O(N) tight-binding molecular dynamics on massively parallel computers: An orbital decomposition approach

The implementation of an O(N) tight-binding molecular dynamics code on the Gray no parallel computer is discussed. The O(N) energy functional depends on non-orthogonal, localised orbitals and a chemical potential parameter which determines the number of electrons in the system. The localisation introduces a sparse nature to the orbital data and Hamiltonian matrix, greatly changing the coding on parallel machines compared to non-localised systems. The data distribution, communication routines and dynamic load-balancing scheme of the program are presented in detail together with the speed and scaling of the code on various homogeneous and inhomogeneous physical systems. Performance results will be presented for systems of 2048 to 32768 atoms on 32 to 512 processors. We discuss the relevance to quantum molecular dynamics simulations with localised orbitals, of techniques used for programming short-range classical molecular dynamics simulations on parallel machines. The absence of global communications and the localised nature of the orbitals makes these algorithms extremely scalable in terms of memory and speed on parallel systems with fast communications. The main aim of this article is to present in detail all the new concepts and programming techniques that localisation of the orbitals introduces which scientists, coming from a background in non-localised quantum molecular dynamics simulations, may be unfamiliar with.