Coupled clusters and the electron gas at metallic densities

James J. Shepherd, Tom M. Henderson, Andreas Gr uneis +1 more

Verena A. Neufeld, Timothy C. Berkelbach

Coupled-cluster theory with single, double, and perturbative triple excitations (CCSD(T))-often considered the "gold standard" of main-group quantum chemistry-is inapplicable to three-dimensional metals due to an infrared divergence, preventing its application to many important problems in materials science. We study the full, nonperturbative inclusion of triple excitations (CCSDT) and propose a new, iterative method, which we call ring-CCSDT, that resums the essential triple excitations with the same N^{7} run-time scaling as CCSD(T). CCSDT and ring-CCSDT are used to calculate the correlation energy of the uniform electron gas at metallic densities and the structural properties of solid lithium. Inclusion of connected triple excitations is shown to be essential to achieving high accuracy. We also investigate semiempirical CC methods based on spin-component scaling and the distinguishable cluster approximation and find that they enhance the accuracy of their parent ab initio methods.

K. S. Singwi, Monica Tosi, Alf Sjölander

Nikolaos Masios, Andreas Irmler, Tobias Schäfer +1 more

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.

James J. Shepherd, Andreas Grüneis

We numerically examine divergences of the total energy in metallic systems of approximate many-body theories using Hartree--Fock as a reference, including perturbative (M\oller-Plesset, MP), coupled cluster (CC) and configuration interaction (CI) approaches. Controlling for finite size effects and basis set incompleteness error by comparison with energies from the random phase approximation (RPA), we suggest convincingly that non-perturbative coupled cluster theories are acceptable for modelling electronic interactions in metals whilst perturbative coupled cluster theories are not. Data are provided from the RPA with which it is possible to test other approximate finite-basis methods for divergences with only modest computational cost.

R. F. Bishop