Orbital Entanglement and The Double $d$-Shell Effect in Binary Transition Metal Molecules

TL;DR

This paper investigates the double d-shell effect in transition metal molecules using quantum information techniques to analyze their electronic structure and correlation effects.

Contribution

It introduces a novel application of information entropy analysis to understand the double d-shell effect in transition metal compounds.

Findings

Quantum information methods reveal nuanced electronic correlations.

The double d-shell effect significantly influences the electronic structure.

Insights into weak and strong correlation regimes in transition metals.

Abstract

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 character 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 study of weak and strong correlation in the transition metal $d$ manifold.