Reactions without barriers

Figure A3.4.8. Potential energy profiles for reactions without barrier. Complex fomiing bimolecular reaction (left) and direct barrierless bimolecular reaction (right).

Surprisingly enough, reactions without barriers and discernible transition states are common. Two radicals will typically combine without a barrier, for example, two methyl radicals to form ethane. 

An important refinement of the hard-sphere cross-section formula [Eq. (3.14)] arises when there are long-range attractive interactions. For reaction without barrier this interaction can be described by a spherically symmetric potential of the form... 

Hu X and Hase W L 1989 Properties of canonical variational transition state theory for association reactions without potential energy barriers J. Rhys. Chem. 93 6029-38... 

An interesting question is why reactions without activation barriers actually occur with different rates. The reason has to do with the preexponential term (or A factor ) in the rate expression, which depends both on the frequency of collisions and their overall effectiveness. These factors depend on molecular geometry and accessibility of reagents. Discussion has already been provided in Chapter 1. 

Diffusion-Controlled Reactions. Chemical reactions without Transition States (or energy barriers), the rates of which are determined by the speed in which molecules encounter each other and how likely these encounters are to lead to reaction. 

The deoxygenation of tetrahydrofuran (THE, 90), which yields ethylene and carbon monoxide, is an interesting case. While this and other deoxygenations might be expected to proceed through an yild intermediate and a biradical as shown in Eq. 50, calculations (MP2/6-31G ) indicate that neither ylid 91 nor biradical 92 is an intermediate in this reaction. These calculations reveal a concerted removal of oxygen that proceeds to carbon monoxide and two molecules of ethylene without barrier. Experimental evidence that 91 is not an intermediate is provided by the fact that reaction of carbon with a mixture of 90 and 90-d generates ethylene and ethyl-ene-t/g in a 2.7 1 ratio.This secondary isotope effect of 1.13 (per D) would not be expected if 91 (or 92) were an intermediate. 

The reaction with Fe (Fig. 3) is somewhat more complicated as it also involves participation of an intermediate-spin (IS, S = 1) state between the LS (S = 0) and the HS (S = 2) states in the course of the reaction. From the initial complex 4, the reaction proceeds virtually without barriers until the final complex 6 is formed. In the cases of both ]TS3 and 1TS4, the activation energies with respect to x4 and ]5 were found to be 2.9 and 0.5 kcal mol-1, respectively, without zero-point vibrational energy (ZPVE) correction. With ZPVE, both 1TS3 and ]TS4 become lower on the potential energy surface than the corresponding complexes 4 and 5 by 0.3 and 1.3 kcal mol-1, respectively. In some cases, we were unable to locate transition states and local minima at all three levels of theory. 

Activation energies are energy barriers to chemical reactions. These barriers are crucial to life itself. The rate at which a molecule undergoes a particular reaction decreases as the activation barrier for that reaction increases. Without such energy barriers, complex macromolecules would revert spontaneously to much simpler molecular forms, and the complex and highly ordered structures and metabolic processes of cells could not exist. Over the course of evolution, enzymes have developed lower activation energies selectively for reactions that are needed for cell survival. 

For bimolecular reactions, reactive species such as radicals may undergo reactions without a barrier—in such cases, no saddle point can be found on the potential energy surface, and more advanced TST methods are needed to compute rate constants. The value shown in the table approaches the diffusion limit indeed, with more accurate rate calculations, barrierless reactions occur even closer to the diffusion limit. Again, heating is needed to accelerate reactions with higher barriers—the case with AE = 20kcal/mol would have a rough Xy2 of 11 h at 150°C. 

The course of these additions of lithium hydride resembles that found for the addition of borane (Nagase et al., 1980 Graham et al., 1981). With ethylene, the initial step is exothermic formation of a Jt-complex without barrier, then rate-determining transformation to the borane via a four-centre transition structure. In both the borane and lithium hydride additions, there is relatively little development of the new C—H bond with distances of 1.692 and 1.736 A respectively in the transition structures. When a carbanionic product is not formed, for example in the reaction of lithium hydride with cyclopropenyl cation yielding cyclopropene and lithium cation (Tapia et al., 1985), reaction again occurs via a hydride-bridged complex, but the C- H- -Li array remains nearly linear throughout the reaction. 

Catalyst. Any substance that increases the rate of reaction without itself being used up in the process is called a catalyst. A catalyst increases the rate of reaction by lowering the activation energy (Fig. 20.3). Thus many more molecules can cross the energy barrier (activation energy) in the presence of a catalyst than in its absence. Almost all the chemical reactions in our bodies are catalyzed by specific catalysts called enzymes. 

For the physisorbed structures 1-1, 1-2 and 1-3, the reaction proceeds without barrier. For the cases of chemisorption, we have calculated the energy barriers for the processes that lead from 1-1 to F-l, 1-2 to F-2 and F-l to F-6, respectively. The energy barriers have been calculated by the climbing Nudged Elastic Band method72,73 where six equidistant images have been used. 

Figure 7 shows the excitation fnnetion (the total ICS as a function of the collision energy). The cross section decreases rapidly with increasing energy. This behavior is typical for a reaction without any barrier. 

It is important to note that, in the models chosen for theoretical calculations, the reaction path from cis to the trans form is easy, particularly due to the lack of steric hindrance (R = H) (Scheme 8). If, for example, bulky substituents were linked to the C2 atom, the rotation around the C2-X3 bond would be certainly hindered, increasing the activation barrier of the cis-trans isomerization. In this case, it would be hazardous to take the C-0 bond breaking to be the ratedetermining step in the thermal coloration reaction (Figure 3). It would be possible to observe a ring-opening followed by a ring-closure reaction without any formation of the stable trans colored isomer. 

The adsorption of molecular hydrogen on platinum is produced without barriers and dissocia-tively (432 kJ mol 1 of dissociation energy) in different configurations that are able to reconstruct the surface. This makes the hydrogen adsorption state attractive for reduction reactions because of its low stabilization energy. 

In the case of an elementary reaction (i.e., reaction without energy barrier associated with the formation of an intermediate complex), if AG is negative, then the reaction can proceed spontaneously at the temperature under consideration. Values of AG°, AH0, S° and C° for most atmospheric species can be found in chemical handbooks. 

The use of curvilinear coordinates and optimization of the orientation of the dividing surface are important for quantitative calculations on simple barrier reactions, but even more flexibility in the dividing surfaces is required to obtain quantitative results for very loose variational transition states such as those for barrier-less association reactions or their reverse (dissociation reactions without an intrinsic barrier). 

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