Free energy for proton transfer

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... 

The rate of deprotonation of an acid by a base depends on their structures [41], on the solvent and temperature, and on the difference (ApKa) between the pKa of the acid and that of the base. When acid and base have the same pfCa (ApKa=0) the change of free energy for proton transfer becomes zero and the reaction becomes thermoneutral. Under these conditions the rate of proton transfer is limited only by the so-called intrinsic barrier [34], which is particularly sensitive to structural changes in the reaction partners [39]. When ApKa increases, the rate of proton transfer also increases and approaches a limiting value, which depends on the structures of the acid and base and on the experimental conditions. For normal acids (O-H, N-H) in water the rate of proton transfer becomes diffusion-controlled (ka=10loL mol-1 s"1) when ApKa>2, but in aprotic solvents the limiting proton transfer rate can be substantially lower [42]. 

Term (2) is the gas-phase isodesmic free energy for proton transfer from RCOOH to the conjugate base CH3COO of our reference acid. At the B3PW91/ 6-31G(d,f) level this is [-327.598929 - 228.969707] [ 328.158016... 

Fig. 1. Comparison of substituent effect on gas phase and aqueous acidities of benzoic acids. para, A meta. Gas phase acidity d G corresponds to free energy for proton transfer A +AoH= =AH+Ao where AoH=benzoic acid and AH is the substituted benzoic acid. <7 is defined as ogKIKo where K and Kq are the dissociation constants in aqueous solution.

In electrochemistry the symbol AF is used to denote the value per mole, not the value per particle. To avoid confusion, we shall use dF/dn to denote the change in the free energy per proton transferred then we shall call (70) the cratic part of dF/dn for the proton transfer. 

A second class [ 16] is one that may enjoy increased interest in the future because of the presence of one of its members in the first industrial IL process [lb], and also because of the new finding that its members can have aqueous solution-like conductivities [17] and can serve as novel electrolytes for fuel cells [18]. This class is closely related to the first but differs in that the cation has been formed by transfer of a proton from a Br0nsted acid to a Br0nsted base. The process is reversible, depending on how large the free energy of proton transfer is. When the gap across which... 

Now let us return to the approaches connected with the estimation of the primary medium effect for protons, log y0 n+, that are used for obtaining quantitative information on the acidity of pure protolytic or aprotic solvents relative to the standard solution of a strong acid in water. From the thermodynamics, these are known to be a measure of the Gibbs free energy of proton transfer from the standard solution in water to the one in a non-aqueous solvent (M). This parameter is connected with the energy of proton resolvation in the following way ... 

In other words, the medium-specific contribution is not easily measured or quantified for probe molecules in interaction with solid surfaces. Moreover, in the case of microporous solids, the short-distance interactions known as "confinement effects" are even more difficult to evaluate. In all comparisons of experimental data one should be aware that the reactivity of probe base molecules is largely influenced by the size of adsorbates and micropore dimensions. As a result, the acidity scales based on the free energy of proton transfer to a specific base are expected to depend on the choice of reference base. This fact has been confirmed experimentally, as calorimetric heats of adsorption of various bases on, e.g., zeolites, depend on the base chosen. For example, a ZH zeolite may be a stronger acid... 

Computed average vibrational free energies for H-transfer (blue) and D-transfer (green) in wild-type DHFR. The results are fitted to an inverse Eckart function, and the locations of the transition state at 5 °C and 45 °C are indicated by the vertical lines. The Boltzmann factor of between H- and D-transfers gives the vibrational free energy contribution (dominantly zero-point effects) to the overall KIE. The reaction coordinate, ARc, is defined as the difference of the distances of the transferring proton from the donor (NADPH) and acceptor (dihydrofolate) atoms. 

Finally, Nagaoka et al have made a very interesting study applying MC-FEP techniques to the vinyl alcohol - acetaldehyde tautomerism.32 Using a cluster of the solute with three water molecules as a solute , the free energy for the tautomerism was calculated along different reaction pathways, which had been previously found by ab initio calculations including an SCRF solvation term. They were able to deduce that a two-step mechanism is favoured over a concerted one for the transfer of the proton. 

Since the rate for the tunneling of a proton is strongly dependent on barrier width, it is necessary that the molecular systems to be studied constrain the distance of proton transfer. Also, since the various theoretical models make predictions as to how the rate of proton transfer should vary with a change in free energy for reaction as well as how the rate constant should vary with solvent, it is desirable to study molecular systems where both the driving force for the reaction and the solvent can be varied widely. 

Fig. 16 Free energy/reaction coordinate diagram for proton transfer from the 4,6-bis(phenylazo)resorcinol monoanion to give the dianion in the presence of 2-methylphenol buffers at a 1 1 buffer ratio and at buffer concentrations of (a) 0.001 and (b) 0.10mol" dm. ...

Figure 3.4 Hypothetical free energy vs. reaction coordinate curves for proton transfer from four different acids, AxH, A2H, A3H, A4II, to base B. The Bronsted catalysis law presumes that the effects of structural change on the transition-state free energies will be some constant fraction of their effects on the overall free-energy changes.

ICR techniques or high-pressure mass spectrometry have been used to determine the equilibrium constants for proton transfer between two bases (equation 23). The determined relative free energies of protonation are accurate ( 0.2 kcalmol-1 in most instances). 

---