Structural Information on Supramolecular Copper(II) β-Diketonate Complexes from Atomic Force Microscopy and Analytical Ultracentrifugation

Supramolecular Cu(II) complexes were prepared from two trifunctional β-diketone ligands. The ligands (CH3Si(phacH)3 and CH3Si(phprH)3, represented by LH3) contain three aryl-β-diketone moieties joined by an organosilicon group. The complexes have the empirical formula Cu3L2, as expected for combinations of Cu2+ and L3–. Several metal–organic polyhedra (MOPs) [Cu3L2]n are possible (n = 1–10); a dodecahedron (Cu30L20; n = 10; estimated diameter of ca. 5 nm) should be the most stable because its internal bond angles would come closest to ideal values. Atomic force microscopy (AFM), performed on samples deposited from solution onto mica substrates, revealed a distribution of sample heights in the 0.5–3.0 nm range. The most commonly observed heights were 0.5–1.5 nm, corresponding to the smallest possible molecules (Cu3L2, i.e., n = 1). Some molecular cubes (Cu12L8; ca. 2.5 nm) or larger molecules or aggregates may be present as well. Equilibrium analytical ultracentrifugation (AUC) was also used to probe the compounds. A previously reported reference compound, the molecular square Cu4(m-pbhx)4 (M = 2241 g mol–1), behaved well in AUC experiments in four nonpolar organic solvents. AUC data for the new tris(β-diketonate) MOPs [Cu3L2]n in toluene and fluorobenzene did not agree well with the theoretical results for a single solute. The data were fit well by a two-solute model, but these results were not consistent in the two solvents used, and some run-to-run variability was noted even in the same solvent. Also, the calculated molecular weights differed significantly from those expected for [Cu3L2]n ([Cu3(CH3Si(phac)3)2]n, multiples of 1322 g mol–1; or [Cu3(CH3Si(phpr)3)2]n, multiples of 1490 g mol–1).


A. Additional AFM Images
The D-Z formula for the partial molar volume Vc ¯ is where the Vi are increments for individual atoms and functional groups, VCV is a covolume correction of +12.4 cm 3 mol −1 , the VRF are corrections for ring formation, and the VES are electrostriction corrections (which are zero for the neutral MOPs discussed here).
Replacing a C atom by Si in these compounds increases the molar volume by 15-17 cm 3 .The average of the three increases is 16.2 cm 3 mol −1 , which gives a D-Z value of 26.1 cm 3 mol −1 for Si.
Note: Changing the volume increment for Si by ±2 cm 3 mol −1 leads to changes in Estimated density = 1.376 g cm −3 ; estimated partial specific volume v ¯ = 0.727 cm 3 g −1 .

S6
The experimental v ¯ value for the known Cu4(m-pbhx)4 molecular square is 0.886 cm 3 g −1 , compared with the D-Z estimated value of 0.839 cm 3 g −1 .Based on this result, the partial specific volumes for the Cu-Si compounds are likely to be slightly higher than those obtained from D-Z values.Approximate v ¯ values for the new Cu-Si MOPs can be obtained by adding 0.047 cm 3 g −1 to the D-Z values, or by multiplying the D-Z values by 0.886/0.839.The suggested values listed below are the averages of the two corrected results (which differed by less than 0.01 cm 3 g −1 in each case).

Partial specific volumes for the different [Cu3L2]n oligomers
The D-Z method yields the same estimate of v ¯ for the different oligomers [Cu3(CH3Si(phac)3)2]n, because they all have the same constituents in the same ratios.However, the experimental partial specific volumes of the oligomers may not all be the same.The smaller oligomers (n = 1-3) have smaller internal volumes and smaller pore sizes as compared to the larger molecules.This could make the smaller oligomers less accessible to solvent, which would increase their partial specific volumes.
For example, if the smallest oligomer, [Cu3(CH3Si(phac)3)2], has a larger partial specific volume than the D-Z estimate, the value of M calculated from AUC data will be too small.If the correct value of v ¯ for this compound is 0.9 cm 3 g −1 , then the AUC data summarized in Table 1 would yield values of M1 of 690 g mol −1 (in toluene) and 1800 g mol −1 (in fluorobenzene).
Similarly, a value of v ¯ of 0.88 cm 3 g −1 for [Cu3(CH3Si(phpr)3)2] would yield values of M1 closer to the calculated molecular weight.The combinations of solutes and solvents studied here have v ¯ρ close to 1.This situation increases the of the calculated M values to small changes in v ¯.This problem could be mitigated by using solvents of lower density for the AUC measurements.However, the MOPs are not soluble in common lower-density solvents (such as alkanes and ethers).
estimated v¯ values of <0.01 cm 3 g −1 for the three reference compounds.The new Cu-MeSi MOPs have an even smaller fraction of Si, so any errors in the volume increment for Si probably do not affect the calculated v ¯ values for our MOPs significantly.Assignments of ring corrections in the D-Z formula were made as follows: A Cu(βdiketonate)2 moiety contains two 6-membered rings (VRF = 8.1 cm 3 mol −1 ).The molecular square Cu4(m-pbhx)4 contains one large ring (VRF = 14.1 cm 3 mol −1 ), and the Cu-Si MOPs contain three large rings per Cu3L2 unit.Results for the Cu4 molecular square and the two MOPs are shown below.
Choosing larger v ¯ increases the calculated M values from the fluorobenzene experiments faster than those in toluene, because of the greater density of fluorobenzene.This exacerbates the differences between calculated M values in the two solvents.One could propose that v ¯ is not the same in the two solvents.However, this would run counter to our experiments with the Cu molecular square [Cu4(m-pbhx)4], which gave very similar values of v ¯ in four different solvents.