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.