The Solid-State Structures of Dimethylzinc and Diethylzinc

The synthesis of dimethylzinc (Me 2 Zn) and diethylzinc (Et 2 Zn) by Frankland in the mid-nineteenth century marks a cornerstone in the history of chemistry. [1] Not only were they among the first organometallic compounds, but studies on their chemical reactions and vapor densities led to the first clear exposition of valency theory. [2] Since then both compounds have found widespread applications: They are important reagents in organic synthesis, [3] for example in the enantioselective alkylation of carbonyls [4] and imines [5] and in cyclopropanation reactions. [6] Their high vapor pressures have led to extensive uses in metalorganic chemical vapor deposition (MOCVD) for the preparation of wide band gap II–VI semiconducting films (e.g. ZnS, ZnSe, ZnTe), [7] ZnO nano-structures, and as p -dopant precursors for III–V semiconduc-tors (e.g. GaAs, InP, Al x Ga 1 (cid:2) x As), which have numerous electronic and photonic applications. [8] Despite their prominence in chemical and materials synthesis, the solid-state structures of these prototypical organometallic systems remained elusive. [9] Me 2 Zn and Et 2 Zn feature the smallest and lightest molecules containing metal atoms in the condensed phase. At standard conditions they exist as volatile, pyrophoric liquids (Me 2 Zn: m.p. (cid:2) 42 8 C, b.p. 46 8 C; Et 2 Zn: m.p. (cid:2) 28 8 C, b.p. 118 8 C), which are moderately soft Lewis acids that form adducts with a variety of ligands. [10] Structural studies of the gas crystal structure remains challenging for density functional methods. This demonstrates that the lower dialkylzinc systems continue to be very intriguing and still provide valuable data for ongoing scientific discussions more than 160 years after their discovery.

4. Two-dimensional disorder of α-Me 2 Zn S10 5. Assessment of the conformation of the methyl groups of β-Me 2 Zn S11 6. Details of Density Functional Calculations S12 7. Atomic coordinates for all calculated crystal structures S14

Crystal data and structure refinement
Samples were contained in quartz capillaries (0.5 mm bore diameter), which were flame sealed. The capillaries were mounted vertically on the X-ray goniometer and cooled with a cold stream of N 2 . Crystals of α-Me 2 Zn and Et 2 Zn were grown from the melt by gradually cooling the samples. Crystals of β-Me 2 Zn were obtained by moving a hot wire along the outside of the capillary. Crystal data were collected on a Bruker Apex diffractometer using MoK α radiation (λ = 0.71073 Å). Crystal structures were refined with SHELX by full-matrix least squares against F 2 using all data. [S1] Note, that the coverage of reflection data was limited due to the experimental setup, which only enabled ω rotation of the vertically aligned capillary.
[S1] G. M. Sheldrick, Acta Crystallogr. 2008, A64, 112. highlights the stacking of molecules along c; such stacks are shown in red. β-Me 2 Zn forms compact layers parallel to the ab-plane, which are more or less planar. These layers contain molecules aligned in two different orientations perpendicular to each other forming T-shaped interactions which yield a square grid type of layer arrangement. The structure of α-Me 2 Zn also features molecules of two orientations that are perpendicular to each other, but these are arranged in alternate layers. Thus a set of two neighboring layers (shown in red in (a)) can be regarded as a corrugated analogue of the planar layer of β-Me 2 Zn. Compared to β-Me 2 Zn, the structure of α-Me 2 Zn is compressed in a and b direction (cell parameters a and b decrease S5 from around 7.5 Å in β-Me 2 Zn to around 6.8 Å in α-Me 2 Zn, while on the other hand the distance between layer planes increases from 3.4 Å (β-Me 2 Zn) to 4.2 Å (α-Me 2 Zn). Hence, the structures of both phases can be compared as follows: While β-Me 2 Zn forms more compact layers in the form of a planar square grid in the ab-plane, these layers are stacked in lower symmetric fashion along the c-direction. In contrast, molecules of α-Me 2 Zn are aligned effectively in the form of linear stacks along c but show a less compact arrangement in both a and b directions.

Hirshfeld surface analysis
Hirshfeld surface analysis was carried out for the X-ray crystal structures of α-Me 2 Zn (Fig.  S3), β-Me 2 Zn (Fig. S4) and Et 2 Zn (Fig. S5) using the program CrystalExplorer (see ref. [S2] for a detailed description of the method).
The Hirshfeld surface partitions the crystal into molecular entities. Color coding the surface according to certain surface properties, such as distance to nearest atom and curvedness, provides a useful visual tool to examine the intermolecular interactions in crystals structures. Note that C-H bond lengths are normalized by CrystalExplorer to 1.083Å. The curvedness is a function of the root-mean-square curvature of the surface, with flat areas of the surface having a low curvedness and areas of sharp curvature having a high curvedness. Areas on the Hirshfeld surface with high curvedness tend to divide the surface into contact patches with each neighboring molecule, so that the curvedness of the Hirshfeld surface could be used to define a coordination number in the crystal.
2D 'fingerprint' plot: Each point corresponds to a unique (d e , d i ) pair. Points are colored blue for a small, green medium to red for points with the greatest contribution. These plots are pseudo-mirrored along the d e = d i diagonal. Features along the diagonal occur due to H···H contacts, while the 'wings' are due to H···Zn interactions.
The surfaces of αand β-Me 2 Zn show very similar features: 85% of the molecular surface is taken up by hydrogen and 15% by zinc, while H…H contacts engage about ¾ and H…Zn contacts ¼ of the molecular surface. The Hirshfeld surfaces of both Me 2 Zn phases show small contributions of direct Zn...Zn contacts (0.9 % for the αand 0.6 % for the β-phase). However, the corresponding Zn…Zn distances of 4.183(3) (Me 2 Zn) and 4.079(7) Å (β-Me 2 Zn) are somewhat long suggesting the absence of significant interactive forces between the metal atoms. In Et 2 Zn the surface contribution of Zn is reduced to about 10%, while Zn…H contacts make up 17 %. The shortest H…H interactions of β-Me 2 Zn and Et 2 Zn measure about 2.4 Å, which is equal to the sum of the Van-der-Waals radii. Slightly longer H…H contacts of 2.6 Å are observed in the more loosely packed α-phase of Me 2 Zn. On the other hand, the shortest Zn…H contacts in all three structures are very similar (around 2.8 Å).
[ The similarity of fingerprint plots shows that the intermolecular interactions are virtually identical in both the ordered and disordered form. This suggests that crystals of α-Me 2 Zn are likely to be affected by two-dimensional disorder in a and b, while onedimensional order is maintained within the stacks of molecules along c. Diffuse scattering, which is indicative of this type of disorder, was too weak to be detected, possibly due to the Icentered superlattice of Zn atoms, which is not affected by the disorder but dominates the reflection pattern.  Figure S7: Hirshfeld surface analysis was used to determine the most appropriate orientation for the methyl groups in the structure of β-Me 2 Zn. Methyl groups were rotated and their Hirshfeld surfaces assessed at various stages. The conformer A shows the most appropriate intermolecular distances, which are very similar to those observed in α-Me 2 Zn and Et 2 Zn. All other conformers (such as B, C and D) generate excessively short intermolecular contacts as indicated by the spikes in the fingerprint plots (excessively short contacts are underlined in the table above). Central spikes are due to short H…H contacts and those at the wings due to short Zn…H contacts. Also note that these structures tend to generate fringes in the region of longer contacts, which is symptomatic of void space. S12

Details of Density Functional Calculations
Initial calculations were performed with the plane-wave basis set VASP [S3] code using the Projector Augmented Wave method [S4] and the PBE functional. [S5] k-point sets were varied from 3x3x4 to 5x5x8 with little effect. A plane-wave cutoff energy of 600 eV was used with geometry optimization continued until the forces per atom were either 0.01 eV/Å or 0.005 eV/Å (both yielded essentially similar results). In the absence of van der Waals corrections, this approach unsurprisingly leads to overestimation of the lattice constants by 5% for a and 10% for c for α-Me 2 Zn, with the overstimation of ~4 % for Et 2 Zn. Using VASP version 5.2.11, calculations were also run with van der Waals corrections included with the Grimme DFT-D [S6] approximation. This substantially overbinds the solid causing contractions of 7% and 11% for a and c respectively.
Subsequently all structures were relaxed using dispersion-corrected density functional theory with the PBE generalized gradient approximation [S5] and the TS'09 dispersion correction [S7] as implemented in all-electron code FHI-aims. [S8] We first relaxed the structure and unit cell using a tier1 basis set (e.g. double-numeric plus polarization), [S8] followed by a highly converged relaxation of the atoms only using a tier2 basis set. [S8] In each case, the calculation was continued until the forces on each atom or the energy gradient with respect to each lattice vector coordinate was less than 0.01 eV/Å. The Brillouin zone was sampled with a 3x3x4 Monkhorst-Pack [S9] k-point grid for relaxing the high-T structure of Me 2 Zn and a 3x3x2 grid for the other unit cells. This gave the best agreement with experiment for the lattice constants of α -Me 2 Zn, with errors of 0.9% and 3.4% for a and c respectively. To obtain the projected density of states, a much denser grid of 16x16x24 k-points was used together with a Mulliken analysis. Finally, an uncertainty analysis [S10] was performed on the van der Waals contribution to the binding energy, which provides some measure of the absolute accuracy of the methods for this particular system.
The final structure obtained with FHI-aims for α -Me 2 Zn was used as the start point for optimization with the van der Waals density functional (optB86b-vdwDF) as implemented in VASP. [S11] With a cutoff energy of 600 eV and a 3x3x5 k-point set the lattice constants reduce slightly to a = 6.74 Å (6.79 Å from FHI-aims) and c = 3.93 Å (4.04 from FHI-aims).