Efficient Assessment of 'Instantaneous pK' Values from Molecular Dynamics Simulations

We present a molecular simulation approach to studying the role of local and momentary molecular environment for potential acid-base reactions. For this, we combine thermodynamic considerations on the pK of ionic species with rapid sampling of energy changes related to (de)protonation. Using dispersed carbonate ions in water as a reference, our approach aims at the fast assessment of the momentary protonation energy, and thus the 'instantaneous pK', of calcium-carbonate ion aggregates. The latter include transient complexes that are elusive to long sampling runs. This motivated the elaboration of approximate, yet particularly fast assessable sampling strategies. Along this line, we were able to characterize instantaneous pK values at a statistical accuracy of 0.4 pK units within sampling runs of only 10 ps duration, whereas statistical errors reduce to 0.1 pK units in 75 ps sampling runs, respectively. This readily enabled the required time resolution for the characterization of [Ca_x (CO₃ )_y ]^2(x-y) aggregates with x=1,2 and y=1,2,3, respectively. In turn, the analysis of the pH-dependent nature of calcite-water interfaces and dynamically ordered liquid-like oxyanion polymers (dollop) domains is outlined at 10 ps resolution.