Initial and Final Systems

The above proposition leads to the following relations. The ratio of the activity product of F (s) to that of I (s), i.e.,,  

The affinity —AG of the steady reaction, i.e., the decrease of Helmholtz (Gibbs) energy of the steady reaction, equals, on the other hand, v, times that due to the conversion of I (5) into F (s), i.e., 

Consider the case of dependent intermediate absent. Equations (III.22) consist, in the present case of single route, of M(i) + Jf(i) = M = 8 — 1 equations with /S — 1 unknowns, v, /s. A theorem of algebra states that the equations have a definite solution, provided that the determinant. 

It follows that D g 0, hence that there exists such a set of p /s as to convert a set I (s) of reactants and products alone into I(s) without creating or consuming any intermediate besides. 

Such a set of p /s may not exist in the presence of dependent intermediates, since the number of simultaneous equations (III.22) is greater than that of the unknowns. Since all the equations need not be independent, such a set of i/, - s may exist but not necessarily. 

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If Y, V are the total volumes of the initial and final systems, Xv and Xv the total numbers of mols in these respectively ... 

From this presentation it is seen that the overall probability P of electron transfer is approximated by P = Pn Pe, where Pn is the probability that the nuclei achieve a configuration so that the electron energy is identical for the initial and final systems (Fig. 5b). In usual kinetic terms, this means that the rate constant is given by kf = /r(kp )ad, where k is the transmission coefficient k = 1 for an adiabatic electron transfer k < 1 for nondiabatic transfers) and (k ) is the rate constant observed for an adiabatic electron transfer. The latter then depends only on nuclear motions that affect the potential energy of the electron. In usual chemical terms, (kf ) is directly related to the height of the activation barrier, that is, to the energetic separation between the state where the electron may tunnel and that corresponding to the initial system at equilibrium (compare Fig. 5b), denoted [A, D] in Scheme 3. 

Probability of electron tunnelling between the initial and final systems i nuclear coordinate (i = 1, N)... 

Assuming that the fluctuation of the environment of the initial and final system oscillates like a harmonic oscillator, then the enthalpies are given by (compare with Fig. 6.3)... 

The set of particles involved in an elementary reaction is called its system, as mentioned in Section I. The system in the state prior or posterior to its occurrence is called the initial or the final system and the relevant state the initial or the final state of the system, respectively. Initial and final systems may include species which are neither reactants nor products of the over-all reaction the latter species are called intermediates. 

The driving force may be identified with the difference of the free energies of the initial and final systems (see p. 614) but the interpretation of the chemical resistance is more difficult. In recent theories, energy barriers are assumed, the interpretation of which is also not completely clear. 

HIA values reflect differences in the energies of the initial and final systems under analysis, not just carbocation stabilities (see Section 2.2.2 for similar reasoning related to radicals), However, in the case of HIAs, factors other than cation stability are not as influential as with radicals and carbanions (see below), and therefore the HIA values track very nicely carbocation stability. This is in part because the differences between the HIA values for various cations are much larger than the differences between BDEs for various bonds, and thus the HIA trends are less sensitive to other factors. 

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