Deprotonation, free energy

The pKa obtained this way is often referred to as the absolute pKa. Thus, pKa can be computed if the gas-phase deprotonation free energy and solvation energies of AH, A- and H+ are known [60, 81]. 

Another method to obtain absolute pKa s for small molecules is to compute deprotonation free energy directly from the free energies of species in the reaction using quantum mechanical and continuum solvation methods (Eq. 10-1),... 

As errors in ionic solvation free energies are often on the order of 5 kcal moP, and as errors in the gas-phase deprotonation free energies may be of similar magnitude even with reasonably good levels of theory, errors in predicted absolute pA/a values of 5 or more pA units are not terribly unusual, which is not particularly satisfying insofar as experimental measurements can be accurate to 0.01 pAC units. 

Term (1) is the gas-phase isodesmically calculated deprotonation free energy of the big acid CH2FCOOH it is to be calculated from terms (2) and (3). 

The deprotonation free energy is estimated from a thermodynamic integral Equation 13.35 as... 

The expression for pK of Equation 13.41 also contains the work function of the proton. Computation of W + is the key step in the proton insertion scheme. It is estimated by the deprotonation free energy of the hydronium cation (H3O+). The HjO ion is modeled by a (flexible) pyramidal structure stabilized by the restraining potential. Thus, identifying with ADP j t, we apply Equation 13.43 and find... 

Assuming that differences in zero-point motion of hydronium and acid can be ignored, pKa is the difference in deprotonation free energies adjusted by a constant. The constant, -3.2 units, is effectively the pKa of the constrained hydronium ion, because, in this case, the deprotonation integrals and zero-point motion terms rigorously cancel. The model H3O+ is therefore 1.5 pX units more acid than the pKa = -1.74 of the hydronium in the Brpnsted theory. 

The kinetic stability of 17 increases on deprotonation. The half-life times of 17 and its anion N 19 have been estimated [104] from the observed [105, 106] and computed free energy to be only 10 min and 2.2 days, respectively. The high kinetic stability of the anion 19 can be understood in terms of enhanced pentgon stability and aromaticity. The deprotonation raises the energy of lone pair orbitals and promotes cyclic delocalization of o- and rr-electrons. 

In principle, one can calculate pKa by making use of the thermodynamic cycle as shown in Figure 10-1 and a relationship between the free energy of deprotonation in aqueous phase and pKa,... 

The titration coordinates evolve along with the dynamics of the conformational degrees of freedom, r, in simulations with GB implicit solvent models [37, 57], An extended Hamiltonian formalism, in analogy to the A dynamics technique developed for free energy calculations [50], is used to propagate the titration coordinates. The deprotonated and protonated states are those, for which the A value is approximately 1 or 0 (end-point states), respectively. Thus, in contrast to the acidostat method, where A represents the extent of deprotonation, is estimated from the relative occupancy of the states with A 1 (see later discussions). The extended Hamiltonian in the CPHMD method is a sum of the following terms [42],... 

Umod(6j) represents the potential of mean force (PMF) for deprotonating a model compound along the titration coordinate. This ensures that the titration simulation of a model compound at pH = p.K od, yields approximately 50% protonated and 50% deprotonated states. In other words, the PMF along the titration coordinate for a model compound is flattened out at pH = p/f od, thus allowing us to model only the difference between the free energy of deprotonation in protein and that in... 

Fig. 1 Free energy reaction coordinate profiles for hydration and isomerization of the alkene [2] through the simple tertiary carbocation [1+], The rate constants for partitioning of [1 ] to form [l]-OSolv and [3] are limited by solvent reorganization (ks = kteorg) and proton transfer (kp), respectively. For simplicity, the solvent reorganization step is not shown for the conversion of [1+] to [3], but the barrier for this step is smaller than the chemical barrier to deprotonation of [1 ] (kTtOTg > kp).

Fig. 4 Free energy reaction coordinate profiles that illustrate a change in the relative kinetic barriers for partitioning of carbocations between nucleophilic addition of solvent and deprotonation resulting from a change in the curvature of the potential energy surface for the nucleophile addition reaction. This would correspond to an increase in the intrinsic barrier for the thermoneutral carbocation-nucleophile addition reaction.

Fig. 6 Hypothetical free energy reaction coordinate profiles for the interconversion of X-[8]-OH and X-[9] (R = H) and X-[10]-OH and X-[ll] (R = CH3) through the corresponding carbocations. The arrows indicate the proposed eifects of the addition of a pair of ortAo-methyl groups to X-[8]-OH, X-[8+] and X-[9] to give X-[10]-OH, X-[10+] and X-[ll]. A Effect of a pair of or/Ao-methyl groups on the stability of cumyl alcohols. B Effect of a pair of or/Ao-methyl groups on the stability of cumyl carbocations. C Effect of a pair of ortho-methyl groups on the stability of the transition state for nucleophilic addition of water to cumyl carbocations. D Effect of a pair of orf/io-methyl groups on the stability of the transition state for deprotonation of cumyl carbocations.

TLM Activity Coefficients. In the version of the TLM as discussed by Davis et al. (11), mass action equations representing surface complexation reactions were written to include "chemical" and "coulombic" contributions to the overall free energy of reaction, e.g., the equilibrium constant for the deprotonation reaction represented by Equation 2 has been given as... 

If kepi, k-epi are much larger than the rates k, ki of substitution, the enantiomeric ratio Hepi-1 is similar to kxjk (path C, dynamic kinetic resolution . Both mechanisms are performing when the rates of the two steps are similar. Since rates and equilibrium are temperature-dependent, enhancement of stereoselectivities can be achieved by sophisticated protocols (see Section m.E). The equilibrium 6/epi-6 is determined by the difference of free energy A AG. This effective energy difference is enlarged if it can be coupled with a second order transformation such as the selective crystallization of one diastere-omer dynamic thermodynamic resolution ). In fact, this applies to the first successful (—)-sparteine-mediated deprotonation (Section FV.C.l). 

Figure 3.3. Plot of gas-phase free energies of deprotonation versus those found in DMSO. ...

Calorimetric data on azoles are given in Tables II and III. Figure 1 shows the linear relationship between the ionization enthalpies (AH°) and free energies (AG°). It is noteworthy that protonation and deprotonation generate two nearly parallel lines. Di- and tri-positive (or negative) ions are clearly off these lines, suggesting that the AH° — AG° relationship is sensitive to the overall charge of the ions. 

Advantage has been taken of the ready accessibility of eleven para-substituted trityl and 9-phenylxanthyl cations, radicals, and carbanions in a study of the quantitative relationship between their stabilities under similar conditions.2 Hammett-type correlations have also been demonstrated for each series. Heats and free energies of deprotonation and the first and second oxidation potentials of the resulting carbanions were compared. The first and second reduction potentials and the p/CR values of the cations in aqueous sulfuric acid were compared, as were calorimetric heats of hydride transfer from cyanoborohydride ion. For radicals, consistent results were obtained for bond dissociation energies derived, alternatively, from the carbocation and its reduction potential or from the carbanion and its oxidation potential. 

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