Optimized nonorthogonal localized orbitals for linear scaling quantum Monte Carlo calculations

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 $7r_s$, opening the possibility of linear scaling QMC calculations for realistic metallic systems.

Figure 1

(Color online) Comparison of the norm of orthogonal (red, solid lines) and nonorthogonal (black, dashed lines) localized orbitals in (a) bulk silicon and (b) a HEG at the same $r_s$. The error bars show the spread in norm. The insets compare the orthogonal and nonorthogonal localized orbitals. The truncation potential is labeled $\Theta$.

Figure 2

(Color online) Comparison of the truncated norm of orthogonal (red, solid lines, circles), self-consistent, nonorthogonal (black, dashed lines, squares), and fixed radius, nonorthogonal (blue, dotted lines, triangles) localized orbitals in (a) bulk silicon and (b) HEG $(r_s=2)$.

Figure 3

(Color online) (a) Convergence of DMC total energy of bulk silicon with truncation radius for orthogonal and nonorthogonal orbitals. (b) Convergence of DMC total energy of the HEG as a function of $R_{\mathit{cut}}∕r_s$.