Navigating the 18-n+m Isomers of PdSn₂: Chemical Pressure Relief through Isolobal Bonds and Main Group Clustering

The 18-n electron-counting rule provides structural guidelines for electronically feasible transition metal (T)-main group (E) phases, contributing toward the goal of material design. However, the availability of numerous potential structure types at any electron count creates a challenge for the prediction of the preferred structures of specific compounds, as is illustrated by the concept of 18-n+m isomerism. In this Article, we explore the driving forces stabilizing one 18-n+m isomer over another with an analysis of the structure of PdSn₂, a layered intergrowth of the fluorite and CuAl₂ structure types. The DFT-reversed approximation Molecular Orbital (DFT-raMO) method reveals that PdSn₂ and its hypothetical parent structures all adhere to bonding schemes approximating the electronic configurations expected from the 18-n rule, with various degrees of isolobal Pd-Pd bonding and Sn clustering. However, partial electron transfer between the Pd 5p orbitals to the Sn 5s orbitals contributes to the absence of convincing electronic pseudogaps near their Fermi energies. As such, there is no clear electronically driven preference among the structure types. This situation allows for atomic packing effects to prevail: DFT-Chemical Pressure (DFT-CP) analysis illustrates that in the fluorite-type parent structure, positive Pd-Sn CPs lead to overcompression of the Pd atoms and a stretching of the relatively open Sn sublattice. In contrast, in the CuAl₂-type parent structure, Sn atoms cluster into tetrahedra, opening space for an expanded Pd environment and the formation of Pd-Pd interactions. However, the tetrahedral packing of the Sn atoms here leads to frustration between negative and positive Sn-Sn CPs. Through the development of the angular CP correlation function (CP_cor+) as a tool to quantify frustration among interatomic interactions, we demonstrate how the observed PdSn₂ structure balances these effects by tuning the degree of Sn-Sn clustering and expansion of the Pd environment. These observations point to generalizations for most 18-n+m isomers, where increased main group ligand clustering (+m) and isolobal bonds (+n) can accommodate compositions with different T and E atomic sizes.