Proton transfer activation free energy

Figure A3.8.3 Quantum activation free energy curves calculated for the model A-H-A proton transfer reaction described 45. The frill line is for the classical limit of the proton transfer solute in isolation, while the other curves are for different fully quantized cases. The rigid curves were calculated by keeping the A-A distance fixed. An important feature here is the direct effect of the solvent activation process on both the solvated rigid and flexible solute curves. Another feature is the effect of a fluctuating A-A distance which both lowers the activation free energy and reduces the influence of the solvent. The latter feature enliances the rate by a factor of 20 over the rigid case.

Lobaugh, J. and Voth, G. A. Calculation of quantum activation free energies for proton transfer reactions in polarsolvents, Chem. Phys. Lett., 198(1992), 311-315... 

Ah initio calculations to map out the gas-phase activation free energy profiles of the reactions of trimethyl phosphate (TMP) (246) with three nucleophiles, HO, MeO and F have been carried out. The calculations revealed, inter alia, a novel activation free-energy pathway for HO attack on TMP in the gas phase in which initial addition at phosphorus is followed by pseudorotation and subsequent elimination with simultaneous intramolecular proton transfer. Ah initio calculations and continuum dielectric methods have been employed to map out the lowest activation free-energy profiles for the alkaline hydrolysis of a five-membered cyclic phosphate, methyl ethylene phosphate (247), its acyclic analogue, trimethyl phosphate (246), and its six-membered ring counterpart, methyl propylene phosphate (248). The rate-limiting step for the three reactions was found to be hydroxyl ion attack at the phosphorus atom of the triester. ... 

The final step of the convolution analysis is the determination of the transfer coefficient a. This coefficient, sometimes called the symmetry factor, describes how variations in the reaction free energy affect the activation free energy (equation 26). The value of a does not depend on whether the reaction is a heterogeneous or a homogeneous ET (or even a different type of reaction such as a proton transfer, where a is better known as the Bronsted coefficient). Since the ET rate constant may be described by equation (4), the experimental determination of a is carried out by derivatization of the ln/Chet-AG° and thus of the experimental Inkhei- plots (AG° = F E — E°)) (equation 27). 

Fig. 15. Conceptualization of processes leading to amine protonation and gel swelling at swelling front. Initially proton attached to carrier diffuses from outer solution (I) to vicinity of front (II). Transfer of proton to amine occurs when amine is still in unhydrated region (III) this represents a transition state. Upon protonation the amine moves into hydrated portion of gel (IV). Plotted is the free energy G at different stages. Activation free energy is AG. This figure illustrates case where proton is attached to a monoacidic buffer. Proton can also be in form of hydronium ion, with accompanying counterion.

We now turn to a detailed discussion of the activation free energy AG which determines the adiabatic PT TSTrate constant Eq. (10.4). In particular, we discuss the derived activation free energy-reaction free energy relation Eq. (10.5) and its components, in a molecular description. We focus on transfer of a proton, but include some aspects for deuteron transfer in preparation for a discussion of KIEs in Section 10.2.3. 

Figure 18. PI-QTST activation free-energy curves as a function of the proton asymmetric stretch coordinate for a A-H-A proton transfer model (see Ref. 77). The solid line depicts the classical free-energy curve for the solute in isolation with a rigid A-A distanee, while the dotted line is the quantum free energy for the rigid, isolated solute with a fully quantized proton. The long-dashed line is the quantum free-energy curve for the isolated solute in which the A-A distance is allowed to fluctuate. The dot-dashed and short-dashed lines depict the quantum free-energy curves for the rigid and flexible solutes, in the polar solvent.

For a given water content and by applying the Stokes-Einstein equation and the rate process to ionic migration s , it is possible to calculate, for two dilferent ions, the difference between their activation free energies for the elementary ion transfer reactions, the proton being chosen as the reference ion... 

It is notable that the behavior of the quantitative values of the free energies that we have analyzed at a molecular level here mimic the rates of isocoulombic proton transfer (and thus activation free energies)[32]., as has been discussed previously[40]. The principles governing both are seen to be the same, and thus a deeper understanding of both proton transfer equilibria and kinetics results from the combination of theory and experiment. 

The free energy of formation of the S-02 species should be quite high, particularly if the ionization constant for reaction (LXIV) is relatively low, and hence the formation of S-O2H is likely to proceed from S-O2 through a simultaneous electron and proton transfer. Such a process would be expected to have a higher activation free energy than just the electron transfer and hence the kinetics to be much slower. 

There is also a relationship between the dihydrogen bond strength and the activation free energy of proton transfer. The latter decreases with the increase of -AT/qjjb (Fig. 8.5). This experimental trend is also predicted by theoretical calculations, which show the ultimate disappearance of the dihydrogen bond minimum and a spontaneous proton transfer with the increase of dihydrogen bond strength [38-40]. 

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