Relativistic effect influencing the diverse bonding character of the interfacial Ag staple motifs in thiolate-protected nanoclusters

Thiolate-protected noble-metal nanoclusters have recently attracted extensive attention due to their appealing properties in optics, catalysis, etc. Within the same group element, experiments indicate that Ag staples exhibit di-, tri-, or even tetra-coordination, in contrast to the di-coordination observed in Au staples, rendering the structures of Ag nanoclusters more intricate. However, the underlying chemical insight of the bonding feature of multiple-coordinated Ag staples remains unclear. In this study, we employed density functional theory coupled with all-electron scalar relativistic calculations to elucidate the critical role of relativistic effect in determining the conformational complexity of Ag staples. Unlike Au, the relatively weaker relativistic effect induces fewer contributions of d orbitals in bonding for the Ag atom, showing an extreme sensitivity to the structural architecture in liganded clusters. A relatively higher d orbital percentage favors di-coordination with a shortened Ag-S bond, while a relatively lower d orbital percentage favors tri- and tetra-coordinations with an elongated Ag-S bond. The Lewis structures of the multi-coordinated Ag motifs were also unveiled. In addition, two AgNCs, including the [Ag-29(SCH3)(18)](3)- cluster with tri-coordinated Ag motifs and [Ag-29(SCH3)(18)(PCH3)(6)](3- )with tetra-coordinated Ag motifs, were predicted after clarifying the bonding characters of the multiple-coordinated Ag motifs. This work not only deepens the understanding of the bonding characteristics of the Ag staple motif in AgNCs and AuAg alloy clusters but also provides a new perspective to understand the relativistic effect in the thiolate-protected noble-metal nanocluster.