The eight-valence-electron systems re-examined: convergence of the coupled-cluster series and performance of quasiperturbative methods for quadruple excitations

We present the results of a coupled-cluster basis-set convergence study on 12 eight-valence-electron systems. These small systems span a wide range of correlation character (from purely dynamical correlation to pathological static correlation) as well as of chemical bonding (from ionic with some backdonation to quadruple covalent bonding). Indicators such as the correlation entropy and the CASSCF 1-C₀², which primarily sample type A static correlation, are good predictors for the energetic importance of connected quintuple excitations, T₅, and to a lesser extent of higher order triple excitations, T₃–(T). The percentage of the total atomisation energy recovered by connected triple excitations, %TAE[(T)], is however a fair predictor for the importance of connected quadruples, T₄. Of the various ansätze for quasiperturbative connected quadruples, CCSDT(Q)/B appears to be the most robust, even as it is still outperformed by the much more expensive CCSDT(Q)_Λ.