Reaction potential energy curve

Figure A3.12.5. A model reaction coordinate potential energy curve for a fluxional molecule. (Adapted from [30].)...

Figure C3.2.1. A slice tlirough tlie intersecting potential energy curves associated witli tlie K-l-Br2 electron transfer reaction. At tlie crossing point between tlie curves (Afy, electron transfer occurs, tlius Tiarjiooning tlie species,...

A transition structure is the molecular species that corresponds to the top of the potential energy curve in a simple, one-dimensional, reaction coordinate diagram. The energy of this species is needed in order to determine the energy barrier to reaction and thus the reaction rate. A general rule of thumb is that reactions with a barrier of 21 kcal/mol or less will proceed readily at room temperature. The geometry of a transition structure is also an important piece of information for describing the reaction mechanism. 

FIGURE 17.2 Illustration of the reaction coordinate for a reaction with a change in the electronic state, (a) Potential energy curves for the two electronic states of the system. (A) Avoided crossing that can be seen in single-detenninant calculations. 

A kinetic scheme and a potential energy curve picture ia the ground state and the first excited state have been developed to explain photochemical trans—cis isomerization (80). Further iavestigations have concluded that the activation energy of photoisomerization amounts to about 20 kj / mol (4.8 kcal/mol) or less, and the potential barrier of the reaction back to the most stable trans-isomer is about 50—60 kJ/mol (3). 

Such diagrams make clear the difference between an intermediate and a transition state. An intermediate lies in a depression on the potential energy curve. Thus, it will have a finite lifetime. The actual lifetime will depend on the depth of the depression. A shallow depression implies a low activation energy for the subsequent step, and therefore a short lifetime. The deeper the depression, the longer is the lifetime of the intermediate. The situation at a transition state is quite different. It has only fleeting existence and represents an energy maximum on the reaction path. 

What are the energies for each species Plot the general shape of the potential energy curve for this reaction. 

Potential energy curves for a reaction proceeding homogenously (full curve) or on a surface (dotted line). 

The original ideas of Evans and Polanyi [1] to explain such a Hnear relation between activation energy and reaction energy can be illustrated through a two-dimensional analysis of two crossing potential energy curves. 

If one assumes the potential energy curves to have a similar parabolic dependence on the displacement of the atoms, a simple relation can be deduced between activation energy, the crossing point energy of the two curves, and the reaction energy. One then finds for a ... 

Fig. 22 a and b. Schematic representation of the potential energy curves for a M +. L ion pair, (a) the excited pair M. L returns nonradiatively to the ground state. L. (b) in competition with the process in (a) a photochemical reaction (P products) is possible (modified from Ref. [1])... 

From these potential energy curves, the reaction rate can be calculated with the aid of Kramers theory. In the limit of a high solvent friction y, the rate is given by Kramers [1940] and Zusman [1980]... 

Reaction mechanisms in chemistry are often written as a sequence of chemical structures, and such structures are referred to as reactive intermediates. Indeed, these intermediates often correspond to local minima on the potential energy curve—as shown in Figure 9.1—but need not do so, and the definition of a reactive intermediate... 

Let us now turn to the description of the reaction pathways. Figure 13-5 schematically depicts the shapes of the corresponding potential energy curves for the sextet and quartet spin-states and Table 13-11 contains the thermochemical information obtained at different levels of theory. 

Figure 4.61 Potential-energy curves for reactions inserting singlet (circles), triplet (triangles), and quintet (squares) Ti into H2. The reaction coordinate R is the distance between Ti and the midpoint of H2, and the zero of energy corresponds to R = oo for ground-state (triplet) Ti + H2.

Figure 4.67 depicts the potential-energy curve for reaction (4.102) along an adiabatic reaction coordinate (R = /Oimc) obtained by stepping along the H—CH3 stretching coordinate with full optimization of geometries at each step. As shown in Fig. 4.67, the reaction exhibits a substantial barrier ( 20.5 kcal mol-1) and overall exothermicity. 

Figure 4.71 The potential-energy curve for the Ti- C2H4 insertion reaction (4.103) (circles, solid line), with leading long-range donor-acceptor interactions of nTi->-7Tcc+ (triangles, dotted line) and ncc n-rF (crosses, dashed line) types. (.R is the distance from Ti to the midpoint of C2.)...

Figure 5.1 Potential energy curves for an outer-sphere reaction the upper curve is for the standard equilibrium potential oo the lower curve for

In the general case R denotes a set of coordinates, and Ui(R) and Uf (R) are potential energy surfaces with a high dimension. However, the essential features can be understood from the simplest case, which is that of a diatomic molecule that loses one electron. Then Ui(R) is the potential energy curve for the ground state of the molecule, and Uf(R) that of the ion (see Fig. 19.2). If the ion is stable, which will be true for outer-sphere electron-transfer reactions, Uf(R) has a stable minimum, and its general shape will be similar to that of Ui(R). We can then apply the harmonic approximation to both states, so that the nuclear Hamiltonians Hi and Hf that correspond to Ui and Uf are sums of harmonic oscillator terms. To simplify the mathematics further, we make two additional assumptions ... 

Figure 1, Potential energy curves for the reaction NH3+ HCL NH4CI. Each curve, corresponding to a fixed N-CI distance, is obtained by varying the position of the hydrogen atom lying between the N and Cl atoms. Top calculations in vacuo. Bottom calculations in solvent.

Figure 2. Potential energy curves for the reaction NH3 + HCL NH4CI. The curves are for fixed N-Cl distance, R(N-C1) = 5.91 a.u., and variation of the H positions.

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