A study of the dense Uniform Electron Gas with high orders of Coupled Cluster

We investigate the accuracies of different coupled cluster levels in a finite model solid, the 14 electron spin-non-polarised uniform electron gas. For densities between ${\mathrm{r}}_{\mathrm{s}}$ = 0.5 ${\mathrm{a}}_0$ and ${\mathrm{r}}_{\mathrm{s}}$ = 5 ${\mathrm{a}}_0$, we calculate ground state correlation energies with stochastic coupled cluster ranging from coupled cluster singles and doubles (CCSD) to coupled cluster including all excitations up to quintuples (CCSDTQ5). We find the need to add triple excitations for an accuracy of 0.01eV/electron beyond ${\mathrm{r}}_{\mathrm{s}}$ = 0.5 ${\mathrm{a}}_0$. Quadruple excitations start being significant past ${\mathrm{r}}_{\mathrm{s}}$ = 3 ${\mathrm{a}}_0$ . At ${\mathrm{r}}_{\mathrm{s}}$ = 5 ${\mathrm{a}}_0$, CCSD gives a correlation energy with a 16% error and CCSDT is in error by 2% compared to the CCSDTQ5 result. CCSDTQ5 gives an energy in agreement with full configuration interaction quantum Monte Carlo results.