Spin State Energetics in First-Row Transition Metal Complexes: Contribution of (3s3p) Correlation and Its Description by Second-Order Perturbation Theory.

This paper presents an in-depth study of the performance of multiconfigurational second-order perturbation theory (CASPT2, NEVPT2) in describing spin state energetics in first-row transition metal (TM) systems, including bare TM ions, TM ions in a field of point charges (TM/PC), and an extensive series of TM complexes, where the main focus lies on the (3s3p) correlation contribution to the relative energies of different spin states. To the best of our knowledge, this is the first systematic NEVPT2 investigation of TM spin state energetics. CASPT2 has been employed in several previous studies but was regularly found to be biased toward high spin states. The bias was attributed to a too low value of the so-called IPEA shift ϵ, an empirical correction in the CASPT2 zeroth-order Hamiltonian with a standard value of 0.25 hartree. Based on comparisons with experiment (TM ions) and calculations with the multireference configuration interaction (TM ions and TM/PC systems) and coupled-cluster (TM complexes) methods, we demonstrate in this work that standard CASPT2 works well for valence correlation and that its bias toward high-spin states is caused by an erratic description of (3s3p) correlation effects. The latter problem only occurs for spin transitions involving a ligand field (de)excitation, not in bare TM ions. At the same time the (3s3p) correlation contribution also becomes strongly ϵ dependent. The error can be reduced by increasing ϵ but only at the expense of deteriorating the CASPT2 description of valence correlation in the TM complexes. The alternative NEVPT2 method works well for bare TM and TM/PC systems, but its results for the TM complexes are disappointing, with large errors both for the valence and (3s3p) correlation contributions to the relative energies of different spin states.