Nonadiabatic Dynamics of Condensed Phase Rate Processes

The quantum-classical Liouville equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantum-classical Liouville equation consists of a Poisson bracket contribution and a more complex term. By transforming the evolution equation, term-by-term, back to the subsystem basis, the complex term (excess coupling term) is identified as being due to a fraction of the back reaction of the quantum subsystem on its environment. A simple approximation to quantum-classical Liouville dynamics in the mapping basis is obtained by retaining only the Poisson bracket contribution. This approximate mapping form of the quantum-classical Liouville equation can be simulated easily by Newtonian trajectories. We provide an analysis of the effects of neglecting the presence of the excess coupling term on the expectation values of various types of observables. Calculations are carried out on nonadiabatic population and quantum coherence dynamics for curve crossing models. For these observables, the effects of the excess coupling term enter indirectly in the computation and good estimates are obtained with the simplified propagation.

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“…Inserting these results into Eq. (19), the QCLE in the subsystem basis (Eq. (2)) is obtained as expected.…”

Section: B Excess Coupling Termmentioning

confidence: 99%

Analysis of the quantum-classical Liouville equation in the mapping basis

Nassimi

Bonella

Kapral

2010

The Journal of Chemical Physics

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“…The proton transfer rate constant and kinetic isotope effect (KIE) have been computed for this model using a wide variety of techniques [5,6,10,47,70,80,105,121]. The specific forms of the interaction potentials, parameter values used, and the remaining details of the model can be found in [47,48] and [49]. In a previous work, they calculated the proton transfer rate constant for this model with the AB distance constrained at R AB = 2.7Å.…”

Section: Quantum-classical Liouville Dynamics Of Proton and Deuteron mentioning

confidence: 99%

Some Aspects of the Liouville Equation in Mathematical Physics and Statistical Mechanics

et al. 2011

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“…Quantum rate processes in a condensed phase has been studied extensively by a variety of methods. [28][29][30][31][32][33][34][35][36][37][38] We apply the corrected propagator to the study of a model system, consisting of a symmetric double-well potential, bilinearly coupled to a bath of harmonic oscillators. The thermal rate constant for this model system has been calculated using a number of approximate methods.…”

Section: Introductionmentioning

confidence: 99%

Finite temperature application of the corrected propagator method to reactive dynamics in a condensed-phase environment

Gelman

Schwartz

2011

The Journal of Chemical Physics

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The recently proposed mixed quantum-classical method is extended to applications at finite temperatures. The method is designed to treat complex systems consisting of a low-dimensional quantum part (the primary system) coupled to a dissipative bath described classically. The method is based on a formalism showing how to systematically correct the approximate zeroth-order evolution rule. The corrections are defined in terms of the total quantum Hamiltonian and are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The evolution of the primary system is governed by the corrected propagator yielding the exact quantum dynamics. The method has been tested on a standard model system describing proton transfer in a condensed-phase environment: a symmetric double-well potential bilinearly coupled to a bath of harmonic oscillators. Flux correlation functions and thermal rate constants have been calculated at two different temperatures for a range of coupling strengths. The results have been compared to the fully quantum simulations of Topaler and Makri [J. Chem. Phys. 101, 7500 (1994)] with the real path integral method.

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Nonadiabatic Dynamics of Condensed Phase Rate Processes

Cited by 38 publications

References 49 publications

Analysis of the quantum-classical Liouville equation in the mapping basis

Analysis of the quantum-classical Liouville equation in the mapping basis

Some Aspects of the Liouville Equation in Mathematical Physics and Statistical Mechanics

Finite temperature application of the corrected propagator method to reactive dynamics in a condensed-phase environment

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