Reaction mechanisms variational transition state theory

Benzofuroxan 79 can be generated from 2-nitrophenyl azide 80 (Scheme 49). Neighboring-group assistance within the pyrolysis leads to a one-step mechanism with an activation barrier of 24.6 kcal/mol at the CCSD(T)/6-31 lG(2d,p) level [99JPC(A)9086]. This value closely resembles the experimental one of 25.5 kcal/mol. Based on the ab initio results for this reaction, rate constants were computed using variational transition state theory. 

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. 

T. V. Albu, J. C. Corchado, D. G. Truhlar, J. Phys. Chem. A 105, 8465 (2001). Molecular Mechanics for Chemical Reactions A Standard Strategy for Using Multiconfiguration Molecular Mechanics for Variational Transition State Theory with Optimized Multidimensional Tunneling. 

There are two corrections to equation (12) that one might want to make. The first has to do with dynamical factors [19,20] i.e., trajectories leave Ra, crossing the surface 5/3, but then immediately return to Ra. Such a trajectory contributes to the transition probability Wfia, but is not really a reaction. We can correct for this as in variational transition-state theory (VTST) by shifting Sajj along the surface normals. [8,9] The second correction is for some quantum effects. Equation (14) indicates one way to include them. We can simply replace the classical partition functions by their quantum mechanical counterparts. This does not correct for tunneling and interference effects, however. 

Various quantum-mechanical theories have been proposed which allow one to calculate isotopic Arrhenius curves from first principles, where tunneling is included. These theories generally start with an ab initio calculation of the reaction surface and use either quantum or statistical rate theories in order to calculate rate constants and kinetic isotope effects. Among these are the variational transition state theory of Truhlar [15], the instanton approach of Smedarchina et al. 

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. 

Warshel and Chu [42] and Hwang et al. [60] were the first to calculate the contribution of tunneling and other nuclear quantum effects to PT in solution and enzyme catalysis, respectively. Since then, and in particular in the past few years, there has been a significant increase in simulations of quantum mechanical-nuclear effects in enzyme and in solution reactions [16]. The approaches used range from the quantized classical path (QCP) (for example. Refs. [4, 58, 95]), the centroid path integral approach [54, 55], and variational transition state theory [96], to the molecular dynamics with quantum transition (MDQT) surface hopping method [31] and density matrix evolution [97-99]. Most studies of enzymatic reactions did not yet examine the reference water reaction, and thus could only evaluate the quantum mechanical contribution to the enzyme rate constant, rather than the corresponding catalytic effect. However, studies that explored the actual catalytic contributions (for example. Refs. [4, 58, 95]) concluded that the quantum mechanical contributions are similar for the reaction in the enzyme and in solution, and thus, do not contribute to catalysis. 

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. 

In microscale model, the reactions generally refer to elementary reaction steps. The reaction network is closely related to the reaction mechanism and could be well obtained by quantum chemistry or ab initio calculations. The corresponding parameters, such as pre-exponential factors and activation energies, could be predicted based on transition state theory (TST) or variational transition state theory (VTST). 

Mechanics for Chemical Reactions A Standard Strategy for Using Multiconfiguration Molecular Mechanics for Variational Transition State Theory with Optimized Multidimensional Tunneling. 

Summary. Rate constants of chemical reactions can be calculated directly from dynamical simulations. Employing flux correlation functions, no scattering calculations are required. These calculations provide a rigorous quantum description of the reaction process based on first principles. In addition, flux correlation functions are the conceptual basis of important approximate theories. Changing from quantum to classical mechanics and employing a short time approximation, one can derive transition state theory and variational transition state theory. This article reviews the theory of flux correlation functions and discusses their relation to transition state theory. Basic concepts which facilitate the calculation and interpretation of accurate rate constants are introduced and efficient methods for the description of larger systems are described. Applications are presented for several systems highlighting different aspects of reaction rate calculations. For these examples, different types of approximations are described and discussed. 

Albu TV, Corchado JC, Truhlar DG (2001) Molecular mechanics for chemical reactions a standard strategy for using multiconfiguration molecular mechanics for variational transition state theory with optimized multidimensional tunneling. J Phys Chem A 105 8465-8487... 

Accurate quantum mechanical calculations on the D -f H2 reaction allow one to test the quantitative predictive ability of variational transition state theory with multidimensional tunneling contributions. Such VTST calculations agree with accurate quantum dynamics with an average eiTor of only... 

Transition state theory is based on the assumption of a dynamical bottleneck. The dynamical bottleneck assumption would be perfect, at least in classical mechanics, if the reaction coordinate were separable. Then one could find a dividing surface separating reactants from products that is not recrossed by any trajectories in phase space. Conventional transition state theory assumes that the unbound normal mode of the saddle point provides such a separable reaction coordinate, but dividing surfaces defined with this assumption often have significant recrossing corrections. Variational transition state theory corrects this problem, eliminating most of the recrossing. 

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