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Title: Mean-field dynamics with stochastic decoherence (MF-SD): A new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence

Abstract

The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence--the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state--and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ('surface hops') and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schroedinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains inmore » a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems.« less

Authors:
; ;  [1]
  1. Department of Chemistry and Biochemistry, University of California, 607 Charles E. Young Drive East, Los Angeles, California 90095-1569 (United States)
Publication Date:
OSTI Identifier:
20783195
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 123; Journal Issue: 23; Other Information: DOI: 10.1063/1.2131056; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; DENSITY MATRIX; MEAN-FIELD THEORY; MIXED STATE; MOLECULAR DYNAMICS METHOD; QUANTUM DECOHERENCE; QUANTUM MECHANICS; SCHROEDINGER EQUATION; SIMULATION; STOCHASTIC PROCESSES; TRAJECTORIES; WAVE FUNCTIONS

Citation Formats

Bedard-Hearn, Michael J., Larsen, Ross E., and Schwartz, Benjamin J. Mean-field dynamics with stochastic decoherence (MF-SD): A new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence. United States: N. p., 2005. Web. doi:10.1063/1.2131056.
Bedard-Hearn, Michael J., Larsen, Ross E., & Schwartz, Benjamin J. Mean-field dynamics with stochastic decoherence (MF-SD): A new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence. United States. doi:10.1063/1.2131056.
Bedard-Hearn, Michael J., Larsen, Ross E., and Schwartz, Benjamin J. Thu . "Mean-field dynamics with stochastic decoherence (MF-SD): A new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence". United States. doi:10.1063/1.2131056.
@article{osti_20783195,
title = {Mean-field dynamics with stochastic decoherence (MF-SD): A new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence},
author = {Bedard-Hearn, Michael J. and Larsen, Ross E. and Schwartz, Benjamin J.},
abstractNote = {The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence--the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state--and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ('surface hops') and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schroedinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems.},
doi = {10.1063/1.2131056},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 23,
volume = 123,
place = {United States},
year = {2005},
month = {12}
}