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.