Dimensional Reduction:  A Practical Formalism for Manipulating Solid Structures

Conceptually, it is not difficult to imagine reaching into a solid structure and carving out just that portion of the framework we desire. Solid-state reactions incorporating an ionic component into a covalent structure have long been recognized as experimental means for accomplishing just such feats. However, the method does not always succeed, and so, in an effort to extend its use in more logical approaches to solid synthesis, we herein provide an assessment of the scope and limitations of the reaction type. Dimensional reduction is set forth as a general formalism describing how the metal−anion (M−X) framework of a parent compound, MXx, is dismantled upon reaction with an ionic reagent AaX to form a child compound AnaMXx+n. The added anions serve to terminate M−X−M bridges, yielding a less tightly connected framework that retains the metal coordination geometry and polyhedron connectivity mode of the original parent structure. In most instances, the connectedness of the ensuing framework can also be predicted, facilitating enumeration of likely structures. A database containing more than 3000 relevant crystal structures has been compiled (available at http://alchemy.cchem.berkeley.edu/dimred) and is employed in evaluating the applicability of dimensional reduction to various systems. Examples are provided and results are tabulated for the deconstruction of parent solids featuring octahedral, tetrahedral, square planar, and linear metal coordination polyhedra linked through corner-, edge-, and face-sharing interactions. The success of dimensional reduction is observed to depend significantly on the choice of the countercation A (with smaller cations typically giving more reliable results), suggesting that this should be considered a variable parameter when targeting a specific child framework. The utility of the method in dismantling cluster-containing frameworks is also discussed.