Incorporation reactions play an important role in dictating immobilization and release pathways for chemical species in low-temperature geologic environments. Quantum-mechanical investigations of incorporation seek to characterize the stability and geometry of incorporated structures, as well as the thermodynamics and kinetics of the
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Incorporation reactions play an important role in dictating immobilization and release pathways for chemical species in low-temperature geologic environments. Quantum-mechanical investigations of incorporation seek to characterize the stability and geometry of incorporated structures, as well as the thermodynamics and kinetics of the reactions themselves. For a thermodynamic treatment of incorporation reactions, a source of the incorporated ion and a sink for the released ion is necessary. These sources/sinks in a real geochemical system can be solids, but more commonly, they are charged aqueous species. In this contribution, we review the current methods for ab initio
calculations of incorporation reactions, many of which do not consider incorporation from aqueous species. We detail a recently-developed approach for the calculation of incorporation reactions and expand on the part that is modeling the interaction of periodic solids with aqueous source and sink phases and present new research using this approach. To model these interactions, a systematic series of calculations must be done to transform periodic solid source and sink phases to aqueous-phase clusters. Examples of this process are provided for three case studies: (1) neptunyl incorporation into studtite and boltwoodite: for the layered boltwoodite, the incorporation energies are smaller (more favorable) for reactions using environmentally relevant source and sink phases (i.e.
(oxides) > ΔErxn
(silicates) > ΔErxn
(aqueous)). Estimates of the solid-solution behavior of Np5+
- and U6+
-boltwoodite and Np5+
- and U6+
-boltwoodite solid solutions are used to predict the limit of Np-incorporation into boltwoodite (172 and 768 ppm at 300 °C, respectively); (2) uranyl and neptunyl incorporation into carbonates and sulfates: for both carbonates and sulfates, it was found that actinyl incorporation into a defect site is more favorable than incorporation into defect-free periodic structures. In addition, actinyl incorporation into carbonates with aragonite structure is more favorable than into carbonates with calcite structure; and (3) uranium incorporation into magnetite: within the configurations tested that preserve charge neutrality (U6+
), uranium incorporation into magnetite is most favorable when U6+
replaces octahedral Fe3+
with charge balancing accomplished by an octahedral Fe3+
iron vacancy. At the end of this article, the limitations of this method and important sources of error inherent in these calculations (e.g., hydration energies) are discussed. Overall, this method and examples may serve as a guide for future studies of incorporation in a variety of contexts.