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.

Investigating the Basis Set Convergence of Diagrammatically Decomposed Coupled-Cluster Correlation Energy Contributions for the Uniform Electron Gas.

We investigate the convergence of coupled-cluster (CC) correlation energies and related quantities with respect to the employed basis set size for the uniform electron gas (UEG) to gain a better understanding of the basis set incompleteness error (BSIE). To this end, coupled-cluster doubles (CCD) theory is applied to the three-dimensional UEG for a range of densities, basis set sizes, and electron numbers. We present a detailed analysis of individual diagrammatically decomposed contributions to the amplitudes at the level of CCD theory. In particular, we show that only two terms from the amplitude equations contribute to the asymptotic large-momentum behavior of the transition structure factor, corresponding to the cusp region at short interelectronic distances. However, due to the coupling present in the amplitude equations, all decomposed correlation energy contributions show the same asymptotic convergence behavior to the complete basis set limit. These findings provide an additional rationale for the success of a recently proposed correction to the BSIE of CC theory. Lastly, we examine the BSIE in the CCD plus perturbative triples [CCD(T)] method, as well as in the newly proposed CCD plus complete perturbative triples [CCD(cT)] method.