Variational transition-state theory systems

Poliak E 1993 Variational transition state theory for dissipative systems Acf/Vafed Barrier Crossinged G Fleming and P Hanggi (New Jersey World Scientific) p 5... 

Poliak E, Tucker S C and Berne B J 1990 Variational transition state theory for reaction rates in dissipative systems Phys. Rev. Lett. 65 1399... 

Poliak E 1990 Variational transition state theory for activated rate processes J. Chem. Phys. 93 1116 Poliak E 1991 Variational transition state theory for reactions in condensed phases J. Phys. Chem. 95 533 Frishman A and Poliak E 1992 Canonical variational transition state theory for dissipative systems application to generalized Langevin equations J. Chem. Phys. 96 8877... 

Song K and Chesnavich W J 1989 Multiple transition states in chemical reactions variational transition state theory studies of the HO2 and HeH2 systems J. Chem. Rhys. 91 4664-78... 

The most satisfactory situation for making an extrapolation of rate data to the true threshold arises when the threshold is uncertain, but we can confidently calculate the functional form of the rate-energy curve from accurate kinetic theory. For small systems, it is feasible to calculate dissociation rates by quantum methods, but this is not yet feasible for the systems of interest to us. Various approaches to variational transition-state theory (VTST) provide classical or semiclassical calculations that are feasible for large systems and seem to be accurate when carefully... 

Alhambra and co-workers adopted a QM/MM strategy to better understand quantum mechanical effects, and particularly the influence of tunneling, on the observed primary kinetic isotope effect of 3.3 in this system (that is, the reaction proceeds 3.3 times more slowly when the hydrogen isotope at C-2 is deuterium instead of protium). In order to carry out their analysis they combined fully classical MD trajectories with QM/MM modeling and analysis using variational transition-state theory. Kinetic isotope effects (KIEs), tunneling, and variational transition state theory are discussed in detail in Chapter 15 - we will not explore these topics in any particular depth in this case study, but will focus primarily on the QM/MM protocol. 

Figure 13.8 A 25-atom quantum subsystem embedded in an 8863-atom classical system to model the catalytic step in the conversion of D-2-phosphoglycerate to phosphoenolpyruvate by enolase. What factors influence the choice of where to set the boundary between the QM and MM regions Alhambra and co-workers found, using variational transition-state theory with a frozen MM region that was selected from a classical trajectory so as to make the reaction barrier and thermochemistry reasonable, that the breaking and making bond lengths were 1.75 and 1.12 A, respectively, for H, but 1.57 and 1.26 A, respectively, for D...

R. Sayos, J. Hernando, J. Flijazo, M. Gonzalez, An analytical potential energy surface of the HFCL(2A ) system based on ab initio calculations. Variational transition state theory study of the H+C1F F+HC1,C1+HF, and F+HCl Cl+HF reactions and their isotope variants, Phys. Chem. Chem. Phys. 1 (1999) 947. 

In ESP theory [30-32] we treat the system by the same methods that we would use in the gas phase except that in the nontunneling part of the calculation we replace V(R) by TT(R), and in the tunneling part we approximate V(R) by TT(R) or a function of TT(R). Next we review what that entails. In particular we will review the application of variational transition state theory [21-25] with optimized multidimensional tunneling [33,34] to liquid-phase reactions for the case [31,32] in which TT(R) is calculated from V(R) by... 

The SES, ESP, and NES methods are particularly well suited for use with continuum solvation models, but NES is not the only way to include nonequilibrium solvation. A method that has been very useful for enzyme kinetics with explicit solvent representations is ensemble-averaged variational transition state theory [26,27,87] (EA-VTST). In this method one divides the system into a primary subsystem and a secondary one. For an ensemble of configurations of the secondary subsystem, one calculates the MEP of the primary subsystem. Thus the reaction coordinate determined by the MEP depends on the coordinates of the secondary subsystem, and in this way the secondary subsystem participates in the reaction coordinate. 

For these reasons we cannot use (7(R) as a rigid support for dynamical studies of trajectories of representative points. G(R) has to be modified, at every point of each trajectory, and these modifications depend on the nature of the system, on the microscopic properties of the solution, and on the dynamical parameters of the trajectories themselves. This rather formidable task may be simplified in severai ways we consider it convenient to treat this problem in a separate Section. It is sufficient to add here that one possible way is the introduction into G (R) of some extra coordinates, which reflect the effects of these retarding forces. These coordinates, collectively called solvent coordinates (nothing to do with the coordinates of the extra solvent molecules added to the solute ) are here indicated by S, and define a hypersurface of greater dimensionality, G(R S). To show how this approach of expanding the coordinate space may be successfully exploited, we refer here to the proposals made by Truhlar et al. (1993). Their formulation, that just lets these solvent coordinates partecipate in the reaction path, allows to extend the algorithms and concepts of the above mentioned variational transition state theory to molecules in solution. 

E. Poliak, Variational Transition State Theory for dissipative systems, in Activated Barrier Crossing, edited by Fleming, G. R. and Hanggi, P. (World Scientific, 1993), pp. 5-41. 

In this chapter we provide a review of variational transition state theory with a focus on how quantum mechanical effects are incorporated. We use illustrative examples of H-transfer reactions to assist in the presentation of the concepts and to highlight special considerations or procedures required in different cases. The examples span the range from simple gas-phase hydrogen atom transfer reactions (triatomic to polyatomic systems), to solid-state and liquid-phase reactions, including complex reactions in biomolecular enzyme systems. 

The higher dimensionality of polyatomic reactions makes them more of a challenge to treat theoretically. Variational transition state theory with multidimensional tunneling has been developed to allow calculations for a wide variety of polyatomic systems. In this section we consider issues that arise when treating polyatomic systems. The Cl -1- CH4 reaction provides a good system for this pur-... 

Volume 2 concludes in Part VII with contributions on the variational transition state theory approach to hydrogen transfer in various contexts (Truhlar and Garrett, Ch. 27), on experimental evidence of hydrogen atom tunneling in simple systems (Ingold, Ch. 28), and finally on a theoretical perspective for multiple hydrogen transfers (Smedarchina, Siebrand and Fernandez-Ramos, Ch. 29). 

The rate constants were calculated with the transition state theory (TST) for direct abstraction reactions and the Rice-Ramsperger-Kassel-Marcus (RRKM) theory for reactions occuring via long-lived intermediates. For reactions taking place without well-defined TS s, the Variflex [35] code and the ChemRate [36] code were used for one-well and multi-well systems, respectively, based on the variational transition-state theory approach... 

In our recent work [89], the reaction of HO2 with CIO has been investigated by ab initio molecular orbital and variational transition state theory calculations. The geometric parameters of the reaction system HO2 + CIO were optimized at the B3LYP and BH HLYP levels of theory with the basis set, 6-311+G(3df,2p), which can be found in Ref. [89]. Both singlet and triplet potential energy surfaces were predicted by the G2M method, as shown in Fig. 24. 

We present an overview of variational transition state theory from the perspective of the dynamical formulation of the theory. This formulation provides a firm classical mechanical foundation for a quantitative theory of reaction rate constants, and it provides a sturdy framework for the consistent inclusion of corrections for quantum mechanical effects and the effects of condensed phases. A central construct of the theory is the dividing surface separating reaction and product regions of phase space. We focus on the robust nature of the method offered by the flexibility of the dividing surface, which allows the accurate treatment of a variety of systems from activated and barrierless reactions in the gas phase, reactions in rigid environments, and reactions in liquids and enzymes. 

Another system where accurate microcanonical rate constants have been calculated is Li + HF - LiF + H with 7 = 0 (172). This reaction has variational transition states in the exit valley. Variational transition state theory agrees very well with accurate quantum dynamical calculations up to about 0.15 eV above threshold. After that, deviations are observed, increasing to about a factor of 2 about 0.3 eV above threshold. These deviations were attributed to effective barriers in the entrance valley these are supernumerary transition states. After Gaussian convolution of the accurate results, only a hint of step structure due to the variational transition states remains. Densities of reactive states, which would make the transition state spectrum more visible, were not published (172). 

In the previous section we demonstrated how variational transition state theory may be usefully applied to systems described by a space- and time-dependent generalized Lan-gevin equation. The harmonic nature of the bath implicit in the STGLE led to a compact analytical expression for the optimized planar dividing surface result. Except for very low temperatures, most reactive systems cannot be described in terms of a harmonic bath. In this section we demonstrate how the VTST formalism may be applied to general condensed phase reactive systems. For a recent review, see Ref. 80. 

E. Poliak, S. C. Tucker, and B. J. Berne, Phys. Rev. Lett., 65, 1399 (1990). Variational Transition State Theory for Reaction Rates in Dissipative Systems. 

There have been many reviews of H + H2 and related topics, and it is useful to summarize them here so that the stage can be set for the more recent results that are of interest to this paper. The most extensive reviews devoted specifically to H + H2 are two by Truhlar and Wyatt. These reviews cover all aspects of the H3 system up through 1976, including the potential surface, theoretical dynamical studies of the reactive, nonreactive and dissociative collision dynamics, and experimental studies. More recent reviews which consider H + H2 as a special topic include reviews of reactive scattering by Walker and Lightby Schatz, and by Connor of variational transition state theory (VTST) by Truhlar and Garrett (see Ref. 17 also for references to earlier VTST reviews) of reduced dimensionality exact quantum (RDEQ) dynamical approximations by Bowman and of... 

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