Comparison of the T1 and D1 diagnostics for electronic structure theory: a new definition for the open-shell D1 diagnostic

It is shown that the coupled-cluster T1 operator used in a previous study to define the open-shell D1 diagnostic is ill defined, and leads to an arbitrary definition of the open-shell D1 diagnostic. A new definition is proposed that eliminates this ambiguity and approximately restores the mathematical relationship previously noted between the closed-shell D1 and T1 diagnostics. Statistical comparison of the T1 and D1 diagnostics shows a very high degree of correlation between them for the molecular systems studied thus far, although it is argued that both diagnostics used together can provide more information than either can separately.