A transferable dual-tuning framework for range-separated double hybrids: Accurate prediction of inverted and conventional singlet–triplet gaps

Accurate prediction of inverted singlet–triplet gaps (ΔST < 0) remains a major challenge for conventional linear-response time-dependent density functional theory because the adiabatic exchange–correlation kernel fails to properly account for double-excitation effects. Although range-separated and double hybrid functionals partially improve the description of such systems, their performance strongly depends on the choice of the range-separation parameter (μ) and perturbative correlation fraction (ac). In the present study, we develop a dual-tuned range-separated double hybrid framework based on the LC-BLYP(D) functional, in which both μ and ac are determined using physically motivated electronic-structure descriptors. The range-separation parameter is obtained through a single-step tuning scheme derived from the electron localization function, while the perturbative correlation fraction is expressed as a function of the tuned μ∗ and the HOMO–LUMO overlap integral. The resulting framework simultaneously balances long-range Hartree–Fock exchange and MP2/CIS(D) correlation contributions, thereby improving the description of excited states possessing strong double-excitation character. The proposed methodology was validated using an extensive benchmark consisting of the original INVEST systems, 15 additional molecules exhibiting inverted singlet–triplet gaps, substituted azulene derivatives with conventional positive gaps, and a broad set of common molecular excitations. For weak-overlap INVEST chromophores such as substituted heptazines and pentaazaphenalene derivatives, the dual-tuned functional significantly reduces the absolute error relative to fixed-parameter approaches while consistently preserving the inverted excited-state ordering. Importantly, the method also maintains balanced performance for molecules with conventional positive singlet–triplet gaps and for ordinary valence excitation energies, demonstrating that the additional perturbative correlation does not artificially overstabilize singlet states.