Energy diagrams continued

Figure 1.14 shows the potential energy diagram for the decomposition of HI. As can be seen, in-order to reach the activated complex or transition state the proper orientaion (and JsufFicent collision energy must be achieved. Once these requirements/areyiCnieved the reaction continues on to completion and the products are fc... 

Winstein et al. [45] first presented evidence for the concept that different types of electrophilic species, each with distinct reactivities, may participate in reactions involving cationic intermediates. As shown in Eq. (36), Winstein et al. proposed that four species are in equilibrium, including covalent electrophiles, contact ion pairs, solvent-separated ion pairs, and free ions. In addition, ion pairs may aggregate in more concentrated solutions- According to this concept, electrophilic species do not react with a continuous spectrum of charge separation, but rather in well-quantified minima in the potential energy diagram. 

Both exothermic and endothermic reactions are often represented graphically with potential energy diagrams, as seen in Figure l-5b. Maybe you can see why endothermic reactions are sometimes called uphill reactions, as they need energy to be continuously added in order to continue. 

Fig. 8. Potential energy diagram illustrating effect of extra resonance energy in transition state (dotted line) compared with absence of negative group effect (continuous line).

Fig. 26. Potential energy diagrams showing possible types of transition from octahedral (II) to tetrahedral (I) coordination —, stable - - -, unstable, (a) Transformation from stable octahedral to stable tetrahedral coordination, (b) development of unstable octahedral coordination before transition to stable tetrahedral coordination, (c) unstable octahedral coordination changing continuously to tetrahedral coordination (109).

Figure 14 Third order correlation energy diagrams involving singly excited intermediate states and one one-electron interactions for a closed-shell system described in zero order by a single determinantal wave function. The eight Brandow diagrams of this type are shown in (a). The exchange diagrams are shown in Goldstone form in (b) (continued overleaf)...

The main difference between the Hamiltonian and dissipative systems arises from the conservation condition that applies to the former. In Hamiltonian systems, the total energy is fixed. A trajectory with a given initial condition and energy will continue with that same energy for the remainder of the trajectory. In the phase space representation, this will result in a stable trajectory that does not pull in toward an attractor. A periodic trajectory in a Hamiltonian system will have an amplitude and position in the phase space that is determined by the initial conditions. In fact, the phase space representation of a Hamiltonian system often includes many choices of initial conditions in the same phase space portrait. The Poincare section, to be described below, likewise contains many choices of initial conditions in one diagram. 

In order to understand the Woodward-Hoffmann rules for determining the stereochemistry of several different types of concerted reactions, let us first consider the ground and excited states of a normal reaction. The ground state energy rises continuously to the transition state and then falls to the product. Often, this is the only state shown in such reaction profile diagrams. The excited state is not generally involved in the reaction, but often has a minimum above the transition state, as shown in Fig. 4.4. 

Figure 13 Schematic energy diagram of a sputtered atom leaving a metal surface. Electron tunneling can occur If the electronic level of the outgoing particle has the same energy as electronic levels in the metals. In reality, the width and energy position of such a level vary continuously with distance from the surface.

The evaluation of the permeability is simple in principle, depending upon the conditions of continuity for the wave function in passing from one part of the energy diagram to another, and it is frequently unnecessary to obtain an explicit expression for the wave function. It is convenient to define the curvature of the barrier at the top by a frequency Vj given by... 

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