Looking for a double-hybrid recipe to accurately predict spin-state energy gaps of transition metal complexes

We assess the performance of double-hybrid density functionals for spin-state energetics and state ordering in transition-metal complexes using the SSE17 dataset composed of 17 experimental references. Among the eight double hybrids examined, B2-PLYP emerges as the only approach combining robust accuracy and reliability, particularly for the challenging spin-crossover (SCO) complexes. By analyzing the interplay between exact-like exchange (EXX) and PT2 correlation contributions, we show that successful double hybrids follow a quadratic relation between the two fractions (ac=ax2). Finally, an analysis of a representative iron SCO complex further reveals that increasing PT2 correlation and/or decreasing EXX enhances ligand-to-metal σ-donation, highlighting the need for a balanced treatment of both terms.