A Parallel Implementation of Tight-binding Molecular Dynamics based on Reordering of Atoms and the Lanczos Eigen-solver

Abstract

We introduce an efficient and scalable parallel implementation of tight-binding molecular dynamics (TBMD) which employs reordering of the atoms in order to maximize data- locality of the distributed tight-binding (TB) Hamiltonian matrix. Reordering of the atom labels allows our new algorithm to scale well on parallel machines since most of the TB hopping integrals for a given atom are local to the processing element (PE) therefore minimizing communication. The sparse storage format and the distribution of the required eigenvectors reduces memory requirements per PE. The sparse storage format and a stabilized parallel Lanczos eigen-solver allow consideration of large problem sizes relevant to materials science. In addition, the implementation allows the calculation of the full spectrum of individual eigen-values/-vectors of the TB matrix at each time-step. This feature is a key issue when the dielectric and optical response must be computed during a TBMD simulation. We present a benchmark of our code and an analysis of the overall efficiency.