Thermal reactions energy profiles

Fig. 19 The reaction energy profiles for thermal (on the left) and radical-anionic (on the right) C1-C6 and C1-C5 cyclizations of the parent enediyne computed at the B3LYP/ 6-31G level.

Figure 9.1. Energy profile for (a) a thermal reaction showing a high-energy intermediate, and (b) a photochemical reaction showing a conical intersection.

Fig. 3 Potential energy profiles for the concerted and the stepwise mechanism in the case of a thermal reductive process. E is the electrode potential for an electrochemical reaction and the standard potential of the electron donor for a homogeneous reaction. For an oxidative process, change - into + and donor into acceptor.

Figure 3.1 Energy profiles for photochemical and thermal reactions.

FIGURE 3.1 Comparison of the energy profile of thermal and photochemical reaction courses. R and R are reactants, TS and TS are transition states, E, and E,, activation energies for the ground and excited states, respectively IP, intermediate photochemical product P and Pph, products of thermal and photochemical reactions, respectively. 

Equation for Electric Field Strength. To include electron-impact source terms in continuity equations for neutral species and to include the effect of ion bombardment on the rate of surface reactions, equations that predict electron and ion densities, momentums, and energy profiles are required. The profiles require an equation for the electric field strength. In general equations for electron and ion continuities (these equations yield electron density and ion density, respectively), electron and ion momentums (for electron and ion net or directed velocity), and electron and ion energies (for electron and ion random or thermal energy) must be solved. Finally, the electric field profile is obtained from Poisson s equation. 

You should already be familiar with the mechanism for the thermal chlorination of methane. We will use Figure 1.17 to review briefly the net equation, the initiation step, and the propagation steps of the monochlorination of methane. Figure 1.18 shows the energy profile of the propagation steps of this reaction. 

The basic principles describing the efFects of CT complexes on the energy profile along the reaction coordinate stem from the theory of electron transfer. Redox processes may occur (i) as ground-state thermal reactions, (ii) by direct irradiation of the CT band, and (iii) upon photoexcitation of one of the redox partners followed by diffusional complex formation [4, 24], as depicted in Chart 3. 

It has in fact been anticipated for many years that the CT free energy surfaces may deviate from parabolas. A part of this interest is provoked by experimental evidence from kinetics and spectroscopy. Eirst, the dependence of the activation free energy, Ff , for the forward (/ = 1 ) and backward i = 2) reactions on the equilibrium free energy gap AFq (ET energy gap law) is rarely a symmetric parabola as is suggested by the Marcus equation,Eq. [9]. Second, optical spectra are asymmetric in most cases and in some cases do not show the mirror symmetry between absorption and emission.In both types of experiments, however, the observed effect is an ill-defined mixture of the intramolecular vibrational excitations of the solute and thermal fluctuations of the solvent. The band shape analysis of optical lines does not currently allow an unambiguous separation of these two effects, and there is insufficient information about the solvent-induced free energy profiles of ET. 

Figure 1.4 A schematic diagram of chemical potential changes at the stationary occurrence of a stepwise reaction R Yq Y2 P, where R and P are the initial reactant and final product of the reaction, while Yq and Y2 are thermalized Intermediates. The minimums in the traditional potential energy profile relate to the standard chemical potentials of thermalized external reactants and intermediates. However, actual chemical transformations of the intermediates occur at stationary values Pyi and pvz (bold lines), the rates of these transformations being dependent on the difference of the corresponding thermodynamic rushes and the values of truncated rate constants e-,j (the latter are functions of standard chemical potentials of the transition states only).

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