All-Purpose Measure of Electron Correlation for Multireference Diagnostics

We present an analytical
relationship between two natural orbital
occupancy-based indices, IND̅ and INDmax, and two established electron
correlation metrics: the leading term of a configuration interaction
expansion, c0, and the D2 diagnostic. Numerical validation revealed that IND̅ and INDmax 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 INDmax, 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.