Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Abstract

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry—for example, in characterization of spin crossover materials and in theoretical modeling...

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

“…3 [ ] + and the triplet−singlet splitting of FeCp 2 (for the latter metallocene molecule, both adiabatic and vertical energies are considered as they differ considerably 9,27 ). Note that for FeL 2 , FeL 2 (NH 3 ), and FeL 2 (Cl), which are simplistic models of metalloporphyrins, 17 we consider the energy differences involving not only their low-spin (LS) and highspin (HS) states but also the intermediate-spin (IS) state.…”

“…Altogether, there are nine energy differences with Δ S = 2 and 9 with Δ S = 1 (where S is the total spin quantum number). Most of them are adiabatic energies (i.e., each spin state is calculated in its own energy minimum) with the exception of two vertical energies, identified with the suffix “(ve)”: the sextet–quartet splitting of false[ F e false( H 2 normalO false) 6 false] 3 + and the triplet–singlet splitting of FeCp 2 (for the latter metallocene molecule, both adiabatic and vertical energies are considered as they differ considerably , ). Note that for FeL 2 , FeL 2 (NH 3 ), and FeL 2 (Cl), which are simplistic models of metalloporphyrins, we consider the energy differences involving not only their low-spin (LS) and high-spin (HS) states but also the intermediate-spin (IS) state.…”

“…These values agree to within 1.6 kcal/mol with the previously reported estimates (3.0 and 4.6 kcal/mol, respectively), which were based on the calculations for a much more simplified model, FeL 2 (NH 3 ). 17 No quantitative experimental values are available for the discussed energy differences, but in view of the existing benchmark studies, 9,26,27 it is reasonable to take the present CC results as the reference data for the assessment of DFT methods. The results for some representative functionals are included in Table 4, where the cells are color-mapped by deviation of a given DFT result from the mean of the CCSD(T) and KS-CCSD(T) results.…”

“…Our main goal will be to learn about the transferability of the BSIEs in the spin-state energetics computed using different WFT methods. The concept of BSIE transferability will bring insight into the accuracy of focal-point approaches for computing TM spin-state energetics, but is also relevant for the construction of benchmark studies in which the results of different methods are compared with experimentally derived reference data. ,, …”

“…Spin states resulting from different distributions of electrons on the metal d orbitals in transition metal (TM) complexes are highly relevant in inorganic chemistry, biochemistry, catalysis, and materials science. − Nevertheless, reliable computation of spin-state energetics (i.e., the energy differences between alternative spin states; also termed spin-state splittings) poses a formidable challenge for computational chemistry methods. − During the past decade, there have been numerous attempts to compute the spin-state energetics accurately using density functional theory (DFT) − or wave function theory (WFT) methods. ,− Despite the progress made, it also has been realized that the problem is very challenging due to a complicated interplay of dynamic and nondynamic correlation effects in TM complexes, so that divergent results are often reported even at high theory levels . Partly for this reason, but also due to the scarcity of definite benchmarks, practical computational protocols for predicting TM spin-state energetics unarguably within the chemical accuracy (i.e., ±1 kcal/mol) from the experimental values are still to be sought.…”