Possible electronic decay channels in the ionization spectra of small clusters composed of Ar and Kr: a four-component relativistic treatment

In this work single and double ionization spectra of the homo- and heteronuclear argon/krypton dimers and trimers are calculated by means of propagator methods where a four-component implementation was employed for the single ionizations. Scalar relativistic effects play only a minor role for the outer valence spectral structure, whereas spin-orbit coupling and electron correlation have to be treated adequately in order to reproduce the features correctly. Nonradiative decay mechanisms of subvalence vacancies in the argon and krypton dimers and trimers are discussed both for the interatomic Coulombic decay and the electron transfer mediated decay (ETMD). In the heteronuclear triatomic system which serves as a model for larger clusters, a possible ETMD process of the Ar 3s vacancy is found for the linear arrangement of the atoms. In the bent configuration the ETMD channel is closed.     

Quantum tunneling effect in entanglement dynamics

Quantum tunneling effect in entanglement dynamics between two coupled particles with separable Gaussian initial state is investigated using entangled trajectory molecular dynamics method in terms of the reduced‐density linear entropy. It has been presented through showing distinguish contribution of single trajectory to linear entropy between classical trajectory and entangled trajectory with same initial state. We find that quantum tunneling effect makes single trajectory's contribution remarkably decrease under quantum dynamics compared to classical dynamics. The nonlocality of quantum entanglement is presented, and the energy transfer between two coupled particles through quantum correlations and classical ones is also discussed in the end. © 2015 Wiley Periodicals, Inc.     

Electronic decay following ionization of aqueous Li+ microsolvation clusters

Ionization in the energetical range between 35 eV and 75 eV of aqueous Li(+) microsolvation clusters may initialize several different electronic decay processes. Electronic decay following H(2)O 2s ionization in a cationic cluster is reported. Li ionization probes the efficiency of electron transfer mediated decay (ETMD) processes. We report estimated ETMD lifetimes in the range of 20-100 fs for clusters with one to five water monomers. Furthermore, tertiary electron emission may occur via a combined cascade of electron transfer mediated decay and intermolecular Coulombic decay.     

Massively parallel spin–orbit configuration interaction

We describe a new approach to incorporating quantum effects into chemical reaction rate theory using quantum trajectories. Our development is based on the entangled trajectory molecular dynamics method for simulating quantum processes using trajectory integration and ensemble averaging. By making dynamical approximations similar to those underlying classical transition state theory, quantum corrections are incorporated analytically into the quantum rate expression. We focus on a simple model of quantum decay in a metastable system and consider the deep tunneling limit where the classical rate vanishes and the process is entirely quantum mechanical. We compare our approximate estimate with the well-known WKB tunneling rate and find qualitative agreement.     

Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations

The non-relativistic quantum dynamics of nuclei and electrons is solved within the framework of quantum hydrodynamics using the adiabatic representation of the electronic states. An on-the-fly trajectory-based nonadiabatic molecular dynamics algorithm is derived, which is also able to capture nuclear quantum effects that are missing in the traditional trajectory surface hopping approach based on the independent trajectory approximation. The use of correlated trajectories produces quantum dynamics, which is in principle exact and computationally very efficient. The method is first tested on a series of model potentials and then applied to study the molecular collision of H with H(2) using on-the-fly TDDFT potential energy surfaces and nonadiabatic coupling vectors.     

Computation of correlation functions and wave function projections in the context of quantum trajectory dynamics

The de Broglie-Bohm formulation of the Schrodinger equation implies conservation of the wave function probability density associated with each quantum trajectory in closed systems. This conservation property greatly simplifies numerical implementations of the quantum trajectory dynamics and increases its accuracy. The reconstruction of a wave function, however, becomes expensive or inaccurate as it requires fitting or interpolation procedures. In this paper we present a method of computing wave packet correlation functions and wave function projections, which typically contain all the desired information about dynamics, without the full knowledge of the wave function by making quadratic expansions of the wave function phase and amplitude near each trajectory similar to expansions used in semiclassical methods. Computation of the quantities of interest in this procedure is linear with respect to the number of trajectories. The introduced approximations are consistent with approximate quantum potential dynamics method. The projection technique is applied to model chemical systems and to the H+H(2) exchange reaction in three dimensions.     

Quantum evolution speed and its limit in the driven double-well system

We investigate quantum evolution speed in the driven double-well system using the entangled trajectory molecular dynamics method. We emphasize not only the evolution speed of the quantum state but also its limit according to different definitions. The Wasserstein 1-distance is used to quantify the distance between distinguishable quantum states in the phase space, the quantum speed limit based on the geometry has been shown to be the strictest one. The single trajectory's contribution to the quantum speed limit is discussed, which is related to both the time evolution of the trajectory and its position in the total Wigner function. The resonance and chaos strongly enhance the evolution speed and its limit in the driven double-well system. The resonance effect makes a large proportion of representative points pass through the well as a whole, nevertheless, the chaos makes the Wigner function disperse in the phase space.     

Electronic quantum trajectories in a quantum dot

This article gives a quantum‐trajectory demonstration of the observed electric, magnetic, and thermal effects on a quantum dot with circular or elliptic shape. By applying quantum trajectory method to a quantum dot, we reveal the quantum‐mechanical meanings of the classical concepts of backscattering and commensurability, which were used in the literature to explain the peak locations of the magnetoresistance curve. Under the quantum commensurability condition, electronic quantum trajectories in a circular quantum dot are shown to be stationary like a standing wave, whose presence increases the electrical resistance. A hidden quantum effect called magnetic stagnation is discovered and shown to be the main cause of the observed jumps of the magnetoresistance curve. Quantum trajectories in an elliptic quantum dot are found to be chaotic and an index of chaos called Lyapunov exponent is proposed to measure the irregularity of the various quantum trajectories. It is shown that the response of the Lyapunov exponent to the applied magnetic field captures the main features of the experimental magnetoresistance curve. © 2014 Wiley Periodicals, Inc.     

Classical probability matrix: Prediction of quantum-state distributions by a moment analysis of classical trajectories

A new method is presented for extracting approximate quantum mechanical state-to-state transition probabilities from the results of classical trajectory calculations. The method recognizes quantum discreteness by dealing with the quantum mechanical probability matrix, but all dynamical quantities are evaluated by classical mechanics. It is illustrated by application to the linear atom-diatom collision (vibrational excitation); it is capable of treating both classically allowed and classically forbidden processes.     

Non-Born-Oppenheimer molecular dynamics of Na...FH photodissociation

The accuracy of non-Born-Oppenheimer (electronically nonadiabatic) semiclassical trajectory methods for simulations of "deep quantum" systems is reevaluated in light of recent quantum mechanical calculations of the photodissociation of the Na...FH van der Waals complex. In contrast to the conclusion arrived at in an earlier study, semiclassical trajectory methods are shown to be qualitatively accurate for this system, thus further validating their use for systems with large electronic energy gaps. Product branching in semiclassical surface hopping and decay-of-mixing calculations is affected by a region of coupling where the excited state is energetically forbidden. Frustrated hops in this region may be attributed to a failure of the treatment of decoherence, and a stochastic model for decoherence is introduced into the surface hopping method and is shown to improve the agreement with the quantum mechanical results. A modification of the decay-of-mixing method resulting in faster decoherence in this region is shown to give similarly improved results.     

Theories and Applications of Mixed Quantum-Classical Non-adiabatic Dynamics

Electronically non-adiabatic processes are essential parts of photochemical process, collisions of excited species, electron transfer processes, and quantum information processing. Various non-adiabatic dynamics methods and their numerical implementation have been developed in the last decades. This review summarizes the most significant development of mixed quantum-classical methods and their applications which mainly include the Liouville equation, Ehrenfest mean-field, trajectory surface hopping, and multiple spawning methods. The recently developed quantum trajectory mean-field method that accounts for the decoherence corrections in a parameter-free fashion is discussed in more detail.     

Constraints at the transition state of the D + H2 reaction: quantum bottlenecks vs. stereodynamics

This article presents a quasiclassical trajectory method for the calculation of cumulative reaction probabilities by sampling of the helicity quantum number of the reagents (k). The method is applied to the D + H(2) reaction at various total angular momentum (J) values, and the helicity-resolved quasiclassical cumulative reaction probabilities are compared to their quantum mechanical counterparts. The agreement between the two sets of results is fairly good. In particular, k-dependent, J-independent reaction thresholds found with quantum methods are reproduced by the quasiclassical calculations. The shift of these thresholds with increasing k, which has been previously attributed to the quantum bottleneck states taking part in the reaction, is revisited and discussed also in terms of the reaction stereodynamics.     

Energy conserving approximations to the quantum potential: dynamics with linearized quantum force

Solution of the Schrodinger equation within the de Broglie-Bohm formulation is based on propagation of trajectories in the presence of a nonlocal quantum potential. We present a new strategy for defining approximate quantum potentials within a restricted trial function by performing the optimal fit to the log-derivatives of the wave function density. This procedure results in the energy-conserving dynamics for a closed system. For one particular form of the trial function leading to the linear quantum force, the optimization problem is solved analytically in terms of the first and second moments of the weighted trajectory distribution. This approach gives exact time-evolution of a correlated Gaussian wave function in a locally quadratic potential. The method is computationally cheap in many dimensions, conserves total energy and satisfies the criterion on the average quantum force. Expectation values are readily found by summing over trajectory weights. Efficient extraction of the phase-dependent quantities is discussed. We illustrate the efficiency and accuracy of the linear quantum force approximation by examining a one-dimensional scattering problem and by computing the wavepacket reaction probability for the hydrogen exchange reaction and the photodissociation spectrum of ICN in two dimensions.     

Quantum initial value representation simulation of water trimer far infrared absorption spectrum

We extend the technique of quantum propagation on a grid of trajectory guided coupled coherent states to simulate experimental absorption spectra. The approach involves calculating the thermally averaged dipole moment autocorrelation function by means of quantum propagation in imaginary time. The method is tested on simulation of the far infrared spectrum of water trimer based on a three-dimensional model potential. Results are in good agreement with experiment and with other calculations.     

Synthesizing quantum probability by a single chaotic complex‐valued trajectory

The current trajectory interpretation of quantum mechanics is based on an ensemble viewpoint that the evolution of an ensemble of Bohmian trajectories guided by the same wavefunction Ψ converges asymptotically to the quantum probability . Instead of the Bohm's ensemble‐trajectory interpretation, the present paper gives a single‐trajectory interpretation of quantum mechanics by showing that the distribution of a single chaotic complex‐valued trajectory is enough to synthesize the quantum probability. A chaotic complex‐valued trajectory manifests both space‐filling (ergodic) and ensemble features. The space‐filling feature endows a chaotic trajectory with an invariant statistical distribution, while the ensemble feature enables a complex‐valued trajectory to envelop the motion of an ensemble of real trajectories. The comparison between complex‐valued and real‐valued Bohmian trajectories shows that without the participation of its imaginary part, a single real‐valued trajectory loses the ensemble information contained in the wavefunction Ψ, and this explains the reason why we have to employ an ensemble of real‐valued Bohmian trajectories to recover the quantum probability . © 2015 Wiley Periodicals, Inc.     

Non-Born-Oppenheimer trajectories with self-consistent decay of mixing

A semiclassical trajectory method, called the self-consistent decay of mixing (SCDM) method, is presented for the treatment of electronically nonadiabatic dynamics. The SCDM method is a modification of the semiclassical Ehrenfest (SE) method (also called the semiclassical time-dependent self-consistent-field method) that solves the problem of unphysical mixed final states by including decay-of-mixing terms in the equations for the evolution of the electronic state populations. These terms generate a force, called the decoherent force (or dephasing force), that drives the electronic component of each trajectory toward a pure state. Results for several mixed quantum-classical methods, in particular the SCDM, SE, and natural-decay-of-mixing methods and several trajectory surface hopping methods, are compared to the results of accurate quantum mechanical calculations for 12 cases involving five different fully dimensional triatomic model systems. The SCDM method is found to be the most accurate of the methods tested. The method should be useful for the simulation of photochemical reactions.     

Multidimensional reactive scattering with quantum trajectories: dynamics with Morse vibrational modes

The reactive scattering of a wave packet is studied by the quantum trajectory method for a model system with up to 25 Morse vibrational modes. The equations of motion are formulated in curvilinear reaction path coordinates with the restriction to a planar reaction path. Spatial derivatives are evaluated by the least squares method using contracted basis sets. Dynamical results, including trajectory evolution and time-dependent reaction probabilities, are presented and analyzed. For the case of one Morse vibrational mode, the results are in good agreement with those derived through direct numerical integration of the time-dependent Schrodinger equation.