Activated complex and solvent

The repulsive term of equation (3.34) is related to the sizes of reactants, activated complex and solvent molecules, closely akin to AFiJtrOf the classical interpretation i.e. positive for a bond-breaking process. The compressibility effect on the critical-region activation volume contributes very significantly via the attractive term. Once it has been normalised out, specific solute solvent electrostatic interactions (dipole-dipole and induction forces) form the remaining attractive contribution. The van der Waals equation of state yields the following expression at infinite dilution ... 

In transition state theory, a reaction takes place only if two molecules acquire enough energy, perhaps from the surrounding solvent, to form an activated complex and cross an energy barrier. 

Should a complete potential energy surface be subjected to outer and inner effects, then a new potential energy surface is obtained on which the corresponding rection paths can be followed. This is described in part 4.3.1 by the example of the potential energy surface of the system C2H5+ jC2H4 under solvent influence. After such calculations, reaction theory assertions concerning the reaction path and the similarity between the activated complex and educts or products respectively can be made. 

Hydrolyses of p-nitrophenyl and 2,4-dinitrophenyl sulfate are accelerated fourfold and eightfold, respectively, by cycloheptaamylose at pH 9.98 and 50.3° (Congdon and Bender, 1972). These accelerations have been attributed to stabilization of the transition state by delocalization of charge in the activated complex and have been interpreted as evidence for the induction of strain into the substrates upon inclusion within the cycloheptaamylose cavity. Alternatively, accelerated rates of hydrolysis of aryl sulfates may be derived from a microsolvent effect. A comparison of the effect of cycloheptaamylose with the effect of mixed 2-propanol-water solvents may be of considerable value in distinguishing between these possibilities. 

Figure 3. Equipotential sections through the potential energy surface for an exchange reaction, as in Figure 2. The heavy horizontal line indicates the solvent configuration appropriate to the activated complex and is the solvent configuration at which inner-sphere tunneling takes place.

The barrier that the reaction must overcome in order to proceed is determined by the difference in the solvation of the activated complex and the reactants. The activated complex itself is generally considered to be a transitory moiety, which cannot be isolated for its solvation properties to be studied, but in rare cases it is a reactive intermediate of a finite lifetime. The solvation properties of the activated complex must generally be inferred from its postulated chemical composition and conformation, whereas those of the reactants can be studied independently of the reaction. For organic nucleophilic substitution reactions, the Hughes-lngold rales permit qualitative predictions on the behavior of the rate when the polarity increases in a series of solvents, as is shown in Reichardt (Reichardt, 1988). 

When an ion is solvated the solvent molecules are packed around the ion, and occupy a smaller volume than they would in pure solvent. For reaction between two ions of opposite charge, formation of the activated complex releases solvent molecules from their solvation sheaths, thereby increasing their volume compared... 

The opposite is found when like charged ions react. Overall, solvent molecules become more tightly packed on forming the activated complex and the overall volume decreases, giving a positive pressure effect. 

From this equation originates the statement that the rate constant is determined by the free energy of activation. Furthermore, as also discussed in Section 6.6, the preexponential factor in front of the activation energy AE is related to the entropy of activation. For reactions in solution, it is important to notice that the values of AA , AS , and AEf are determined by the activated complex and the reactant as well as by the surrounding solvent molecules. 

The Hamiltonian of Eq. (10.15) is, of course, valid for any configuration of the system, and also when an activated complex AB is formed and the identity of the reactants is lost. It will then be natural to restructure the terms in Eq. (10.15), so the Hamiltonian will be a sum of a Hamiltonian for the activated complex, a Hamiltonian for the solvent, and an interaction energy term between the activated complex and the solvent ... 

Fig. 10.2.1 Reactants A and B in a solvent cage . V b is the intramolecular gas-phase potential of the activated complex. Fsoi is the intermolecular potential of the pure solvent. V t is the intermolecular potential that describes the interaction between the activated complex and all the solvent molecules.

From this it is clear that the solvent effect on the rate constant amounts to a renormalization of the energy barrier from being Ec in the gas phase to Ec + Wmean in solution. This represents the net effect of stabilization of the activated complex and the reactants in the solution. 

The structure of the activated complex, and thus y may depend on the nature of the solvent for liquid-phase reactions. Here, we focus on gas-phase reactions therefore, we assume that y is unity in subsequent analyses and replace the activity at by the partial pressure P, for an ideal gas. The rate rAB thus becomes... 

Fig. 5-3. One-dimensional Gibbs energy diagram for a chemical reaction in two different solvents I and II [cf. Figs. 5-1 and 5-2). AGj and AG, standard molar Gibbs energies of activation in solvents I and II AG jj and AGj jj standard molar Gibbs energies of transfer of the reactants R and the activated complex from solvent I to solvent II, respectively.

Fig. 5-5. Schematic one-dimensional relative enthalpy diagram for the exothermic bimolecular displacement reaction HO + CH3—Br —> HO—CH3 + Br in the gas phase and at various degrees of hydration of the hydroxide ion [485]. Ordinate standard molar enthalpies of (a) the reactants, (b, d) loose ion-molecule clusters held together by ion-dipole and ion-induced dipole forces, (c) the activated complex, and (e) the products. Abscissa not defined, expresses only the sequence of (a). .. (e) as they occur in the chemical reaction. The barrier heights ascribed to the activated complex at intermediate degrees of hydration were chosen to be qualitatively consistent with the experimental rate measurements cf. Table 5-3 [485]. Possible hydration of the neutral reactant and product molecules, CH3—Br and HO—CH3, is ignored. The barrier height ascribed to the activated complex in aqueous solution corresponds to the measured Arrhenius activation energy. A somewhat different picture of this Sn2 reaction in the gas phase, which calls into question the simultaneous solvent-transfer from HO to Br , is given in reference [487].

Concerted + n s] cycloadditions are, in principle, forbidden by orbital symmetry [90]. This restriction is bypassed when these reactions occur via zwitterions or biradicals, or by the symmetry-allowed [A + 2 ] process. Since cycloadditions proceeding through zwitterionic intermediates or dipolar activated complexes should be affected by solvent polarity, the investigation of the solvent effects on rates can be of considerable value when considering potential models for the activated complex and the reaction mechanism [91-93]. The possible solvent effects on one-step and two-step cycloaddition reactions are shown schematically in Fig. 5-6 [92] ... 

Fig. 5-6. Gibbs energy diagram for (a) one-step cycloaddition reactions proceeding via a dipolar activated complex, and (b) two-step cycloaddition reactions proceeding via a zwitterionic intermediate, in both nonpolar (solvent 1) and polar solvents (solvent II) [92]. For the sake of simplicity, no notice is taken of the different solvation of the initial reactants.

Ab initio MO calculations for the uncatalyzed [2 + 2]cycloaddition reaction between ketenes e.g. chloroketene) and carbonyl compounds e.g. formaldehyde) to yield oxetan-2-ones (y9-lactones) predict a relatively synchronous, concerted process, with a [ 2s + 2s +, i2s)] arrangement of the reactants in the activated complex and a negligible solvent effect [813],... 

In any solution reaction, cavities in the solvent must be created to accommodate reactants, activated complex, and products. Thus, the ease with which solvent molecules can be separated from each other to form these cavities is an important factor in solute solubility cf. Section 2.1). Furthermore, because solubility and reactivity are often related phenomena, the intermolecular forces between solvent molecules must also influence rates of reaction. The overall attractive forces between solvent molecules gives the solvent as a whole a cohesion which must be overcome before a cavity is created. The degree of cohesion may be estimated using the surface tension, but a more reliable estimate is obtained by considering the energy necessary to separate the solvent molecules. This is known as the cohesive pressure c (also called cohesive energy density) [228-... 

Examples of the solvent-influenced competition between concerted [4 -I- 2]Diels-Alder type cycloaddition reactions and 1,4-dipolar reaction pathways with zwitterionic intermediates can be found in references [677-679], For example, in solvents of low polarity (CHCI3, CH2CI2), homofuran reacts with tetracyanoethene to form the seven-membered [4 -I- 2]cycloadduct A in quantitative yield. In solvents of high polarity (CH3CN), however, the [2- -2]cycloadduct B predominates, formed via a 1,4-dipolar activated complex and a zwitterionic intermediate [679] cf. Eq. (5-142). 

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