Approaching the Complete Basis Set Limit for Transition Metal Spin–State Energetics

Convergence to the complete basis set (CBS) limit is analyzed for the problem of transition metal (TM) spin-state energetics by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term, (T#). This computational protocol recovers relative spin–state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation 0.4, mean signed deviation 0.2, and maximum deviation 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin–state energetics calculated using CCSD(T) and other wave-function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, MRCI+Q), which justifies efficient focal-point approximations and simplifies construction of multi-method benchmark studies.