Wider research context. Many of the current technological challenges facing our society are related to materials science. Efficient computer simulations of molecules, solids and their interaction have become indispensable in this research field. In the past years machine learning (ML) techniques massively extended the scale of simulations both in time and size. But, at the atomic scale, ML strongly depends on calibration from highly accurate solutions to the Schrödinger equation (SE) that describes the electronic structure. To this end density functional theory (DFT) forms an unchallenged standard, which however, also depends on calibration, due to uncontrollable errors in available approximate functionals. For molecules, breaking the computational cost bottleneck of the coupled cluster (CC) method opened the path for highly accurate solutions of the SE. For solids, however, it remains an open challenge. While CC is equally accurate here, the available low-cost approximations lose this accuracy, especially for polarizable materials and metals.
Objectives. My goal is to develop a general purpose low-cost approach that enables highly accurate CC calculations on realistic three dimensional materials: large periodic simulation cells including at least 103 correlated electrons and correlation lengths of at least 20 Angström. I will consider the following applications in the scope of international cooperations, all of which require beyond DFT accuracy: (i) oxygen vacancy formation in complex oxides: the case of the 4f band material cerium oxide, and (ii) van-der Waals heterostructures: the interface of $\text{MoS}_2$ and graphene. It is also planned to release the algorithm to the scientific community as part of the software packages VASP and Cc4s.
Approach. As I have recently shown, specific approximations at different correlation lengths allow for a significant reduction of the computational cost whilst retaining the high accuracy of the CC method for solids. Different length scales can easily be addressed by truncations of the Coulomb potential. For the technical realization in a periodic plane-wave based approach I plan to (i) develop robust schemes to transfer both occupied and virtual Bloch orbitals into localized Wannier functions in insulators and metals, (ii) reduce the computational cost of the CC method by taking advantage of sparse truncated Coulomb integrals in the localized Wannier basis using tensor contraction frameworks, (iii) investigate the contribution of different subsets of the diagrammatic CC representation at different length scales in order to identify new low-cost approximations.
Level of originality. While numerous CC approaches exist for large molecules, their direct transfer to solids remains questionable. Our approach (not to be confused with local correlation approaches) will not only fill this gap, but it is characterized by its conceptual simplicity. This opens a path to interatomic forces or excited states in solids. While this goes beyond the stated goals, it is of great interest to the international research community in the long run.
