Microscopic description of acid-base equilibrium

Abstract

Acid-base reactions are ubiquitous in nature. Understanding their mechanisms is crucial in many fields, from biochemistry to industrial catalysis. Unfortunately, experiments give only limited information without much insight into the molecular behavior. Atomistic simulations could complement experiments and shed precious light on microscopic mechanisms. The large free-energy barriers connected to proton dissociation, however, make the use of enhanced sampling methods mandatory. Here we perform an ab initio molecular dynamics (MD) simulation and enhance sampling with the help of metadynamics. This has been made possible by the introduction of descriptors or collective variables (CVs) that are based on a conceptually different outlook on acid-base equilibria. We test successfully our approach on three different aqueous solutions of acetic acid, ammonia, and bicarbonate. These are representative of acid, basic, and amphoteric behavior.

Keywords: acid–base; collective variables; enhanced sampling; metadynamics.

Fig. 1.

Two examples of partitioning the space. (Left) We show a convectional approach in which the distance from the oxygen atom is used to define its surroundings. Clearly artificial superpositions can be seen. (Right) The Voronoi tessellation does not suffer from these shortcomings.

Fig. 2.

Smooth tessellation of a 2D space with cells centered on the three water molecule oxygen atoms. The flat blue regions represent the portion of space in which the function assumes a value of 1 and the yellow ones represent the borders among cells. This surface has been obtained with a value of $\lambda =4$.

Fig. 3.

(A–C) Free-energy surfaces along $s_p$ and $s_d$ of acetic acid (A), ammonia (B), and bicarbonate (C) in aqueous solution. Color bars indicate the free energy expressed in kJ$\cdot$mol⁻¹ units. The CV $s_d$ is expressed in angstroms.