Coupled Cluster Theory in Materials Science

The workhorse method of computational materials science is undeniably the density functional theory (DFT) in the Kohn-Sham framework of approximate exchange and correlation energy functionals. However, the need for highly accurate electronic structure theory calculations in materials science motivates the further development and exploration of alternative as well as complementary techniques. Among these alternative approaches, quantum chemical wavefunction based theories and in particular coupled cluster theory hold promise in filling the gap in the toolbox of computational materials scientists. Coupled cluster (CC) theory provides a compelling framework of approximate infinite-order perturbation theory, in the form of an exponential of cluster operators describing the true quantum many-body effects of the electronic wave function at a computational cost that, despite being significantly more expensive than DFT, scales polynomially with system size. The hierarchy of size-extensive approximate methods established in the framework of CC theory, achieves systematic improvability for many materials properties. This is in contrast to currently available density functionals that often suffer from uncontrolled approximations that limit the accuracy in the prediction of materials properties. In this tutorial-style review we will introduce basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the connection between coupled cluster theory and the random-phase approximation that is widely used in the field of solid-state physics. We will discuss various approaches to improve the computational performance without compromising on accuracy. These approaches include large-scale parallel design as well as techniques that reduce the pre-factor of the computational complexity. A central part of this article discusses the convergence of calculated properties to the thermodynamic limit, which is of significant importance for reliable predictions of materials properties and constitutes an additional challenge compared to calculations of large molecules. We mention technical aspects of computer code implementations of periodic coupled cluster theories in different numerical frameworks of the one-electron orbital basis; the projector-augmented-wave formalism using a plane wave basis set and the numeric atom-centered-orbital (NAO) with resolution-of-identity. We will discuss results and the possible scope of these implementations and how they can help advance the current state of the art in electronic structure theory calculations of materials.