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.