Coupled cluster methods for periodic systems

The importance of modelling continues to grow in research and development, including chemistry and solid state physics, and supplementing experiment and theory, computation now constitutes the third pillar of modern science. This situation has emerged from a combination of the ever-increasing computer power, improved numerical algorithms arising from still deeper insight into the underlying physics, and the unique opportunities offered by modelling. Computations can be used to reduce or replace experimental work, thus saving time and costs. Even more important, perhaps, is the information which can be deduced from modelling and which is difficult or impossible to extract experimentally. The success of modelling thus crucially depends on high reliability and low computational cost. The grand challenge is to transfer coupled cluster methods from the realm of small molecules, where these methods are known to predict molecular properties with a precision rivalling that of experiment, to large extended systems in one, two, and three dimensions. In collaboration with Prof. L. Maschio, University of Turin, a scientific paper has been written (accepted for publication in Molecular Physics in 2020) where we document that socalled Project Atomic Orbitals (PAOs) are superior to localised orthonormal virtual orbitals (LVOs) with respect to the calculation of electron correlation energies. The paper also contains a thorough analysis of these findings. Based on this observation, we have developed a new version of the X-DEC algorithm, which can use either PAOs or LVOs. In addition, the new version contains significant performance improvements due to full exploitation of translation symmetry and automatic detemination of cutoff distances for the long-range electronic interactions. Its improved modularity allows for easy implementation of more advanced coupled-cluster models. We are preparing a new manuscript on the ability of the new X-DEC algorithm to produce continuous potential-energy surfaces, which is essential for future applications of the X-DEC algorithm to, e.g., computational studies of adsorption processes on surfaces or zeolites. Finally, in collaboration with SINTEF and Prof. A. Alavi, Max Planck Institute for Solid-State Research and Cambridge University, we have developed a pilot code for multiconfigurational studies of strongly correlated solids. We expect to publish a manuscript on this development during 2020.

Treningen av de tre midlertidig ansatte på prosjektet har gitt dem videre karrierer innen akademisk forskning, privat FOU og utdanning. Prosjektet har ført til nye interne og eksterne prosjekter på Hylleraas-senteret. Et viktig nytt prosjekt om kvantedynamikk til atomære og molekylære elektroner i sterke laser-pulser kan føre til kontroll av materialer på elektron-skala - et forskningsområde utpekt av Department of Energy i USA til en av de største vitenskapelige utfordringer i det 21. århundre. Dette har ført til opprettelsen av et Grunnforskningssenter på Det Norske Vitenskapakademi. I tillegg er det etablert et tett samarbeid mellom Hylleraas-senteret og beregningsfysikk-gruppen på Fysisk Institutt, UiO. Videre er det etablert et samarbeid mellom prosjektlederen, SINTEF og Max Planck Instituttet om utvikling av nye metoder til simulering av sterkt korrelerte materialer. Slike materialer er teknologisk viktige, blant annet for utvikling av nye batterier.

Density functional theory (DFT) is used almost universally for computational studies of periodic systems. While DFT has a relatively low computational cost, it is not a convergent method since approximate density functionals can not be systematically improved. Coupled cluster (CC) theory, on the other hand, converges to the exact result but has a devastating computational cost. This project aims at reducing the computational cost and thus make CC theory the preferred choice for periodic systems. The recently developed divide-expand-consolidate (DEC) approach to linear-scaling CC theory for molecules will be adapted to periodic boundary conditions. The DEC approach relies on strongly localized occupied and virtual orbitals and the first crucial step of the project is to implement the transformation from inherently delocalized Bloch orbitals to localized Wannier orbitals. The accuracy of the DEC approach is controlled by a single parameter, which also affects the computational efficiency. The computational efficiency will be further improved using density fitting and pair-natural orbitals. Exploiting the connection between CC theory and the random phase approximation (RPA) to ground state correlation energies, the project will also explore range-separated DFT with several RPA flavors. Since RPA gives an accurate account of dispersion effects in molecules, it is expected that structures of covalent and molecular crystals can be accurately and swiftly predicted by this approach.