Energy as a function of reaction

Figure 1.1 Transition-state saddle point diagram. Schematic representation of potential energy as a function of reaction coordinate.

Figure 1. Potential energy as a function of reaction coordinate for a self-exchange reaction. AE, energy barrier for thermal electron transfer (weak coupling) AE2, energy of an intervalence transition which is possible for the system.

The free energy as a function of reaction coordinates has been explicitly represented by Quack and Troe [36. 112] for the reaction... 

Figure 10.36 Activation strain model analysis of the CH, dissociation on the Rh(lll) surface. Interaction energy as a function of reaction coordinate (black line). of the CH,...

Figure 2.2 Schematic reaction activation energies as a function of reaction coordination. (For color version of this figure, the reader is referred to the oniine...

In addition to QC studies, reactive molecular dynamics (RMD) simulations using the reactive force field ReaxFF have been used to gain insight into reactions of singly reduced EC in the condensed (solution) phase [31]. In this study the reaction of Li /o-EC with both LiVo-EC and LiVc-EC has been studied in a solution of EC molecules. A snapshot of the system is shown in Fig. 7.5. RMD simulations were used to determine the free energy as a function of reaction coordinate (see below) and to examine the propensity of various radical combination reactions to occur in the condensed phase of an EC solvent. 

Fig. 36 Electron binding energies as a function of reaction progress for C-Cl reductive elimination from dinuclear Pd(in) structure A...

Photochemical reactions are the same as other chemical reactions, like addition, cleavage, or rearrangements of molecules. The actual difference is the way to supply energy. Here we discuss the classification of photochemical reactions on the basis of potential energy as a function of reaction coordinates. On this basis photochemical reaction is of following three types ... 

Figure 1. Quasiclassical cross-sections for the reaction D -I- H2 (w — 1,2 — 1) DH (v — 1, /) -f H at 1.8-eV total energy as a function of/. The solid line indicates results obtained without including the geometric phase effect. Boxes show the results with the geometric phase included using either 9o = 0 (dashed) or 9o = 11.5 " (dotted).

Figure 2.7 Potential energy as a function of location along the reaction coordinate. The solid line describes an undisturbed liquid the broken line applies to liquids subjected to shearing force.

The potential energy surface consists of two valleys separated by a col or saddle. The reacting system will tend to follow a path of minimum potential energy in its progress from the initial state of reactants (A + BC) to the final state of products (AB -F C). This path is indicated by the dashed line from reactants to products in Fig. 5-2. This path is called the reaction coordinate, and a plot of potential energy as a function of the reaction coordinate is called a reaction coordinate diagram. 

Actually the assumptions can be made even more general. The energy as a function of the reaction coordinate can always be decomposed into an intrinsic term, which is symmetric with respect to jc = 1 /2, and a thermodynamic contribution, which is antisymmetric. Denoting these two energy functions h2 and /zi, it can be shown that the Marcus equation can be derived from the square condition, /z2 = h. The intrinsic and thermodynamic parts do not have to be parabolas and linear functions, as in Figure 15.28 they can be any type of function. As long as the intrinsic part is the square of the thermodynamic part, the Marcus equation is recovered. The idea can be taken one step further. The /i2 function can always be expanded in a power series of even powers of hi, i.e. /z2 = C2h + C4/z. The exact values of the c-coefficients only influence the... 

Figure 1.5 Schematic state correlation diagram for radical addition to a carbon-carbon double bond showing configuration energies as a function of the reaction...

As discussed in previous chapters, one is often interested in calculating the free energy as a function of a given reaction coordinate . Such a free energy profile A( ) is defined as... 

Figure 5.4 Gibbs energy as a function of the extent of reaction.

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