Spin-free orbital entropy, mutual information, and correlation analysis

TL;DR

This paper introduces a modified spin-free approach to orbital entropy and mutual information analysis, simplifying interpretation and ensuring invariance to spin projection, thereby improving the understanding of electron correlation patterns in complex molecules.

Contribution

The authors develop a spin-free, invariant version of orbital entropy and mutual information measures, enhancing the analysis of electron correlation in large active spaces.

Findings

Spin-free measures are invariant to $M_s$ and distinguish static from strong correlation.

Application to diradicals and iron-sulfur complexes demonstrates improved interpretability.

Modified measures effectively separate spin coupling effects from multiconfigurational correlation.

Abstract

Orbital entropies, pair entropies, and mutual information have become popular tools for analysis of strongly correlated wave functions. They can quantitatively measure how strongly an orbital (e.g. from the DMRG active space) participates in the strong correlation and reveal the entanglement pattern between different orbitals. However, this pattern can become rather complicated and sometimes difficult to interpret for large active spaces and is not invariant with respect to the spin projection ($M_s$) component of the spin multiplet state. We introduce a modified spin-free orbital entropy, pair entropy, and mutual information, which simplify the entanglement analysis and are invariant with respect to $M_s$. By comparison of these quantities with their ``original'' spin-including counterparts one can distinguish static correlation due to spin couplings from the ``genuine'' strong correlation due to a multiconfigurational character of the wave function. We illustrate the approach on a model consisting of a non-interacting dimer of triplet diradicals and on a more realistic example of iron-sulfur bound complexes with one and two iron atoms.