Uncovering the Activity of Alkaline Earth Metal Hydrogenation Catalysis Through Molecular Volcano Plots

Recent advances in alkaline earth (Ae) metal hydrogenation catalysis have broadened the spectrum of potential catalysts to include candidates from the main group, providing a sustainable alternative to the commonly used transition metals. Although Ae-amides have already been demonstrated to catalyze hydrogenation of imines and alkenes, a lucid understanding of how different metal/ligand combinations influence the catalytic activity is yet to be established. In this article, we use linear scaling relationships and molecular volcano plots to assess the potential of the Ae metal-based catalysts for the hydrogenation of alkenes. By analyzing combinations of eight metals (mono-, bi-, tri-, and tetravalent) and seven ligands, we delineate the impact of metal-ligand interplay on the hydrogenation activity. Our findings highlight that the catalytic activity is majorly determined by the charge and the size of the metal ions. While bivalent Ae metal cations delicately regulate the binding and the release of the reactants and the products, respectively, providing the right balance for this reaction, ligands play only a minor role in determining their catalytic activity. We show how volcano plots can be utilized for the rapid screening of prospective Ae catalysts to establish a guideline to achieve maximum activity in facilitating the hydrogenation process. Supplementary Information The online version of this article at 10.1007/s11244-021-01480-7.


Additional computational details
The NCI plots were computed with the NCIPLOT program, starting from the M06 wave functions of the optimized geometries. 1 The NCI index is based on the electron density and its derivatives. The relationship between the reduced density (s) and the electron density (ρ) is: When representing s versus ρ, the presence of non-covalent interactions is shown by the characteristic peaks at low density values, originating from the annihilation of the density gradient at these points. 2 The reduced density gradient and the electron density are evaluated at a set of grid points around the system of interest. The sign of the second eigenvalue (λ 2 ) of the electron-density Hessian matrix allows to distinguish between the type of interaction.
A negative eigenvalue (λ 2 < 0) denotes a bonding interaction, while a positive eigenvalue (λ 2 > 0) characterizes nonbonding interactions. The strength of the interaction is derived from the density values of the low-gradient spikes. The Laplacian sign is a widely used tool to distinguish between different types of strong interactions. 3 Bonded interactions give rise to a charge accumulation (∇ 2 ρ < 0), whereas a density depletion is the result from antibonding interactions (∇ 2 ρ > 0). For weaker, noncovalent interactions, the Laplacian in the interatomic region is dominated by the positive contribution for both bonding and nonbonding interactions. Therefore, to distinguish between attractive and repulsive interactions, one must consider density accumulation or depletion in the plane perpendicular to the interaction. This is mainly characterized by the second eigenvalue (λ 2 ) of the electron-density matrix. The Laplacian can be written as follows, using the three components of the maximal variation.
In this equation, the λ i values are the three eigenvalues of the electron-density Hessian matrix. Since it is the sign of the second eigenvalue that is indicative for the type of interaction, the density gradient is plotted against the product of the sign(λ 2 ) and the electron density ρ. The visualization of the gradient isosurface in real space is a useful tool for visualizing non-covalent interactions. The value of the sign(λ 2 )ρ is used to colour the different isosurfaces. In general, a RGB (red-green-blue) scale is used. Red isosurfaces stand for repulsive interactions while on the other hand blue isosurfaces indicate attractive interactions. Green indicates van der Waals-type interactions.

NCI analysis of intermediate 6
To obtain further insight into the cation-π interactions (CPI), the NCI index has been computed for different metal complexes of intermediate 6.
To evaluate the influence of the metal, the ligand (Me − ) was kept constant. For all complexes, a nonbonding interaction is located at the ring center of the substrate (see Figure 6, S4, and S6). Additionally, an attractive and repulsive spike in the s(ρ) diagram was localized for the cation-π interaction (CPI) between the metal and the product. For the same substrate, the CPI weakens significantly with a decreasing cation charge. The shift in the peak is largest between the tetra-, and trivalent, and the tri-and divalent cations. This validates the hypothesis that highly charged cations are limited by product release, due to the strong CPI with the Ph ring of ethylbenzene, leading to an overstabilization of complex 6. The shift in the peak describing the metal-product interaction is rather small when going from Ca 2+ to Na + , while a large shift ( Figure S5) is visible in the peak that is responsible for the interaction between the cation and the Me − ligand and the cation and the hydride. The positions of the low gradient spikes corresponding to the CPI for evenly charged cations are very similar. Figure   S6 and S7 provide the NCI analysis for a few representative catalysts containing Ae metals.
To evaluate the influence of the ligand on the substrate activity, we looked at the NCI analysis of two Ti 4+ complexes, since the ligand effect was expected to be amplified for highly charged cations. A small shift towards higher density values ( Figure S4 and S5) was observed for the attractive peak of the CPI when changing from a more electron-donating ligand like NMe − 2 towards an electron-withdrawing ligand like F − . As expected, the NCI analysis validates that the metal charge plays a more crucial role in determining the activity of the catalysts towards the hydrogenation.