Toward an Affordable Density-Based Measure for the Quality of a Coupled Cluster Calculation

We propose two new diagnostics for the degree to which static correlation impacts the quality of a coupled cluster calculation. The first is the change in the Matito static correlation diagnostic IND¯ between CCSD and CCSD(T), ΔIND¯[(T)]=IND¯[CCSD(T)]−IND¯[CCSD]. The second is the ratio of the same and of the corresponding change in the total correlation diagnostic IT¯=IND¯+ID¯, i.e., rI[(T)]=ΔIND¯[(T)]/ΔIT¯[(T)]. The first diagnostic can be extended to higher-order improvements in the wave function, e.g., ΔIND¯[(Q)]=IND¯[CCSDT(Q)]−IND¯[CCSDT]. In general, a small ΔIND¯[level1] value indicates that at this level1 of theory, the density is converged and any further changes to the energy come from dynamical correlation, while larger ΔIND¯[level2] indicates that the density is still not converged at level2 and some static correlation remains. rI[(T)] is found to be a moderately good predictor for the importance of post-CCSD(T) correlation effects.