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.     

Ehrenfest dynamics is purity non-preserving: A necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.     

Influences of molecular packing on the charge mobility of organic semiconductors: from quantum charge transfer rate theory beyond the first-order perturbation

The electronic coupling between adjacent molecules is an important parameter for the charge transport properties of organic semiconductors. In a previous paper, a semiclassical generalized nonadiabatic transition state theory was used to investigate the nonperturbative effect of the electronic coupling on the charge transport properties, but it is not applicable at low temperatures due to the presence of high-frequency modes from the intramolecular conjugated carbon-carbon stretching vibrations [G. J. Nan et al., J. Chem. Phys., 2009, 130, 024704]. In the present paper, we apply a quantum charge transfer rate formula based on the imaginary-time flux-flux correlation function without the weak electronic coupling approximation. The imaginary-time flux-flux correlation function is then expressed in terms of the vibrational-mode path average and is evaluated by the path integral approach. All parameters are computed by quantum chemical approaches, and the mobility is obtained by kinetic Monte-Carlo simulation. We evaluate the intra-layer mobility of sexithiophene crystal structures in high- and low-temperature phases for a wide range of temperatures. In the case of strong coupling, the quantum charge transfer rates were found to be significantly smaller than those calculated using the weak electronic coupling approximation, which leads to reduced mobility especially at low temperatures. As a consequence, the mobility becomes less dependent on temperature when the molecular packing leads to strong electronic coupling in some charge transport directions. The temperature-independent charge mobility in organic thin-film transistors from experimental measurements may be explained from the present model with the grain boundaries considered. In addition, we point out that the widely used Marcus equation is invalid in calculating charge carrier transfer rates in sexithiophene crystals.     

Markov models of molecular kinetics: generation and validation

Markov state models of molecular kinetics (MSMs), in which the long-time statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting long-time kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modeling molecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if non-metastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data.     

On the correspondence between classical and quantum mechanics in macromolecular systems: Too much classical chaos

In a recent study we found the classical dynamics of a polyethylene (PE) chain to exhibit low dimensional chaos at temperatures as low as a few Kelvin. These results strongly suggest that classical molecular dynamic simulations in polymer systems can grossly overestimate vibrational motion, which consequently results in disordered structures. In contrast, quantum mechanical calculations using Internal Coordinate Quantum Monte Carlo (an improved method with an initial conjecture for the correct wave function) indicate that the quantum ground state for a three-dimensional model PE chain is far more rigid than determined from molecular dynamics (MD) simulations, even at energies as low as a small fraction of the ground state energy. This result casts uncertainty on the reliability of MD estimates of dynamical or structural quantities relevant to the study of some macromolecular systems.     

Semi-classical generalized Langevin equation for equilibrium and nonequilibrium molecular dynamics simulation

Molecular dynamics (MD) simulation based on Langevin equation has been widely used in the study of structural, thermal properties of matter in different phases. Normally, the atomic dynamics are described by classical equations of motion and the effect of the environment is taken into account through the fluctuating and frictional forces. Generally, the nuclear quantum effects and their coupling to other degrees of freedom are difficult to include in an efficient way. This could be a serious limitation on its application to the study of dynamical properties of materials made from light elements, in the presence of external driving electrical or thermal fields. One example of such system is single molecule dynamics on metal surface, an important system that has received intense study in surface science. In this review, we summarize recent effort in extending the Langevin MD to include nuclear quantum effect and their coupling to flowing electrical current. We discuss its applications in the study of adsorbate dynamics on metal surface, current-induced dynamics in molecular junctions, and quantum thermal transport between different reservoirs.     

量子耗散与量子输运的级联方程组方法

级联方程已成为研究量子开放系统的稳态性质和动力学过程的重要方法。本文旨在系统综述量子耗散和量子输运的级联方程组方法的建立、发展以及在理论、算法和应用方面的一些最新进展。级联方程形式理论的建立以影响泛函路径积分为基础,并具有数值上的高效性和应用上的灵活性,可用于研究分子体系的复杂动力学过程以及强关联电子体系中的量子输运。其级联耦合结构以非微扰的方式揭示了多体相互作用、体系-环境耦合、非马尔可夫记忆等的综合效应。作为应用示例,我们采用级联方程模拟了生物光富集体系的二维相干动力学光谱以及含时电子输运过程中的动态近藤效应。     

A hybrid explicit/implicit solvation method for first-principle molecular dynamics simulations

In this work, we present a hybrid explicit/implicit solvation model, well suited for first-principles molecular dynamics simulations of solute-solvent systems. An effective procedure is presented that allows to reliably model a solute with a few explicit solvation shells, ensuring solvent bulk behavior at the boundary with the continuum. Such an approach is integrated with high-level ab initio methods using localized basis functions to perform first-principles or mixed quantum mechanics/molecular mechanics simulations within the extended-Lagrangian formalism. A careful validation of the model along with illustrative applications to solutions of acetone and glycine radical are presented, considering two solvents of different polarity, namely, water and chloroform. Results show that the present model describes dynamical and solvent effects with an accuracy at least comparable to that of conventional approaches based on periodic boundary conditions.     

A theoretical study of the charge transfer behavior of the highly regioregular poly-3-hexylthiophene in the ordered state

We use quantum mechanical (QM) methods to interpret the charge transport properties of the self-assembled poly-3-hexylthiophene (P3HT) molecules along the intrachain and interchain directions. Our approach is illustrated by a hopping transport model, in which we examine the variation of the electron-coupling strength (transfer integral) with the torsional angle and the intermolecular distance between two adjacent thiophene segments. We also simulate the packed P3HT structures at various values of temperature and regioregularity via the molecular dynamics (MD) simulations. The MD results indicate that with decreasing the molecular regioregularity and/or increasing temperature, the P3HT backbone chains experience a larger distortion of the thiophene rings out of coplanarity, and thus the charge mobility along the main chains is reduced. However, as long as the P3HT molecules remain in the ordered lamellar state due to the presence of the pi-pi interaction, the resultant mobility along the pi-pi interchain direction is still significantly less than that along the intrachain direction. Accordingly, the main charge transfer route within the P3HT ordered domains is along the intrachains instead of the interchains.     

An accurate and simple quantum model for liquid water

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.     

共轭高分子光电功能材料的多尺度性能研究——聚合物电子学领域中的新机遇

共轭高分子材料特异的金属或半导体的电子特性兼有质轻、价廉、易于加工的优点使其在有机场效应晶体管、有机太阳能电池和有机发光二极管等领域显示了重要的应用前景.然而,尽管经过几十年的不断研究,共轭高分子材料种类及其相关器件性能均已得到显著发展,但是共轭高分子材料的本征电荷传输特性仍不清楚,其研究面临巨大挑战,这主要是由共轭高分子材料本身分子量分布弥散、分子间相互缠结以及在常规旋涂薄膜器件中分子高度无序等特性所决定的.从调控共轭高分子聚集态结构的角度出发,不断提高共轭高分子的结构有序性及减小电荷传输过程中的晶界及缺陷密度,是实现共轭高分子材料本征性能认识的有效途径之一.本文首先简单归纳总结了研究者在共轭高分子多尺度聚集态结构调控及性能研究方面的初步结果,进一步结合国内外相关研究进展,重点对共轭高分子晶体方面的工作展开详细介绍,最后对该领域未来发展的挑战及机遇进行了简单评述.     

Photoinduced electron transport process in electrochemical cell I. Phenomenological description

The process of electron transport plays an essential role in the fundamental phenomena of life like photosynthesis, respiration and vision as well as in photoelectronic devices. However, the molecular mechanisms of the electron way and factors governing the transport rate in such systems are still unclear. Several groups have reported theoretical approaches for searching the mechanisms by using statistical mechanics, coherent dynamics and quantum mechanics. The current density vector inside the semiconducting layer is determined. In this paper we consider the problem of transport of electron promoted in the electrochemical cell constructed of two electrodes with the dye molecules immersed in. We describe the process of electron promotion by refractive light wave on the vacuum–semiconductor boundary as well as on the semiconducting electrode and the dye molecule layer in terms of extended phenomenological electrodynamics formalism. The results of our theoretical model show that such a theoretical approach will give more information on the mechanism of electron transport and will give insight in the determination of some electric features of materials.     

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.     

Dynamical mean-field theory from a quantum chemical perspective

We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.     

A statistical mechanical theory of proton transport kinetics in hydrogen-bonded networks based on population correlation functions with applications to acids and bases

Extraction of relaxation times, lifetimes, and rates associated with the transport of topological charge defects in hydrogen-bonded networks from molecular dynamics simulations is a challenge because proton transfer reactions continually change the identity of the defect core. In this paper, we present a statistical mechanical theory that allows these quantities to be computed in an unbiased manner. The theory employs a set of suitably defined indicator or population functions for locating a defect structure and their associated correlation functions. These functions are then used to develop a chemical master equation framework from which the rates and lifetimes can be determined. Furthermore, we develop an integral equation formalism for connecting various types of population correlation functions and derive an iterative solution to the equation, which is given a graphical interpretation. The chemical master equation framework is applied to the problems of both hydronium and hydroxide transport in bulk water. For each case it is shown that the theory establishes direct links between the defect's dominant solvation structures, the kinetics of charge transfer, and the mechanism of structural diffusion. A detailed analysis is presented for aqueous hydroxide, examining both reorientational time scales and relaxation of the rotational anisotropy, which is correlated with recent experimental results for these quantities. Finally, for OH(-)(aq) it is demonstrated that the "dynamical hypercoordination mechanism" is consistent with available experimental data while other mechanistic proposals are shown to fail. As a means of going beyond the linear rate theory valid from short up to intermediate time scales, a fractional kinetic model is introduced in the Appendix in order to describe the nonexponential long-time behavior of time-correlation functions. Within the mathematical framework of fractional calculus the power law decay ～t(-σ), where σ is a parameter of the model and depends on the dimensionality of the system, is obtained from Mittag-Leffler functions due to their long-time asymptotics, whereas (stretched) exponential behavior is found for short times.