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As popular mixed quantum–classical dynamics methods, trajectory surface hopping and Ehrenfest mean field have been widely utilized to simulate nonadiabatic dynamics. Recently, we have proposed the branching-corrected surface hopping and the branching-corrected mean field methods, both of which closely reproduce the exact quantum dynamics in a series of standard scattering models. Here, the mixed surface hopping and mean field with branching correction (BCSHMF) is presented as a unified framework of mixed quantum–classical dynamics. As benchmarked in thousands of diverse three-level and four-level scattering models, BCSHMF achieves high reliability and flexibility, implying that surface hopping and mean field are compatible with each other in nature, and trajectory branching is essential for the mixed quantum–classical description of nonadiabatic dynamics. [ABSTRACT FROM AUTHOR]

We report a surface hopping approach in which the implemented linear vibronic coupling Hamiltonian is constructed and the electronic wavefunction is propagated in the reciprocal space. The parameters of the linear vibronic coupling model, including onsite energies, phonon frequencies, and electron–phonon couplings, are calculated with density-functional theory and density-functional perturbation theory and interpolated in fine sampling points of the Brillouin zone with maximally localized Wannier functions. Using this approach, we studied the relaxation dynamics of the photo-excited hot carrier in a one-dimensional periodic carbon chain. The results show that the completeness of the number of Hilbert space k points and the number of phonon q points plays an important role in the hot carrier relaxation processes. By calculating the relaxation times of hot carriers under different reciprocal space sampling and extrapolating with the stretched–compressed exponential function, the relaxation times of hot electrons and holes in the quasi-continuous energy band are obtained. By considering the feedback effect in the hopping processes and analyzing the time-dependent phonon energy in different normal modes, we found that the long-wave longitudinal optical phonons play a major role in the relaxation dynamics of hot electrons and holes. We, therefore, provided herein an efficient and accurate approach for modeling the photophysical processes in periodic solid-state material systems. [ABSTRACT FROM AUTHOR]

We present a new algorithm of the branching corrected mean field (BCMF) method for nonadiabatic dynamics [J. Xu and L. Wang, J. Phys. Chem. Lett. 11, 8283 (2020)], which combines the key advantages of the two existed algorithms, i.e., the deterministic BCMF algorithm based on weights of trajectory branches (BCMF-w) and the stochastic BCMF algorithm with random collapse of the electronic wavefunction (BCMF-s). The resulting mixed deterministic–stochastic BCMF algorithm (BCMF-ws) is benchmarked in a series of standard scattering problems with potential wells on the excited-state surfaces, which are common in realistic systems. In all investigated cases, BCMF-ws holds the same high accuracy while the computational time is reduced about two orders of magnitude compared to the original BCMF-w and BCMF-s algorithms, thus promising for nonadiabatic dynamics simulations of general systems. [ABSTRACT FROM AUTHOR]

Disordered or even seemingly amorphous, donor–acceptor type, conjugated copolymers with high charge-carrier mobility have emerged as a new class of functional materials, where transport along the conjugated backbone is key. Here, we report on non-adiabatic molecular dynamics simulations of charge-carrier transport along chains of poly (indacenodithiophene-co-benzothiadiazole), within a model Hamiltonian parameterized against first-principles calculations. We predict thermally activated charge transport associated with a slightly twisted ground-state conformation, on par with experimental results. Our results also demonstrate that the energy mismatch between the hole on the donor vs the acceptor units of the copolymer drives localization of the charge carriers and limits the intra-chain charge-carrier mobility. We predict that room-temperature mobility values in excess of 10 cm2 V−1 s−1 can be achieved through proper chemical tuning of the component monomer units. [ABSTRACT FROM AUTHOR]

Cadmium zinc telluride (CZT) is an ideal material for room temperature nuclear radiation detection, but CZT crystals of high quality and low defects concentration are difficult to obtain. Therefore, in order to improve the performance of the CZT detector, the working conditions of the CZT detector could be appropriately changed to make the internal electric field of the CZT detector close to uniform distribution so as to improve the electron transport performance. In this paper, alpha induced transient charge analysis has been used to study the internal electric field of the CZT detector, and deep level defects in CZT were linked with internal electric field distribution. Based on the process, a variety of deep level defects on electron trapping and detrapping by changing the temperature, the output waveform change of charge sensitive preamplifier (the pulse height spectra for alpha radiation at different temperatures) was observed, and then the effects of deep level defects on electron mobility (μ e), electron transport time (T R), the internal electric field, and the electron collection efficiency of the CZT detector were analyzed. The experimental results indicated that the influence of deep level defects was a main factor to the internal electric field in the range of −140 to 40 °C. As the temperature rises, the influence of these defects weakens, μ e and electron collection efficiency both increase, and internal electric field distribution tends to be uniform. Moreover, with the further increasing temperature (−40 to 20 °C), μ e decreased and internal electric field distribution became fluctuating, but electron collection efficiency was basically unchanged, which suggested that the influence of lattice vibration in the range of −40 to 20 °C turned to be the main factor. The above conclusions demonstrated that although the CZT detector has excellent room temperature detection ability, room temperature was not its optimal working temperature due to the influence of high concentration deep level defects. At −20 °C, the CZT detector presented the highest electron collection efficiency and maximum which limited the influence of deep level defects on electron transport, performing the optimal properties. [ABSTRACT FROM AUTHOR]

Since the seminal work of Tully [J. Chem. Phys. 93, 1061 (1990)], two-level scattering models have been extensively adopted as the standard benchmark systems to assess the performance of different trajectory surface hopping methods for nonadiabatic dynamics simulations. Here, we extend the branching and phase corrections to multilevel systems and combine them with both the traditional fewest switches surface hopping (FSSH) and its variant global flux surface hopping (GFSH) algorithms. To get a comprehensive evaluation of the proposed methods, we construct a series of more challenging and diverse three-level and four-level scattering models and use exact quantum solutions as references. Encouragingly, both FSSH and GFSH with the branching and phase corrections produce excellent and nearly identical results in all investigated systems, indicating that the new surface hopping methods are robust to describe multilevel problems and the reliability is insensitive to the definition of self-consistent hopping probabilities in the adiabatic representation. Furthermore, the branching correction is found to be especially important when dealing with strongly repulsive potential energy surfaces, which are common in realistic systems, thus promising for general applications. [ABSTRACT FROM AUTHOR]

We propose a fuzzy global optimization (FGO) algorithm to identify the lowest-energy structure of nanoclusters. In contrast to traditional methods implemented in the real space, FGO utilizes mostly the discrete space in a fuzzy search framework. Starting from random initial configurations, we carry out directed Monte Carlo and surface Monte Carlo in the discrete space to obtain low-energy candidate clusters and make real-space local optimizations finally to get the real global minimum structure. The performance of FGO is demonstrated in a large set of standard Lennard-Jones (LJ) clusters with up to 1000 atoms. All the putative global minima reported in the literature are successfully obtained with a low scaling of CPU time with cluster size, and new global minimum structures for LJ clusters with 894, 974, and 991 atoms are identified. Due to the unbiased nature, FGO can potentially deal with the global optimization of other nanomaterials with high efficiency and reliability. [ABSTRACT FROM AUTHOR]

Surface hopping (SH) is a popular mixed quantum-classical method for modeling nonadiabatic excited state processes in molecules and condensed phase materials. The method is simple, efficient, and easy to implement, but the use of classical and independent nuclear trajectories introduces an overcoherence in the electronic density matrix which, if ignored, often leads to spurious results, such as overestimated reaction rates. Several methods have been proposed to incorporate decoherence into SH simulations, but a lack of insightful benchmarks makes their relative accuracy unknown. Herein, we run numerical simulations of common coherence-corrected SH methods including Truhlar's decay-of-mixing (DOM) and Subotnik's augmented SH using a Donor-bridge-Acceptor (DbA) model system. Numerical simulations are carried out in the superexchange regime, where charge transfer proceeds from a donor to an acceptor as a result of donor-bridge and bridge-acceptor couplings. The computed donor-to-acceptor reaction rates are compared to the reference Marcus theory results. For the DbA model under consideration, augmented SH recovers Marcus theory with quantitative accuracy, whereas DOM is only qualitatively accurate depending on whether predefined parameters in the decoherence rate are chosen wisely. We propose a general method for parameterizing the decoherence rate in the DOM method, which improves the method's reaction rates and presumably increases its transferability. Overall, the decoherence method of choice must be chosen with great care and this work provides insight using an exactly solvable model. [ABSTRACT FROM AUTHOR]

We present a new interpretation of the decoherence correction in surface hopping by examining the inconsistency of the traditional time-dependent Schrödinger equation and propose an elegant decoherence correction algorithm to deal with wave packet branching. In contrast to the widely used approaches based on decoherence rates, our branching corrected surface hopping (BCSH) resets the wavefunction directly after wave packet branching is identified through prediction of trajectory reflection. The appealing simplicity and reliability of BCSH are demonstrated in a series of widely studied one-dimensional and two-dimensional scattering models using exact quantum solutions and existing surface hopping approaches as references. The BCSH approach exhibits a high performance in all investigated systems, showing good potential for applications in general nonadiabatic dynamics simulations. [ABSTRACT FROM AUTHOR]

We present a semiclassical Moyal dynamics (SMD) method based on the phase space formulation of quantum dynamics. In contrast to the quantized Hamiltonian dynamics approach by Prezhdo et al. using the Heisenberg equation of motion, SMD adopts the Moyal equation of motion to derive the time evolution of expectation values and uses an auxiliary phase space distribution technique to systematically terminate the coupled equations of motion. Thereby, tedious derivation of commutators is essentially not required, and semiclassical dynamics of arbitrary orders can be realized. The appealing simplicity, flexibility, and reliability of SMD are demonstrated in three representative model systems with strong quantum effects. [ABSTRACT FROM AUTHOR]

The branching corrected surface hopping (BCSH) has been demonstrated as a robust approach to improve the performance of the traditional fewest switches surface hopping (FSSH) for nonadiabatic dynamics simulations of standard scattering problems [J. Chem. Phys. 150, 164101 (2019)]. Here, we study how reliable populations of both adiabatic and diabatic states can be interpreted from BCSH trajectories. Using exact quantum solutions and FSSH results as references, we investigate a series of one-dimensional two-level scattering models and illustrate that excellent time-dependent populations can be obtained by BCSH. Especially, we show that different trajectory analysis strategies produce noticeable differences in different representations. Namely, the method based on active states performs better to get populations of adiabatic states, while the method based on wavefunctions produces more reliable results for populations of diabatic states. [ABSTRACT FROM AUTHOR]

Global optimization of Morse clusters with shortrange potential is a great challenge. Here, we apply our recently developed unbiased fuzzy global optimization method to systematically study Morse clusters with the potential range ρ = 14 and the number of atoms N up to 400. All the putative global minima reported in the literature have been successfully reproduced with relatively high success ratios. Compared to the available results for N ≤ 240 and several larger Morse clusters, new global minima (and local minima) with lower energies have been found out for N = 164, 175, 188, 193, 194, 197, 239, 246, 260, 318, and 389. Clusters with magic numbers are figured out through fitting the size-dependent global minimum energies. The cluster structures tend to be close-packed for short-range potential with large N. [ABSTRACT FROM AUTHOR]

The performance of the mean field theory to account for charge transfer rate in molecular dimers and charge transport mobility in molecular stacks with small intermolecular electronic coupling and large local electron-phonon coupling (i.e., in the hopping regime) is carefully investigated against various other approaches. Using Marcus formula as a reference, it is found that mean field theory with system-bath interaction and surface hopping approaches yield fully consistent charge transfer rates in dimers. However, in contrast to the dimer case, incorporating system-bath interaction in the mean field approach results in a completely wrong temperature dependence of charge carrier mobility in larger aggregates. Although the mean field simulation starting from the relaxed geometry of a charged molecule and neglecting system-bath interaction can reproduce thermally activated transport, it is not able to characterize properly the role of additional nonlocal electron-phonon couplings. Our study reveals that the mean field theory must be used with caution when studying charge transport in the hopping regime of organic semiconductors, where the surface hopping approach is generally superior. [ABSTRACT FROM AUTHOR]

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 cm2/Vs (∼0.14 cm2/Vs) in one-dimensional (two-dimensional) crystals. [ABSTRACT FROM AUTHOR]

Semiclassical Marcus electron transfer theory is often employed to investigate the charge transport properties of organic semiconductors. However, quite often the electronic couplings vary several orders of magnitude in organic crystals, which goes beyond the application scope of semiclassical Marcus theory with the first-order perturbative nature. In this work, we employ a generalized nonadiabatic transition state theory (GNTST) [Zhao et al., J. Phys. Chem. A 110, 8204 (2004)], which can evaluate the charge transfer rates from weak to strong couplings, to study charge transport properties in prototypical organic semiconductors: quaterthiophene and sexithiophene single crystals. By comparing with GNTST results, we find that the semiclassical Marcus theory is valid for the case of the coupling <10 meV for quaterthiophene and <5 meV for sexithiophene. It is shown that the present approach can be applied to design organic semiconductors with general electronic coupling terms. Taking oligothiophenes as examples, we find that our GNTST-calculated hole mobility is about three times as large as that from the semiclassical Marcus theory. The difference arises from the quantum nuclear tunneling and the nonperturbative effects. [ABSTRACT FROM AUTHOR]

Overall population errors (k) of FSSH, GFSH, PC-FSSH, PC-GFSH, BC-PC-FSSH, and BC-PC-GFSH averaged over all the 750 models in the MB1 model base. Apparently, PC-FSSH and PC-GFSH eliminate the errors in the high energy region with I k i > 25, while both BC-PC-FSSH and BC-PC-GFSH show excellent performance in all cases. Apparently, PC-FSSH and PC-GFSH eliminate the errors in the high energy region with I k i > 25, while both BC-PC-FSSH and BC-PC-GFSH show excellent performance in all cases. [Extracted from the article]

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. [ABSTRACT FROM AUTHOR]

The quantized Hamiltonian dynamics (QHD) theory provides a hierarchy of approximations to quantum dynamics in the Heisenberg representation. We apply the first-order QHD to study charge transport in molecular crystals and find that the obtained equations of motion coincide with the Ehrenfest theory, which is the most widely used mixed quantum-classical approach. Quantum initial conditions required for the QHD variables make the dynamics surpass Ehrenfest. Most importantly, the first-order QHD already captures the low-temperature regime of charge transport, as observed experimentally. We expect that simple extensions to higher-order QHDs can efficiently represent other quantum effects, such as phonon zero-point energy and loss of coherence in the electronic subsystem caused by phonons. [ABSTRACT FROM AUTHOR]

Surface hopping is the most popular method for nonadiabatic molecular dynamics. Many have reported that it does not rigorously attain detailed balance at thermal equilibrium, but does so approximately. We show that convergence to the Boltzmann populations is significantly improved when the nuclear velocity is reversed after a classically forbidden hop. The proposed prescription significantly reduces the total number of classically forbidden hops encountered along a trajectory, suggesting that some randomization in nuclear velocity is needed when classically forbidden hops constitute a large fraction of attempted hops. Our results are verified computationally using two- and three-level quantum subsystems, coupled to a classical bath undergoing Langevin dynamics.

Recent years have witnessed substantial progress in the surface hopping (SH) formulation of non-adiabatic molecular dynamics. A generalization of the traditional fewest switches SH (FSSH), global flux SH (GFSH) utilizes the gross population flow between states to derive SH probabilities. The Liouville space formulation of FSSH puts state populations and coherences on equal footing, by shifting the hopping dynamics from Hilbert to Liouville space. Both ideas have shown superior results relative to the standard FSSH in Hilbert space, which has been the most popular approach over the past two and a half decades. By merging the two ideas, we develop GFSH in Liouville space. The new method is nearly as straightforward as the standard FSSH, and carries comparable computational expense. Tested with a representative super-exchange model, it gives the best performance among all existing techniques in the FSSH series. The obtained numerical results match almost perfectly the exact quantum mechanical solutions. Moreover, the results are nearly invariant under the choice of a basis state representation for SH, in contrast to the earlier techniques which exhibit notable basis set dependence. Unique to the developed approach, this property is particularly encouraging, because exact quantum dynamics is representation independent. GFSH in Liouville space significantly improves accuracy and applicability of SH for a broad range of chemical and physical processes.

Global flux surface hopping (GFSH) generalizes fewest switches surface hopping (FSSH)—one of the most popular approaches to nonadiabatic molecular dynamics—for processes exhibiting superexchange. We show that GFSH satisfies detailed balance and leads to thermodynamic equilibrium with accuracy similar to FSSH. This feature is particularly important when studying electron-vibrational relaxation and phonon-assisted transport. By studying the dynamics in a three-level quantum system coupled to a classical atom in contact with a classical bath, we demonstrate that both FSSH and GFSH achieve the Boltzmann state populations. Thermal equilibrium is attained significantly faster with GFSH, since it accurately represents the superexchange process. GFSH converges closer to the Boltzmann averages than FSSH and exhibits significantly smaller statistical errors.

We present a nonperturbative quantum master equation to investigate charge carrier transport in organic molecular crystals based on the Liouville space hierarchical equations of motion method, which extends the previous stochastic Liouville equation and generalized master equation methods to a full quantum treatment of the electron-phonon coupling. Diffusive motion of charge carriers in a one-dimensional model in the presence of nonlocal electron-phonon coupling was studied, and two different charge carrier diffusion mechanisms are observed for large and small average intermolecular couplings. The new method can also find applications in calculating spectra and energy transfer in various types of quantum aggregates where the perturbative treatments fail.