Transition state and reactants

The rates of radical-forming thermal decomposition of four families of free radical initiators can be predicted from a sum of transition state and reactant state effects. The four families of initiators are trarw-symmetric bisalkyl diazenes,trans-phenyl, alkyl diazenes, peresters and hydrocarbons (carbon-carbon bond homolysis). Transition state effects are calculated by the HMD pi- delocalization energies of the alkyl radicals formed in the reactions. Reactant state effects are estimated from standard steric parameters. For each family of initiators, linear energy relationships have been created for calculating the rates at which members of the family decompose at given temperatures. These numerical relationships should be useful for predicting rates of decomposition for potential new initiators for the free radical polymerization of vinyl monomers under extraordinary conditions. 

In Eq. (44), gei(T ) is the ratio of transition state and reactant electronic partition functions [31] and the rotational degeneracy factor = (2ji + l)(2/2 + 1) for heteronuclear diatomics, and will also include nuclear spin considerations in the case of homonuclear diatomics. 

For the present reaction, the presence of surrounding protein only marginally affects the barrier (it increases by 0.7 kcal/mol). A possible reason for the small protein effects could be that in the present model, the active site is not deeply buried inside the enzyme instead it is located on the interface of two monomers. Still, addition of the protein environment had effects on the active-site geometry. The reason this does not affect the total barrier height is that when comparing transition state and reactant, the protein effect appears to be relatively constant. 

Reactions defining absolute acidity, e.g., the reaction above for the acidity of HF, and absolute basicity are important special cases. Some comparisons between transition states and reactants will also likely fall into this category. These will be considered in Chapter 9. 

The transition state sum omits the reaction coordinate degree of freedom since it is not a bound vibration and does not contribute to the zero-point energy in the transition state. E% and Er are respectively the energy of the potential energy surface at transition state and reactants. Then,... 

Energies of molecules and transition states this tells us which isomer is favored at equilibrium, and (from transition state and reactant energies) how fast a reaction should go. 

Fig. 5.25 The reaction energy, the energy difference of products and reactants, determines the extent of a reaction, i.e. its equilibrium constant. The activation energy (the simple ab initio energy difference shown here is not exactly the conventional Arrhenius activation energy), the energy difference of transition state and reactants, partially determines the rate constant. Unfortunately, energy is ambiguous, since chemists use the terms potential energy, enthalpy (heat energy), and free energy see Section 5.5.2.1...

The two products are taken over the sets of equivalent hydrogen atoms in transition state and reactants, respectively, and t and r represent the numbers of equivalent hydrogen atoms in each set. 

First of all, let us compare transition state and reactants with regard to electron distribution. In the transition state, there is a partly formed bond between carbon and hydroxide ion and a partly broken bond between carbon and halide ion hydroxide ion has brought electrons to carbon, and halide ion has taken electrons away. Unless one of the two processes, bond-making or bond-breaking, has gone much further than the other, the net charge on carbon is not greatly different from what it was at the start of the reaction. Electron withdrawal or electron release by substituents should affect stability of transition state and reactant in much the same way, and therefore should have little influence on reaction rate. 

To understand how structure does influence the rate, let us compare transition state and reactants with regard to shape starting with the methyl bromide reaction. The carbon in reactant and product is tetrahedral, whereas carbon in the transition state is bonded to five atoms. As indicated before, the C—H bonds are arranged like the spokes of a wheel, with the C--OH and C—Br bonds lying along the axle (Fig. 14.2). 

The use of the same potential surface has allowed a detailed comparison of results obtained by trajectory calculations and by calculations using the transition-state model 199>. In the H + H2 reaction, the two assumptions incorporated in transition-state theory, i.e. equilibrium between transition state and reactants, and transmission coefficient equal to unity, seem to hold very well, but in the colhnear H +HBr H2 +Br reaction the transmission coefficient is found to be less than one, while in the reverse reaction H2 +Br - H +HBr the equilibrium condition is not satisfied. 

The first three terms on the right-hand side correspond to the Marcus relation for the nonadiabatic case where there is no coupling between the diabatic energy states (i.e. E = 0 at all values of the reaction coordinate). The fourth and fifth terms reflect the effect of the adiabatic coupling of the two surfaces on the transition state and reactant state, respectively, and < /2 AGjxn + 4AGin,l. ... 

Table 13. The difference in atomic Muliken s charges on two carbons involved in C-C bond breaking for monosubstituted cyclobutene between the corresponding transition state and reactant...

For unimolecular reactions, the transition state and reactant can differ by only one degree of vibrational freedom, thus... 

From the way that the reaction sequence (XXIV) is written, one might suppose that it is possible to look at the overall problem also in terms of macroscopic thermodynamic functions defined on a molal basis. Certainly this is so the equilibrium between transition state and reactants can be expressed in terms of a classical free energy of activation as... 

The term AAG in Eq. 5 is concerned with the differential effects of the solvent and the enzyme environment on the transition state and reactant state. If the enzyme provides stronger stabilizing interactions to the transition state than the reactant state relative to the difference in water, such an... 

Eyring s equation assumes that a thermodynamic equilibrium exists between the transition state and the state of the reactants and that the reaction rate is proportional to the concentration of particles at the high-energy transition state, k accounts for the fraction of molecules going into product state and AG represents the difference between Gibbs energy of transition state and reactants. If AG is expressed in terms of enthalpy (AH ) and entropy (AS ) of activation, fromEq. 3.114 ... 

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