Survey of short and long cuprophilic d¹⁰-d¹⁰ contacts for tetranuclear copper clusters. Understanding of bonding and ligand role from a planar superatom perspective

Polynuclear copper(i) complexes involving d¹⁰-d¹⁰ interactions have been studied to a lesser extent in comparison to their gold counterparts. Here, we attempt to gain a deeper understanding of ligand-protected d¹⁰ copper clusters based on density functional theory calculations, based on the evaluation of several tetranuclear copper arrays offering different cuprophilic interactions, showing short- and long-contact d¹⁰-d¹⁰ situations. Our results show that the protecting ligands display a fundamental role in the stabilization of the closed-shell central core since there is a direct relationship between ligand charge donation to the ns combinations of multinuclear metallic center and the collateral increasing of the copper-copper stabilizing interactions. Further, quantification of the incoming population of ns shell levels through a selective analysis of coefficients of its corresponding wave functions depicts a useful and novel methodology toward the characterization of the copper-metallophilic phenomena that appears in these closed-shell systems. Thereby, here we use the planar superatom approach to describe the ns valence population in terms of superatomic two-dimensional shell set levels, namely, 1s, 1p_x, 1p_y, and 1d_xy. Thus, the tetranuclear clusters can be viewed as formally 8-valence electron systems, which gives a better understanding of the stable core structures. The formation of different types of cuprophilic interaction in d¹⁰-d¹⁰ Cu-Cu structures can be used to generate strongly bound closed-shell interactions in lighter counterparts from the coinage metal group, similarly to gold-gold compounds. We expect that this analysis can be extended to linear and polymeric d¹⁰-d¹⁰ Cu-Cu arrays in order to gain a deeper understanding of the closed-shell bonding situation.