Above: the largest dication in the study (barium) produces the most asymmetric coordination complex in the crystal phase (and retains a THF to boot).
Published in the Journal of Coordination Chemistry (article link) and "…dedicated to Professor Jim Atwood to honor his many years as Editor-in-Chief of the Journal or Coordination Chemistry [huzzah!]." I most definitely still have my copy of Inorganic and Organometallic Reaction Mechanisms; that cover stared back at me for six months in one of my grad school offices. The raw data for this paper goes back several years and has finally been put into form – "several years" being long enough that the theory work for this one didn't overlap with the method work that went into the Azobenzene as an Effective Ligand in Europium Chemistry article I posted several days back (as to whether the predictions would have been different or not, we may never know).
We've solved the protein folding problem (fairly well as of late) but still haven't solved the (molecular) crystal polymorphism problem. While this paper and field of work focuses on the presented alkali (Li -> Fr) and alkaline earth (Be -> Ra) metals, in these systems those metals really are just charged, spherical linkers that will preferentially stick to some organic functional groups better than others (ignoring the chemistry to get those metals there, of course). For anyone pondering the design of crystals or (macro)molecular complexes out of these spheres, the key issues are (a) dicationic radius, (b) effective charge at the metals, (c) the strength of the interaction of these spheres with the functional groups, and (d) the preferred means of these metals to interacting with varied ligands due to the varied dependencies within the other three items.
These tetrahedral tetraarylborate anions are valuable molecules because their high symmetry means that many coordination modes are available that can still retain some of the symmetry elements of the isolated anion – this provides the theoretician with a healthy opportunity to speed the calculations along and impose symmetry-constrained geometries that let us explore binding preferences at higher levels of theory. In terms of developing computational models to explore preferred binding modes, these ligands are excellent test cases because they are highly symmetric molecules that, except for barium, prefer to produce highly (locally) symmetric coordination complexes. This was exploited to great extent in the Gaussian 09 (I did say this theory work was older) calculations performed to try to draw firm conclusions about the preferred binding modes across the Ca-Sr-Ba series – and the calculations well-reproduced the observed trends (so there).
Some additional work was done to model the preferred numbers of coordinated solvent molecules (THF and Et2O) down the alkali earth series, but that's an even more academic question given the known coordination energies of both molecules, and so was not included in the article.
Catherine M. Lavin, Damian G. Allis, Miriam M. Gillett-Kunnath, Ashley Clements, Alan G. Goos, Joshua J. Woods, Paul Hager, Donyell S. Logan, and Karin Ruhlandt-Senge
Abstract: The use of the weakly binding tetraarylborate ligands and the careful selection of co-ligands affords novel contact ion pairs exclusively stabilized by Ae-π (Ae = calcium, strontium and barium) interactions of the form [Ae(B{(3,5-Me2)C6H3}4)2(thf)n] (Ae = Ca, n = 0, 1; Sr, n = 0, 2), [Ba(B{(3,5-Me2)C6H3}4)2(thf)]. HN(SiMe3)2, 3 and [Ba(B{(4-tBu)C6H4}4)2].Et2O, 4. The variety of and preference for binding geometries with choice of metal is considered using theoretical calculations.