The Statistical Mechanics of Solution-Phase Nucleation: CaCO$$_$$ Revisited

Providing a molecular level description of amorphous CaCO\(_3\) nucleation in aqueous solutions necessitates the use of theory and simulation in addition to a direct connection to experiments. Furthermore, the ability to simulate experimental conditions relevant to nucleation requires a systematic reduction in the complexity of a molecular-based model that can be compared to experimental observations and tested for self-consistency. In this review, we further expand on the theoretical details described in (Henzler et al. Sci Adv 4:eaa06283, (2018)), where a molecular-based solution model was constructed based on a solvent-mediated quantum mechanical potential of mean force for Ca\(^{2+}\) and CO\(_3^{2-}\) ion pairing. The statistical mechanics and simulation approaches for solution-phase nucleation are presented and connected to the various CaCO\(_3\) polymorph chemical potentials and interfacial surface energies. The resulting theory presented herein is general and is shown to accurately describe the initial stages of amorphous calcium carbonate nucleation.