Auxiliary field quantum Monte Carlo in the PAW method

Density functional theory (DFT) is undoubtedly the best-established method for making predictions about solids and materials. This is because the method is both very efficient and relatively accurate. However, the known approximations for the density funct ional very often lead to uncontrollable errors, especially when chemical processes take place, i.e. if bonds are broken or reformed. Among other things, the so important energy barriers in catalytic processes are hence often described inaccurately. Therefore, for many years, methods have been worked on to determine the exact wave function and exact energy of the multi -electron Schrödinger equation. This is a very difficult task, as the wave function is so complex and multilayered that even the most powerful supercomputers in the world cannot store it. The second important aspect to consider is that the computing power of the supercomputers is constantly increasing, but no longer due to an increase in the power of the individual processors, but by increasing the number of processors. These two problems can only be solved conclusively with Monte-Carlo methods. In this proposal the so-called auxiliary field quantum Monte Carlo (AF-QMC) method for Fermions shall be implemented and materials properties predicted. The AF -QMC is still a relatively new and not widely used method but it has numerous properties that make it particularly attractive. On the one hand, the individual calculation steps are very elementary, not dissimilar to those in the density functional theory mentioned ab ove, so that the memory requirements remain low and we can reuse our expertise in DFT . On the other hand, the individual calculations can be easily distributed among thousands of processors, making the algorithm ideally suited for next-generation supercomputers (Austria has just become a member of PRACE and thus also has access to such computers). After successful implementation and extensive testing of the method on simple solids, we will apply it to prototypical but important problems. We want to concen trate on the adsorption of molecules on solids, which is important for catalysis, as well as on correlated solids than can hardly be described with traditional methods now.

Understanding the properties of molecules and solids is crucial for advancing new materials, drugs, and technologies. For decades, the workhorse method for these predictions has been Density Functional Theory (DFT). While DFT is remarkably versatile and computationally fast, it often suffers from a significant drawback: accuracy. Its predictions for properties like energy and structure aren't always precise enough, especially for complex or challenging materials. This lack of precision limits our ability to confidently design new substances based on simulation alone. Auxiliary Field Quantum Monte Carlo - The Accuracy Breakthrough The Auxiliary Field Quantum Monte Carlo (AFQMC) method offers a powerful solution to this accuracy dilemma. Our project focuses on dramatically advancing AFQMC, creating exceedingly efficient computer codes that are tailor-made for today's high-performance supercomputers. These technical advancements represent a significant leap forward in the state of the art. With these new, faster codes, we can now achieve highly accurate predictions for both small molecules and periodic solids, reaching a level of precision previously considered impossible. A key innovation is the use of multi-determinantal wavefunctions as 'trial wavefunctions' within the AFQMC method. This technical improvement allows us to capture the complex behavior of electrons with unprecedented accuracy, particularly in systems where electrons strongly interact, known as strongly correlated solids. In addition, we have developed a deep understanding of the method itself. This will enable the researchers involved to achieve further significant improvements in the coming years, making Vienna the leading location for research into quantum Monte Carlo methods. Calibrating the Future of Materials Science Crucially, we can now routinely apply AFQMC to perform calculations on simple solid-state systems, defects, and surfaces. For these materials, a reliable, highly accurate "gold standard" reference method was essentially non-existent. The ability to run these accurate AFQMC simulations provides a powerful new tool: we can now use our precise AFQMC results to calibrate much cheaper DFT methods, making them more reliable and accurate for broader use. This ability to cross-check and improve existing methods is a major breakthrough. It opens a new realm for reproducible, high-accuracy calculations and promises to revolutionize the computer modeling of materials, especially those with strong electron correlations, paving the way for the discovery of next-generation materials.