Duality of Ring and Ladder Diagrams and Its Importance for Many-Electron Perturbation Theories

We present a diagrammatic decomposition of the transition pair correlation function for the uniform electron gas. We demonstrate explicitly that ring and ladder diagrams are dual counterparts that capture significant long- and short-ranged interelectronic correlation effects, respectively. Our findings help to guide the further development of approximate many-electron theories and reveal that the contribution of the ladder diagrams to the electronic correlation energy can be approximated in an effective manner using second-order perturbation theory. We employ the latter approximation to reduce the computational cost of coupled cluster theory calculations for insulators and semiconductors by 2 orders of magnitude without compromising accuracy.

Figure 1

(a) Pair correlation function contributions according to Eq. (4) using 1863 plane waves at $r_s=5a_0$. (b) Difference between pair correlation function contributions obtained using 1863 plane waves and 1021 plane waves. (c),(d) CBS limit error of corresponding correlation energy contributions retrieved as a function of the plane wave basis set size for densities corresponding to $r_s=1.8a_0$ and $r_s=5a_0$, respectively.

Figure 2

CBS limit errors of CCSD (dashed) and CCSD PPL (solid) correlation energies for ab initio systems with respect to the number of natural orbitals employing eight atomic supercells.