2013
DOI: 10.1063/1.4799272
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A mixed quantum-classical Liouville study of the population dynamics in a model photo-induced condensed phase electron transfer reaction

Abstract: We apply two approximate solutions of the quantum-classical Liouville equation (QCLE) in the mapping representation to the simulation of the laser-induced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the Forward-Backward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standar… Show more

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Cited by 37 publications
(38 citation statements)
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“…[44 -47] PBME simulations of the symmetric spin-boson model, [28] simple curve crossing models [34] and the Fenna -Mathews -Olsen complex [48] have yielded results that agree well with the exact results. However, in the case of simple conical intersection and collinear reactive collision models [29] and an asymmetric spinboson model, [39] the agreement ranges from moderate to poor. In an in-depth analysis of QCL dynamics in the mapping representation, Kelly et al found that the dynamics prescribed by the solution of the PBME can take the system outside of the physical space (and thereby lead to a variety of dynamical instabilities), whereas the dynamics prescribed by the solution of the mapping-QCLE confines the system to the physical space.…”
Section: The Pbme Solutionmentioning
confidence: 95%
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“…[44 -47] PBME simulations of the symmetric spin-boson model, [28] simple curve crossing models [34] and the Fenna -Mathews -Olsen complex [48] have yielded results that agree well with the exact results. However, in the case of simple conical intersection and collinear reactive collision models [29] and an asymmetric spinboson model, [39] the agreement ranges from moderate to poor. In an in-depth analysis of QCL dynamics in the mapping representation, Kelly et al found that the dynamics prescribed by the solution of the PBME can take the system outside of the physical space (and thereby lead to a variety of dynamical instabilities), whereas the dynamics prescribed by the solution of the mapping-QCLE confines the system to the physical space.…”
Section: The Pbme Solutionmentioning
confidence: 95%
“…Specifically, we review the results for the dynamics of a three-state model of a laser-induced electron transfer (ET) reaction in a harmonic oscillator bath, previously studied by our group in Refs [39,40], and present new results for the dynamics of a realistic, atomistic model of a proton transfer (PT) complex in a nanocluster of polar molecules. It should be noted that this is the first time that any of these approximate methods have been applied to a realistic system.…”
Section: Introductionmentioning
confidence: 99%
“…When such coordinates are canonically conjugate momenta and positions, one approach to treat these situations is provided by the quantum-classical Liouville equation. [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] Nevertheless, there are also many interesting cases when the bath is described in terms of classical spins, e.g., in order to model complex molecules where magnetic effects are important. 29,30 Such models can be studied by means of Monte Carlo methods or by molecular dynamics simulations.…”
mentioning
confidence: 99%
“…In practice, fast bath decoherence alleviates this problem and, indeed, the canonical version of the quantum-classical bracket, or of the quantum-classical Liouville equation, is used for many applications in chemistry and physics. [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] Moreover, it is worth reminding that the non-Lie (or, as they are also called, non-Hamiltonian) brackets, with their lack of time translation invariance, are also used to impose thermodynamical (such as constant temperature and/or pressure) [36][37][38] and holonomic constraints 39,40 in classical molecular dynamics simulations. 31,32 In order to represent the abstract equation (6) the quantum-classical Hamiltonian of Eq.…”
mentioning
confidence: 99%
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