Averting the Infrared Catastrophe in the Gold Standard of Quantum Chemistry

Coupled-cluster theories can be used to compute ab initio electronic correlation energies of real materials with systematically improvable accuracy. However, the widely used coupled cluster singles and doubles plus perturbative triples [CCSD(T)] method is only applicable to insulating materials. For zero-gap materials the truncation of the underlying many-body perturbation expansion leads to an infrared catastrophe. Here, we present a novel perturbative triples formalism denoted as (cT) that yields convergent correlation energies in metallic systems. Furthermore, the computed correlation energies for the three-dimensional uniform electron gas at metallic densities are in good agreement with quantum Monte Carlo results. At the same time the newly proposed method retains all desirable properties of CCSD(T) such as its accuracy for insulating systems as well as its low computational cost compared to a full inclusion of the triples. This paves the way for ab initio calculations of real metals with chemical accuracy.

Figure 1

(a) and (b) UEG transition structure factor contributions at different levels of theory for 246 electrons with 2178 spatial orbitals, 266 twists for rCCD, 166 twists for CCD, (T) and (cT) and $r_s=20\mathrm{a}.\mathrm{u}.$ (c) Contributions to $t_{ij}(\mathbf{q})$ at different levels of theory for 730 electrons with 6254 spatial orbitals, 40 twists and $r_s=20\mathrm{a}.\mathrm{u}.$ (d) and (e) CBS correlation energies per electron with 40 twists at $r_s=3\mathrm{a}.\mathrm{u}.$ for the UEG retrieved as $N^{-2/3}$, where $N$ is the electron number. (d) MP2, rCCD, and CCD correlation energies. (e) (T) and (cT) energies. (e) (T) and (cT) correlation energy per electron with 20 twists for Li denoted as Li-(T) and Li-(cT). Details in the Supplemental Material [21].