Barrier for reaction

Figure A3.12.1. Schematic potential energy profiles for tluee types of iinimolecular reactions, (a) Isomerization, (b) Dissociation where there is an energy barrier for reaction in both the forward and reverse directions, (c) Dissociation where the potential energy rises monotonically as for rotational gronnd-state species, so that there is no barrier to the reverse association reaction. (Adapted from [5].)...

In Ref.125) the calculation of an activation barrier for reaction (21) in the gas phase is considered to be an error of the MINDO/3 method and the process is assumed to be activationless. But in respect to the medium effect a barrier of 54 k J mol-1 is obtain-ed which agrees again with the results from Huron-Claverie calculations. Bertran et al. calculated the influence of the solvation on the electrophilic attack of a proton 133) or a methyl cation 134,135) on ethene using a MINDO/3 supermolecule model. Smaller reaction enthalpies also result in solution than in the gas phase in addition to the appearance (H+ + ethene) or the increase (CH 4 + ethene) of an activation barrier1361. 

The same energetic modifications also affect the CO bulk oxidation. Because of the lower binding energy of the adsorbed reactants (COad and OHad) on the intermixed surface, the barrier for reaction of these species and hence for CO2 formation is significantly reduced compared with reaction on Ru(OOOl)... 

Table 1 includes partitioning data only for carbocations that are sufficiently stable to form in the nucleophilic aqueous/organic solvents used in these experiments. For example, it is not possible to obtain values of ks for reaction of secondary aliphatic carbocations in water and other nucleophilic solvents, because the chemical barrier to ks is smaller than that for a bond vibration.83 The vanishingly small barriers for reaction of secondary carbocations with nucleophilic solvents results in enforced concerted mechanisms2-3 for the nucleophilic substitution and elimination reactions of secondary derivatives in largely aqueous solvents.83-84... 

Barriers for reaction (7.1), calculated at a wide variety of levels, are presented in Table 6.14. The theoretical results [41] are compared with the experimental barriers obtained from condensed phase (21.3 kJ/mol) [40, 42] and gas-phase (25.7 kJ/mol) [43] studies, back-corrected for temperature and zero-point energy effects [41, 44],... 

Providing that the interactions between the reactant and the electrode in the electrochemical transition state, and between the two reactants in the homogeneous transition state, are negligible ("weak overlap" limit), the activation barriers for reactions 10 and 11 will be closely related. 

One formalism which has been extensively used with classical trajectory methods to study gas-phase reactions has been the London-Eyring-Polanyi-Sato (LEPS) method . This is a semiempirical technique for generating potential energy surfaces which incorporates two-body interactions into a valence bond scheme. The combination of interactions for diatomic molecules in this formalism results in a many-body potential which displays correct asymptotic behavior, and which contains barriers for reaction. For the case of a diatomic molecule reacting with a surface, the surface is treated as one body of a three-body reaction, and so the two-body terms are composed of two atom-surface interactions and a gas-phase atom-atom potential. The LEPS formalism then introduces adjustable potential energy barriers into molecule-surface reactions. 

The cycloaddition reaction of methyleneketene 25 and 5-methylene-l,3-dioxan-4,6-dione 26 was studied by DFT at the B3LYP/6-31G" level of theory both in the gas phase and in chloroform solution <1999JMT(488)187>. In the gas phase, the activation barriers for reactions to 27, 28, or 29 (Scheme 1) were calculated to be 21.81, 0.25, and 2.96 kcal mol respectively thus, the reaction leading to the 1,2-adduct 28 was lowest, in agreement with the... 

Surface science studies of CO oxidation on Au(llO) single crystals have been made previously in which a Pt filament was used to adsorb oxygen adatoms ( o 0.25) on the Au(llO) surface and a CO titration was performed subsequently (7). CO did react to form CO2 with Eapp = 2 1 kcal/mole. Since CO was not observed to adsorb on Au(llO) at 125 K, it is only physisorbed (as on Au(lll)) and we can estimate that Elh = 7 kcal/mol on Au(llO). The difference from Au(lll) is probably due to a weaker Au-O bond on Au(lll) which leads to a lower barrier for reaction. No surface carbonate was formed from CO2 + Oa on Au(llO) either (7). This is in contrast to the behavior on Ag. Exposing oxygen covered Ag(llO) (16) or Ag(lll) (17) to CO2 produces carbonate species which are stable to 485 K on the surface. 

A common approach for the study of activated barrier crossing reactions is the transition state theory (TST), in which the transfer rate over the activation barrier V is given by (0)R/2jt)e where 0)r (the oscillation frequency of the reaction coordinate at the reactant well) is an attempt frequency to overcome the activation barrier. For reactions in solution a multi-dimensional version of TST is used, in which the transfer rate is given by... 

Molecules may be strained by a variety of modes of distortion that include angle bending, torsional strain, and steric interactions. In some cases, strain can provide an important driving force for reaction. However, it is not the strain in the molecule that is important, but rather the change in strain in a reaction. Even this is not sufficient because there must also be a mechanism for the conversion of a compound to a lower energy product that leads to a relatively low barrier for reaction. 

If the intersecting curves are parabolic in form, then the reactivity pattern expected is described by the Marcus equation (Marcus, 1964, 1977). The magnitude of a may then be shown to be that in (82). Here AGjisthe intrinsic barrier for reaction and AG° the free energy of reaction. 

The increase in double bond character is assumed to increase the intrinsic barrier for reaction at the a-carbon atom. As this increase is greatest for the thermodynamically least stable (CF3-substituted) carbocation, changes in thermodynamic driving force and intrinsic barrier oppose each other. The constancy of the values of kn2o thus reflects a change in intrinsic barrier overriding the second and third terms in the Marcus expression of Equation (20). This is a more radical effect than the lesser variation preserving the linearity of the plots for the reaction families in Fig. 3 (p. 77), for which only the third term is overridden. 

In estimating these barriers Richard addresses a problem that so far has been avoided. When discussing the correlation of log h2o with pATR in Fig. 3, it was implied that the rate and equilibrium constants refer to the same reaction step. That is not strictly true, because attack of water on a carbocation yields initially a protonated alcohol which subsequently loses a proton in a rapid equilibrium step. As we are reminded in Equation (26) the equilibrium constant AR refers to the combination of these two steps. To calculate an intrinsic barrier for reaction of the carbocation with water therefore the equilibrium constant KR should be corrected for the lack of stoichiometric protonation of the alcohol. Fortunately, there have been enough measurements of pA,s of protonated alcohols240 (e.g. pAa = -2.05 for CthOHi1") for the required corrections to be made readily. 

Fig. 12. Schematic representation of the relation between the spectroscopic Stokes shift and the difference in the reorganization barriers for ground and excited state electron transfer reactions. AB = absorption CD = emission B C + D A = Ahv (Stokes shift) 2Ea = reorganization barrier for reaction (35) 2 Ea = reorganization barrier for reaction (36)...

Ab initio [515, 516] and semi-empirical calculations [517] of the reaction potential-energy surface show that the potential-energy barrier for reaction depends on the angle of the H—H—F transition state and is lowest for the collinear configuration, having a value 4 kJ mole-1. Thus, collisions involving a nearly collinear approach of F to H2 make the major contribution to reaction and give backward-scattered products. All the surfaces are of a repulsive type. 

In the first and second equation, E is the energy of activation. In the first equation A is the so-called frequency factor. In the second equation AS is the entropy of activation, the interatomic distance between diffusion sites, k Boltzmann s constant, and h Planck s constant. In the second equation the frequency factor A is expressed by means of the universal constants X2 and the temperature independent factor eAS /R. For our purposes AS determines which fraction of ions or atoms with a definite energy pass over the energy barrier for reaction. 

The partially charged atom is more readily compressible to its promotion state, as shown by the dotted line in figure 4. When this modified atom of the second kind reaches its valence state two-way delocalization occurs and an electron-pair bond is established as before. It is notable how the effective activation barrier is lowered with respect to 2Vqij the barrier for reaction of homonuclear pair i. The effective reaction profile is the sum of the two promotion curves of atoms 1 and 2, with charge transfer.6... 

If only the thermal energy of the bombarding olefin molecules was available to overcome the activation energy barrier for reaction then there should be a marked dependence of the conversion on the jet temperature. The results (Fig. 15) show clearly that this is not so and in fact the points for different temperatures all fall on the same curve. Therefore the thermal energy of the alighting molecules is unimportant. Either the reactions must occur at 77°K after the molecules have lost their thermal energy, or if they do occur immediately after bombardment... 

The trend of the activation energies Tact (shown in the last column of Table 5) closely follows that of the adsorption energies of the CH and CH2 fragments on the two surfaces. Because the adsorption energies are much higher for the reaction on ruthenium than for that on cobalt, the barrier for reaction on ruthenium is also inferred to be higher. The transition state is late with respect to the nonassociated state. 

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