A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: improving reproducibility and reducing the trial-wave-function bias

Fixed node diffusion quantum Monte Carlo (FN-DMC) is an increasingly used computational approach for investigating the electronic structure of molecules, solids, and surfaces with controllable accuracy. It stands out among equally accurate electronic structure approaches for its favorable cubic scaling with system size, which often makes FN-DMC the only computationally affordable high-quality method in large condensed phase systems with more than 100 atoms. In such systems FN-DMC deploys pseudopotentials to substantially improve efficiency. In order to deal with non-local terms of pseudopotentials, the FN-DMC algorithm must use an additional approximation, leading to the so-called localization error. However, the two available approximations, the locality approximation (LA) and the T-move approximation (TM), have certain disadvantages and can make DMC calculations difficult to reproduce. Here we introduce a third approach, called the determinant localization approximation (DLA). DLA eliminates reproducibility issues and systematically provides good quality results and stable simulations that are slightly more efficient than LA and TM. When calculating energy differences -- such as interaction and ionization energies -- DLA is also more accurate than the LA and TM approaches. We believe that DLA paves the way to the automization of FN-DMC and its much easier application in large systems.