Dissociation Constants of Weak Acids from ab Initio Molecular Dynamics Using Metadynamics: Influence of the Inductive Effect and Hydrogen Bonding on p<i>K</i>_a Values

The theoretical estimation of the dissociation constant, or p<i>K</i>_a, of weak acids continues to be a challenging field. Here, we show that ab initio Car–Parrinello molecular dynamics simulations in conjunction with metadynamics calculations of the free-energy profile of the dissociation reaction provide reasonable estimates of the p<i>K</i>_a value. Water molecules, sufficient to complete the three hydration shells surrounding the acid molecule, were included explicitly in the computation procedure. The free-energy profiles exhibit two distinct minima corresponding to the dissociated and neutral states of the acid, and the difference in their values provides the estimate for p<i>K</i>_a. We show for a series of organic acids that CPMD simulations in conjunction with metadynamics can provide reasonable estimates of p<i>K</i>_a values. The acids investigated were aliphatic carboxylic acids, chlorine-substituted carboxylic acids, <i>cis-</i> and <i>trans-</i>butenedioic acid, and the isomers of hydroxybenzoic acid. These systems were chosen to highlight that the procedure could correctly account for the influence of the inductive effect as well as hydrogen bonding on p<i>K</i>_a values of weak organic acids. In both situations, the CPMD metadynamics procedure faithfully reproduces the experimentally observed trend and the magnitudes of the p<i>K</i>_a values