Article pubs.acs.org/JPCC
Examining the Accuracy of Density Functional Theory for Predicting the Thermodynamics of Water Incorporation into Minerals: The Hydrates of Calcium Carbonate Raffaella Demichelis,*,† Paolo Raiteri,† Julian D. Gale,† and Roberto Dovesi‡ †
Nanochemistry Research Institute, Department of Chemistry, Curtin University, GPO Box U1987, Perth, WA 6845, Australia Dipartimento di Chimica and NIS (Nanostructured Interfaces and Surfaces) Centre of Excellence, Università degli Studi di Torino, Via P. Giuria, 7, 10125 Torino, Italy
‡
ABSTRACT: The thermodynamics of water incorporation into calcium carbonate to form hydrates has been computed quantum mechanically using density functional theory (DFT). The structure of both the hydrated and the anhydrous phases are accurately reproduced by pure-DFT, hybrid Hartree−Fock/DFT, and DFT-D2 (long-range empirical correction). However, all of the aforementioned schemes fail to correctly reproduce the experimental energetics for the hydration process. In particular, functionals that provide reliable values for the anhydrous and low water content phases (calcite, aragonite, monohydrocalcite) fail to predict the energetics for the highly hydrated phase (ikaite) and vice versa, such that a comprehensive reliable study cannot be performed with a single method. Given that the available C6 parameters for the dispersive contributions in augmented DFT schemes typically are derived for atoms in molecular environments, we have refitted this parameter specifically for carbonates based on the relative enthalpy of aragonite versus calcite. This leads to a major improvement of the computed relative enthalpy and free energy of the anhydrous and hydrated phases. This paper therefore confirms that (i) the most widely used DFT schemes are unable to predict the energetics of reactions involving systems with very different structures or those that are characterized by different kinds of interactions; (ii) van der Waals interactions are important even in systems dominated by strong ionic and covalent interactions; (iii) using literature C6 parameters that have been derived for molecular systems can lead to significant errors for solid systems; and (iv) PBE-type functionals specifically tailored for solids are able to predict at least the stability order of two polymorphs and the sign of ΔH and ΔG of a reaction, despite the fact that long-range correlation effects are not explicitly included in their formulation. a range of temperatures and pressures,8−10 and their relatively stability with respect to calcite and water has been11 or can be12,13 derived on the basis of experimental data, the reasons for their formation, their low stability and their specific stoichiometry are largely unexplored. In addition, accurate knowledge of the structure and properties of these hydrated phases is very important because they are used as a reference point to investigate ACC, especially in the case of monohydrocalcite.6,14−17 Atomistic theoretical and computational techniques have the potential to provide useful information in the field of crystallization, since they allow the investigation of the interatomic interactions within a given structure and thereby can shed light on the reasons for its stability or otherwise. Although several questions related to nucleation, crystal growth, and polymorphism have already been successfully addressed using both force field and first principles methods,18−20 the problem of determining accurate thermodynamic predictions for water incorporation into carbonate mineral phases has rarely been considered. In contrast, water incorporation into silicate minerals such as olivine has received extensive attention because of the relevance to the Earth’s mantle.21
1. INTRODUCTION Calcium carbonates play an important role in the biochemistry of our body and in the geochemistry of our environment, where they are mostly present as a result of biomineralization. Recent studies have shown that carbonate minerals nucleate and crystallize via a more complex series of pathways than envisaged within classical nucleation theory.1,2 As a result, there has been heightened interest in characterizing the intermediate phases that appear during the formation of calcium carbonate, with the aim of understanding the mechanism itself and the factors that lead to the selection of the final polymorph. In particular, the anhydrous CaCO3 crystalline phases (aragonite, calcite, vaterite) are the final products of a dehydration and structural reorganization step that starts from amorphous calcium carbonate (ACC) particles that can possess variable water content and proceeds via the formation of crystalline hydrated calcium carbonates intermediates.3−7 The latter have the general formula of CaCO3· xH2O, with x being either 1 (monohydrocalcite), or 6 (ikaite). Due to their relatively low stability at ambient temperature and pressure, these compounds are rarely found in nature, and are difficult to obtain as pure crystals.8,9 Several questions related to the role of monohydrocalcite and ikaite in the transformation of hydrated ACC to anhydrous crystals are still a matter of ongoing investigation. While the structures of both monohydrocalcite and ikaite are reasonably well-known over © 2013 American Chemical Society
Received: May 16, 2013 Revised: July 19, 2013 Published: July 24, 2013 17814
dx.doi.org/10.1021/jp4048105 | J. Phys. Chem. C 2013, 117, 17814−17823
The Journal of Physical Chemistry C
Article
In this paper we apply first -principles methods to study the thermodynamics associated with the following reaction: CaCO3 + x H 2O → CaCO3 ·x H 2O
bipolar expansion. The latter approximation, which allows a reduction of the computing time, affects the relative energy between calcite and aragonite by ≃0.7 kJ/mol per formula unit when using the default tolerances. By reducing the thresholds to the above more precise values this error is reduced to
