Investigation of a diagnostic for perturbation theory. Comparison to the T₁ diagnostic of coupled-cluster theory

A diagnostic for perturbation theory calculations, L₂, is defined and numerical results compared to the established L₁ diagnostic from coupled-cluster theory. L₂ is the lowest-order non-zero contribution to a Møller-Plesset perturbation expansion of T₁. L₂ is a reasonable estimate of the importance of non-dynamical electron correlation, although not as reliable as T₁. L₂ values ≤0.012 suggest that low orders of perturbation theory should yield reasonable results; L₂ values between 0.012 and 0.015 suggest that caution is required in interpreting results from low orders of perturbation theory; L₂ values ≥0.015 indicate that low orders of perturbation theory are not reliable for accurate results. Although not required mathematically, L₂ is always less than T₁ for the examples studied here.