Energy barrier to proton transfer

Proton transfer reactions are fast and essentially diffusion controlled if a hydrogen bond can be formed between proton donor and acceptor. They are slow if a hydrogen bond cannot be formed [129] (see Vol. 2, pp. 346—351). The rates of slow proton transfer reactions may be correlated with the differences of pK values of donor and acceptor. On the other hand, the pK difference cannot be the only important quantity. Therefore, a need exists for a better qualitative or semi-quantitative understanding of the factors which govern the height of the energy barrier to proton transfer. 

A semi-empirical model of the energy barrier to proton transfer is based on a Johnston type equation. According to Johnston [131], the energy barrier in gas phase hydrogen atom abstraction reactions is described by the equation... 

Recently, a new category of methods, the cavity model, has been proposed to account for the solvent effect. Molecules or supermolecules are embedded in a cavity surrounded by a dielectric continuum, the solvent being represented by its static dielectric constant. The molecules (supermolecules) polarize the continuum. As a consequence this creates an electrostatic potential in the cavity. This reaction potential interacts with the molecules (supermolecules). This effect can be taken into account through an interaction operator. The usual SCF scheme is modified into a SCRF (self consistent reaction field) scheme, and similar modifications can be implemented beyond the SCF level. Several studies based on this category of methods have been published on protonated hydrates. They account for the solvent effect on the filling of the first solvation shell (53, 69), the charges (69, 76) and the energy barrier to proton transfer (53, 76). 

NHb bond. As reported in the second row of Table 3, this bond becomes progressively longer as n is increased. The energy barriers to proton transfer from one N atom to the other show a marked dropoff as the strain of the n=l structure is relieved. The highly angularly distorted H-bond in H2N(CH2)iNH3+ leads to a barrier in excess of 30 kcal/mol, which drops below 10 kcal/mol as a second CH2 group is added. 

Marcus showed that if within a log k — log X relationship variations in the rate constant solely reflect changes in the equilibrium constant, then log k, or in Marcus s formulation the free energy of activation AG may be expressed in terms of a free energy of the proton-transfer step of the reaction AGr, and an intrinsic energy barrier to proton-transfer for reaction of a substrate and. acid for which AGg = 0 ... 

As seen in Fig. 5.35, the highest TS barrier to proton transfer along the reaction coordinate lies significantly (>7 kcal mol 1) below the energy of either reactant or product asymptote. Thus, unless trapped in the deep H H20 well, an H- ion impinging on a water molecule will undergo spontaneous proton transfer to form H2 + OH-, without an apparent barrier. 

The nature of the methanol-zeolite interaction has been shown to be sensitive to a number of parameters and as such has proved to be a good benchmark for judging the reliability of quantum chemical methods. Not only are there a number of possible modes whereby one and two molecules interact with an acidic site (245), the barrier to proton transfer is small and sensitive to calculation details. Recent first-principles simulations (236-238) suggest that the nature of adsorbed methanol may be sensitive to the topology of the zeolite pore. The activation and reaction of methane, ethane, and isobutane have been characterized by using reliable methods and models, and realistic activation energies for catalytic reactions have been obtained. 

From the point of view of this review the most important energy level difference relative to the cis enol Cs is the cis enol Qv, the symmetrical or chelate tautomer. Several calculated values for this quantity, AE, the energy barrier to the transfer of the proton from one oxygen to the other, have been obtained and are listed in Table 12. Of these the most acceptable should be that of 36 kJ mol-1 computed with the largest basis set1001. XH NMR studies461 however on MDA place an upper limit of ca. 25 kJ mol-1 for the effective barrier to interconversion of the two Cs forms via the C2v. 

Fig. 4.126. Potential-energy barrier for proton transfer from to HgO.

A more theoretical model of the energy barrier of proton transfer reactions has been introduced by Marcus [133]. This simple semi-empirical model is, to some extent, related to Marcus model. 

In table 2 we report the deviations for the geometrical parameters and harmonic vibrational fiequencies of 32 molecules belonging to the G2 set. Here, the deviations of PBE are close to those provided by the BLYP functional, thus giving further support to the reliability of this model. It is clear, anyway, that these results are stiU far from the accuracy required for chemical applications (e.g. about 5 kJ/mol for atomization energies). Furthermore, the PBE functional suffers from other problems. For instance, the energy barriers for proton transfer reactions [22], as well as some chemisorption energies [31] are still significantly underestimated. 

From these curves it is apparent that the energy barrier to proton motion in the transfer of an H3O+ state between neighbouring moleeules is less than that for the transfer of an 0H state, in agreement with the mobility data of table 7.1. This is not unexpected since, in the first case, we are transferring an excess proton between two basically neutral molecules while, in the... 

Proton transfers from strong acids to water and alcohols rank among the most rapid chemical processes and occur almost as fast as the molecules collide with one another. Thus the height of the energy barrier for proton transfer must be quite low. 

Thus, the apparently most accurate theoretical estimate of the barrier to proton transfer in a malonaldehyde molecule, determined as a difference between the energies of the structures XIa and XIc, is so far 4.3-5.0 kcal/mol. This value explains well fast (k > 10 s" ) tautomerization XIa F XIb observed in solution by the NMR method. Note, however, that calculations by means of a reaction surface Hamiltonian constructed for malonaldehyde [63] gave the barrier of 6.6 0.5 kcal/mol. 

This simple model was extended by adding clusters of 25 water molecules on both sides of the wire [75]. This more accurately emulates a water wire in a true water-bilayer system, where there would be a reservoir of water on either end of the wire, and where the membrane head groups are solvated by water. In this extended system, the proton becomes markedly better solvated at the ends of the water chain. As a result, its free energy is almost constant everywhere along the chain and proton transfer becomes barrierless and rapid (on a picosecond timescale). It may be anticipated that including full lamellae of water, instead of clusters, would further stabilize the proton at the ends of the wire producing a free energy barrier to proton transport at the center of the membrane. However, this barrier will not only be substantially lower than that obtained from equation (11) but, most likely, will also be lower than the barrier calculated for an ion in a flexible membrane. 

Here AG is the free energy of activation, w, is the free energy required to bring the reactants into an encounter complex, with reactants and solvation spheres correctly oriented for reaction, Wp is the corresponding term for the separation of the products, 2/4 is the free-energy barrier for proton transfer within the encounter complex if AG is zero, and A = AG - w, - Wp. 

Figure 13. Exaggerated free energy surface showing two volcanoes with contours for a concerted proton transfer. At all values of the C-O distance there is a barrier to proton transfer. The Marcus theory of proton transfer predicts that a = since the saddle occurs at the value of x where the thermodynamics driving the proton transfer is in balance (QRS). The surface has been drawn for a symmetrical case, but this conclusion still holds for an unsymmetrical case. The strip cartoon shows the mechanism for the hydration dehydration reaction of a ketone.

Figure 6.11 shows a similar test case for an anionic system here we transfer a proton in a 0H -H20 dimer. In this case the most stable configuration of the dimer has a 0-0 distance of 2.48 A. In contrast to the H30 -H20 case discussed previously, for the anionic dimer the proton is shared between the oxygen atoms in the global energy minimum. At increased 0-0 distances a barrier to proton transfer appears this barrier increase to more than 60 kcal moR for an 0-0 distance of 3.6 A. 

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