CONSPECTUS: All-atom methods treat solute and solvent at the same level of electronic structure theory and statistical mechanics. All-atom computation of acidity constants (pKa) and redox potentials is still a challenge. In this Account, we review such a method combining density functional theory based molecular dynamics (DFTMD) and free energy perturbation (FEP) methods. The key computational tool is a FEP based method for reversible insertion of a proton or electron in a periodic DFTMD model system. The free energy of insertion (work function) is computed by thermodynamic integration of vertical energy gaps obtained from total energy differences. The problem of the loss of a physical reference for ionization energies under periodic boundary conditions is solved by comparing with the proton work function computed for the same supercell. The scheme acts as a computational hydrogen electrode, and the DFTMD redox energies can be directly compared with experimental redox potentials. Consistent with the closed shell nature of acid dissociation, pKa estimates computed using the proton insertion/removal scheme are found to be significantly more accurate than the redox potential calculations. This enables us to separate the DFT error from other sources of uncertainty such as finite system size and sampling errors. Drawing an analogy with charged defects in solids, we trace the error in redox potentials back to underestimation of the energy gap of the extended states of the solvent. Accordingly the improvement in the redox potential as calculated by hybrid functionals is explained as a consequence of the opening up of the bandgap by the Hartree-Fock exchange component in hybrids. Test calculations for a number of small inorganic and organic molecules show that the hybrid functional implementation of our method can reproduce acidity constants with an uncertainty of 1-2 pKa units (0.1 eV). The error for redox potentials is in the order of 0.2 V.

Acid-base chemistry of clay minerals is central to their interfacial properties, but up to 10 now a quantitative understanding on the surface acidity is still lacking. In this study, with first principles 11 molecular dynamics (FPMD) based vertical energy gap technique, we calculate the acidity constants of 12 surface groups on (010)-type edges of montmorillonite and kaolinite, which are representatives of 2:1 13 and 1:1-type clay minerals, respectively. It shows that ≡Si-OH and ≡Al-OH 2 OH groups of kaolinite 14 have pKas of 6.9 and 5.7 and those of montmorillonite have pKas of 7.0 and 8.3, respectively. For each 15 mineral, the calculated pKas are consistent with the experimental ranges derived from fittings of 16 titration curves, indicating that ≡Si-OH and ≡Al-OH 2 OH groups are the major acidic sites responsible to 17 pH-dependent experimental observations. The effect of Mg substitution in montmorillonite is 18 investigated and it is found that Mg substitution increases the pKas of the neighboring ≡Si-OH and ≡Si-19 OH 2 groups by 2~3 pKa units. Furthermore, our calculation shows that the pKa of edge ≡Mg-(OH 2 ) 2 is 20 as high as 13.2, indicating the protonated state dominates under common pH. Together with previous 21 adsorption experiments, our derived acidity constants suggest that ≡Si-O-and ≡Al-(OH) 2 groups are the 22 most probable edge sites for complexing heavy metal cations.

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