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.