Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes

Convergence to the complete basis set (CBS) limit is
analyzed for
the problem of spin-state energetics in mononuclear first-row transition
metal (TM) complexes 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 the relative spin-state energetics of the benchmark
set in excellent agreement with the reference CCSD(T)/CBS limits (mean
absolute deviation of 0.4, mean signed deviation of 0.2, and maximum
deviation of 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 computed using
CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2,
and MRCI + Q), which justifies efficient focal-point approximations
and simplifies the construction of multimethod benchmark studies.