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.