Massively parallel linear-scaling algorithm in an ab initio local-orbital total-energy method

Similar to the manner of S. Itoh et al. [Comp. Phys. Commun. 88 (1995) 173], we report implementation of a massively parallel linear-scaling algorithm into an ab initio tight-binding method called Fireball [Phys. Rev. B (2001)]. The use of local-orbitals yields a very sparse Hamiltonian matrix which facilitates using a linear-scaling algorithm to obtain the electronic band-structure energy. The general functional form of Kim et al. [Phys. Rev. B 52 (1995) 1640], which minimizes a functional to obtain the electronic band-structure energy, has been parallelized utilizing the conjugate gradient method. The results of this approach are reported here. In addition, the use of “fireball” wavefunctions, where the wavefunctions are explicitly zero beyond some cutoff, allows for pre-generating all integrals describing two- and three-center interactions. The computation of these integrals is then an easily parallelizable problem for which the results are reported. Both integral generation and the linear-scaling optimization procedures are parallelized using the standard MPI message passing interface mixed with an OpenMP strategy.