The use of Density Functional Theory (DFT) has, in many instances, enabled the prediction of materials properties to accuracies of tenths to several hundredths of an electron-volt. However, it is often the case that energetic quantities of interest, such as adsorption and vacancy formation energies, are themselves of this order of magnitude. In such situations, it is desirable to employ many-body electronic structure theories to probe the physics of these systems more accurately and to highlight potential shortcomings of DFT approaches. While Quantum Monte Carlo (QMC) methods such as Diffusion Monte Carlo (DMC) have emerged as effective tools to elucidate surface chemistry at the required levels of accuracy, their computational expense frequently renders them prohibitive for studying these systems. A significant contributor to this computational cost is the need for calculations on progressively large simulation cells (supercells) in order to eliminate many-body finite-size effects and carry out extrapolations to the thermodynamic limit.<br/><br/>In this work, we demonstrate that the process of taking differences between total-energies in DMC calculations of adsorption and vacancy formation energies leads to appreciable cancellation of many-body finite-size errors. By systematically analyzing the extent of this error cancellation in a few representative surface systems, we show that it is often practical to bypass finite-size extrapolations or to carry them out using only a few small supercells. Since this can lead to a several-fold reduction in the number of electrons that need to be simulated, computational gains of an order of magnitude or more can be achieved by appropriately leveraging error cancellation in DMC calculations.

Error cancellation in diffusion Monte Carlo surface calculations

ACS Spring 2022

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