Toward more robust tuned range-separated DFT for heavy-element clusters

Range-separated hybrid (RSH) density functionals with ionization potential theorem based tuning are widely used for excited-state and response-property calculations in metal clusters and related systems, yet their tuned variants are often numerically unstable and poorly reproducible for small-gap, near-degenerate cases, particularly for frequency-dependent and higher-order responses. Here, we analyze the origin of these difficulties using heavy-element gold clusters as representative examples. Focusing on Au₅V as a detailed case study and Au₄ and Au₈ clusters as additional benchmarks with available reference data, we show that the instability and poor reproducibility of conventional tuned RSH calculations are closely linked to an underconstrained immediate-frontier tuning strategy and to the treatment of spin multiplicity. Based on these insights, we establish a more robust tuning workflow and introduce cross-functional robustness as a practical criterion for assessing the reliability of frequency-dependent response calculations when high-level but computationally demanding benchmarks are unavailable. The present results provide practical guidance for applying tuned RSH methods to heavy-element clusters and related systems with dense frontier manifolds.