Optimized Non-Orthogonal Localized Orbitals for Linear Scaling Quantum Monte Carlo calculations

Habiburrahman Zulfikri, C. Amovilli, Claudia Filippi

Arne Lüchow, Sebastian Manten

Fernando Agustín Reboredo, Andrew Williamson

We derive an automatic procedure for generating a set of highly localized, non-orthogonal orbitals for linear scaling quantum Monte Carlo calculations. We demonstrate the advantage of these orbitals in calculations of the total energy of both semiconducting and metallic systems by studying bulk silicon and the homogeneous electron gas. For silicon, the improved localization of these orbitals reduces the computational time by a factor five and the memory by a factor of six compared to localized, orthogonal orbitals. For jellium, we demonstrate that the total energy is converged for orbitals truncated within spheres with radii 7-8 $r_s$, opening the possibility of linear scaling QMC calculations for realistic metallic systems.

Fernando Agustín Reboredo, Andrew Williamson

We derive an automatic procedure for generating a set of highly localized, nonorthogonal orbitals for linear scaling quantum Monte Carlo (QMC) calculations. We demonstrate the advantage of these orbitals for calculating the total energy of both semiconducting and metallic systems by studying bulk silicon and the homogeneous electron gas. For silicon, the improved localization of these orbitals reduces the computational time by a factor of 5 and the memory by a factor of 6 compared to localized, orthogonal orbitals. For jellium at typical metallic densities, we demonstrate that the total energy is converged to 3 meV per electron for orbitals truncated within spheres with radii $7{r}_{s}$, opening the possibility of linear scaling QMC calculations for realistic metallic systems.

Eduardo Alberto Castro

Dario Alfè, Michael J. Gillan

We have reformulated the quantum Monte Carlo (QMC) technique so that a large part of the calculation scales linearly with the number of atoms. The reformulation is related to a recent alternative proposal for achieving linear-scaling QMC, based on maximally localized Wannier orbitals (MLWO), but has the advantage of greater simplicity. The technique we propose draws on methods recently developed for linear-scaling density functional theory. We report tests of the new technique on the insulator MgO, and show that its linear-scaling performance is somewhat better than that achieved by the MLWO approach. Implications for the application of QMC to large complex systems are pointed out.