A Benchmark Database for Spin-Flip Gap Calculations in Single- and Multireference Systems Using ΔDFT and Beyond

Accurate calculation of spin-flip gaps (SFGs) in molecular systems remains challenging due to the lack of benchmark data and the multireference nature of many open-shell singlet states. Here, we constructed a benchmark SFG database comprising 419 vertical gaps, partitioned into two subsets: SFG-SR (379 gaps from single-reference systems) and SFG-MR (40 gaps from multireference diradicals). Reference values were obtained using CCSD(T) for SFG-SR and MS-CASPT2 or experimental data for SFG-MR. This data set provides a reliable basis for future benchmarking and functional development. For the SFG-SR subset, 32 functionals were assessed using the ΔDFT method. Hybrid functionals significantly outperformed semilocal ones. The amount of Hartree–Fock exchange was found critical for accuracy and size scaling, with optimal performance achieved through careful parameter tuning or theoretical justification. Compared to (SF-)TDDFT, ΔDFT with optimized functionals offers a practical and accurate strategy for SFG prediction. For the SFG-MR subset, we evaluated the hierarchically correlated orbital functional theory (HCOFT). Among its variants, 1-HCOFT showed excellent accuracy for singlet diradicals and remarkably low basis set dependence. This robustness persists with increasing system size, making 1-HCOFT promising for large-scale multireference systems. By incorporating strong correlation within a single-determinant framework, HCOFT extends beyond KS-DFT’s limitations. Altogether, this work connects benchmark data with emerging theory, advancing scalable and accurate modeling of spin states in complex systems.