Multireference and multiconfiguration Ab initio methods in heme-related systems: What have we learned so far?

This work reviews the recent applications of ab initio multireference/ multiconfiguration (MR/MC) electronic structure methods to heme-related systems, involving tetra-, penta-, and hexa-coordinate species, as well as the high-valent iron-oxo species. The current accuracy of these methods in the various systems is discussed, with special attention to potential sources of systematic errors. Thus, the review summarizes and tries to rationalize the key elements of MR/MC calculations, namely, the choice of the employed active space, especially the so-called double-shell effect that has already been recognized to be important in transition-metal-containing systems, and the impact of these elements on the spin-state energetics of heme species, as well as on the bonding mechanism of small molecules to the heme. It is shown that expansion of the MC wave function into one based on localized orbitals provides a compact and insightful view on some otherwise complex electronic structures. The effects of protein environment on the MR/MC results are summarized for the few available quantum mechanical/molecular mechanical (QM/MM) studies. Comparisons with corresponding DFT results are also made wherever available. Potential future directions are proposed.