Large-Scale Coupled Cluster Calculations for real Materials

Tobias Schäfer is working at the Vienna University of Technology on the computational modeling of quantum phenomena in materials. At the atomic level, these quantum phenomena are described mathematically by the Schrödinger equation. The key here is to take into account the complicated interaction of electrons. However, a highly accurate description of the electronic correlations pushes even modern supercomputers to their limits. This is because the computational effort required to solve the Schrödinger equa tion grows exponentially with the number of interacting electrons. In the research project "Large-Scale Coupled Cluster Calculations for Real Materials", Tobias Schäfer aims at simulating quantum mechanical effects in surface catalysis as well as the calculation of weak bonds of layered two-dimensional materials induced by quantum fluctuations. However, due to the large number of atoms and electrons involved, quantitatively high -precision modeling of such situations is beyond what is feasible today. Theref ore, the first step of the research project is to develop a new, more efficient algorithm for the established coupled -cluster method for solving the Schrödinger equation of large periodic simulation cells. By combining different techniques, such as the exploitation of numerically sparse tensors or the approximation of selected mathematical expressions, memory requirements and computation time can be drastically reduced while maintaining the high accuracy of the coupled -cluster method. In cooperation with international research groups, the algorithm will be applied to the aforementioned quantum mechanical processes in a second step. In doing so, precise reference data for the formation of oxygen perturbations in surfaces of cerium oxide as well as for binding energies of two-dimensional materials will be calculated. While binding energies are relevant for the design of new functional materials, oxygen vacancies form the reactive sites in processes of heterogeneous catalysis, which are of high interest for science and industry.

Large-Scale Coupled Cluster Calculations for Real Materials Computer simulations are essential for understanding materials at the atomic level, but they rely on mathematical approximations. The overarching goal of our project was to advance "large-scale coupled cluster calculations"-a highly reliable but computationally demanding quantum mechanical method-so it could be applied to complex, real-world materials. Our work successfully realized this goal, resulting in two main scientific advances. First, we scaled up this high-level method to resolve a known issue where different standard simulations gave conflicting predictions regarding how large molecules interact. In a study published in Nature Communications, we identified the source of these discrepancies. By refining the coupled cluster approach, we can now provide highly reliable calculations for large-scale molecular systems containing hundreds of atoms. Because molecular interactions are fundamental to chemistry, these calculations help establish better reference points for future research. Second, we successfully extended our large-scale coupled cluster calculations to metallic systems. Applying this level of theory to metals has traditionally been very difficult due to a mathematical hurdle known as the "infrared divergence." We implemented a computational workaround to solve this issue. As a result, we were able to calculate highly accurate surface energies for metals like aluminum and platinum directly from quantum mechanical principles. This represents the first time large-scale coupled cluster theory has been successfully applied to derive reliable surface energies in metals. Societal and Technological Impact Improving the accuracy of computer simulations reduces the need for extensive trial-and-error experiments in the laboratory. By providing the scientific community with reliable, large-scale computational tools for both complex molecules and metallic surfaces, this work supports basic research in surface chemistry. In the long term, these methods can help researchers more efficiently design and evaluate new catalysts, energy storage solutions, and advanced materials.