All-Purpose Measure of Electron Correlation for Multireference Diagnostics

Abstract

We present an analytical relationship between two natural orbital occupancy-based indices, $\overline{I_{ND}}$ and I_ND^max, and two established electron correlation metrics: the leading term of a configuration interaction expansion, c₀, and the D₂ diagnostic. Numerical validation revealed that $\overline{I_{ND}}$ and I_ND^max can effectively substitute for c₀ and D₂, respectively. These indices offer three distinct advantages: (i) they are universally applicable across all electronic structure methods, (ii) their interpretation is more intuitive, and (iii) they can be readily incorporated into the development of hybrid electronic structure methods. Additionally, we draw a distinction between correlation measures and correlation diagnostics, establishing MP2 and CCSD numerical thresholds for I_ND^max, which are to be used as a multireference diagnostic. Our findings further demonstrate that establishing thresholds for other electronic structure methods can be easily accomplished using small data sets.

Figure 1

Relationship between 4(1-c₀²)/N and for (left) Set A, including various diatomic molecules at equilibrium and 50% larger interatomic distances at the CISD level, and (right) Set B containing several 18-electron systems studied at the selected CI (SCI) level.

Figure 2

I_ND^max and against D₂ for the molecules in Set C (left) and I_ND^max against D₂ for the molecules in Set D (right). All calculations were performed at the MP2 level.

Figure 3

Relationship between D₂ and I_ND^max for Set A (left) and Set E (right) at the CCSD level.