Linear scaling algorithm of real-space density functional theory of electrons with correlated overlapping domains

The real-space grid based implementation of the Kohn-Sham density functional theory of electrons using the finite difference method for derivatives of variables, has attractive features of parallelizability and applicability to various boundary conditions in addition to universality in target materials. Following the divide-and-conquer strategy, we propose a linear scaling algorithm of it by advancing the algorithm in [F. Shimojo et al., Comput. Phys. Comm. 167 (2005) 151]. In the Kohn-Sham-type equation for a domain, we introduce (i) the density-template potential for density continuity with simple stepwise weight functions and (ii) the embedding potential to take into account all the quantum correlation effects with other overlapping domains in addition to the classical effects of ionic and electronic Coulomb potentials. We thereby realize reasonably high accuracies in atomic forces with relatively small numbers of buffer ions irrespective of the electronic characters of materials. The timing tests on parallel machines demonstrate the linear scaling of the code with little communication time between the domains.