Reaction coordinate profile

Fig. 1 Free energy reaction coordinate profiles for hydration and isomerization of the alkene [2] through the simple tertiary carbocation [1+], The rate constants for partitioning of [1 ] to form [l]-OSolv and [3] are limited by solvent reorganization (ks = kteorg) and proton transfer (kp), respectively. For simplicity, the solvent reorganization step is not shown for the conversion of [1+] to [3], but the barrier for this step is smaller than the chemical barrier to deprotonation of [1 ] (kTtOTg > kp).

Fig. 2 Free energy reaction coordinate profiles for the stepwise acid-catalyzed hydration of an alkene through a carbocation intermediate (Scheme 5). (a) Reaction profile for the case where alkene protonation is rate determining (ks kp). This profile shows a change in rate-determining step as a result of Bronsted catalysis of protonation of the alkene. (b) Reaction profile for the case where addition of solvent to the carbocation is rate determining (ks fcp). This profile shows a change in rate-determining step as a result of trapping of the carbocation by an added nucleophilic reagent.

Fig. 4 Free energy reaction coordinate profiles that illustrate a change in the relative kinetic barriers for partitioning of carbocations between nucleophilic addition of solvent and deprotonation resulting from a change in the curvature of the potential energy surface for the nucleophile addition reaction. This would correspond to an increase in the intrinsic barrier for the thermoneutral carbocation-nucleophile addition reaction.

Fig. 6 Hypothetical free energy reaction coordinate profiles for the interconversion of X-[8]-OH and X-[9] (R = H) and X-[10]-OH and X-[ll] (R = CH3) through the corresponding carbocations. The arrows indicate the proposed eifects of the addition of a pair of ortAo-methyl groups to X-[8]-OH, X-[8+] and X-[9] to give X-[10]-OH, X-[10+] and X-[ll]. A Effect of a pair of or/Ao-methyl groups on the stability of cumyl alcohols. B Effect of a pair of or/Ao-methyl groups on the stability of cumyl carbocations. C Effect of a pair of ortho-methyl groups on the stability of the transition state for nucleophilic addition of water to cumyl carbocations. D Effect of a pair of orf/io-methyl groups on the stability of the transition state for deprotonation of cumyl carbocations.

Fig. 8. Reaction coordinate profiles for aminolysis of an organic ester. For esters with moderately poor leaving groups (i.e., R = alkyl) reacting with a moderately good nucleophilic amine (i.e., NH2R), deprotonation of the first-formed addition intermediate, T , by NH2R is considered to be rate determining at high pH, while at lower pH loss of RO from T is considered rate determining (specific OH catalysis).

Fig. 9. Reaction coordinate profile for (A) a two-stage reaction for the addition of NH2R to a Co(III)-active ester (ti), followed by the loss of ROH from T° ( j 2), observed in the absence of protonated amine. (B and C) One-stage reaction observed in the presence of protonated amine (B) rate-determining general acid (NH3R+, BH+) catalyzed loss of ROH from T° (C) rate-determining deprotonation of T+.

Diphosphinedihalonickel(II) complexes planar-tetrahedral spin equilibrium, 32 29-30 reaction coordinate profile, 32 31 Diphosphoric acid, dissociation constants for, 4 25... 

Figure 2.1. One-dimensional (ID) free energy reaction coordinate profiles that show the Dn + An reaction mechanism through a carhocation intermediate and the change to an AnDn reaction in which the intermediate is too unstable to exist in an energy weU for the time of a bond vibration.

Fig. 4.5 Schematic energy - reaction coordinate profiles for symmetrical ET processes having small and large energy splittings at the intersection point.

Fig. 5. Reaction coordinate profile for the octahedral spin equilibrium of [Fe(HB(pz)3)2],...

Fig. 6. Reaction coordinate profile for the planar-tetrahedral spin equilibrium of a diphosphinedihalonickel(II) complex.

Fig. 7. Alternative reaction coordinate profiles for planar-octahedral equilibria of nickel(II).

Fig. 9.1. Free energy/reaction coordinate profile for two competing associative pathways the dashed line leads to less stable products via a less stable intermediate than the full line, but is faster because of smaller activation barriers.

Fig. 1. Energy versus reaction coordinate profiles for two concerted and a noncon-certed process...

Fig. 1. Schematic free energy-reaction coordinate profiles for a single-electron electroreduction involving solution reactant O and product R at a given electrode potential E, occurring via three different reaction pathways, PAS, P A S, and P A S". Pathway PAS involves energetically favorable precursor and successor states (P and S) but with a weak-overlap transition state. Pathways P A S and P A"S involve energetically similar precursor and successor states, but with the latter involving strong overlap in the transiton state.

Fig. 2. Schematic plots outlining outer-shell free energy-reaction coordinate profiles for the redox couple O + e R on the basis of the hypothetical two-step charging process (Sect. 3.2) [40b]. The y axis is (a) the ionic free energy and (b) the electrochemical free energy (i.e. including free energy of reacting electron), such that the electrochemical driving force, AG° = F(E - E°), equals zero. The arrowed pathways OT S and OTS represent hypothetical charging processes by which the transition state, T, is formed from the reactant.

Hypothetical potential-energy reaction coordinate profiles for each term of the rate law of Eq. 3 arc shown in Figure . The first term of the rate law of Eq. 3... 

The Marcus equation was first formulated to model the dependence of rate constants for electron transfer on the reaction driving force [47-49]. Marcus assumed in his treatment that the energy of the transition state for electron transfer can be calculated from the position of the intersection of parabolas that describe the reactant and product states (Fig. 1.2A). This equation may be generalized to proton transfer (Fig. 1.2A) [46, 50, 51], carbocation-nucleophile addition [52], bimolecular nucleophilic substitution [53, 54] and other reactions [55-57] by assuming that their reaction coordinate profiles may also be constructed from the intersection of... 

Figure 1.2. A, Reaction coordinate profiles for proton transfer at carbon constructed from the intersection of parabolas for the reactant and product states. B, The reaction coordinate profile for a reaction where AC° = 0 and ACt is equal to the Marcus intrinsic barrier A...

In unstrained substrates it is possible that a discrete adduct does not form, but that the trigonal bipyramidal species is the high point, that is, the transition state, on the energy level-reaction coordinate profile. 

Figure 8.54 Schematic illustration of reaction coordinate diagram for the simplest Uni Uni Kinetic Scheme (Scheme 8.1) for bio-catalysis. The reaction coordinate profile is drawn under the assumption that excess substrate is present so that fccat conditions prevail. Two types of free energy of activation exist, from E -I- S (AG ) and from ES AG. ...

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