Incorporation of quantum effects for selected degrees of freedom into the trajectory-based dynamics using spatial domains

Garashchuk, Sophya; Volkov, Mikhail V.

doi:10.1063/1.4746156

Cited by 14 publications

(17 citation statements)

References 33 publications

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“…This idea has been illustrated in Ref. [43] for QT dynamics with the LQF that depended explicitly on the coordinates of QDOFs, and parametrically on the CDOFs. The procedure was shown to converge with respect to the number of domains for model systems of reactive and non-reactive scattering.…”

Section: Molecular Simulation 93mentioning

confidence: 98%

“…The stretch of HBr bond is the QDOF, x, and the separation of He and centre of mass of the diatomic is the CDOF, y. The parameters, listed in Table 1, come from the fit of ES data to simple functions, [43] …”

Section: 22mentioning

confidence: 99%

“…(For treatment of the interface of adjacent domains see Ref. [43]) For simplicity, consider domains that are associated with a single classical coordinate y, correlating, for example, with the separation of the reactive fragments. The simplest way to set up the domains is to define strips in the y-coordinate, or cells for a multiple CDOFs.…”

Section: Molecular Simulation 93mentioning

confidence: 99%

“…The lth domain, out of their total number L, is defined by a function V l ; V l ðỹÞ. [43] The resulting quantum potential is a sum over the domains of the domain-specific contributions U l :…”

Section: Molecular Simulation 93mentioning

confidence: 99%

“…Separate subsection is devoted to the approximation to the quantum potential defined on subspaces of the classical DOF. [43] The approach is introduced at the formal theoretical level and is, then, illustrated by an example of a collision of He with HBr.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Approximate quantum trajectory dynamics for reactive processes in condensed phase

Garashchuk

Jakowski

Rassolov

2014

Molecular Simulation

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A method of molecular dynamics with quantum corrections, practical for studies of large molecular systems, is reviewed. The approach is based on the Bohmian formulation of the time-dependent Schrödinger equation in which a wavefunction is represented by an ensemble of interdependent trajectories. The quantum effects come from the quantum potential acting on trajectories on par with the usual classical potential. The quantum potential is determined from the evolving nuclear wavefunction, i.e. from the quantum trajectory (QT) ensemble itself. For practical and conceptual reasons the quantum potential and corresponding quantum nuclear effect are computed only for the selected light nuclei. For studies of reactive chemical processes, the classical potential is computed on-the-fly using the density functional tight binding method of electronic structure. A massively parallel implementation, based on the message passing interface allows for efficient simulations of ensembles of thousands of trajectories describing systems of up to 200 atoms. As a biochemical application, the approximate QT approach is used to model the tunnelling-dominated proton transfer in soybean-lipoxygenase-1. A materials science application is represented by a study of the nuclear quantum effect on adsorption of hydrogen and deuterium on a C 37 H 15 molecule, which is a model 'flake' of graphene.Keywords: quantum effect; hybrid dynamics of quantum/classical nuclei; on-the-fly electronic structure; densityfunctional tight-binding method

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Section: Molecular Simulation 93mentioning

confidence: 98%

Section: 22mentioning

confidence: 99%

Section: Molecular Simulation 93mentioning

confidence: 99%

Section: Molecular Simulation 93mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Approximate quantum trajectory dynamics for reactive processes in condensed phase

Garashchuk

Jakowski

Rassolov

2014

Molecular Simulation

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Two-dimensional reactive scattering with transmitted quantum trajectories

Chou

2014

Int. J. Quantum Chem.

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A simple and easy-to-implement method is presented for the study of time-dependent reaction dynamics by propagating an ensemble of transmitted quantum trajectories. During the trajectory evolution, reflected trajectories are gradually removed and all the remaining trajectories represent the transmitted subensemble. The removal process of reflected trajectories avoids numerical instabilities arising from node formation in the reactant region, and allows stable long-time propagation of transmitted trajectories. This method is applied to a twodimensional model chemical reaction. Excellent computational results are obtained for the time-dependent reaction probabilities evaluated by the time integration of the probability flux.

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Pilot-Wave Quantum Theory with a Single Bohm’s Trajectory

2015

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The representation of a quantum system as the spatial configuration of its constituents evolving in time as a trajectory under the action of the wave-function, is the main objective of the de Broglie–Bohm theory (or pilot wave theory). However, its standard formulation is referred to the statistical ensemble of its possible trajectories. The statistical ensemble is introduced in order to establish the exact correspondence (the Born’s rule) between the probability density on the spatial configurations and the quantum distribution, that is the squared modulus of the wave-function. In this work we explore the possibility of using the pilot wave theory at the level of a single Bohm’s trajectory, that is a single realization of the time dependent configuration which should be representative of a single realization of the quantum system. The pilot wave theory allows a formally self-consistent representation of quantum systems as a single Bohm’s trajectory, but in this case there is no room for the Born’s rule at least in its standard form. We will show that a correspondence exists between the statistical distribution of configurations along the single Bohm’s trajectory and the quantum distribution for a subsystem interacting with the environment in a multicomponent system. To this aim, we present the numerical results of the single Bohm’s trajectory description of the model system of six confined planar rotors with random interactions. We find a rather close correspondence between the coordinate distribution of one rotor, the others representing the environment, along its trajectory and the time averaged marginal quantum distribution for the same rotor. This might be considered as the counterpart of the standard Born’s rule when the pilot wave theory is applied at the level of single Bohm’s trajectory. Furthermore a strongly fluctuating behavior with a fast loss of correlation is found for the evolution of each rotor coordinate. This suggests that a Markov process might well approximate the evolution of the Bohm’s coordinate of a single rotor (the subsystem) and, under this condition, it is shown that the correspondence between coordinate distribution and quantum distribution of the rotor is exactly verified

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Incorporation of quantum effects for selected degrees of freedom into the trajectory-based dynamics using spatial domains

Cited by 14 publications

References 33 publications

Approximate quantum trajectory dynamics for reactive processes in condensed phase

Approximate quantum trajectory dynamics for reactive processes in condensed phase

Two-dimensional reactive scattering with transmitted quantum trajectories

Pilot-Wave Quantum Theory with a Single Bohm’s Trajectory

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