Entropic Control of Bonding, Guided by Chemical Pressure: Phase Transitions and 18- n + m Isomerism of IrIn 3 .

As with other electron counting rules, the 18- n rule of transition metal-main group (T-E) intermetallics offers a variety of potential interatomic connectivity patterns for any given electron count. What leads a compound to prefer one structure over others that satisfy this rule? Herein, we investigate this question as it relates to the two polymorphs of IrIn 3 : the high-temperature CoGa 3 -type and the low-temperature IrIn 3 -type forms. DFT-reversed approximation Molecular Orbital analysis reveals that both structures can be interpreted in terms of the 18- n rule but with different electron configurations. In the IrIn 3 type, the Ir atoms obtain largely independent 18-electron configurations, while in the CoGa 3 type, Ir-Ir isolobal bonds form as 1 electron/Ir atom is transferred to In-In interactions. The presence of a deep pseudogap for the CoGa 3 type, but not for the IrIn 3 type, suggests that it is electronically preferred. DFT-Chemical Pressure (CP) analysis shows that atomic packing provides another distinction between the structures. While both involve tensions between positive Ir-In CPs and negative In-In CPs, which call for the expansion and contraction of the structures, respectively, their distinct spatial arrangements create very different situations. In the CoGa 3 type, the positive CPs create a framework that holds open large void spaces for In-based electrons (a scenario suitable for relatively small T atoms), while in the IrIn 3 type the pressures are more homogenously distributed (a better solution for relatively large T atoms). The open spaces in the CoGa 3 type result in quadrupolar CP features, a hallmark of low-frequency phonon modes and suggestive of higher vibrational entropy. Indeed, phonon band structure calculations for the two IrIn 3 polymorphs indicate that the phase transition between them can largely be attributed to the entropic stabilization of the CoGa 3 -type phase due to soft motions associated with its CP quadrupoles. These CP-driven effects illustrate how the competition between global and local packing can shape how a structure realizes the 18- n rule and how the temperature can influence this balance.