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An efficient and accurate method for computing the equilibrium reduced density matrix is presented for treating open quantum systems characterized by the system-bath model. The method employs the multilayer multiconfiguration time-dependent Hartree theory for imaginary time propagation and an importance sampling procedure for calculating the quantum mechanical trace. The method is applied to the spin-boson Hamiltonian, which leads to accurate results in agreement with those produced by the multi-electronic-state path integral molecular dynamics method.

In this paper, we report a magnetic and conductive textile made from a mixture of NdFeB microparticles, multi-walled carbon nanotubes, and polydimethylsiloxane. The textile can (i) shield 99.8% of electromagnetic signals ranging from 30 MHz to 3 GHz, thereby protecting people from damage caused by the electromagnetic radiation, (ii) be hydrophobic and fire retardant, making it a possible choice for raincoat and fire protection clothing, and (iii) convert mechanical energy into electricity through both electromagnetic induction and triboelectrification. The textile creates many opportunities in the fields of multifunctional protective equipment and energy harvesting.

We present a self-cleaning organic solar cells (OSCs) with a light-trapping structure by introducing a groove-shaped micro/nanostructured haze thin films (GHFs). The GHF with periods larger than wavelengths of incident light can broaden the effective optical paths and promote the diffused lights, while keeping high (low) total transmission (reflectance) properties. When laminated GHF on top of the light-in side of OSCs, the power conversion efficiency of OSCs is improved more than 10%. Simultaneously, the superhydrophobic GHF composed of the groove structure allows the droplets to successfully remove dust particles from the polydimethylsiloxane (PDMS) surface during the roll-off process of the drop. Under 10 cycles of dust contamination and cleaning treatment, OSCs with GHF can still guarantee an initial efficiency of 84% (76%), showing great potentials of OSCs in practical applications.

The stochastic differential equation is a powerful tool for describing the dynamics of a dissipative system in which noise characterizes the influence of the environment. For the Ornstein-Uhlenbeck noise, both the formula of differentiation and the hierarchy approach provide efficient numerical simulations, with the stochastic differential equation transformed into a set of coupled, linear ordinary differential equations. We show that while these two deterministic schemes result in different sets of equations, they can be regarded as two representations of an underlying linear-dynamics. Moreover, by manipulating the involved Ornstein-Uhlenbeck noise, we propose a unified algorithm that may reduce to the hierarchy approach or the formula of differentiation in different limits. We further analyze the numerical performance of this algorithm and find that the hierarchy approach appears to be more efficient for our numerical model studies.

We relate the memory kernel in the Nakajima–Zwanzig–Mori time-convolution approach to the reduced system propagator which is often used to obtain the kernel in the Tokuyama–Mori time-convolutionless approach. The connection provides a robust and simple formalism to compute the memory kernel for a generalized system-bath model circumventing the need to compute high order system-bath observables, thus streamlining the use of numerically exact solvers for calculating the memory kernel. We illustrate this for a model system with electron-electron and electron-phonon couplings, driven away from equilibrium.

Within the framework of the hierarchy equation of motion (HEOM), the quantum kinetic expansion (QKE) method of the spin-boson model is reformulated in the matrix representation. The equivalence between the two formulations (HEOM matrices and quantum operators) is numerically verified from the calculation of the time-integrated QKE rates. The matrix formulation of the QKE is extended to the system-bath factorized initial state. Following a one-to-one mapping between HEOM matrices and quantum operators, a quantum kinetic equation is rederived. The rate kernel is modified by an extra term following a systematic expansion over the site-site coupling. This modified QKE is numerically tested for its reliability by calculating the time-integrated rate and non-Markovian population kinetics. For an intermediate-to-strong dissipation strength and a large site-site coupling, the population transfer is found to be significantly different when the initial condition is changed from the local equilibrium to system-bath factorized state.

The semiclassical (SC) initial value representation (IVR) provides a way for including quantum effects into classical molecular dynamics simulations. Implementation of the SC-IVR to the thermal rate constant calculation, based on the reactive flux correlation function formalism, has two major obstacles: (1) the SC integrand may be highly oscillatory with respect to the initial phase space variables; and (2) matrix elements of the Boltzmannized flux operator, which are crucial in generating the initial (or final) distribution for the SC trajectories, are generally not available in analytic forms. In this paper, we present practical ways of overcoming these two barriers for the SC calculation of thermal rate constants. For the first problem, we show that use of a symmetric flux–flux correlation function, together with the generalized Filinov transformation technique, can significantly smooth the corresponding SC integrand and make the calculation practical for quite large systems. For the second problem, we propose a general method for evaluating matrix elements of the Boltzmannized flux operator “on-the-fly,” based on the combination of the imaginary-time path integral technique with the Metropolis random walk algorithm. Using these approaches, it is shown that thermal rate constants can be obtained for systems with more than 100 degrees of freedom, as well as for reactions in the deep tunneling regimes where quantum effects are significant.

The multilayer multiconfiguration time-dependent Hartree method is applied in an interaction picture to simulate dynamics of the spin-boson model in the reaction-coordinate representation. The use of the interaction picture allows a more effective description of correlation effects, especially when the coupling strength between the reaction coordinate and the bath is very strong. Examples show that in most physical regimes the efficiency is improved significantly, in some cases up to several orders of magnitude. This opens up new avenues for studying quantum dynamical problems.

The self-consistent hybrid approach [H. Wang, M. Thoss, and W. H. Miller, J. Chem. Phys. 115, 2979 (2001), preceding paper] is applied to the spin-boson problem with Debye spectral density as a model for electron-transfer reactions in a solvent exhibiting Debye dielectric relaxation. The population dynamics of the donor and acceptor states in this system is studied for a broad range of parameters, including the adiabatic (slow bath), nonadiabatic (fast bath), as well as the intermediate regime. Based on illustrative examples we discuss the transition from damped coherent dynamics to purely incoherent decay. Using the numerically exact results of the self-consistent hybrid approach as a benchmark, several approximate theories that have been widely used to describe the dynamics in the spin-boson model are tested: the noninteracting blip approximation, the Bloch–Redfield theory, the Smoluchowski-equation treatment of the reaction coordinate (Zusman equations), and the classical path approach (Ehrenfest model). The parameter range where the different methods are applicable are discussed in some detail.

An efficient method, the self-consistent hybrid method, is proposed for accurately simulating time-dependent quantum dynamics in complex systems. The method is based on an iterative convergence procedure for a dynamical hybrid approach. In this approach, the overall system is first partitioned into a “core” and a “reservoir” (an initial guess). The former is treated via an accurate quantum mechanical method, namely, the time-dependent multiconfiguration self-consistent field or multiconfiguration time-dependent Hartree approach, and the latter is treated via a more approximate method, e.g., classical mechanics, semiclassical initial value representations, quantum perturbation theories, etc. Next, the number of “core” degrees of freedom, as well as other variational parameters, is systematically increased to achieve numerical convergence for the overall quantum dynamics. The method is applied to two examples of quantum dissipative dynamics in the condensed phase: the spin-boson problem and the electronic resonance decay in the presence of a vibrational bath. It is demonstrated that the method provides a practical way of obtaining accurate quantum dynamical results for complex systems.

The capability of two different, recently proposed semiclassical (SC) forward–backward (FB) initial value representations (IVR) to describe quantum interference and coherence effects is investigated. It is shown that depending on the way the observable under consideration is represented by unitary operators one can obtain rather different results. Although the FB-IVR based on an integral representation as a rule is capable of describing quantum interference, a closer analysis reveals that it depends on the observable under consideration if all interference that can be described semiclassically is actually included in the calculation. To overcome this problem a new, generalized FB-IVR method (GFB-IVR) is proposed, which combines the capability of the SC-IVR to describe quantum interference effects independent of the observable and the better convergence properties of the FB-IVR. The performance of this new approach is studied in some detail. In particular, it is shown that the GFB-IVR can describe both the...

It is shown that the forward–backward (FB) version of the semiclassical (SC) initial value representation (IVR) is able to describe quantum interference/coherence (i.e., diffraction) of particles transmitted by a two-slit potential. (In contrast, the linearized approximation to the SC-IVR, which leads to the classical Wigner model, is unable to do so.) FB-IVR calculations are also used to describe the (partial) quenching of this interference structure (i.e., “de-coherence”) when the two-slit potential is coupled to a bath of harmonic oscillators.

The forward–backward (FB) version of the semiclassical (SC) initial value representation (IVR) is used to study quantum coherence effects in the time-dependent probability distribution of an anharmonic vibrational coordinate and its quenching when coupled to a thermal bath. It is shown that the FB-IVR accurately reproduces the detailed quantum coherent structure in the weak coupling regime, and also describes how this coherence is quenched with an increase of the system–bath coupling and/or the bath temperature. Comparisons are made with other approximations and the physical implications are discussed.

The feasibility of using a basis set approach to the study of quantum dissipative dynamics is investigated for the spin-boson model, a system of two discrete states linearly coupled to a harmonic bath. The infinite Hamiltonian is discretized to a finite number of degrees of freedom. Traditional basis set approach, in a multiconfiguration time-dependent Hartree context, is used to solve the time-dependent Schrodinger equations by explicitly including all the degrees of freedom (“system”+“bath”). Quantities such as the reduced density matrix are then evaluated via a quadrature summation/Monte Carlo procedure over a certain number of time-dependent wave functions. Numerically exact results are obtained by systematically increasing the number of bath modes used to represent the condensed phase environment, as well as other variational parameters (number of basis functions, configurations, etc.). The potential of the current method is briefly discussed.

The semiclassical (SC) initial value representation (IVR) provides a potentially practical way for including quantum effects into classical molecular dynamics simulations. The forward–backward (FB) version of the IVR provides an especially attractive way for calculating time correlation functions, in particular the reactive flux correlation function which determines chemical reaction rates. This paper presents a further analysis and development of the FB-IVR approach. Applications show that it is feasible and accurate for a reaction coordinate coupled to up to 40 degrees of freedom.

The linearized semiclassical initial value representation (LSC-IVR) [H. Wang, X. Sun and W. H. Miller, J. Chem. Phys. 108, 9726 (1998)] is used to study the nonadiabatic dynamics of the spin-boson problem, a system of two electronic states linearly coupled to an infinite bath of harmonic oscillators. The spectral density of the bath is chosen to be of the Debye form, which is often used to model the solution environment of a charge transfer reaction. The simulation provides a rather complete understanding of the electronically nonadiabatic dynamics in a broad parameter space, including coherent to incoherent transitions along all three axes (the T-axis, the η-axis, and the ωc-axis) in the complete phase diagram and the determination of rate constants in several physically interesting regimes. Approximate analytic theories are used to compare with the simulation results, and good agreement is found in the appropriate physical limits.

A linearized approximation to the semiclassical initial value representation (SC-IVR), referred to herein as the LSC-IVR, was used by us in a recent paper [J. Chem. Phys. 108, 9726 (1998)] to calculate reactive flux correlation functions for a model of a chemical reaction on a single potential energy surface. This paper shows how the LSC-IVR—which is much easier to apply than the full SC-IVR because it linearizes the phase difference between interfering classical trajectories—can be applied to electronically nonadiabatic processes, i.e., those involving transitions between different potential-energy surfaces. Applications to several model problems are presented to show its usefulness: These are the nonadiabatic scattering problems used by Tully to test surface-hopping models, and also the spin–boson model of coupled electronic states in a condensed phase environment. Though not as accurate as the full SC-IVR, the LSC-IVR does a reasonably good job for all these applications, even describing correctly Stuc...

An earlier paper of ours [J. Chem. Phys. 108, 9726 (1998)] used an approximate (linearized) version of the semiclassical initial value representation (SC-IVR) to calculate reactive flux correlation functions for a model of unimolecular isomerization, namely a 1-d double well potential coupled to an infinite set of harmonic oscillators, obtaining excellent agreement with accurate quantum results for this system. Here we analyze this linearized approximation (LA) further, however, and show that it is not capable of describing quantum interference/coherence effects in the longer time recrossing behavior of the isomerization dynamics. (The recrossing effects seen in our earlier work were due to classical mechanics.) To accentuate quantum effects in the recrossing dynamics, the present article considers the double well potential without the harmonic bath, using both the LA and the full SC-IVR. The results of the calculations show that the flux correlation functions given by the LA agrees well with the exact qu...

Two different semiclassical approaches are presented for extending flux correlation function methodology for computing thermal reaction rate constants, which has been extremely successful for the “direct” calculation of rate constants in small molecule (∼3–4 atoms) reactions, to complex molecular systems, i.e., those with many degrees of freedom. First is the popular mixed quantum-classical approach that has been widely used by many persons, and second is an approximate version of the semiclassical initial value representation that has recently undergone a rebirth of interest as a way for including quantum effects in molecular dynamics simulations. Both of these are applied to the widely studied system-bath model, a one-dimensional double well potential linearly coupled to an infinite bath of harmonic oscillators. The former approximation is found to be rather poor while the latter is quite good.

An efficient method was recently introduced by Thompson and Miller [J. Chem. Phys. 106, 142 (1997)] for calculating thermal rate constants using the flux–flux autocorrelation function with absorbing boundary conditions. The method uses an iterative method to exploit the low rank feature of the Boltzmannized flux operator and subsequently only propagates the eigenvectors that have significant contributions to the rate constant. In the present article, this method is used to calculate the thermal rate constants of the Cl+H2→HCl+H reaction in the temperature range of 200–1500 °K. Total angular momentum is treated by employing the body-fixed axis frame, both exactly and also via various approximations. Comparisons with previous exact and approximate theoretical results are made.

The quasiclassical trajectory (QCT) method was used to study the dynamics of the OH(X 2Π) and OD(X 2Π)+HBr chemical reactions on an empirical potential energy surface (PES). The main emphasis in the calculation was the vibrational energy distributions of H2O (and HDO) and the magnitude and temperature dependence of the rate constant. However, this PES also serves as a generic model for the dynamics of direct H atom abstraction by OH radicals. Since this PES has no formal potential energy barrier, variational transition‐state theory was used to obtain rate constants for comparison with the QCT calculations and experimental results. The parameters of the potential energy surface were adjusted to obtain better agreement with the experimentally measured fraction of H2O vibrational energy, 〈fV(H2O)〉=0.6, without significantly changing the entrance channel. No isotope effect for the partition of energy to H2O vs HOD was found. Analysis of the trajectories indicates that the reactant OH(OD) bond is a spectator, ...

A previous trajectory study of the dissociation of Cl−...CH3Cl complexes formed by Cl−+CH3Cl association is further analyzed to determine (1) the relationship between classical and quantum Rice–Ramsperger–Kassel–Marcus (RRKM) rate constants for Cl−...CH3Cl→Cl−+CH3Cl dissociation; (2) the importance of anharmonicity in calculating the RRKM dissociation rate constant; (3) the role of angular momentum in interpreting the trajectory distribution N(t)/N(0) of Cl−...CH3Cl complexes versus time; and (4) the pressure‐dependent collision‐averaged rate constant k(ω,E) for Cl−...CH3Cl dissociation. It is found that only the low‐frequency intermolecular modes of Cl−...CH3Cl are initially excited by Cl−+CH3Cl association. Classical and quantum RRKM rate constants for dissociation of this intermolecular complex are in excellent agreement. Anharmonicity lowers the rate constant by a factor of 4–8 from its harmonic value. The dissociation rate for the long‐time tail of the trajectory N(t)/N(0) distribution is much smaller than predicted by a RRKM model, which accurately treats angular momentum. It is suggested that the long‐lived trajectories may arise from motion on vague tori. The trajectory collision‐averaged rate constant k(ω,E) is in agreement with an experimental study at 300 K.

Up to now, in most of the research work done on the effect of hydrogen on a Schottky barrier, the hydrogen was introduced into the semiconductor before metal deposition. This letter reports that hydrogen can be effectively introduced into the Schottky barriers (SBs) of Au/n-GaAs and Ti/n-GaAs by plasma hydrogen treatment (PHT) after metal deposition on [100] oriented n-GaAs substrates. The Schottky barrier height (SBH) of a SB containing hydrogen shows the zero/reverse bias annealing (ZBA/RBA) effect. ZBA makes the SBH decrease and RBA makes it increase. The variations in the SBHs are reversible. In order to obtain obvious ZBA/RBA effects, selection of the temperature for plasma hydrogen treatment is important, and it is indicated that 100-degrees-C for Au/n-GaAs and 150-degrees-C for Ti/n-GaAs are suitable temperatures. It is concluded from the analysis of experimental results that only the hydrogen located at or near the metal-semiconductor interface, rather than the hydrogen in the bulk of either the semiconductor or the metal, is responsible for the ZBA/RBA effect on SBH.

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory within second quantization representation of the Fock space, a novel numerically exact methodology to treat many-body quantum dynamics for systems containing identical particles, is applied to study the effect of vibrational motion on electron transport in a generic model for single-molecule junctions. The results demonstrate the importance of electronic-vibrational coupling for the transport characteristics. For situations where the energy of the bridge state is located close to the Fermi energy, the simulations show the time-dependent formation of a polaron state that results in a pronounced suppression of the current corresponding to the phenomenon of phonon blockade. We show that this phenomenon cannot be explained solely by the polaron shift of the energy but requires methods that incorporate the dynamical effect of the vibrations on the transport. The accurate results obtained with the ML-MCTDH in this parameter regime are compared to results of nonequilibrium Green's function (NEGF) theory., Comment: 39 pages, 11 figures

A generalized master equation approach is developed to describe electron transfer (ET) dynamics in the presence of mode mixing. Results from this approximate approach are compared to the numerically exact simulations using the multilayer multiconfiguration time-dependent Hartree theory. The generalized master equation approach is found to work well for nonadiabatic resonant ET. Depending on the specific situation, it is found that the introduction of mode mixing may either increase or decrease the ET time scale. The master equation fails in the adiabatic ET regime, where the introduction of mode mixing may lead to electron trapping. From both the approximate theory and the numerically exact simulation it is shown how neglecting mode mixing in practical calculations may lead to inaccurate predictions of the ET dynamics.

We investigate the influence of strong femtosecond optical pulses on the ultrafast dynamics of molecular systems. The study is based on a series of generic molecular models of increasing complexity, which incorporate multiple and mutually coupled electronic states, electronic-vibrational interaction, and vibrational relaxation. The influence of vibrational relaxation is treated using multilevel Redfield theory. Comparisons to benchmark results of the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method demonstrate the validity of the field-free implementation of Redfield theory employed in this work for weak system-bath interaction. The calculated electronic population and vibrational wave-packet dynamics demonstrate the intricate interplay of strong-field excitation, laser-induced Rabi oscillations, electronic interaction, vibronic coupling, and dissipation. In particular, we show that the interaction with a strong laser pulse may result in pronounced coherent vibrational motion in a dissipative system, even for laser pulses that are longer than the vibrational period. Furthermore, vibrational relaxation in combination with strong laser pulse excitation can lead to revivals of the electronic population after the excitation pulse is over.

A linear Langevin equation that governs the population dynamics of electron transfer reactions is derived. The noise in the Langevin equation is eliminated by treating the diabatic population fluctuations as the relevant variables, leaving only the memory kernel responsible for the population relaxation. Within the memory kernel, the diabatic coupling is treated perturbatively and a second order expansion is found to give a simple closed form expression for the kernel. The accuracy of the second order truncation is maximized by performing a fixed rotation of the diabatic electronic states that minimizes the first order free energy of the system and thus minimizes the effect of the perturbation on the thermodynamics. The resulting two-hop Langevin equation (THLE) is then validated by applying it to a simple spin-boson model, where exact results exist. Excellent agreement is found in a wide parameter range, even where the perturbation is moderately strong. Results obtained in the rotated electronic basis are found to be consistently more accurate than those from the unrotated basis. These benchmark calculations also allow us to demonstrate the advantage of treating the population fluctuations instead of the populations as the relevant variables, as only the former lead to reliable results at long time. Thus, the THLE appears to provide a viable alternative to established methods--such as Ehrenfest dynamics or surface hopping--for the treatment of nonadiabatic effects in electron transfer simulations.

A classical trajectory simulation performed on the PES1(Br) analytic potential energy surface is used to study the atomic-level dynamics of the Cl−+CH3Br→ClCH3+Br−SN2 nucleophilic substitution reaction. At low reactant relative translational energies Erel of less than 5 kcal/mol, the reaction is dominated by an indirect mechanism in which the Cl−⋯CH3Br complex or both the Cl−⋯CH3Br and ClCH3⋯Br− complexes are formed. For Erel>10 kcal/mol a direct reaction mechanism dominates without the formation of either complex. For Erel of 5–10 kcal/mol there is a minimum in the SN2 rate constant which, for a CH3Br vibrational/rotational temperature Tvr of 300 K, is ∼400 times smaller than the rate at Erel of 0.1 kcal/mol. The dependence of the trajectory SN2 rate constants on Erel, Tv, and Tr is significantly different than the prediction of a statistical theoretical model. For Erel⩽10 kcal/mol there is a much more pronounced decrease in the trajectory SN2 rate constant as Erel is increased as compared to the statistical model, which arises from the inadequacy of the ion–molecule capture component of the statistical model. As Erel is increased the trajectory Cl−+CH3Br association rate constant becomes much smaller than that predicted by the ion–molecule capture model. Increasing the CH3Br rotational temperature from 300 to 600 K decreases the trajectory SN2 rate constant more than the prediction of the statistical model. At low Erel, where the reaction occurs by an indirect mechanism, the product energy is preferentially partitioned to CH3Cl vibration. For the direct mechanism, which dominates at high Erel, the majority of the energy is partitioned to product relative translation.