## Reports: UNI655243-UNI6: Structure and Energetics of Calcium Carbonate Pre-Nucleation Clusters from Atomic-Scale Simulations: Development of a Novel Interatomic Potential

**Patrick Huang, PhD**, California State University, East Bay

**Introduction**

The eventual goal of this project is to develop a novel
interatomic potential that will enable atomic-scale simulations for the
structure and thermodynamics of calcium carbonate (CaCO_{3})
pre-nucleation clusters in water. To do this, we need benchmark information on
the hydration of the CaCO_{3}(*aq*) contact ion
pair, which is not available. Thus, we first establish the structure and
energetics of CaCO_{3}(*aq*) hydration using
first-principles techniques.

**Progress to date**

Previously, we found that the structure of hydrated CaCO_{3}(*aq*) as derived from classical molecular dynamics (MD) with
model interatomic potentials [1] disagreed with first-principles MD using
density functional theory (DFT) and the generalized gradient approximation
(GGA). The classical MD predicted a 7-coordinate Ca^{2+} complex with
six waters plus a carbonate coordinated in a monodentate
fashion. In contrast, first-principles MD gave a 6-coordinate Ca^{2+},
where the carbonate coordination shifts between mono- and bidentate
on the time scale of the simulation (Figure 1).

*Figure 1**: Dynamics of the
order parameter from first-principles MD simulation of CaCO _{3}(aq), defined as the difference in the Ca^{2+} and
carbonate oxygen distances. An order parameter of ~ 0 corresponds to bidentate coordination; a non-zero order parameter
represents monodentate coordination. One the time
scale of the simulation (~ 30 ps), the carbonate
coordination switches between monodentate with five
waters of hydration around Ca^{2+}, and bidentate
carbonate with four waters of hydration.*

However, there are well-known weaknesses in the DFT-GGA description of liquid water and metal ion hydration [2]. In order to confirm the first-principles MD findings, we embarked on a complementary approach to study metal ion hydration using finite cluster models, which can be treated using quantum chemical techniques and Gaussian-type basis sets. Such models permit the use of a wider variety of DFT functionals (i.e., hybrid functionals) that are not possible in first-principles MD, which rely primarily on plane-wave basis sets and the GGA.

We have approached this with a simpler system, the hydrated Ce(OH)_{4}(*aq*) complex,
employing DFT with the hybrid exchange-correlation density functional PBE0 [3].
A preference for a particular hydration environment can be established by
comparing the energetics of different coordination structures; in this case, we
have optimized clusters of 6, 7, and 8-coordinate Ce^{4+} (Figure 2).
Such cluster models require at least two complete solvation shells, which correspond
to a minimum of about 30 water molecules. Future work will apply this cluster
approach to establish the preferred hydration structure of CaCO_{3}(*aq*).

*Figure 2**: Finite cluster
models for the hydrated Ce(OH) _{4}(aq) complex.
Clusters have varying coordination numbers (CN) have been optimized:
6-coordinate (left), 7-coordinate (middle), and 8-coordinate (right). In order
to compare their energetics, one has to take care that each cluster is
constructed to have the same number of hydrogen bonds to ensure proper cancellation
of errors.*

**Impact**

The ACS-PRF award has supported a total of two graduate (MS) students and two undergraduate (BS) students. Two of these students have graduated and successfully transitioned to jobs in industry; a third student is expected to graduate later this year and is applying to pursue a Ph.D. in chemistry.

**References**

[1] Raiteri, P.; Gale, J.D.;
Quigley, D.; Rodger, P.M. Derivation of an Accurate Force-Field for Simulating
the Growth of Calcium Carbonate from Aqueous Solution: A New Model for the
Calcite-Water Interface. *J. Phys. Chem. C*
**2010**, *114*, 5997–6010. DOI: 10.1021/jp910977a

[2] Gillan, M.J.; Alfe, D.; Michaelides, A.
Perspective: How good is DFT for water? *J. Chem. Phys.* **2016**, *144*, 130901. DOI:
10.1063/1.4944633

[3] Perdew, J.P.; Ernzerhof, M.; Burke, K. Rationale for mixing exact
exchange with density functional approximations. *J. Chem. Phys.* **1996**, *105*, 9982.
DOI: 10.1063/1.472933