Path Integral Calculation of Quantum Nonadiabatic Rates in Model Condensed Phase Reactions

Topaler, Maria; Makri, Nancy

doi:10.1021/jp951673k

Cited by 76 publications

(99 citation statements)

References 47 publications

(104 reference statements)

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“…We have analysed the use of the Kubo-transformed fluxside correlation function, with reactants and products defined as usual by projections onto electronic states, 12 to compute the nonadiabatic rate constant for systems with weak electronic coupling. It was shown to be very inefficient due to strong oscillatory behaviour stemming from spurious diabatic transitions occurring between low-and high-energy states, which due to phase cancellation at long times do not contribute to the rate constant.…”

Section: Discussionmentioning

confidence: 99%

“…A more appropriate dividing-surface concept is provided by considering projections onto electronic states. 10,12,37 However, with this form, there are strong oscillations in the flux correlation functions in some parameter regimes. 42 We discuss this issue in Sec.…”

Section: Linear Response Theorymentioning

confidence: 99%

“…It is unfortunately exactly this type of correlation function that one would like to compute with trajectory simulations including nonadiabatic RPMD. 40 Many previous approaches have concentrated on computing the smoother symmetric correlation function, whether based on trajectories employing mapping variables, 37 real-time path integrals 12 or MCTDH. 10 We note, however, that for lower temperatures or strongly biased systems, even the symmetric correlation function can become oscillatory and could cause problems for these methods as well.…”

Section: Flux Correlation Functions In the Nonadiabatic Limitmentioning

confidence: 99%

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Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

Richardson

Thoss

2014

The Journal of Chemical Physics

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Quantum mechanical canonical rate theory: A new approach based on the reactive flux and numerical analytic continuation methods J. Chem. Phys. 112, 2605 (2000); 10.1063/1.480834Erratum: "A unified framework for quantum activated rate processes. II. The nonadiabatic limit" [J. Chem. Phys. 106, 1769 There is currently much interest in the development of improved trajectory-based methods for the simulation of nonadiabatic processes in complex systems. An important goal for such methods is the accurate calculation of the rate constant over a wide range of electronic coupling strengths and it is often the nonadiabatic, weak-coupling limit, which being far from the Born-Oppenheimer regime, provides the greatest challenge to current methods. We show that in this limit there is an inherent sign problem impeding further development which originates from the use of the usual quantum flux correlation functions, which can be very oscillatory at short times. From linear response theory, we derive a modified flux correlation function for the calculation of nonadiabatic reaction rates, which still rigorously gives the correct result in the long-time limit regardless of electronic coupling strength, but unlike the usual formalism is not oscillatory in the weak-coupling regime. In particular, a trajectory simulation of the modified correlation function is naturally initialized in a region localized about the crossing of the potential energy surfaces. In the weak-coupling limit, a simple link can be found between the dynamics initialized from this transition-state region and an generalized quantum goldenrule transition-state theory, which is equivalent to Marcus theory in the classical harmonic limit. This new correlation function formalism thus provides a platform on which a wide variety of dynamical simulation methods can be built aiding the development of accurate nonadiabatic rate theories applicable to complex systems. © 2014 AIP Publishing LLC. [http://dx

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Section: Discussionmentioning

confidence: 99%

Section: Linear Response Theorymentioning

confidence: 99%

Section: Flux Correlation Functions In the Nonadiabatic Limitmentioning

confidence: 99%

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Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

Richardson

Thoss

2014

The Journal of Chemical Physics

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“…Alternatively, quantum mechanical path integrals can be used to describe nuclear motion. 34,35 A huge variety of semiclassical methods for nonadiabatic dynamics have been proposed, [17][18][19][36][37][38][39][40][41] many building on the early work by Miller. 42 Density matrix, quantum Liouville, and quantum trajectory approaches also appear quite promising.…”

Section: Dynamicsmentioning

confidence: 99%

Perspective: Nonadiabatic dynamics theory

Tully

2012

The Journal of Chemical Physics

566

589

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Nonadiabatic dynamics-nuclear motion evolving on multiple potential energy surfaces-has captivated the interest of chemists for decades. Exciting advances in experimentation and theory have combined to greatly enhance our understanding of the rates and pathways of nonadiabatic chemical transformations. Nevertheless, there is a growing urgency for further development of theories that are practical and yet capable of reliable predictions, driven by fields such as solar energy, interstellar and atmospheric chemistry, photochemistry, vision, single molecule electronics, radiation damage, and many more. This Perspective examines the most significant theoretical and computational obstacles to achieving this goal, and suggests some possible strategies that may prove fruitful.

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“…The dynamics can be found from numerical path integration schemes, [28][29][30] or from the hierarchy of equations of motion. 4,[24][25][26][31][32][33][34] In this paper, we will use the hierarchy of equations of motion, where the reduced density matrix is propagated alongside a set of auxiliary density matrices, which allows for the correct inclusion of the system bath correlations.…”

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confidence: 99%

System Bath Correlations and the Nonlinear Response of Qubits

Dijkstra

Tanimura

2012

J. Phys. Soc. Jpn.

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In this letter we study qubits coupled to the bath formed by their environment. Although entanglement of the qubits is a well-known topic, much less effort has gone into the description of the correlations between the qubits and the bath. Here, we investigate these correlations, and study their effect on the qubits in equilibrium and their dynamics following the interaction with one or several external pulses. We find that a correct description of the correlations at the moment of these interactions is essential for a correct understanding of the dynamics.KEYWORDS: qubit, system-bath, nonlinear response, initial correlations, non-MarkovianThe entanglement of two qubits (two-level systems) measures the extent to which they are not separable, and is a purely quantum effect. It is formed and destroyed by the interaction of the qubit system with its environment. Formation of entanglement is often the result of a deliberate preparation procedure, while the destruction occurs because of uncontrollable interactions. After the preparation of an entangled state, the entanglement typically decays with time to an equilibrium value. In the case of Markovian dynamics, the entanglement smoothly decays with time, while temporary increases are possible if the evolution is nonMarkovian. The dynamics of entanglement shows some surprising characteristics. Even if the single qubit coherence decays smoothly, the entanglement can go to zero in a finite time, a phenomenon called ''sudden death'' of entanglement.1) Furthermore, the entanglement can be revived from death, i.e., the system can become entangled after a period of zero entanglement.All these time dependent phenomena are caused by the interaction of the qubits with a bath. Entanglement which is lost from the system during the time evolution is stored in the bath.2) Crucially, correlations are created between the qubit system and the bath. Their presence influences the dynamics in the system. In particular, correlations present at the moment of the interaction with an external force are not well studied. Their detailed understanding is the topic of this letter. Of course, correlations are formed continuously when a system is placed in contact with a heat bath. This is closely related to the reorganization energy known in chemical physics. 3,4) In the case of non-Markovian dynamics, the correlations acts as a memory for the system, and influences the system entanglement at a later point in time.5) Besides this, there is another phenomenon which is important for a complete description of the dynamics: the entanglement of system and bath states at time zero (where zero can be chosen arbitrarily, but in this paper will represent the moment of interaction with an external pulse). In general, this quantity, which reports on initial correlations, 6-9) does not vanish and can influence the system during its time evolution. 10)Theoretically, the dynamics of a system in contact with its environment is often studied using master equations, which have been extended to include initial cor...

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Path Integral Calculation of Quantum Nonadiabatic Rates in Model Condensed Phase Reactions

Cited by 76 publications

References 47 publications

Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory

Perspective: Nonadiabatic dynamics theory

System Bath Correlations and the Nonlinear Response of Qubits

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