Reactive flux formalism

The calculation of reaction rate constants with the transition path sampling methods does not require understanding of the reaction mechanism, for instance in the form of an appropriate reaction coordinate. If such information is available other methods such as the reactive flux formalism are likely to yield reaction rate constants at a lower computational cost than transition path sampling. 

Equivalently, we could use q- x) instead of g+(x) in this expression.) Since the derivation of (43) from (42) involves a few technical steps we postpone it till the end of this section. To the best of our knowledge, this expression was first given in [14]. It provides an exact alternative to the expression for the reaction rate given by TST and the reactive flux formalism (see Sect. 5). Finally, notice that (11) and (43) can be combined with (16) to give the following expression for the mean reaction time tAB defined in (14) ... 

Abstract. This paper provides a perspective on the use of the reactive flux formalism for calculating rate constants in condensed phase systems through molecular dynamics simulations. This approach makes possible the computation of rate constants even for systems with very high energy barriers. 

Barrier crossing phenomena are fundamental in chemistry. In many situations barrier crossing events correspond to first-order kinetics characterized by a rate constant. Because the dynamics of such processes corresponds to infrequent events, direct simulation of a reaction from reactants to products can be extremely inefficient- A much better approach is offered by the reactive flux formalism which expresses the reaction rate in terms of the flux crossing a fictitious dividing surface that separates reactants from products. Even though the reactive flux method offers a numerically advantageous approach compared with direct simulation of the reaction itself, fully... 

The rate coefficient of a reactive process is a transport coefficient of interest in chemical physics. It has been shown from linear response theory that this coefficient can be obtained from the reactive flux correlation function of the system of interest. This quantity has been computed extensively in the literature for systems such as proton and electron transfer in solvents as well as clusters [29,32,33,56,71-76], where the use of the QCL formalism has allowed one to consider quantum phenomena such as the kinetic isotope effect in proton transfer [31], Here, we will consider the problem of formulating an expression for a reactive rate coefficient in the framework of the QCL theory. Results from a model calculation will be presented including a comparison to the approximate methods described in Sec. 4. 

Equations (359) and (361) indicate that the reason that the flux-flux autocorrelation formalism gives exact quantum reaction rate constants is simply that all the dynamical information from time zero to time inflnity has been included. Indeed, as shown by Eqs. (360) and (362), in the classical limit the flux-flux autocorrelation formalism requires us to follow all classical trajectories until t = +00 so as to rigorously tell which trajectory is reactive and which trajectory is nonreactive. Evidently, then, the flux-flux autocorrelation formalism is not a statistical reaction rate theory insofar as no approximation to the reaction dynamics is made. 

Several other related aspects of TCFs can be mentioned, but will not be covered here to concentrate instead on calculational methods and applications of collisional TCFs. An earlier alternative approach in terms of superoperators [18] suggests ways of extending the formalism to include phenomena where the total energy is not conserved due to interactions with external fields or media. It has led to different TCFs which however have not been used in calculations. Information-theory concepts can be combined with TCFs [10] to develop useful expressions for collisional problems [19]. Collisional TCFs can also be expressed as overlaps of time-dependent transition amplitude functions that satisfy differential equations and behave like wavepackets. This approach to the calculation of TCFs was developed for Raman scattering [20] and has more recently been extended using collisional TCFs for general interactions of photons with molecules [21] and for systems coupled to an environment [22-25]. This approach has so far been only applied to the interaction of photons with molecular systems. Flux-flux TCFs [26-28] have been applied to reactive collision and molecular dynamics problems, but their connection to collisional TCFs have not yet been studied. 

The reduction potentials for O2 and various intermediate species in H2O at pH 0, 7, and 14 are summarized in Table IV similar data for -02 in MeCN at pH —8.8, 10.0, and 30.4 are presented in Table V. For those couples that involve dioxygen itself, formal potentials are given in parentheses for -02- at unit molarity ( 10 atm [ O2 ] Ri 1 mM at 1 atm partial pressure). The reduction manifolds for O2 (Tables IV and V) indicate that the limiting step (in terms of reduction potential) is the first electron transfer to 02- and that an electron source adequate for the reduction of 02- will produce all of the other reduced forms of dioxygen (O2, HOO, HOOH, HOO, HO-, H2O, H0 ) via reduction, hydrolysis, and disproportionation steps. Thus, the most effective means to activate -02 is the addition of an electron (or hydrogen atom H O -b H ), which results in significant fluxes of several reactive oxygen species. 

The next problem is the formulation of the transport fluxes. The precision with which it must be done for multicomponent mixtures is a matter on which there is diversity of opinion. This arises because the more precise formulations rapidly become more expensive in computer time but have uncertain returns in terms of accuracy because of shortcomings in the primary data. The author is of the opinion that a detailed transport flux model is a necessary reference representation on which approximations may be based so as to give the most satisfactory compromise for a specific problem. Fortunately, the various degrees of approximation result in formally similar continuity equations which can be treated by the same numerical techniques. Readers interested in the general aspects of modeling reactive flows are advised to omit this section on first reading and to accept the results given at the commencement of Section 4. 

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