Theory of Rate Processes in Condensed Media

Fain, Benjamin

doi:10.1007/978-3-642-93153-6

Cited by 55 publications

(33 citation statements)

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“…(111) for K (2). This verifies that for the master equation with rate constants calculated to order 0', detailed balance is satisfied.…”

Section: N(wo)+1supporting

confidence: 64%

“…The first two equations, for the TLS populations, are gain-loss type rate equations, and are the simplest example of the so-called master equation. 2 Observing that the populations of the ground and excited states must relax to their Boltzmann equilibrium values in the limit of infinite time leads to the detailed balance condition:…”

Section: -01 (T) = [I(lij O + Lllij) -L/t2 ]0-01 (T)mentioning

confidence: 99%

“…(2)- (5), can be more or less divided into two types. Theories of the first type involve the treatment of the bath degrees offreedom in a purely stochastic way.…”

Section: -01 (T) = [I(lij O + Lllij) -L/t2 ]0-01 (T)mentioning

confidence: 99%

“…If one could show that Eqs. (2) and (3) were valid in higher-order perturbation theory, this would provide an example of a master equation valid outside the weak-coupling limit. Moreover, the higher-order expressions for the rate constants would produce an extension of Fermi's Golden Rule. In this paper we derive generalized Bloch equations (Redfield equations 5 ) to fourth order in the system/bath interaction, for a completely quantum-mechanical Hamiltonian involving a TLS coupled linearly and off-diagonally to a bath of harmonic oscillators.…”

Section: -01 (T) = [I(lij O + Lllij) -L/t2 ]0-01 (T)mentioning

confidence: 99%

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Quantum-mechanical derivation of the Bloch equations: Beyond the weak-coupling limit

Laird

Budimir

Skinner

1991

The Journal of Chemical Physics

151

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Two nondegenerate quantum levels coupled off-diagonally and linearly to a bath of quantummechanical harmonic oscillators are considered. In the weak-coupling limit one finds that the equations of motion for the reduced density-matrix elements separate naturally into two uncoupled pairs of linear equations for the diagonal and off-diagonal elements, which are known as the Bloch equations. The equations for the populations form the simplest twocomponent master equation, and the rate constant for the relaxation of nonequilibrium population distributions is liT), defined as the sum of the "up" and "down" rate constants in the master equation. Detailed balance is satisfied for this master equation in that the ratio of these rate constants is equal to the ratio of the equilibrium popUlations. The relaxation rate constant for the off-diagonal density-matrix elements is known as l/T 2 . One finds that this satisfies the well-known relation l/T2 = 1/2TI' In this paper the weak-coupling limit is transcended by deriving the Bloch equations to fourth order in the coupling. The equations have the same form as in the weak-coupling limit, but the rate constants are calculated to fourth order. For the population-relaxation rate constants this results in an extension to fourth order of Fermi's golden rule. We find that these higher-order rate constants do indeed satisfy detailed balance. Comparing the dephasing and population-relaxation rate constants, we find that in fourth order lIT 2 # lI2T!.

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“…(111) for K (2). This verifies that for the master equation with rate constants calculated to order 0', detailed balance is satisfied.…”

Section: N(wo)+1supporting

confidence: 64%

Section: -01 (T) = [I(lij O + Lllij) -L/t2 ]0-01 (T)mentioning

confidence: 99%

“…(2)- (5), can be more or less divided into two types. Theories of the first type involve the treatment of the bath degrees offreedom in a purely stochastic way.…”

Section: -01 (T) = [I(lij O + Lllij) -L/t2 ]0-01 (T)mentioning

confidence: 99%

Section: -01 (T) = [I(lij O + Lllij) -L/t2 ]0-01 (T)mentioning

confidence: 99%

See 2 more Smart Citations

Quantum-mechanical derivation of the Bloch equations: Beyond the weak-coupling limit

Laird

Budimir

Skinner

1991

The Journal of Chemical Physics

151

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“…In the electronically nonadiabatic limit, the vibronic coupling can be expressed as the product of the electronic coupling V el and the Franck-Condon overlap S μν of the reactant and product proton vibrational wavefunctions: (6) In the electronically adiabatic limit, the proton dynamics occur on the electronically adiabatic ground state potential energy surface, and the vibronic coupling can be calculated by standard semiclassical methods. [49,50] For a symmetric system, the vibronic coupling is half the splitting between the symmetric and antisymmetric proton vibrational states for the electronic ground state potential energy surface.…”

Section: Vibronic Coupling Calculationsmentioning

confidence: 99%

Theoretical studies of proton-coupled electron transfer: Models and concepts relevant to bioenergetics

Hammes‐Schiffer¹,

Hatcher²,

Ishikita³

et al. 2008

Coordination Chemistry Reviews

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Theoretical studies of proton-coupled electron transfer (PCET) reactions for model systems provide insight into fundamental concepts relevant to bioenergetics. A dynamical theoretical formulation for vibronically nonadiabatic PCET reactions has been developed. This theory enables the calculation of rates and kinetic isotope effects, as well as the pH and temperature dependences, of PCET reactions. Methods for calculating the vibronic couplings for PCET systems have also been developed and implemented. These theoretical approaches have been applied to a wide range of PCET reactions, including tyrosyl radical generation in a tyrosine-bound rhenium polypyridyl complex, phenoxyl/ phenol and benzyl/toluene self-exchange reactions, and hydrogen abstraction catalyzed by the enzyme lipoxygenase. These applications have elucidated some of the key underlying physical principles of PCET reactions. The tools and concepts derived from these theoretical studies provide the foundation for future theoretical studies of PCET in more complex bioenergetic systems such as Photosystem II.

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Classical description of activated conformational processes in molecular systems coupled to solvent degrees of freedom

Nordio

Polimeno

1996

Int. J. Quantum Chem.

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rnExtended Fokker-Planck (FP) equations are generalized stochastic equations which describe the evolution of a set of coordinates, loosely referred to as solute, coupled with a relevant set of solvent variables. They are useful for the analysis of molecular dynamics in liquids, when a time-scale separation between probe motions and relaxation times of interactions with surroundings particles cannot be performed, because of persistence of slowly fluctuating components. In this article, we focus attention on a model system, made up of an angular coordinate and its conjugate momentum, submitted to a bistable potential, and coupled to a dissipative harmonic mode, to investigate the influence of polar solvents on reactive dynamics. The results are appropriate to describe dielectric effects, solvent-controlled conformational changes involving charge transfer which occur in photophysical processes, and the dynamic Stokes shifts observed in time-resolved fluorescence experiments.

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Theory of Rate Processes in Condensed Media

Cited by 55 publications

References 0 publications

Quantum-mechanical derivation of the Bloch equations: Beyond the weak-coupling limit

Quantum-mechanical derivation of the Bloch equations: Beyond the weak-coupling limit

Theoretical studies of proton-coupled electron transfer: Models and concepts relevant to bioenergetics

Classical description of activated conformational processes in molecular systems coupled to solvent degrees of freedom

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