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 functional 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 above, 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 concentrate 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.