Intrinsic reaction path

A transition structure is, of course, a maximum on the reaction pathway. One well-defined reaction path is the least energy or intrinsic reaction path (IRC). Quasi-Newton methods oscillate around the IRC path from one iteration to the next. Several researchers have proposed methods for obtaining the IRC path from the quasi-Newton optimization based on this observation. 

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. 

MODELING CHEMICAL REACTIONS MD ALONG INTRINSIC REACTION PATHS... 

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 ... 

Michalak A, Ziegler T, First-principle molecular dynamic simulations along the intrinsic reaction paths, J Phys Chem A, 105, 4333—4343 (2001)... 

Fukui s reaction path, corresponding to a vibrationless and rotationless trajectory, passes gradually into the normal decomposition mode of the reactants (or products) or into the transition vector of the activated complex. Strictly speaking, Fukui s concept requires the knowledge of an accurately localized saddle point. However, it is also possible to exploit Fukui s procedure for approximately localized saddle points these points are usually obtained by an independent method. The respective resulting path is then an approximation to the real intrinsic reaction path. 

This is supported by computed rate constants with tunneling contributions using the semiclassical Wentzel-Kramers-Brillouin (WKB) theory. The WKB procedure requires a carefully described intrinsic reaction path, and... 

The Intrinsic Reaction Path. - The intrinsic reaction path was originally proposed by Fukui.128,129 In this case structure is changed according to... 

Ultimately, the intrinsic reaction path defines a unique way in which the structure of a system is allowed to evolve. Thus, in a molecular-dynamics calculation the system is no longer allowed to change structure completely freely, but has to change along the intrinsic reaction path. This leads to an extra constraint on the possible structural degrees of freedom that has to be included in a practical molecular-dynamics calculation. This was done recently by Michalak and Ziegler130 who showed how the approach could be combined with the Car-Parrinello method that we discussed in Section 2.3. 

The electronic rearrangements associated with bond breaking/forming processes determined five steps along the intrinsic reaction path, the ELF isosurfaces that characterized... 

The energy variations along the intrinsic reaction path (IRP) and the ADMP trajectory are reported in Figures 2 and 3, respectively. We want to underline that the IRP corresponds to a unique and constrained minimum energy path and does not contain any time information, whereas the ADMP profile is computed along a trajectory issued by a dynamics simulation. Therefore, any direct (i.e. point-to-point) comparison is misleading. Nevertheless, their global differences can be discussed. 

Fig. 7. Intrinsic Reaction Path of H2SO/HSOH rearrangement reaction computed with the 6-3IG basis set...

Wu and Kaeding correlated the product distribution of the conversion of methanol on ZSM-5 catalysts with the a-value, a measure of the catalyst activity. Their results, at complete conversion of methanol, demonstrated that only catalysts with a lower than 30 are able to obtain high selectivities toward light olefins at high conversion. It was also advised that HZSM-5 catalysts with very high Si/Al-ratio (800) should be used to avoid diffusion disguise of the true intrinsic reaction path. ° ... 

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... 

This is an equation for the path of steepest decent. There are two paths of steepest descent from the saddle point, one toward reactants and the other toward the products. The combined path from reactants to products is called the intrinsic reaction path (IRP) [33-39]. Friction has eliminated the oscillatory motion from this path, so that it resembles the dashed path shown in Fig. 3. 

There are two distinct reaction pathways for dissociation of the most stable trans-HCOH structure, denoted as routes A and B. Only the structure at the intermediate minimum for the formaldehyde radical cation has more than a plane of symmetry. These three examples give some impression of the variation in the behavior observed in intrinsic reaction paths. 

Figure 8. Energy profile along the intrinsic reaction paths for reaction (3.15), shown relative to the energy of the formaldehyde radical cation (see Refs. 56 and 57). There are two separate routes for the dissociation of structure 1 through to a weak complex in the product valley, structure S. The paths were calculated at the Hartree-Fock/6-31G level of theory. The molecular structures at the stationary points on the paths are sketched.

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. ... 

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