Intrinsic reaction path coordinates

Although intrinsic reaction coordinates like minima, maxima, and saddle points comprise geometrical or mathematical features of energy surfaces, considerable care must be exercised not to attribute chemical or physical significance to them. Real molecules have more than infinitesimal kinetic energy, and will not follow the intrinsic reaction path. Nevertheless, the intrinsic reaction coordinate provides a convenient description of the progress of a reaction, and also plays a central role in the calculation of reaction rates by variational state theory and reaction path Hamiltonians. 

The choice of reaction path definition used as the reference for such a constrained dynamics is arbitrary any path may be used in practice. However, a natural choice in order to ensure that the simulation moves along the bottom of the potential energy valley connecting reactants/products with TS is the intrinsic reaction path (IRP) of Fukui.46,47 IRP by definition goes along the bottom of such a valley. IRP simply corresponds to a steepest descent path in a mass-weighted coordinates ... 

A. Intrinsic Reaction Paths and Natural Collision Coordinates Variations on the Same Theme Potentials for Distinguished Coordinate Paths IRP Potentials in Internal (Valence) Coordinates Reaction Surfaces V. Dynamics on Path-Based Surfaces... 

A. Intrinsic Reaction Paths and Natural Collision Coordinates... 

This paper reviews recent (and current) work in my research group which is aimed at developing practical methods for describing reaction dynamics in polyatomic systems in as ab initio a framework as possible. To overcome the dimensionality dilemma of polyatomic systems—i.e., the fact that the potential energy surface depends on 3N-6 internal coordinates for an N atom system—we have developed dynamical models based on the intrinsic reaction path", i.e., the steepest descent path which connects reactants and products through the transition state (i.e., saddle point) on the potential energy surface. ... 

With respect to a more quantitative characterization of the PE function along the reaction coordinate, in terms of local minima and barriers between them, the minimum energy reaction (MER) path concept is more promising. The MER path approach, also called the intrinsic reaction path approach [39], is defined as the steepest descent path from the transition state (a saddle point on the PE surface) down to the local minima that are equilibrium geometries of reactant and product. It has been shown [40] how to express the Hamiltonian of an N atom molecular system in terms of the reaction coordinate, and this approach has been used successfully to describe a variety of processes in polyatomic reaction dynamics. It is also well known that for many reactions (PT process among them) the MER path is very sharply curved, so that the relevant dynamical motion deviates far from it. This is not a particularly important point for our present purpose of a qualitative characterization of the PE surfaces relevant for the PT reaction, as far as we do not consider the dynamics of... 

By following the steepest descent path we change the coordinates of all the N atoms of the system. If the atoms were moving infinitely slowly the path would be mapped out by the classical equations of motion. However, the displacement of the atoms should not be mass dependent. This can be avoided by introducing mass-weighted coordinates in a similar manner to what is done in the normal mode treatment of vibrational motion. We therefore introduce the socalled intrinsic reaction path (IRP) [19]. The IRP is defined as the steepest descent path in mass-weighted coordinates. Thus we have the mass weighted cartesian position coordinates and notation, such that... 

The dynamics of a reaction complex is connected with the intrinsic reaction coordinate (IRC) or, better, intrinsic reaction path (IRC path), which is simply the steepest descent path expressed in mass-weighted Cartesian coordinates. The IRC path was first used by Eliason and Hirschfelder, and later investigated in great detail by Fukui and co-workers. ... 

As shown by Valtazanos and Ruedenberg [93], steepest descent paths (e.g., the Fiikui intrinsic reaction coordinate)... 

Techniques have been developed within the CASSCF method to characterize the critical points on the excited-state PES. Analytic first and second derivatives mean that minima and saddle points can be located using traditional energy optimization procedures. More importantly, intersections can also be located using constrained minimization [42,43]. Of particular interest for the mechanism of a reaction is the minimum energy path (MEP), defined as the line followed by a classical particle with zero kinetic energy [44-46]. Such paths can be calculated using intrinsic reaction coordinate (IRC) techniques... 

Fig. 5.29 Method for correcting the path followed by a steepest descents algorithm to generate the intrinsic reaction coordinate. The solid line shows the real path and the dotted line shows the algorithmic approximation to it. (Figure redrawn from Gonzalez C and H B Schlegel 1988. An Improved Algorithm for Reaction Path Following. Journal of Chemical Physics 90 2154-2161.)...

The MEP is defined as the path of steepest descent in mass-weighted Cartesian coordinates. This is also called intrinsic reaction coordinate (IRC). In reality, we know that many other paths close to the IRC path would also lead to a reaction and the percentage of the time each path is taken could be described by the Boltzmann distribution. 

MEP (IRC, intrinsic reaction coordinate, minimum-energy path) the lowest-energy route from reactants to products in a chemical process MIM (molecules-in-molecules) a semiempirical method used for representing potential energy surfaces... 

Reaction path following (using intrinsic reaction coordinates). 

An intrinsic reaction coordinate (IRC) is concerned with travel along the reaction path it can be defined by the path taken by a classical particle sliding from a saddle point down to a minimum. 

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