Time-dependent Wavepacket Diffusion Method Research Articles

Perturbation expansions of stochastic wavefunctions for open quantum systems.

Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.

Charge Carrier Mobilities and Singlet Fission Dynamics in Thienoquinoidal Compounds

The charge carrier mobilities and singlet fission (SF) dynamics in newly synthesized three thienoquinoidal compounds (ThBF, TThBF, and BThBF) are theoretically characterized by combining a time-dependent wavepacket diffusion method and electronic structure calculations. It is found that all three compounds have quite large electron and hole mobilities and that ThBF possesses the property of p-type semiconductor, whereas TThBF and BThBF show the behavior of n-type semiconductor. For the SF efficiency, TThBF should be the best candidate among the three molecular crystals due to a strong electronic coupling. The obvious correlation between charge carrier mobilities and the SF dynamics is not found; however, the expansion of exciton wave function in the aggregates of these compounds can accelerate the SF process, consistent with other experimental and theoretical observations.

Quantum Interference in Singlet Fission: J- and H-Aggregate Behavior.

The quantum interference in singlet fission (SF) among the multiple pathways from singlet excited states to correlated triplet pair states is comprehensively investigated. The analytical analysis reveals that this interference is strongly affected by the exciton-exciton coupling and is closely related to the property of J- and H-type of aggregates. Different from the interference in the spectra of aggregates, which depends only on the sign of exciton-exciton coupling, the interference in SF is additionally related to the signs of couplings between singlet excited states and triplet pair states. The interference dynamics is further demonstrated numerically by a time-dependent wavepacket diffusion method with electron-phonon interactions incorporated. Finally, we take a pentacene dimer as a concrete example to show how to adjust the constructive and destructive interferences in SF dynamics in terms of J-/H-aggregate behaviors. The results presented here may provide guiding principles for designing efficient SF materials through directly tuning quantum interference via morphology engineering.

Effects of Charge Transfer State and Exciton Migration on Singlet Fission Dynamics in Organic Aggregates

A time-dependent wavepacket diffusion method is used to investigate the effects of charge transfer (CT) states, singlet exciton, and multiexciton migrations on singlet fission (SF) dynamics in organic aggregates. The results reveal that the incorporation of CT states can result in SF dynamics different from the direct interaction between singlet exciton and multiexciton, and an obvious SF interference is also observed between the direct channel and the indirect channel mediated by CT states. In the case of direct interaction, although the fast population transfer of singlet exciton in monomers, caused by the increase of exciton–exciton interaction, can accelerate the SF process, the spatial coherence alternatively has a counter-productive effect, and their competition leads to an optimal exciton–exciton interaction at which SF has a maximal rate. This trade-off relationship in SF dynamics is further analyzed from different perspectives, specifically in spatial and energy representations, and is also confi...

Large-scale conductivity-tensor calculations for Hall effects in time-dependent wave-packet diffusion method

We present a computational methodology to evaluate the conductivity tensors of ``large-scale'' systems in a magnetic field based on the time-dependent wave-packet diffusion method. As demonstrations, we first apply the method to the two-dimensional square lattice model with static disorder and confirm appropriate magnetic-field dependence of conductivities from weak to strong magnetic-field regimes. Furthermore, we extend the method to apply to realistic systems and evaluate the influence of dynamical disorder on the Hall effects of organic semiconductors, taking microscopic molecular vibrations into account.

Energy relaxation and separation of a hot electron-hole pair in organic aggregates from a time-dependent wavepacket diffusion method.

The time-dependent wavepacket diffusive method [X. Zhong and Y. Zhao, J. Chem. Phys. 138, 014111 (2013)] is extended to investigate the energy relaxation and separation of a hot electron-hole pair in organic aggregates with incorporation of Coulomb interaction and electron-phonon coupling. The pair initial condition generated by laser pulse is represented by a Gaussian wavepacket with a central momentum. The results reveal that the hot electron energy relaxation is very well described by two rate processes with the fast rate much larger than the slow one, consistent with experimental observations, and an efficient electron-hole separation is accomplished accompanying the fast energy relaxation. Furthermore, although the extra energy indeed helps the separation by overcoming the Coulomb interaction, the width of initial wavepacket is much sensitive to the separation efficiency and the narrower wavepacket generates the more separated charges. This behavior may be useful to understand the experimental controversy of the hot carrier effect on charge separation.

Coherent quantum transport in disordered systems: II. Temperature dependence of carrier diffusion coefficients from the time-dependent wavepacket diffusion method

The time-dependent wavepacket diffusion method for carrier quantum dynamics (Zhong and Zhao 2013 J. Chem. Phys. 138 014111), a truncated version of the stochastic Schrödinger equation/wavefunction approach that approximately satisfies the detailed balance principle and scales well with the size of the system, is applied to investigate the carrier transport in one-dimensional systems including both the static and dynamic disorders on site energies. The predicted diffusion coefficients with respect to temperature successfully bridge from band-like to hopping-type transport. As demonstrated in paper I (Moix et al 2013 New J. Phys. 15 085010), the static disorder tends to localize the carrier, whereas the dynamic disorder induces carrier dynamics. For the weak dynamic disorder, the diffusion coefficients are temperature-independent (band-like property) at low temperatures, which is consistent with the prediction from the Redfield equation, and a linear dependence of the coefficient on temperature (hopping-type property) only appears at high temperatures. In the intermediate regime of dynamic disorder, the transition from band-like to hopping-type transport can be easily observed at relatively low temperatures as the static disorder increases. When the dynamic disorder becomes strong, the carrier motion can follow the hopping-type mechanism even without static disorder. Furthermore, it is found that the memory time of dynamic disorder is an important factor in controlling the transition from the band-like to hopping-type motions.

Wave-packet approach to transport properties of carrier coupled with intermolecular and intramolecular vibrations of organic semiconductors

We present a methodology to study the charge-transport properties of organic semiconductors by the time-dependent wave-packet diffusion method, taking the polaron effects into account. As an example, we investigate the transport properties of single-crystal pentacene organic semiconductors coupled with inter- and intramolecular vibrations within the mixed Holstein and Peierls model, which describes both hopping and bandlike transport behaviors due to small and large polaron formations. Taking into account static disorders, which inevitably exist in the molecular crystals, we present the temperature dependence of charge-transport properties in competition among the thermal fluctuation of molecular motions, the polaron formation, and the static disorders.

Electron Mobilities of n-Type Organic Semiconductors from Time-Dependent Wavepacket Diffusion Method: Pentacenequinone Derivatives

The electron mobilities of two n-type pentacenequinone derivative organic semiconductors, 5,7,12,14-tetraaza-6,13-pentacenequinone (TAPQ5) and 1,4,8,11-tetraaza-6,13-pentacenequinone (TAPQ7), are investigated with use of the methods of electronic structure and quantum dynamics. The electronic structure calculations reveal that the two key parameters for the control of electron transfer, reorganization energy and electronic coupling, are similar for these two isomerization systems, and the charge carriers essentially display one-dimensional transport properties. The mobilities are then calculated by using the time-dependent wavepacket diffusion approach in which the dynamic fluctuations of the electronic couplings are incorporated via their correlation functions obtained from molecular dynamics simulations. The predicted mobility of TAPQ7 crystal is about six times larger than that of TAPQ5 crystal. Most interestingly, Fermi's golden rule predicts the mobilities very close to those from the time-dependent wavepacket diffusion method, even though the electronic couplings are explicitly large enough to make the perturbation theory invalid. The possible reason is analyzed from the dynamic fluctuations.

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.

Hall conductivity calculations by the time-dependent wave-packet diffusion method

We formulate to calculate the Hall conductivities using the time-dependent wave-packet diffusion (TD-WPD) method, which enables us to treat carrier transport in a magnetic field without any direct numerical diagonalization of the Hamiltonian, and thus to obtain a magnetoconductivity in a large system. The obtained Hall mobility from the Hall coefficient ${R}_{H}$ in disordered systems shows good agreement with the mobility obtained from the diagonal part of the conductivity.