Orbital entanglement and the double d-shell effect in binary transition metal molecules

Accurate modeling of transition metal-containing compounds is of great interest due to their wide-ranging and significant applications. These systems present several challenges from an electronic structure perspective, including significant multi-reference characters and many chemically relevant orbitals. A further complication arises from the so-called double d-shell effect, which is known to cause a myriad of issues in the treatment of first-row transition metals with both single- and multi-reference methods. While this effect has been well documented for several decades, a comprehensive understanding of its consequences and underlying causes is still evolving. Here, we characterize the second d-shell effect by analyzing the information entropy of correlated wavefunctions in a periodic series of 3d and 4d transition metal molecular hydrides and oxides. These quantum information techniques provide unique insight into the nuanced electronic structure of these species and are powerful tools for the study of weak and strong correlations in the transition metal d manifold.