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 $\overline{I_{\mathrm{ND}}}$ between CCSD and CCSD(T), $\Delta \overline{I_{\mathrm{ND}}}\left[\left(T\right)\right]=\overline{I_{\mathrm{ND}}}\left[\mathrm{CCSD}\left(T\right)\right]-\overline{I_{\mathrm{ND}}}\left[\mathrm{CCSD}\right]$. The second is the ratio of the same and of the corresponding change in the total correlation diagnostic $\overline{I_T}=\overline{I_{\mathrm{ND}}}+\overline{I_D}$, i.e., $r_I\left[\left(T\right)\right]=\Delta \overline{I_{\mathrm{ND}}}\left[\right(T\left)\right]/\Delta \overline{I_T}\left[\right(T\left)\right]$. The first diagnostic can be extended to higher-order improvements in the wave function, e.g., $\Delta \overline{I_{\mathrm{ND}}}\left[\left(Q\right)\right]=\overline{I_{\mathrm{ND}}}\left[\mathrm{CCSDT}\left(Q\right)\right]-\overline{I_{\mathrm{ND}}}\left[\mathrm{CCSDT}\right]$. In general, a small $\Delta \overline{I_{\mathrm{ND}}}$[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 $\Delta \overline{I_{\mathrm{ND}}}$[level₂] indicates that the density is still not converged at level₂ and some static correlation remains. r_I[(T)] is found to be a moderately good predictor for the importance of post-CCSD(T) correlation effects.