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), $\Delta I_{ ND}[\textrm{ (T)}]=\overline{ I_{ ND}}[\textrm{ CCSD(T)}]-\overline{ I_{ ND}}[\textrm{ CCSD}]$. 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., $r_I[(T)]=\Delta I_{ ND}[\textrm{ (T)}]/\Delta I_{ T}[\textrm{ (T)}]$. The first diagnostic can be extended to higher-order improvements in the wave function, e.g., $\Delta I_{ ND}[\textrm{ (Q)}]=\overline{ I_{ ND}}[\textrm{ CCSDT(Q)}]-\overline{ I_{ ND}}[\textrm{ CCSDT}]$. In general, a small $\Delta I_{ ND}$[\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 $\Delta I_{ ND}$[\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.
Categories: physics.chem-ph