene single crystal from atmospheric pressure up to 2.1 GPa (at room temperature) and from 5 to 296 K (at ambient pressure). It is found that the pressure reduces the electron-phonon coupling strength and enhances the mobilities. Importantly, we point out that only when temperature-dependent structure modifications are taken into account can one better describe the temperature-dependent transport behavior. Especially, the band to hopping crossover transition temperature for the electron transport in the c'-axis is calculated to be around 153 K, which is close to the experimental result of between 100 and 150 K. If this temperature-dependent structure modifications were neglected, the transition temperature would be only about 23 K, as previously obtained [L. J. Wang et al., J. Chem. Phys. 127, 044506 (2007)].     

Charge Carrier Transport Mechanism in Ta2O5, TaON,and Ta3N5 Studied by Applying Polaron Hopping and Bandlike Models

TaON and Ta₃N₅ are considered promising materials for photocatalytic and photoelectrochemical water splitting. In contrast, their counterpart Ta₂O₅ does not exhibit good photocatalytic performance. This may be explained with the different charge carrier transport mechanisms in these materials, which are not well understood yet. Herein, we investigate the charge transport properties in Ta₂O₅, TaON, and Ta₃N₅ by polaron hopping and bandlike models. First, the polaron binding energies were calculated to evaluate whether the small polaron occurs in these materials. Then we performed calculations to localize the excess carriers as small polarons using a hybrid density functional. We find that the small polaron hopping is the charge transfer mechanism in Ta₂O_5, whereas our calculations indicate that this mechanism may not occur in TaON and Ta₃N₅. We also investigated the bandlike model mechanism by calculating the charge carrier mobility of these materials using the effective mass approximation, but the calculated mobility is not consistent with experimental results. This study is a first step towards understanding charge transport in oxynitrides and nitrides and furthermore establishes a simple rule to determine whether a small polaron occurs in a material.     

Electric field independent mobilities in molecular crystals

It is experimentally demonstrated that the electron drift mobility among the c' direction of anthracene and naphthalene is independent of the electric field to high electric fields (≈17 V/μm)at low temperatures (≈100 K). These data provide additional evidence against the applicability of small polaron models to molecular crystals and provide a challenge to recently proposed hopping models of charge transport which can account for the temperatures independence of the drift mobility.     

Dynamics of a Holstein polaron with off-diagonal coupling

Dynamics of a one-dimensional Holstein polaron with off-diagonal exciton-phonon coupling is studied by employing the Dirac-Frenkel time-dependent variational principle. The trial state used is the Davydov D(2) Ansatz with two sets of variational parameters, one for each constituting particle in the linearly coupled exciton-phonon system. Validity of the approach is carefully checked by quantifying how faithfully the trial state follows the Schro?dinger equation. A close examination of variational outputs reveals fine details of polaron dynamics and intricacies of dynamic exciton-phonon correlations. In the absence of diagonal coupling, the change in the polaron effective mass hinges on the sign of the transfer integral due to the antisymmetric nature of the off-diagonal coupling. The role of the off-diagonal coupling switches from being an agent of transport at moderate coupling strengths to that of localization at large coupling strengths. Increasing the phonon bandwidth leads to a reduced polaron effective mass at the zone center and an overall lowering of the polaron band.     

Charge transport in high mobility molecular semiconductors: classical models and new theories

The theories developed since the fifties to describe charge transport in molecular crystals proved to be inadequate for the most promising classes of high mobility molecular semiconductors identified in the recent years, including for example pentacene and rubrene. After reviewing at an elementary level the classical theories, which still provide the language for the understanding of charge transport in these systems, this tutorial review outlines the recent experimental and computational evidence that prompted the development of new theories of charge transport in molecular crystals. A critical discussion will illustrate how very rarely it is possible to assume a charge hopping mechanism for high mobility organic crystals at any temperature. Recent models based on the effect of non-local electron-phonon coupling, dynamic disorder, coexistence of localized and delocalized states are reviewed. Additionally, a few more recent avenues of theoretical investigation, including the study of defect states, are discussed.     

Small polaron hopping conduction mechanism in Fe doped LaMnO3

The structural and electrical transport properties of LaMn(1-x)Fe(x)O(3) (0.1 ≤ x ≤ 0.6) bulk samples have been investigated. The powder x-ray diffraction patterns at room temperature show that all samples are formed in single phase. The temperature dependent resistivity data have been fitted with the Mott's variable-range hopping (VRH) model for an entire studied range of the temperature (77-300 K) to calculate the hopping distance (R(h)) and the density of states at Fermi level (N(E(F))). It is found that all parameters vary systematically with the increase in Fe concentration. Moreover, the resistivity data were also fitted in the small polaron hopping (SPH) model. The non-adiabatic SPH conduction mechanism is followed by all samples. This type conduction mechanism is far accompanied by subtle electronically induced structural changes involving in Fe-O-Fe and Fe-O-Mn bond angles and bond lengths. Thus we suggest that the transport properties can be explained according to the additional localization of charge carriers induced by Fe doping.     

Kinetic Monte Carlo model of charge transport in hematite (alpha-Fe(2)O(3))

The mobility of electrons injected into iron oxide minerals via abiotic and biotic electron transfer processes is one of the key factors that control the reductive dissolution of such minerals. Building upon our previous work on the computational modeling of elementary electron transfer reactions in iron oxide minerals using ab initio electronic structure calculations and parametrized molecular dynamics simulations, we have developed and implemented a kinetic Monte Carlo model of charge transport in hematite that integrates previous findings. The model aims to simulate the interplay between electron transfer processes for extended periods of time in lattices of increasing complexity. The electron transfer reactions considered here involve the IIIII valence interchange between nearest-neighbor iron atoms via a small polaron hopping mechanism. The temperature dependence and anisotropic behavior of the electrical conductivity as predicted by our model are in good agreement with experimental data on hematite single crystals. In addition, we characterize the effect of electron polaron concentration and that of a range of defects on the electron mobility. Interaction potentials between electron polarons and fixed defects (iron substitution by divalent, tetravalent, and isovalent ions and iron and oxygen vacancies) are determined from atomistic simulations, based on the same model used to derive the electron transfer parameters, and show little deviation from the Coulombic interaction energy. Integration of the interaction potentials in the kinetic Monte Carlo simulations allows the electron polaron diffusion coefficient and density and residence time around defect sites to be determined as a function of polaron concentration in the presence of repulsive and attractive defects. The decrease in diffusion coefficient with polaron concentration follows a logarithmic function up to the highest concentration considered, i.e., approximately 2% of iron(III) sites, whereas the presence of repulsive defects has a linear effect on the electron polaron diffusion. Attractive defects are found to significantly affect electron polaron diffusion at low polaron to defect ratios due to trapping on nanosecond to microsecond time scales. This work indicates that electrons can diffuse away from the initial site of interfacial electron transfer at a rate that is consistent with measured electrical conductivities, but that the presence of certain kinds of defects will severely limit the mobility of donated electrons.     

Ab initio electron propagators in molecules with strong electron-phonon interaction. I. Phonon averages

Ab initio electron propagators in molecular systems with strong electron-electron and electron-phonon interactions are considered to study molecular electronic properties. This research is important in electron transfer reactions where the electron transition is not considered any longer as a single electron transfer process or in temperature dependences of current-voltage characteristics in molecular wires or aggregates. To calculate electron Green's functions, the authors apply a small polaron canonical transformation that intrinsically contains strong electron-phonon effects. According to this transformation, the excitation energies of the noninteracting Hamiltonian are shifted down by the relaxation (solvation) energy for each state. The electron-electron interaction is also renormalized by the electron-phonon coupling. For some values of the electron-phonon coupling constants, the renormalized Coulomb integrals can be negative resulting in the attraction between two electrons. Within this transformation, they develop a diagrammatic expansion for electron Green's function in which the electron-phonon interaction is included into the multiple phonon correlation functions. The multiple phonon correlation functions are exactly found. It is pointed out that Wick's theorem for such correlation functions is invalid. Consequently, there is no Dyson equation for electron Green's functions. The proposed approach can be considered for future method developments for quantum chemical calculations that include strong nonadiabatic (non-Born-Oppenheimer) effects.     

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

We calculate the hole and electron mobilities in naphthalene crystal from 10 to 300 K within the framework of the Holstein-Peierls model coupled with first-principles density-functional-theory-projected tight-binding band structures. All the electron-phonon coupling constants, including both local and nonlocal parts for inter- and intramolecular vibrations, have been taken into considerations through density functional theory. The band-hopping crossover transition temperature for the electron transport in the c' axis is calculated to be around 23 K. We have identified a few high frequency intramolecular vibrations which are very important to the charge transport in naphthalene crystal due to their comparatively large electron-phonon coupling constants. However, their contributions to the temperature dependence of mobility are minor because of the small phonon occupations and small nonlocal coupling strengths. The low frequency intermolecular modes (longitudinal optical modes) are found to be the major contributions to the temperature dependent charge transfer properties in naphthalene crystal. Even though the calculated qualitative temperature dependence is in agreement with experiment, the predicted absolute mobility is about one to two orders of magnitude larger.     

Mixed quantum-classical simulations of charge transport in organic materials: numerical benchmark of the Su-Schrieffer-Heeger model

The electron-phonon coupling is critical in determining the intrinsic charge carrier and exciton transport properties in organic materials. In this study, we consider a Su-Schrieffer-Heeger (SSH) model for molecular crystals, and perform numerical benchmark studies for different strategies of simulating the mixed quantum-classical dynamics. These methods, which differ in the selection of initial conditions and the representation used to solve the time evolution of the quantum carriers, are shown to yield similar equilibrium diffusion properties. A hybrid approach combining molecular dynamics simulations of nuclear motion and quantum-chemical calculations of the electronic Hamiltonian at each geometric configuration appears as an attractive strategy to model charge dynamics in large size systems "on the fly," yet it relies on the assumption that the quantum carriers do not impact the nuclear dynamics. We find that such an approximation systematically results in overestimated charge-carrier mobilities, with the associated error being negligible when the room-temperature mobility exceeds ～4.8 cm(2)∕Vs (～0.14 cm(2)/Vs) in one-dimensional (two-dimensional) crystals.     

Base sequence effects on transport in DNA

Given the success of the polaron model based on solvation in accounting for the width of a hole polaron on an all-adenine (A) sequence on DNA, we extend the calculations to other sequences. We find excellent agreement with the free energy differences measured by Lewis et al. (J. Am. Chem. Soc. 2000, 122, 12037-12038) between a guanine (G) cation and a pair of bases, GG, or a triple of bases, GGG, in all cases surrounded by As, by treating AGGA and AGGGA as solvated polarons. There is additional support for hole polaron formation in DNA from experiments in which oxidative damage due to injected holes is investigated in sequences involving Gs and As. Theory and comparison with transport measurements on repeated sequences involving multiple thymines (Ts) or combinations such as ATs or GCs, where C is cytosine, led to the suggestion that the basic sequences in these cases must be polarons whose wave functions have substantial amplitudes on both chains in a duplex. The size of an electron polaron in DNA is predicted to be similar to that of a hole polaron, approximately 4 or 5 bases. Although experiments have shown that polaron hopping is the dominant mode of charge transport in DNA with repeated sequences such as AGGA, further investigations, particularly of temperature dependence of site energies and transfer integrals, are needed to determine to what extent hole transport takes place by polaron hopping for arbitrary DNA sequences.     

A vibronic approach to the band-filling and temperature-dependent metal-insulator transition

A model of vibronic origin is used to investigate the important issue of metal-insulator transition in low-dimensional materials. For zero temperature, the stability of the single-band model chain is controlled by the competition between the internal electron-phonon coupling and the nearest-neighbor hopping integral. Assuming one particular deformation mode, one can analytically derive an instability criterion in which the band filling is explicitly included. The carrier doping directly controls the stability of a one-dimensional chain. For a half-filled band, the Peierls instability is recovered. For finite temperatures, a similar criterion is derived and can be used to investigate the metal-insulator transition temperatures.     

Quantum effect induced kinetic molecular sieving of hydrogen and deuterium in microporous materials

We report here our investigations using Monte Carlo and molecular dynamics (MD) simulations, as well as quasi-elastic neutron scattering experiments, to study the adsorption and diffusion of H₂ and D₂ in zeolite Rho. In the simulations, quantum effects are incorporated via the Feynman-Hibbs variational approach. At low temperatures, we observe a reversal of kinetic molecular sieving in which D₂ diffuses faster than H₂. Based on fits of bulk data, we suggest new set of potential parameters for hydrogen, with the Feynman-Hibbs variational approach used for quantum corrections. The transport properties obtained from MD simulations are in excellent agreement with the experimental results, with both showing significant quantum effects on the transport at low temperature. The MD simulation results on two different structures of zeolite Rho clearly demonstrate that the quantum effect is very sensitive to pore size. High transport flux selectivity is noted at low temperatures, suggesting feasibility of kinetic isotope separation.     

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.     

Monte Carlo simulation based on dynamic disorder model in organic semiconductors: from coherent to incoherent transport

The dynamic disorder model for charge carrier transport in organic semiconductors has been extensively studied in recent years. Although it is successful on determining the value of bandlike mobility in the organic crystalline materials, the incoherent hopping, the typical transport characteristic in amorphous molecular semiconductors, cannot be described. In this work, the decoherence process is taken into account via a phenomenological parameter, say, decoherence time, and the projective and Monte Carlo method are applied for this model to determine the waiting time and thus the diffusion coefficient. It is obtained that the type of transport is changed from coherent to incoherent with a sufficiently short decoherence time, which indicates the essential role of decoherence time in determining the type of transport in organics. We have also discussed the spatial extent of carriers for different decoherence time, and the transition from delocalization (carrier resides in about 10 molecules) to localization is observed. Based on the experimental results of spatial extent, we estimate that the decoherence time in pentacene has the order of 1 ps. Furthermore, the dependence of diffusion coefficient on decoherence time is also investigated, and corresponding experiments are discussed.     

Mechanistic study of proton transfer and HD exchange in ice films at low temperatures (100-140 K)

We have examined the elementary molecular processes responsible for proton transfer and HD exchange in thin ice films for the temperature range of 100-140 K. The ice films are made to have a structure of a bottom D(2)O layer and an upper H(2)O layer, with excess protons generated from HCl ionization trapped at the D(2)OH(2)O interface. The transport behavior of excess protons from the interfacial layer to the ice film surface and the progress of the HD exchange reaction in water molecules are examined with the techniques of low energy sputtering and Cs(+) reactive ion scattering. Three major processes are identified: the proton hopping relay, the hop-and-turn process, and molecular diffusion. The proton hopping relay can occur even at low temperatures (<120 K), and it transports a specific portion of embedded protons to the surface. The hop-and-turn mechanism, which involves the coupling of proton hopping and molecule reorientation, increases the proton transfer rate and causes the HD exchange of water molecules. The hop-and-turn mechanism is activated at temperatures above 125 K in the surface region. Diffusional mixing of H(2)O and D(2)O molecules additionally contributes to the HD exchange reaction at temperatures above 130 K. The hop-and-turn and molecular diffusion processes are activated at higher temperatures in the deeper region of ice films. The relative speeds of these processes are in the following order: hopping relay>hop and turn>molecule diffusion.     

环聚炔苯和环聚炔吡啶组成的盘状液晶中的电荷转移

用电子转移的半经典模型在量子化学B3LYP/6-31G(d)水平(对单体)和B3LYP/STO-3G水平(对二聚物)对环聚炔苯和环聚炔吡啶组成的盘状液晶体系的电荷转移性质进行了研究. 盘状液晶体系的电荷转移速率主要依赖于重组能和电荷转移矩阵元, 重组能越小, 电荷转移矩阵元越大, 则电荷转移速率常数越大. 计算结果表明, 这些大环化合物比目前广泛研究和应用的苯并菲衍生物组成的液晶有较小的重组能, 所以有更好的电荷转移性质. 计算结果对有效地设计和合成高效的光导材料和载流子输送材料是有帮助的.     

Communication: Standard surface hopping predicts incorrect scaling for Marcus' golden-rule rate: the decoherence problem cannot be ignored

We evaluate the accuracy of Tully's surface hopping algorithm for the spin-boson model for the case of a small diabatic coupling parameter (V). We calculate the transition rates between diabatic surfaces, and we compare our results to the expected Marcus rates. We show that standard surface hopping yields an incorrect scaling with diabatic coupling (linear in V), which we demonstrate is due to an incorrect treatment of decoherence. By modifying standard surface hopping to include decoherence events, we recover the correct scaling (~V(2)).