Minimum energy paths , potential surfaces

In the chapter on reaction rates, it was pointed out that the perfect description of a reaction would be a statistical average of all possible paths rather than just the minimum energy path. Furthermore, femtosecond spectroscopy experiments show that molecules vibrate in many dilferent directions until an energetically accessible reaction path is found. In order to examine these ideas computationally, the entire potential energy surface (PES) or an approximation to it must be computed. A PES is either a table of data or an analytic function, which gives the energy for any location of the nuclei comprising a chemical system. 

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... 

After 28 years the perepoxide quasi-intermediate was supported by a two-step no intermediate mechanism [71, 72]. The minimum energy path on the potential energy surface of the reaction between singlet molecular oxygen ( A and dg-teramethylethylene reaches a vaUey-ridge inflection point and then bifurcates leading to the two final products [73]. 

Zhang Y, Liu H, Yang W (2000) Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface. J Chem Phys 112 3483-3492... 

Figure 1. (Left) Potential energy surface for the LiNC/LiCN isomerizing system drawn as a contours plot. The minimum energy path connecting the two stable linear isomers, LiNC (0 = 180°) and LiCN (6 = 0), is shown as a dotted line. 

A very perceptive treatment of chemical reaction dynamics, called the reaction path Hamiltonian analysis, states that the reactive trajectory is determined as the minimum energy path, and small displacements from that path, on the potential-energy surface [64-71]. The usual analysis keeps the full dimensionality of the reacting system, albeit with a focus on motion along and orthogonal to the minimum energy path. It is also possible to define a reaction path in a reduced dimensionality representation. 

Huge amount of studies by means of molecular orbital (MO) calculations have been reported in the literature, which calculate the structures of reactants, products, reactive intermediates, and TSs of possible reaction pathways, as well as minimum energy paths from the TSs to both the reactant and product sides on the potential energy surface (PES). The information thus obtained, together with experimental findings, has been used to deduce reaction mechanisms. The combined use of experiment and MO calculations has become a common method for physical organic chemists. However, it should be noted that the calculated structures and energies are at OK and that therefore the information obtained from MO calculations may not directly be related to experimental observation at a finite temperature. 

Once an adiabatic potential energy surface has been defined, the next step is to determine the minimum energy path (MEP). Within the... 

For JT problems of higher dimensions such as that for the T (e t2) problem, the adiabatic potential V is complicated and cannot be written down in an analytical form. However, in such problems, the least action path can be approximated by the minimum energy path (or path of steepest descent) on the adiabatic potential surface. It is the path for which the tangent to it is parallel to the gradient of the APES. 

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