Spin–State Energetics for Hydride and Helium Models of Transition Metal Complexes: A Benchmark Study of Wave Function Quantum Chemistry Methods

Accurate determination of spin–state energetics in first-row transition metal (TM) complexes is recognized as a challenging problem in computational quantum chemistry because different methods often yield divergent predictions and credible reference data are scarce. Trying to provide a way towards unambiguously accurate reference values from high-level wave function computation, a benchmark set of small TM complexes with hydrides (H^–) or helium atoms as σ-donor ligands is presented. These models have analogous electronic structures as realistic TM complexes and their spin–state energetics feature comparable method- dependence, but their small size enables application of more accurate methods than are applicable to realistic TM complexes. The extrapolated full configuration interaction (exFCI) results are obtained for selected spin–state splittings of the hydride/helium models and used as reference values for benchmarking various wave function methods, including second- and third-order perturbation theory multireference methods, multireference CI, and coupled cluster methods with up to approximate quadruples. It is demonstrated that the exFCI reference values can be reproduced satisfactorily with both multireference and single-reference methods, among which the NEVPT2 and CCSDT(Q)_Λ methods perform best, yielding deviations comparable with the uncertainties of the reference values or smaller than 2 kcal/mol. The CCSD(T) method yields errors of ca. 3 kcal/mol or smaller, with one exception where the CCSD(T)’s error is greater than 6 kcal/mol presumably due to pronounced multireference character. The CASPT2, CASPT3, CASPT2/CC methods are shown to not outperform the CCSD(T) method consistently. The present study, in addition to presenting novel benchmark set for the spin–state energetics problem, establishes hydride/helium models of TM complexes as useful and challenging systems for further investigations with correlated electronic structure methods.