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

Abstract

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.

An Isolated Molecule of Iron(II) Phthalocyanin Exhibits Quintet Ground‐State: A Nexus between Theory and Experiment

“…Performance of the multi‐reference perturbation methods giving, contrary to the experiments, quintet ground‐state was discussed with respect to computational aspects. It was concluded that the disagreement results from a poor description of the Fe(3s3p) electron correlation at the CASPT2 . A combined CASPT2/CC approach which treats the valence and semi‐core Fe(3s3p) correlation effects at the CASPT2 and CCSD(T) methods, respectively, puts triplet 0.15 kcal mol −1 below quintet.…”

RASPT2 study of the valence excited states of an iron–porphyrin–carbonyl model complex

“…Thus, electronic states involving excitations on the pyrazine ligand cannot be obtained by our calculations and are ignored in the present study. The (3s3p) correlation effect has been shown to be important in the spin state energetics of first‐row transition metal complexes as discussed by Pierloot and coworkers . In this work, we handle transition energies between states of same spin.…”

ACCDB: A collection of chemistry databases for broad computational purposes

“…It includes spin states and binding energies data of porphyrin structures, which are ubiquitous in nature (the famous heme group is an example). It is divided into two subsets: PorSS11, which includes the SS energy differences of three Mn‐porphyrins, one Co‐porphyrin, and seven Fe‐porphyrins, bonded to different ligands (NH 3 , OH − , and SH − ); and PorBE10, which includes the binding energies for the complexes between a model system of a heme group and three diatomic molecules: NO, CO, and O 2 (Fig. ) .…”

“…) . Por21 includes 32 structures, and 21 reference energies obtained at the CASPT2 level (different active spaces have been used for each molecule in the database, their details are given in the original publications, and are also reported in our online repository).…”

“…For more details of all the subsets of every database, as well as references to their original sources, and a better overview of their overlaps, see also the Supporting Information. [7,12,[22][23][24][25][26][27][30][31][32][33][34][35][36][37][38][39][40]46,48, Automation Software ACCDB contains 10,049 geometry files-in xyz format, and appropriately named, including charge and spin multiplicity data-collected in one directory called "Geometries." Each file requires a single-point energy calculation, usually performed with quantum chemistry software engines, such as Gaussian [175] or Q-Chem.…”