Stationary phase evaluations of quantum rate constants

We compute the quantum rate constant based on two extended stationary phase approximations to the imaginary-time formulation of the quantum rate theory. The optimized stationary phase approximation to the imaginary-time flux-flux correlation function employs the optimized quadratic reference system to overcome the inaccuracy of the quadratic expansion in the standard stationary phase approximation, and yields favorable agreements with instanton results for both adiabatic and nonadiabatic processes in dissipative and nondissipative systems. The integrated stationary phase approximation to the two-dimensional barrier free energy is particularly useful for adiabatic processes and demonstrates consistent results with the imaginary-time flux-flux correlation function approach. Our stationary phase methods do not require calculation of tunneling paths or stability matrices, and work equally well in the high-temperature and the low-temperature regimes. The numerical results suggest their general applicability for calibration of imaginary-time methods and for the calculation of quantum rate constants in systems with a large number of degrees of freedom.     

The origin of charge localization observed in organic photovoltaic materials

Two of the primary hurdles facing organic electronics and photovoltaics are their low charge mobility and the inability to disentangle morphological and molecular effects on charge transport. Specific chemical groups such as alkyl side chains are often added to enable spin-casting and to improve overall power efficiency and morphologies, but their exact influence on mobility is poorly understood. Here, we use two-photon photoemission spectroscopy to study the charge transport properties of two organic semiconductors, one with and one without alkyl substituents (sexithiophene and dihexyl-sexithiophene). We show that the hydrocarbon side chains are responsible for charge localization within 230 fs. This implies that other chemical groups should be used instead of alkyl ligands to achieve the highest performance in organic photovoltaics and electronics.     

Simultaneous studies of pressure effect on charge transport and photophysical properties in organic semiconductors: A theoretical investigation

High-mobility and strong luminescent materials are essential as an important component of organic photodiodes, having received extensive attention in the field of organic optoelectronics. Beyond the conventional chemical synthesis of new molecules, pressure technology, as a flexible and efficient method, can tune the electronic and optical properties reversibly. However, the mechanism in organic materials has not been systematically revealed. Here, we theoretically predicted the pressure-depended luminescence and charge transport properties of high-performance organic optoelectronic semiconductors, 2,6-diphenylanthracene (DPA), by first-principle and multi-scale theoretical calculation methods. The dispersion-corrected density functional theory (DFT-D) and hybrid quantum mechanics/molecular mechanics (QM/MM) method were used to get the electronic structures and vibration properties under pressure. Furthermore, the charge transport and luminescence properties were calculated with the quantum tunneling method and thermal vibration correlation function. We found that the pressure could significantly improve the charge transport performance of the DPA single crystal. When the applied pressure increased to 1.86 GPa, the hole mobility could be doubled. At the same time, due to the weak exciton coupling effect and the rigid flat structure, there is neither fluorescence quenching nor obvious emission enhancement phenomenon. The DPA single crystal possesses a slightly higher fluorescence quantum yield ～ 0.47 under pressure. Our work systematically explored the pressure-dependence photoelectric properties and explained the inside mechanism. Also, we proposed that the external pressure would be an effective way to improve the photoelectric performance of organic semiconductors.     

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.     

Semiclassical treatment of thermally activated electron transfer in the intermediate to strong electronic coupling regime under the fast dielectric relaxation

The generalized nonadiabatic transition-state theory (NA-TST) (Zhao, Y.; et al. J. Chem. Phys. 2004, 121, 8854) is used to study electron transfer with use of the Zhu-Nakamura (ZN) formulas of nonadiabatic transition in the case of fast dielectric relaxation. The rate constant is expressed as a product of the well-known Marcus formula and a coefficient which represents the correction due to the strong electronic coupling. In the case of general multidimensional systems, the Monte Carlo approach is utilized to evaluate the rate by taking into account the multidimensionality of the crossing seam surface. Numerical demonstration is made by using a model system of a collection of harmonic oscillators in the Marcus normal region. The results are naturally coincident with the perturbation theory in the weak electronic coupling limit; while in the intermediate to strong electronic coupling regime where the perturbation theory breaks down the present results are in good agreement with those from the quantum mechanical flux-flux correlation function within the model of effective one-dimensional mode.     

Charge carrier dynamics in phonon-induced fluctuation systems from time-dependent wavepacket diffusion approach

A time-dependent wavepacket diffusion method is proposed to deal with charge transport in organic crystals. The electron-phonon interactions in both site energies and electronic couplings are incorporated by the time-dependent fluctuations which are generated from the corresponding spectral density functions. The numerical demonstrations reveal that the present approach predicts the consistent charge carrier dynamics with the rigorous quantum approaches. In addition, the diffusion coefficients obtained from the Marcus formula are well reproduced at the weak electronic coupling and high temperature limits. It is also found that the charge mobility feature of the crossover from the band-like to the hopping-type cannot be predicted from the fluctuations induced by the linear electron-phonon interactions with an Ohmic spectral density; however, it indeed appears as the electronic coupling fluctuation exponentially depends on the nuclear coordinates. Finally, it should be noted that although the present approach neglects the imaginary fluctuation, it essentially incorporates the coherent motion of the charge carrier and quantum effect of the phonon motion with a broad regime of the fluctuations for symmetric systems. Besides, the approach can easily be applied to systems having thousands of sites, which allows one to investigate charge transport in nanoscale organic crystals.     

Techniques for characterization of charge carrier mobility in organic semiconductors

The charge transport characteristics of organic semiconductors are one of the key attributes that impacts the performance of organic electronic and optoelectronic devices in which they are utilized. For improved performance in organic photovoltaic cells, light-emitting diodes, and field-effect transistors (FETs), efficient transport of the charge carriers within the organic semiconductor is especially critical. Characterization of charge transport in these organic semiconductors is important both from scientific and technological perspectives. In this review, we shall mainly discuss the techniques for measuring the charge carrier mobility and not the theoretical underpinnings of the mechanism of charge transport. Mobility measurements in organic semiconductors and particularly in conjugated polymers, using space-charge-limited current, time of flight, carrier extraction by linearly increasing voltage, double injection, FETs, and impedance spectroscopy are discussed. The relative merits, as well as limitations for each of these techniques are reviewed. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Theoretical study on the charge transport properties of triphenylene discogens with a phenylpropionyloxy or 3-phenylpropenoyloxy side chain

Charge transport is one of the most important properties in organic materials. Charge transport properties of triphenylene discogens with a phenylpropionyloxy or 3-phenylpropenoyloxy side chain have been investigated computationally on the basis of semi-classical Marcus theory. The results show that three triphenylene derivatives have high charge mobility. Title compounds have much better electronic mobility than the triphenylene. The triphenylenes containing 3-phenylpropenoyloxy have better hole mobility, but smaller electronic mobility than the triphenylenes with phenylpropionyloxy. For the triphenylene discogens with a phenylpropionyloxy, the longer the alkloxy chains, the better the positive charge transfer rate, but the smaller the negative charge transfer rate. Supported by the National Natural Science Foundation of China (Grant No. 50673069), the Research Foundation of Education Bureau of Sichuan Province, China (Grant No. 07ZA093), and Scientific Research Foundation of Sichuan Normal University for Innovation Groups ( Grant No. 025156)     

Crystal packing and charge transport in single crystals of chrysene derivatives: Impact of halogenation

Crystal packing has strong influence on the charge mobility for organic semiconductors, so the elucidation of the structure-property relationship is important for the design of high-performance organic semiconductors. Halogen substitution has been shown to be a promising strategy to alter the crystal structure without significantly changing the molecular size in previous reports. This paper studies the influence of halogenation on charge transport in single crystals of chrysene derivatives from a theoretical standpoint. The structure-property relationship is first rationalized by investigating the reorganization energy and electronic coupling from the density functional theory calculations. Based on the Marcus charge transfer theory, the mobilities in the molecular monolayer are then calculated with the random walk simulation technique from which the angular resolution anisotropic mobilities are obtained on the fly. It is shown that the mobilities become much larger for holes than those for electrons in the molecular monolayer when the halogenation occurs. Furthermore, the intra-layer charge transport is little influenced by the inter-layer pathways in the single crystals of the halogenated chrysene derivatives, while the opposite case is shown for the crystal of the nonhalogenated chrysene derivative. The reason for the variations of charge transport is discussed theoretically.     

Dependence of charge transfer reorganization energy on carrier localisation in organic molecular crystals

Taking the organic molecular material dithiophene-tetrathiafulvalene (DT-TTF) as an example of a high mobility organic molecular material, we use density functional calculations to calculate the dependency of the reorganization energy associated with charge carrier transport on: (i) the geometric and electronic responsiveness of the local molecular crystal environment, and, (ii) the local spatial extent of the charge carrier. We find that in our most realistic extended models the charge transfer reorganization energy is strongly dependent on carrier localization. In particular, whereas highly localized carriers are found to be highly susceptible to their charge transfer efficiency being affected by changes in the local crystal environment, more delocalized carriers are better able to maintain their low reorganization energies. Considering that maintaining a relatively small charge transfer reorganization energy magnitude is an important factor in achieving high carrier mobilities, we suggest that those materials better able to sustain carriers with short-range thermally resistant intermolecular delocalisation should be sought for device applications.     

Excess charge delocalization in organic and biological molecules: some theoretical notions

Theoretical and computational investigations of the excess charge distribution (ECD) in molecular complexes have attracted considerable attention as ECD is closely related to electronic properties of organic semiconductors, such as the efficiency of photoinduced charge separation in organic solar cells and charge transport in DNA and proteins. In this paper, we analyze the ECD in several representative models on the basis of ab initio and DFT calculations. We consider how changes in the reorganization energy, electronic coupling and charge transfer energy affect the ECD in the systems. In particular, we compare ECD in π stacks of polycyclic aromatic hydrocarbons and DNA nucleobases. While the π interaction between subunits in the systems is similar in both cases, ECD is quite different: the excess charge is found to be completely delocalized over the hydrocarbon stacks but strongly confined to a single nucleobase in DNA stacks. We also discuss the effects of conformational fluctuations on ECD in the stacks. Finally, ECD in amino acids and its dependence on the conformational changes are briefly considered.     

Zero-point fluctuations in naphthalene and their effect on charge transport parameters

We calculate the effect of vibronic coupling on the charge transport parameters in crystalline naphthalene, between 0 and 400 K. We find that nuclear fluctuations can cause large changes in both the energy of a charge on a molecule and on the electronic coupling between molecules. As a result, nuclear fluctuations cause wide distributions of both energies and couplings. We show that these distributions have a small temperature dependence and that, even at high temperatures, vibronic coupling is dominated by the effect of zero-point fluctuations. Because of the importance of zero-point fluctuations, we find that the distributions of energies and couplings have substantial width, even at 0 K. Furthermore, vibronic coupling with high energy modes may be significant, even though these modes are never thermally activated. Our results have implications for the temperature dependence of charge mobilities in organic semiconductors.     

Charge transport parameters of the pentathienoacene crystal

Pentathienoacene, the thiophene equivalent of pentacene, is one of the latest additions to the family of organic crystal semiconductors with a great potential for use in thin film transistors. By using density functional theory and gas-phase ultraviolet photoelectron spectroscopy, we investigate the microscopic charge transport parameters of the pentathienoacene crystal. We find that the valence band exhibits a stronger dispersion than those in the pentacene and rubrene single crystals with marked uniaxial characteristics within the molecular layer due to the presence of one-dimensional pi-stacks; a small hole effective mass is also found along the direction perpendicular to the molecular layers. In the conduction band, strong intermolecular sulfur-sulfur interactions give rise to a significant interstack electronic coupling whereas the intrastack dispersion is greatly reduced. The intramolecular vibronic coupling (reorganization energy) is stronger than that in pentacene but comparable to that in sexithiophene; it is larger for holes than for electrons, as a result of low-frequency modes induced by the sulfur atoms. The polarization energy is large, but its effect on the vibronic coupling remains small. Charge transport is discussed in the framework of both band and hopping models.     

Charge transfer between quasi-zero-dimensional nanostructures

In the present paper, we show the main features of the theoretical formula allowing us to understand the irreversible transfer of electrons or holes, as it may be observed in some electrically conducting (conjugated) polymers. The formula reported here is derived with the use of the nonequilibrium quantum transport theory. The key role in the formula is played by the electron–phonon interaction which is included in an approximation going beyond the limits of the finite order of the perturbation calculation. The transfer formula is developed for a simple model of the stacked conjugated polymer, which is represented here by two interacting quantum dots. The numerical calculations show the dependence of the charge carrier mobility on the charge carrier concentration and on the lattice temperature. A comparison with organic field-effect transistor experiments and with molecular-scale modeling on conjugated polymers is promising.     

Single molecule charge transport: from a quantum mechanical to a classical description

This paper explores charge transport at the single molecule level. The conductive properties of both small organic molecules and conjugated polymers (molecular wires) are considered. In particular, the reasons for the transition from fully coherent to incoherent charge transport and the approaches that can be taken to describe this transition are addressed in some detail. The effects of molecular orbital symmetry, quantum interference, static disorder and molecular vibrations on charge transport are discussed. All of these effects must be taken into account (and may be used in a functional way) in the design of molecular electronic devices. An overview of the theoretical models employed when studying charge transport in small organic molecules and molecular wires is presented.     

Anomalous Charge Transfer from Organic Ligands to Metal Halides in Zero-Dimensional [(C6H5)4P]2SbCl5 Enabled by Pressure-Induced Lone Pair-π Interaction

Low-dimensional (low-D) organic metal halide hybrids (OMHHs) have emerged as fascinating candidates for optoelectronics due to their integrated properties from both organic and inorganic components. However, for most of low-D OMHHs, especially the zero-D (0D) compounds, the inferior electronic coupling between organic ligands and inorganic metal halides prevents efficient charge transfer at the hybrid interfaces and thus limits their further tunability of optical and electronic properties. Here, using pressure to regulate the interfacial interactions, efficient charge transfer from organic ligands to metal halides is achieved, which leads to a near-unity photoluminescence quantum yield (PLQY) at around 6.0 GPa in a 0D OMHH, [(C₆H₅)₄P]₂SbCl₅. In situ experimental characterizations and theoretical simulations reveal that the pressure-induced electronic coupling between the lone-pair electrons of Sb³⁺ and the π electrons of benzene ring (lp-π interaction) serves as an unexpected “bridge” for the charge transfer. Our work opens a versatile strategy for the new materials design by manipulating the lp-π interactions in organic–inorganic hybrid systems.     

The effect of substitution on reorganization energy and charge mobility in metal free phthalocyanine

To gain insight into how the electronic properties of discotic organic materials may be modified through substitution, the reorganization energy and the charge mobility of metal free phthalocyanine, and of several mono-substituted derivatives, are studied by electronic structure methods. It is found that the reorganization energy of phthalocyanine is not significantly changed by substitution on an outer phenyl ring, but is more strongly influenced when the inner crown amine ring is substituted. The relationship between reorganization energy and substituent is studied through the use of; substituent constant, HOMO energy, and geometry relaxation. The computed charge mobility shows stronger relationship to coupling matrix element than reorganization energy. A hybrid computational screening method in which the reorganization energy is calculated at the DFT level and the coupling matrix element is calculated at the AM1 level shows good predicting power for trends in charge mobility at reduced computational expense.     

Influence of lattice dynamics on charge transport in the dianthra[2,3-b:2',3'-f]-thieno[3,2-b]thiophene organic crystals from a theoretical study

The influence of lattice dynamics on carrier mobility has received much attention in organic crystalline semiconductors, because the molecular components are held together by weak interactions and the transfer integrals between neighboring molecular orbitals are extremely sensitive to small nuclear displacements. Recently, it has been shown that the dynamic disorder has little effect on hole mobility in the ab plane of pentacene, but a reasonable explanation is absent for such a puzzle. To better understand the effect of lattice vibrations on carrier transport, a further study is required for other organic materials. In this work, a mixed molecular dynamic and quantum-chemical methodology is used to assess the effect of nuclear dynamics on hole mobility in the dianthra[2,3-b:2',3'-f]-thieno[3,2-b]thiophene (DATT) crystals which exhibit high air stability with the hole mobility as large as that in rubrene-based devices. It is found that the lattice vibrations lead to an increasing encumbrance for hole transport in the ab plane of the DATT crystals as the temperature increases. By comparing the crystal structures of DATT and pentacene, the reduced hole mobility in DATT is attributed to the unsymmetric arrays of nearest-neighboring molecular dimers in the ab plane, because the electronic coupling exhibits unbalanced thermal fluctuations for the nearest-neighboring dimers which then induces a stronger oscillation for carriers along the directions with asymmetric packing. To further relate the dynamic disorder with hole transport, the variations of anisotropic mobilities are also analyzed. As a result, the negligible effect of lattice dynamics on the hole mobility in pentacene is explained by the centrosymmetric molecular packing of the nearest-neighboring molecular pairs in the ab plane.