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 $\overline{I_{ND}}$ between CCSD and CCSD(T), $ΔI_{ND}[\textrm{(T)}]=\overline{I_{ND}}[\textrm{CCSD(T)}]-\overline{I_{ND}}[\textrm{CCSD}]$. The second is the ratio of the same and of the corresponding change in the total correlation diagnostic $\overline{I_{T}}=\overline{I_{ND}}+\overline{I_{D}}$, i.e., $r_I[(T)]=ΔI_{ND}[\textrm{(T)}]/ΔI_{T}[\textrm{(T)}]$. The first diagnostic can be extended to higher-order improvements in the wave function, e.g., $ΔI_{ND}[\textrm{(Q)}]=\overline{I_{ND}}[\textrm{CCSDT(Q)}]-\overline{I_{ND}}[\textrm{CCSDT}]$. In general, a small $ΔI_{ND}$[\textrm{level$_1$}] value indicates that at this level$1$ of theory, the density is converged and any further changes to the energy come from dynamical correlation, while larger $ΔI{ND}$[\textrm{level$_2$}] indicates that the density is still not converged at level$_2$ 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.

💡 Research Summary

In this work the authors introduce two inexpensive, density‑based diagnostics to assess the impact of static (nondynamical) correlation on the quality of coupled‑cluster (CC) calculations. The first diagnostic, ΔI_ND