Linear-scaling first-principles molecular dynamics with plane-waves accuracy

We propose a real-space finite differences approach for accurate and unbiased $\mathrm{O}\left(N\right)$ density functional theory molecular dynamics simulations based on a localized orbitals representation of the electronic structure. The discretization error can be reduced systematically by adapting the mesh spacing, while the orbitals truncation error decreases exponentially with the radius of the localization regions. For regions large enough, energy conservation in microcanonical simulations is demonstrated for liquid water. We propose an explanation for the energy drift observed for smaller regions.

Figure 1

Discretization error on the forces for the finite differences “Mehrstellen” and the plane-wave approaches for $({\mathrm{H}}_2\mathrm{O}{)}_{32}$ (average and maximum over sample). The reference values are the result of a fully converged PW calculation $\left(400\mathrm{Ry}\right)$.

Figure 2

Total energy and ALC displacements during molecular dynamics simulation of water (512 molecules) at $300\mathrm{K}$ with localization radius of $9\mathrm{Bohr}$.

Figure 3

Contour plot of one localized obitals for two ground-state local minima for polyacetylene in the plane of the molecule (MD snapshot at $300\mathrm{K}$, $R_c=11\mathrm{Bohr}$). The right picture corresponds to a state lower in energy by $0.00089\mathrm{Ha}$.

Figure 4

Wall clock time as a function of system size (liquid water) for 1 SC step with $R_c=10\mathrm{Bohr}$, for two different ratios of No. molecules/CPU (weak scaling). The numbers next to the data points indicate the number of processors used.

Figure 5

Total CPU time comparison between the cost of one iterative step in our $\mathrm{O}\left(N\right)$ approach (values from previous plot) and a preconditioned steepest descent step in the PW approach (35 CPUs/64 molecules for PW).