Density functional theory proton solvation energy

With trihydroxyethylenephosphorane (91) as a model for RNA hydrolysis, Karplus et al. developed a protocol for calculating the values of pKa and pKa of (91) based on estimates of the pKa for phosphoric acid. The protocol used density functional theory to calculate gas-phase protonation energies and continuum dielectric methods to determine solvation corrections and arrived at values of 7.9 and 14.3 for pKa and pKa respectively. These values are within the experimental ranges of 6.5-11.0 for pKa and 11.3-15.0 for pKa proposed for the molecules. 

Solvation effects have been incorporated into the calculations of anionic proton transfer potentials in a number of ways. The simplest is the microsolvation model where a few solvent molecules are included to form a supermolecular system that is directly characterized by quantum mechanical calculations. This has the advantage of high accuracy, but is limited to small systems. Moreover, one must assume that a limited number of solvent molecules can adequately model a tme solution. A more realistic approach is to explicitly describe the inner solvation shell with quantum calculations and then treat the outer solvation sphere and bulk solvent as a continuum (infinite polarizable dielectric medium). In this way, the specific interactions can be treated by high-level calculations, but the effect of the bulk solvent and its dielectric is not neglected. An ej tension of this approach is to characterize the reaction partners by quantum mechanics and then treat the solvent with a molecular mechanics approach (hybrid quantum mechanics/molecular mechanics QM/MM). The low-cost of the molecular mechanics treatment allows the solvent to be involved in molecular dynamics simulations and consequently free energies can be calculated. In more recent work, solvent also has been treated with a frozen or constrained density functional theory approach. ... 

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