Proton free energy levels

Belieres, J.P. and Angell, C.A., Protonic ionic liquids Preparation, characterization, and proton free energy level representation, J. Phys. Chem. B 111 (18), 4926 937 (2007). 

BeUeres J-P, Angell CA (2007) Protic ionic liquids preparation, characterization, and proton free energy level representation. JPhys Chem B 111(18) 4926—4937. doi 10.1021/jp067589u... 

Belieres J. -P. Angell, C. A. (2007). Protic Ionic Liquids Preparation, Characterization, and Proton Free Energy Level Preparation. /. Phys. Chem., B, 111, 4926-4937. 

One can draw a useful analogy between acid-base and oxidation-reduction reactions. Both involve the transfer of a species from a source, the donor, to a sink, the acceptor. The source and sink nomenclature implies that the tendency of the proton (in the case of acids) or of the electron (for reducing agents) to undergo transfer is proportional to the fall in free energy. From the relation AG° = RTIn Ka. you can see that the acid dissociation constant is a measure of the fall in free energy of the proton when it is transferred from a donor HA to the solvent H2O, which represents the reference (zero) free energy level of the proton in aqueous solution. 

Figure 10.1 Free energy curves versus proton position at the reactant R, transition state TS, and product P solvent configurations for a symmetric reaction. For both R and P, the ground state proton vibrational energy level (solid line) is indicated. For the transition...

Much less information is available for the proton free energy of solvation, most certainly because of problems related to the determination of the entropic contribution TAS i. From a theoretical point of view, this contribution is much more sensitive than the enthalpic term for the choice of a model for the solvated proton and also to the level of theory employed in the calculations. Table VII.9 summarizes the results for the proton solvation free energy reported in the literature. 

The configuration of the Fj center is suggestive of an HJ ion imbedded in a dielectric continuum. The two lattice vacancies play the role of the protons. The energy levels of such an ion are related to the free space case by... 

Figure 1 -4. Aqueous proton levels shown as free energy levels. [See Henry A. Bent, The Second Law, Oxford University Press, New York, 1965, Chapter 32 and R. W. Gurney, Ionic Processes in Solution, McGraw-Hill, New York, 1953 (reprinted Dover, 1962), p. 133.]...

AG can be considered to be the free energy level of the protonated state relative to the deprotonated one. Our method for calculating apparent pK s is based on these energy levels. 

Fig. 6 a Protonation on O and on N of S-SPl conformer, b protonation on O and on N of R-SP2 conformer, as for the neutral case, both enantiomers of a given conformer react in the same way (see Fig. 7). The protonation free energies (kJ mol ) for the reaction SP - -H30 — > SPH + H2O are computed at the CAM-B3LYP/6-311-1- G(d,p) level at room temperature. Note that while protonation on the O leads to the open cir-TCCOH conformer (see Table S7), protonation on the N atom leads to a stable close SP conformer (see Table S8)...

Through all these calculations of the effect of pH and metal ions on the ATP hydrolysis equilibrium, we have assumed standard conditions with respect to concentrations of all species except for protons. The levels of ATP, ADP, and other high-energy metabolites never even begin to approach the standard state of 1 M. In most cells, the concentrations of these species are more typically 1 to 5 mM or even less. Earlier, we described the effect of concentration on equilibrium constants and free energies in the form of Equation (3.12). For the present case, we can rewrite this as... 

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