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

Abstract

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.

Predicting spin states of iron porphyrins with DFT methods including crystal packing effects and thermodynamic corrections

“…Commonly used functionals, including B3LYP-D3, B3LYP*-D3 and TPSSh-D3, produce significant to very large deviations in favor of the quartet (IS) state. We have already diagnosed a similar problem in previous studies of Fe III porphyrins by comparing with the CCSD(T) calculations for small models 65,67 or with the experimental data of microperoxidase. 80 The present results fully confirm the previous diagnoses.…”

“…It is well known 64–66 that four-coordinate Fe II porphyrins have two triplet states lying close in energy: the degenerate ( 3 E) and non-degenerate ( 3 A) one. Pure functionals, including PBE, yield the degenerate triplet 3 E lower in energy, in disagreement with the hybrid functionals, CASPT2, 64 and CCSD(T) 10,65,67 calculations, all of which point to the 3 A being lower in energy. The 3 E state is also in disagreement with the known structure 26 lacking Jahn–Teller distortion of the FeN 4 geometry, which would occur in a degenerate state (and is clearly observed if the geometry is optimized for the 3 E state).…”

“…74, which is still considered as a challenging problem. 66,75,76 The best available CCSD(T) calculations for the porphin model 67 suggest that the quintet–triplet energy difference is very small and, as data in Table 3 show, the δ G corr term additionally favors the quintet state by 2.5 kcal mol −1 . The presently discussed structural CPE effect may thus play a crucial role in explaining why the experimental ground state is the triplet, rather than the quintet.…”

“…Accounting for this effect may be important when discussing the accuracy of wave-function theory methods, which tend to predict a very small quintet–triplet gap in isolated [Fe(P)]. 65–67,74–76 For [Fe(TPP)], side substituents of the porphyrin ring do not affect the spin-state splitting significantly, but this is not true in general. In particular, for [Fe(OETPP)(2-MeIm)] + , the substituent effect has been shown to be almost 3 kcal mol −1 .…”