Transition-state theory energy minimization

Variational transition-state theory (VTST), as its name implies, variationally moves the reference position along the MEP that is employed for the computation of the activated complex free energy, either backwards or forwards from the TS sttuctme, until the rate constant is minimized. Notationally... 

Abbreviations MD, molecular dynamics TST, transition state theory EM, energy minimization MSD, mean square displacement PFG-NMR, pulsed field gradient nuclear magnetic resonance VAF, velocity autocorrelation function RDF, radial distribution function MEP, minimum energy path MC, Monte Carlo GC-MC, grand canonical Monte Carlo CB-MC, configurational-bias Monte Carlo MM, molecular mechanics QM, quantum mechanics FLF, Hartree-Fock DFT, density functional theory BSSE, basis set superposition error DME, dimethyl ether MTG, methanol to gasoline. 

The Canonical Variational Theory [39] is an extension of the Transition State Theory (TST) [40,41]. This theory minimizes the errors due to recrossing trajectories [42-44] by moving the dividing surface along the minimum energy path (MEP) so as to minimize the rate. The reaction coordinate (s) is defined as the distance... 

In view of the variational property of transition state theory it is evident that within the parabolic barrier estimate for the rate, the optimal transformation coefficients are those that minimize the parabolic barrier frequency WPP of the free-energy surface, subject to the constraint that the coefficients a, are normalized. 

The transition state is taken to be the (3V - 7)-dimensional plane orthogonal to the reaction path at that value of s which minimizes the TST rate. For reactions at given energy [microcanonical variational transition-state theory (/uVT)], the bimolecular rate constant is given by [125]... 

An approximate rate constant, fea, can be calculated from probability that the reactants in the distribution of quantum state will collide and react in accord with the collision frequency. The approximate constant is greater than the measured rate constant, k. One approach to improving transition state theory with respect to calculating the rate constant is to alter the configuration of the transition state used in the energy calculations in order to effect a change in In fact, the calculations are performed in such a way that the calculated rate constant is a minimum and thereby approaches the observed k. Just as energy minimization is accomplished by means of the... 

For a reaction with a defined transition state and without recrossing, reaction rate can be well approximated by many methods. For such reaction, we can assume that there is a dynamics bottleneck located at the transition state (conventional transition state theory, TST) or at a generalized transition state obtained by a canonical (CTV) or microcanonical (/zVT) criterion. In the later cases, the dividing surface is optimized variationally to minimize the recrossing. Evans first proposed to place the transition state at the location that maximizes the free energy of activation which provides a key conceptual framework for modern variational transition state theory [33]. However, recrossing always possibly exists and only a full-dimensional reactive scattering dynamics calculations are able to provide us the exact rate constant on a defined PES. Eor a detailed discussion, one may refer to the reviews by Truhlar et al. [38,136]. 

Figure 11.22 A simple unified model for free energy change of a chemical reaction in solution. Each parabola is a function of the solvent displacement coordinate rand the solute reaction coordinate q. The minimal energy path followed by the system, as shown, involves both coordinates, just as in the toy model of Section 11.2.2.1. Here we do not couple the two motions, although we could. To apply transition state theory we need to know where is the lowest energy barrier and what is its height.

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