Investigation of a diagnostic for perturbation theory. Comparison to the [formula omitted]1 diagnostic of coupled-cluster theory

Abstract

A diagnostic for perturbation theory calculations, L 2, is defined and numerical results compared to the established L 1 diagnostic from coupled-cluster theory. L 2 is the lowest-order non-zero contribution to a Møller-Plesset perturbation expansion of T 1. L 2 is a reasonable estimate of the importance of non-dynamical electron correlation, although not as reliable as T 1. L 2 values ⩽0.012 suggest that low orders of perturbation theory should yield reasonable results; L 2 values between 0.012 and 0.015 suggest that caution is required in interpreting results from low orders of perturbation theory; L 2 values ⩾0.015 indicate that low orders of perturbation theory are not reliable for accurate results. Although not required mathematically, L 2 is always less than T 1 for the examples studied here.