Double-substitution-based diagnostics for coupled-cluster and Møller–Plesset perturbation theory

New diagnostics are proposed for coupled-cluster and Møller–Plesset perturbation theory. The diagnostics, designated D2(CCSD) and D2(MP1), are computed from the double-substitution amplitudes in the CCSD and MP1 wavefunctions, and their definitions are analogous to those of the single-substitution-based D1(CCSD) and D1(MP2) diagnostics. The correlation between the magnitude of the new diagnostics and the performance of the CCSD and MP2 methods is demonstrated for prediction of structures and harmonic vibrational frequencies for 34 molecules, and the application of D1 and D2 to diradicals and bond dissociation is also discussed.