Reaction paths, energy

FIGURE 8 A comparison of reaction energy paths for hydrogen-assisted and direct activation of CO on the corrugated Ru(1121) surface. 

Figure 3.48. The activation of NH3 by Pt(lll). Reaction energy paths and structures of reaction intermediates and their corresponding transition states. Reaction energy diagram for the transformation of NH3 to Nad.-------NHs --------NHs+Oads NHs+OHads -...

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... 

Chemical processes, such as bond stretching or reactions, can be divided into adiabatic and diabatic processes. Adiabatic processes are those in which the system does not change state throughout the process. Diabatic, or nonadiabatic, processes are those in which a change in the electronic state is part of the process. Diabatic processes usually follow the lowest energy path, changing state as necessary. 

In order to define how the nuclei move as a reaction progresses from reactants to transition structure to products, one must choose a definition of how a reaction occurs. There are two such definitions in common use. One definition is the minimum energy path (MEP), which defines a reaction coordinate in which the absolute minimum amount of energy is necessary to reach each point on the coordinate. A second definition is a dynamical description of how molecules undergo intramolecular vibrational redistribution until the vibrational motion occurs in a direction that leads to a reaction. The MEP definition is an intuitive description of the reaction steps. The dynamical description more closely describes the true behavior molecules as seen with femtosecond spectroscopy. 

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... 

A postulated reaction mechanism is a description of all contributing elementary reactions (we will call this the kinetic scheme), as well as a description of structures (electronic and chemical) and stereochemistry of the transition state for each elementary reaction. (Note that it is common to mean by the term transition state both the region at the maximum in the energy path and the actual chemical species that exists at this point in the reaction.)... 

FIGURE 2.1. The least-energy path of the CH4 + Cl— CH3 + HC1 reaction. This one-dimensional curve is obtained by cutting the two-dimensional surface of Figure 1.7 along the a—>b— c—path, which is taken here as the reaction coordinate. 

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]. 

In most cases, the observables measured in the study of a chemical reaction are interpreted under the following (often valid) assumptions (1) each product channel observed corresponds to one path on the PES, (2) reactions follow the minimum energy path (MEP) to each product channel, and (3) the reactive flux passes over a single, well-defined transition state. In all of the reactions discussed in this chapter, at least one, and sometimes all of these assumptions, are invalid. 

One disadvantage of statistical approaches is that they rely on two of the assumptions stated in the introduction, namely, that reactions follow the minimum energy path to each product channel, and that the reactive flux passes through a transition state. Several examples in Section V violate one or both of these assumptions, and hence statistical methods generally cannot treat these instances of competing pathways [33]. 

Figure 5. Potential-energy diagram including zero-point energy for the HCC0 + 02 reaction. Energies of reactants and products ignore differences between and Intermediates species are denoted by Roman numerals, saddle points by Arabic numerals, and reactions paths are labeled A-F. Reproduced from [47] by permission of the PCCP Owner Societies.

G. OH + CH3F Avoiding the Minimum Energy Path The reaction... 

Figure 11. The minimum energy path of the OH + CH3F reaction, not including zero-point energy. The four labeled structures are (A), the central barrier TS (B), the nearly collinear backside well complex [HOCH3 F] (C) the transition of the F atom toward the OH moiety (D) the hydrogen-bonded [CH3OH F ] structure. Reprinted from [63] with permission from the American Association for the Advancement of Science.

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