Time-dependent probability of quantum tunneling in terms of the quasisemiclassical method

In view of the rapid progress in experiments of the tunneling dynamics in the time domain, we develop a quasisemiclassical method that is aimed at a study of the proton-transfer dynamics in a large system such as tropolone and its interesting derivatives, to which not only full quantum mechanics, but even a standard semiclassical theory is never easy to apply. In our very tractable method for multidimensional systems, the tunneling paths are generated in terms of the generalized classical mechanics, but the quantum phases arising from the action integral, the Maslov index, and the semicalssical amplitude factor as well in the semiclassical kernels are entirely neglected. This approach is called the quasisemiclassical method. One of the technical issues involved in the general semiclassical scheme is how to locate points from which a tunneling path emanates. Hence the studies of such tunneling points and the quasisemiclassical method should be examined collectively. We test several ways of determining the tunneling point, including those already proposed in the literature and a newly proposed one. It is shown numerically that the quasisemiclassical method with an appropriate choice of tunneling points reproduces the full quantum mechanical tunneling probability reasonably well. This case study indicates that the present conventional approach is promising to the study of large systems. The role of tunneling points in the initial process of tunneling is also discussed.     

Density dynamics in some quantum systems

The quantum domain behavior of classical nonintegrable systems is well‐understood by the implementation of quantum fluid dynamics and quantum theory of motion. These approaches properly explain the quantum analogs of the classical Kolmogorov–Arnold–Moser type transitions from regular to chaotic domain in different anharmonic oscillators. Field‐induced tunneling and chaotic ionization in Rydberg atoms are also analyzed with the help of these theories. Quantum fluid density functional theory may be used to understand different time‐dependent processes like ion‐atom/molecule collisions, atom‐field interactions, and so forth. Regioselectivity as well as confined atomic/molecular systems and their reactivity dynamics have also been explained. © 2013 Wiley Periodicals, Inc.     

Tunneling time in driven double-well system using entangled molecular dynamics method

We calculate quantum tunneling time in the double-well system without perturbation and with symmetry-breaking driven force using the entangled trajectory molecular dynamics method in the present article. Without perturbation, quantum tunneling time decreased with the increase of the energy, and the different contributions of the barrier traversal time and the intrinsic decay time have been shown. The tunneling time dependence on the amplitude and frequency of the symmetry-breaking driven force are present. In the case of weak driven force, tunneling time has a minimum value in the resonant frequency. For strong driven force, chaos brings a huge change to quantum dynamics, tunneling time significantly becomes short. Finally, we directly show the enhancement of quantum tunneling process by chaotic behavior of entangled trajectories and indicate that it was caused by quantum effect.     

Quantum corrections to classical time-correlation functions: hydrogen bonding and anharmonic floppy modes

Several simple quantum correction factors for classical line shapes, connecting dipole autocorrelation functions to infrared spectra, are compared to exact quantum data in both the frequency and time domain. In addition, the performance of the centroid molecular dynamics approach to line shapes and time-correlation functions is compared to that of these a posteriori correction schemes. The focus is on a tunable model that is able to describe typical hydrogen bonding scenarios covering continuously phenomena from tunneling via low-barrier hydrogen bonds to centered hydrogen bonds with an emphasis on floppy modes and anharmonicities. For these classes of problems, the so-called "harmonic approximation" is found to perform best in most cases, being, however, outperformed by explicit centroid molecular dynamics calculations. In addition, a theoretical analysis of quantum correction factors is carried out within the framework of the fluctuation-dissipation theorem. It can be shown that the harmonic approximation not only restores the detailed balance condition like all other correction factors, but that it is the only one that also satisfies the fluctuation-dissipation theorem. Based on this analysis, it is proposed that quantum corrections of response functions in general should be based on the underlying Kubo-transformed correlation functions.     

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.     

Trajectory on-the-fly molecular dynamics approach to tunneling splitting in the electronic excited state: A case of tropolone

The semiclassical tunneling method is applied to evaluate the tunneling splitting of tropolone due to the intramolecular proton transfer in the electronic excited state, first time, in a framework of the trajectory on-the-fly molecular dynamics (TOF-MD) approach. To prevent unphysical zero-point vibrational energy transfer among the normal modes of vibration, quantum zero-point vibrational energies are assigned only to the vibrational modes related to intramolecular proton transfer, whereas the remaining modes are treated as bath modes. Practical ways to determine the tunnel-initiating points and tunneling path are introduced. It is shown that the tunneling splitting decreases as the bath-mode energy increases. The experimental tunneling splitting value is well reproduced by the present TOF-MD approach based on the Wentzel-Kramers-Brillouin (WKB) approximation.     

Quantum tunneling in a periodically driven double well system: Entangled trajectory molecular dynamics method

We study a wavepacket tunneling in one‐dimensional periodically driven double‐well system using entangled trajectory molecular dynamics method. The tunneling dynamics dependents on the amplitude and frequency of the driven force are present. Both resonant and nonresonant tunneling process are enhanced by the driven force when the system is chaotic under classical dynamics. We give entangled trajectory in phase space compared to corresponding classical trajectory with same initial state to visually show quantum tunneling process. The average values of quantum tunneling probability after long time evolution have been shown in the parameter spaces, the effect of resonance and chaos on the tunneling dynamics are present. The relation between chaos and the uncertainly product is discussed in the end. © 2016 Wiley Periodicals, Inc.     

Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.     

Low temperature electron transfer in strongly condensed phase

Electron transfer coupled to a collective vibronic degree of freedom is studied in strongly condensed phase and at lower temperatures where quantum fluctuations are essential. Based on an exact representation of the reduced density matrix of the electronic + reaction coordinate compound in terms of path integrals, recent findings on the overdamped limit in quantum dissipative systems are employed. This allows us to give a consistent generalization of the well-known Zusman equations to the quantum domain. Detailed conditions for the range of validity are specified. Using the Wigner transform these results are also extended to the quantum dynamics in full phase space. As an important application electronic transfer rates are derived that comprise adiabatic and nonadiabatic processes in the low temperature regime including nuclear tunneling. Accurate agreement with precise quantum Monte Carlo data is observed.     

Concerted hydrogen exchange tunneling in formic acid dimer

The effect of conformational relaxation on the quantum dynamics of the hydrogen exchange tunneling is studied in the D2h subspace of formic acid dimer. The fully coupled quantum dynamics in up to six dimensions are derived for potential energy hypersurfaces interpolated directly from hybrid density functional calculations with and without geometry relaxation. For a calculated electronic barrier height of 35.0 kJ/mol the vibrational ground state shows a tunneling splitting of 0.0013 cm(-1). The results support the vibrational assignment of Madeja and Havenith [J. Chem. Phys. 2002, 117, 7162-7168]. Fully coupled ro-vibrational calculations demonstrate the compatibility of experimentally observed inertia defects with in-plane hydrogen exchange tunneling dynamics in formic acid dimer.     

DOIT: a program to calculate thermal rate constants and mode‐specific tunneling splittings directly from quantum‐chemical calculations

In this contribution we discuss computational aspects of a recently introduced method for the calculation of proton tunneling rate constants, and tunneling splittings, which has been applied to molecules and complexes, and should apply equally well to bulk materials. The method is based on instanton theory, adapted so as to permit a direct link to the output of quantum‐chemical codes. It is implemented in the DOIT (dynamics of instanton tunneling) code, which calculates temperature‐dependent tunneling rate constants and mode‐specific tunneling splittings. As input, it uses the structure, energy, and vibrational force field of the stationary configurations along the reaction coordinate, computed by conventional quantum‐chemical programs. The method avoids the difficult problem of calculating the exact least‐action trajectory, known as the instanton path, and instead focusses on the corresponding instanton action, because it governs the dynamic properties. To approximate this action for a multidimensional system, the program starts from the one‐dimensional instanton action along the reaction coordinate, which can be obtained without difficulty. It then applies correction terms for the coupling to the other vibrational degrees of freedom, which are treated as harmonic oscillators (transverse normal modes). The couplings are assumed linear in these modes. Depending on the frequency and the character of the transverse modes, they may either decrease or increase the action, i.e., help or hinder the transfer. A number of tests have shown that the program is at least as accurate as alternative programs based on transition‐state theory with tunneling corrections, and is also much less demanding in computer time, thus allowing application to much larger systems. An outline of the instanton formalism is presented, some new developments are introduced, and special attention is paid to the connection with quantum‐chemical codes. Possible sources of error are investigated. To show the program in action, calculations are presented of tunneling rates and splittings associated with triple proton transfer in the chiral water trimer. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 787–801, 2001     

Resonance enhanced tunneling in an asymmetric double well potential: The 2B1Σ+ state of HCl

We investigate the exact quantum tunneling dynamics using a density matrix approach in the 2B¹Σ⁺ state of HCl which has recently been calculated to be an asymmetric double well potential. With the exact dynamics and a simple model of the collisional interaction process the transfer rate shows strong resonance enhancement for particular rotational states. The transmission coefficient approach, commonly used in tunneling calculations, shows no such features. This system suggests the possibility of the experimental observation of such rotationally induced tunneling resonances (perhaps in HCl in the gas phase). Although not strongly coupled to the environment itself the large resonance effects, caused by near degeneracies, in this system suggest that in treating systems which are strongly coupled to their environment (such as in the solid state) the exact quantum dynamics should be used rather than the transmission coefficient model.     

Vibrational stimulation of the coherent tunneling transition in the cyclopentanone molecule

The tunneling interconversion of the cyclopentanone molecule, which leads to the appearance of tunneling doublets in the microwave spectrum of the system, is studied. The dynamics of interconversion is described by two generalized coordinates, one of which corresponds to bending (non-tunneling promoting mode), while the other of which corresponds to twisting of the molecular plane (tunneling coordinate). The coupling between two coordinates is symmetric. A method for quasi-classical calculation of the wave functions in the tunneling region and of the tunneling splittings of the vibrationally excited states in a two-dimensional potential with symmetric coupling is proposed. The tunneling spectrum of cyclopentanone is calculated. It agrees well with the experimental one, and the tunneling splitting increases by 140 times when the transverse quantum number goes from 0 to 6. The dynamic effect of the vibrationally assisted tunneling is shown to be due to the increase in the width of the tunneling channel with the quantum number of bending mode, as well as to the simultaneous shortening of the tunneling distance. The transition state geometry is found using the wave function at the dividing line of the potential.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2098–2105, December, 1994.This work was supported by the Russian Foundation for Basic Research (Project 94-03-08863). The authors express their gratitude to W. Miller for helpful discussions and to H. Nakamura for a preprint of their work.     

Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.     

Quantum escape kinetics over a fluctuating barrier

The escape rate of a particle over a fluctuating barrier in a double-well potential exhibits resonance at an optimum value of correlation time of fluctuation. This has been shown to be important in several variants of kinetic model of chemical reactions. We extend the analysis of this phenomenon of resonant activation to quantum domain to show how quantization significantly enhances resonant activation at low temperature due to tunneling.     

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.     

Quantum rate dynamics for proton transfer reaction in a model system: effect of the rate promoting vibrational mode

We extended our previous calculation of the quantum rate dynamics for a model system of proton transfer (PT) reaction using the Liouville space hierarchical equations of motion method in this study. A rate promoting vibrational (RPV) mode that symmetrically coupled to the proton coordinate was included in the quantum dynamics calculations, in order to study the effect of enhanced tunneling by the proton donor-acceptor motion. Adding the RPV mode is observed to increase the PT rate and reduce the kinetic isotope effects. We also found that the PT dynamics is influenced by the dissipation of the RPV mode. Besides this extension, in the case without the RPV, we investigated whether the PT rate dynamics in the deep tunneling regime can reduce to an effective two-state spin-boson type of model and found that this is only possible at low reorganization energies.     

Visualizing Progressive Atomic Change in the Metal Surface Structure Made by Ultrafast Electronic Interactions in an Ambient Environment

Understanding the atomic and molecular phenomena occurring in working catalysts and nanodevices requires the elucidation of atomic migration originating from electronic excitations. The progressive atomic dynamics on metal surface under controlled electronic stimulus in real time, space, and gas environments are visualized for the first time. By in situ environmental transmission electron microscopy, the gas molecules introduced into the biased metal nanogap could be activated by electron tunneling and caused the unpredicted atomic dynamics. The typically inactive gold was oxidized locally on the positive tip and field‐evaporated to the negative tip, resulting in the atomic reconstruction on the negative tip surface. This finding of a tunneling‐electron‐attached‐gas process will bring new insights into the design of nanostructures such as nanoparticle catalysts and quantum nanodots and will stimulate syntheses of novel nanomaterials not seen in the ambient environment.