Free energy reaction profiles

The Gibbs free energy reaction profiles in Fig. 16 have been calculated from the results in Table 16 and the mechanism in (30) and refer to reaction in a 1 1 2-methylphenol buffer at buffer concentrations of 0.001 and 0.1 moldm" (Fig. 16(a) and (b), respectively). TS(1) is the transition state for opening of the intramolecular hydrogen bond and TS(2) is the transition... 

Fig. 2.5 Free energy reaction profile for (2.130) for various relative values of the associated rate constants.

Fig. 1 Computed free energy reaction profiles for the decarboxylation of OMP in water and in the wild-type enzyme ODCase. Reprinted with permission from Reference 66. Copyright 2000 National Academy of Sciences.

A complete description of these substituent effects is obtained by comparing the rate and equilibrium constants for the addition of HBr to 48 (Fig. 4A)91 and p-1 (Fig. 4B)52 and the derived free energy reaction profiles shown in Fig. 4.52 The 1.7 kcal/mol larger driving force for addition of FiBr to 48 shows that the... 

Fig. 4 (A) Free energy reaction profile for the reversible addition of Br to the di-Q -CF3-substituted quinone methide 48, constructed using rate and equilibrium data from Ref.91 (B) Free energy reaction profile for the reversible addition of Br to the simple quinone methide p-1, constructed using rate and equilibrium data from Ref.52 These nucleophile addition reactions show similar thermodynamic driving force, but both the formation and reaction of 48 are slow because of the large intrinsic barrier A for nucleophile addition.

Solvent effects can significantly influence the function and reactivity of organic molecules.1 Because of the complexity and size of the molecular system, it presents a great challenge in theoretical chemistry to accurately calculate the rates for complex reactions in solution. Although continuum solvation models that treat the solvent as a structureless medium with a characteristic dielectric constant have been successfully used for studying solvent effects,2,3 these methods do not provide detailed information on specific intermolecular interactions. An alternative approach is to use statistical mechanical Monte Carlo and molecular dynamics simulation to model solute-solvent interactions explicitly.4 8 In this article, we review a combined quantum mechanical and molecular mechanical (QM/MM) method that couples molecular orbital and valence bond theories, called the MOVB method, to determine the free energy reaction profiles, or potentials of mean force (PMF), for chemical reactions in solution. We apply the combined QM-MOVB/MM method to... 

In Fig. 6.11 is depicted a general scheme of a stepwise HH-transfer reaction between the initial state A and the final state D. B and C are intermediates whose concentration is small. In each reaction step a single H is transferred, the other H is bound. Let us denote the formation of the intermediate as dissociation and the backward reaction as neutralization . The corresponding free energy reaction profile is illustrated in Fig. 6.11(b). 

Fig. 12 Simplified computed free energy reaction profiles (kcal/mol) for the coupling of alkynes with 3-phenylpyrazoles in dichloroethane (a) Model 1 HC=CH with lb at CpRh(OAc)2, BP86 functional, (b) Model 2 "PrC=C"Pr with la at Cp Rh(OAc)2, BP86 functional (c) as for Model 2 but with BP86-D3...

Fig. 14 Computed free energy reaction profile (kcal/mol) for catalytic azidocarbonylation at (Xantphos)Pd(CO)2. Inset shows computed geometries of the oxidative addition and C-N coupling transition states, with key distances in A...

Figure 1.24 Computed free energy reaction profiles (kcal mol ) for C-H activation of H-Lj at [MCl Cp ] for M = lr (in CH CI ) and M = Rh (in MeOH). Computed C-H...

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. 4. The free-energy (G) profile of the transfer-reaction mechanism at 423 K with the BP86 method and without any pressure corrections. Reaction going from left to right uses up the sacrificial olefin and from right to left generates the target olefin.

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. 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. 3 (A) Free energy reaction profdes, constructed from intersecting parabolas, for addition of water to a simple carbocation that show the change in reaction barrier with changing reaction driving force. (B) Free energy profile for thermoneutral addition of water to a carbocation for which the observed activation barrier is equal to the intrinsic barrier A.

Figure 3.3.10 (A) The electrode potential dependence of the Gibbs free energy reaction pathway of the ORR. While the overall reaction has elementary steps that are energetically uphill at +1.23 V (red pathway), all elementary steps become downhill at +0.81 V (yellow pathway) (i.e. at an overpotential of approximately -0.42 V. At this point, the reaction is not limited by kinetics anymore. (B) The experimentally observed current-potential (j-E) relation of the ORR is consistent with the computational conclusions from (A) between +1.23 V and +0.81 V the j-E curve shows an exponential behavior, while at electrode potentials below +0.81 V, the ORR reaction rate becomes oxygen mass-transport limited, which is reflected by a flat ( j-E) profile. Figure adapted with permission from [19]. 

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.

Fig. 4. Free energy (hartree) profile along the reaction coordinate (A) for the electrophilic attachment of chlorine to ethylene in aqueous solution. The symbols TS and P refer respectively to the position of the transition state and the ionic intermediate. The dashed line indicates the free energy of the reactants at infinite separation.

Example 5.1 Determine the overpotential and free energy change profiles as functions of the reaction constant at varying temperature. Explain the electrochemical behavior. 

PEP theory has also been applied to modelling the free energy profiles of reactions in solution. An important example is the solvent effect on the SN2 reaction... 

Figure A2.3.21 Free energy profile of the SN2 reaction Cl +CH2CI— [Cl-CHg-Cl]— CICH +Cl in the gas phase, dimethyl fonnamide and in water (from [93]).

Outer sphere electron transfer (e.g., [11-19,107,160-162]), ion transfer [10,109,163,164] and proton transfer [165] are among the reactions near electrodes and the hquid/liquid interface which have been studied by computer simulation. Much of this work has been reviewed recently [64,111,125,126] and will not be repeated here. All studies involve the calculation of a free energy profile as a function of a spatial or a collective solvent coordinate. 

FIGURE 14.1 Reaction profile showing large AG for glucose oxidation, free energy change of —2,870 kj/mol catalysts lower AG, thereby accelerating rate. 

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