State transition diagram

It is desirable and perhaps necessary to make the conditions, (21) and (23), explicit, since substitution of the equilibrium condition (12) into either (18) or (19), separately, gives results that makes this derivation appear suspect. The derivation is, however, valid, and it corresponds to a transition-state diagram containing three peaks. The last and highest one, which is lowered as the concentration of base increases, corresponds to the conversion of IV to product the first... 

Scheme 20. Transition state diagrams for oxo-imido reactions, illustrating steric effects.

Figure 9-15 (A) Transition state diagram illustrating Gibbs energy vs reaction coordinate for conversion of reactants to products in a chemical reaction. (B) Contour map of Gibbs energy vs interatomic bond distances for reaction B + X - A —> B-X+A.

A detailed molecular-level understanding of the role of solvation on the nature of Sn2 reaction pathways has been revealed only during the last decades. Fig. 5 compares the gas-phase Sn2 enthalpy diagram with two minima, first proposed by Brauman et al. [474], with the more familiar single transition-state diagram obtained in solution. 

Fio. 11. Transition state diagram for a two-step reaction showing how changes in structure which aSect principally the second step result in a nonlinear structure-reactivity correlation. From Kirsch and Jencks, (1964a). Reproduced with permission of the American Chemical Society. 

Nikolaidis, A. and Labuza, T.E Glass transition state diagram of a baked cracker and its relationship to gluten, /. Food Sci., 61, 803, 1996. 

Heterogeneous electron transfer can be envisioned with the aid of transition state diagrams. First consider the forward reaction, the transfer of an electron from the electrode to the oxidized species in solution adjacent to the electrode. A transition state diagram will in the first place reflect the reactant and the product free energy. The reactants are the oxidized species in solution and the electron in... 

Figure 1-10 Transition state diagrams for reduction at different electrode potentials.

Figure 1-14 Transition state diagram for electron transfer according to Marcus theory.

Figure 7.9 Transition state diagram illustrating the deuterium isotope effect the lower zero point energy of the carbon-deuterium bond is responsible for a correspondingly larger activation energy and lower reaction rate for bond cleavage.

These equations lead to fomis for the thermal rate constants that are perfectly similar to transition state theory, although the computations of the partition functions are different in detail. As described in figrne A3.4.7 various levels of the theory can be derived by successive approximations in this general state-selected fomr of the transition state theory in the framework of the statistical adiabatic chaimel model. We refer to the literature cited in the diagram for details. 

Figure A3.12.10. Schematic diagram of the one-dimensional reaction coordinate and the energy levels perpendicular to it in the region of the transition state. As the molecule s energy is increased, the number of states perpendicular to the reaction coordinate increases, thereby increasing the rate of reaction. (Adapted from [4].)...

The most stable nuclear configuration of this system is a pair of H2 molecules. There are three possible spin coupling combinations for H4 corresponding to three distinct stable product H2 pairs H1 H2 with H3 H4, H1 H3 with H2 H4, and H1 H4 with H2 H3. Each H atom contributes one electron, the dot diagrams indicate spin pairing. The three combinations are designated as Hfl), HOT), and H(III), respectively. They may be interconverted via square transition states, Figure 2. 

A potential energy diagram for nng inversion m cyclohexane is shown m Figure 3 18 In the first step the chair conformation is converted to a skew boat which then proceeds to the inverted chair m the second step The skew boat conformation is an inter mediate in the process of ring inversion Unlike a transition state an intermediate is not a potential energy maximum but is a local minimum on the potential energy profile... 

With the potential energies shown on a common scale we see that the transition state for formation of (CH3)3C is the highest energy point on the diagram A reaction can proceed no faster than its slowest step which is referred to as the rate determining step In the reaction of tert butyl alcohol with hydrogen chloride formation of the... 

Sketch a potential energy diagram for the reaction of 1 heptanol with hydrogen bromide paying careful attention to the positioning and structures of the intermediates and transition states... 

Section 4 9 The potential energy diagrams for separate elementary steps can be merged into a diagram for the overall process The diagram for the reac tion of a secondary or tertiary alcohol with a hydrogen halide is charac terized by two intermediates and three transition states The reaction is classified as a ummolecular nucleophilic substitution, abbreviated as SnI... 

Potential energy diagram (Section 4 8) Plot of potential en ergy versus some arbitrary measure of the degree to which a reaction has proceeded (the reaction coordinate) The point of maximum potential energy is the transition state Primary alkyl group (Section 2 13) Structural unit of the type RCH2— in which the point of attachment is to a pnmary carbon... 

Figure 5 The transition state ensemble is the set of trajectories that are crossing the transition state from reactant to product at equilibrium (shown as black dots). There are four types of trajectories, shown top to bottom in the diagram. (1) Starting as reactant, the trajectory crosses and recrosses the transition state and is deactivated as reactant. It does not add to the reactive flux. (2) Starting as reactant, the trajectory is deactivated as product. It adds +1 to the reactive flux. (3) Starting as product, the trajectory crosses and recrosses the transition state and is deactivated as product. Such a trajectory must be subtracted from the ensemble, so it counts —1 to the reactive flux. (4) Starting as product, the trajectory is deactivated as reactant. It does not contribute to the reactive flux.

A more complete analysis of interacting molecules would examine all of the involved MOs in a similar wty. A correlation diagram would be constructed to determine which reactant orbital is transformed into wfiich product orbital. Reactions which permit smooth transformation of the reactant orbitals to product orbitals without intervention of high-energy transition states or intermediates can be identified in this way. If no such transformation is possible, a much higher activation energy is likely since the absence of a smooth transformation implies that bonds must be broken before they can be reformed. This treatment is more complete than the frontier orbital treatment because it focuses attention not only on the reactants but also on the products. We will describe this method of analysis in more detail in Chapter 11. The qualitative approach that has been described here is a useful and simple wty to apply MO theory to reactivity problems, and we will employ it in subsequent chapters to problems in reactivity that are best described in MO terms. I... 

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. 

Fig. 5.11. Contrasting potential energy diagrams for stable and unstable bridged norbomyl cation. (A) Bridged ion is a transition state for rearrangement between classical structures. (B) Bridged ion is an intermediate in rearrangement of one classical structure to the other. (C) Bridged nonclassical ion is the only stable structure.

Z7. The cotr arison of activation parameters for reactions in two different solvents requires consideration of differences in solvation of both the reactants and the transition states. This can be done using a potential energy diagram such as that illustrated below, where A and B refer to two different solvents. By thermodynamic methods, it is possible to establish values which correspond to the enthalpy... 

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