Quantum-classical Liouville dynamics of nonadiabatic proton transfer

Hanna, Gabriel; Kapral, Raymond

doi:10.1063/1.1940051

Cited by 107 publications

(181 citation statements)

References 33 publications

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“…Furthermore, during the coherent evolution segments, the observable of interest accumulates a phase to reflect the creation of quantum coherence. In addition to creating and destroying quantum coherence throughout the evolution, the quantum-classical propagator ensures that energy is exactly conserved along a trajectory even if the momentum-jump approximation 33 is made. Of course, physical significance should only be attached to expectation values computed from averages over the ensemble.…”

Section: Discussionmentioning

confidence: 99%

“…In contrast, the upper trajectory immediately hops onto the coherent state surface (denoted by 1.5) and remains there for 0.8 ps until it falls back down to the ground state surface. These nonadiabatic transitions occur when the trajectory is in the vicinity of the barrier top (since the probability of a transition is highest in this region according to our sampling scheme 33,34 ). We note that the dynamics on the coherent state surface is associated with excursions in ∆E(t) across the barrier top.…”

Section: Dynamics Of Condensed Phase Rate Processes Hanna and Kapralmentioning

confidence: 99%

“…The subsequent evolution to time t takes place on the single adiabatic potential energy surface E (R) giving N (R′,P′,t) at bath coordinates (R′,P′). Finally, the matrix element N RR′ (R,P,t) is appropriately constructed 33,34 from all such trajectories in which quantum transitions can occur stochastically at any intermediate time.…”

Section: Combining Quantum and Classical Dynamicsmentioning

confidence: 99%

“…33 The potential energy function describing the hydrogen bonding within the complex is chosen to model a slightly strong hydrogen bond between the hydroxyl and amine groups in phenol (A) trimethylamine (B) in the absence of a solvent. 40 We assume that the dynamics of the proton is electronically adiabatic.…”

Section: Proton Transfermentioning

confidence: 99%

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Nonadiabatic Dynamics of Condensed Phase Rate Processes

Hanna

Kapral

2005

Acc. Chem. Res.

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The study of quantum rate processes occurring in condensed phase environments is difficult because of the large number of degrees of freedom involved. Since a full quantum mechanical treatment is not computationally feasible, one is motivated to use mixed quantum-classical dynamical methods. This type of dynamics is applicable when one can single out a few degrees of freedom to be quantum in nature while treating the remainder classically. We describe a method that is based on the quantum-classical Liouville equation, which clearly prescribes the details of the coupling between the quantum and classical degrees of freedom. With the aid of this machinery, we show how to compute rate constants of reactions involving quantum particles immersed in a classical bath. We illustrate the use of this method on a model for proton transfer in a molecular complex dissolved in a polar solvent.

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Section: Discussionmentioning

confidence: 99%

Section: Dynamics Of Condensed Phase Rate Processes Hanna and Kapralmentioning

confidence: 99%

Section: Combining Quantum and Classical Dynamicsmentioning

confidence: 99%

Section: Proton Transfermentioning

confidence: 99%

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Nonadiabatic Dynamics of Condensed Phase Rate Processes

Hanna

Kapral

2005

Acc. Chem. Res.

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“…[12][13][14][15][16][17][18] In these methods, the classical trajectories evolve on adiabatic potential energy surfaces with transitions governed by a stochastic algorithm, which varies in different schemes. While quantum decoherence is neglected in the original surface-hopping method, it has been introduced in later extensions.…”

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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Proton and Deuteron Transfer Reactions in Molecular Nanoclusters

Kim

Kapral

2008

ChemPhysChem

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Proton and deuteron transfer rates and mechanisms are studied in polar molecular nanoclusters. The cluster environment strongly influences the reaction rate and the nature of these changes is studied as a function of the cluster size. The stabilities of the covalent reactant and polar product states change with cluster size and this effect alters both the equilibrium properties and transfer rate. The proton and deuteron are light quantum particles and the quantum character of the rate process is reflected in the magnitude of the kinetic isotope effect. Our mixed quantum-classical rate simulations indicate that the magnitude of the isotope effect decreases as the cluster size increases. More generally, our study shows how quantum effects combined with structural nanosolvation effects can lead to changes in reaction rates and mechanisms which should be applicable to many quantum charge transfer reactions in molecular nanoclusters.

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Quantum-classical Liouville dynamics of nonadiabatic proton transfer

Cited by 107 publications

References 33 publications

Nonadiabatic Dynamics of Condensed Phase Rate Processes

Nonadiabatic Dynamics of Condensed Phase Rate Processes

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

Proton and Deuteron Transfer Reactions in Molecular Nanoclusters

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