First-principle electronic structure calculations have proven to be a very powerful and accurate tool for investigating the properties of matter at microscopic scales, where they extend or complement the domain of experiments. Their strength comes from the precision and predictive power that is inherent in a parameter-free quantum-mechanical approach, from the fine level of detail of the spatial and temporal description they provide at the atomic level, and from the recent expansion in the availability of powerful computational resources. However, the time needed to solve a given system using conventional implementations of these methods is proportional to the third power of the number of atoms, thus preventing the extension of this otherwise extremely successful approach to a great many systems of interest. This limitation is algorithmic in nature; the physics and its associated complexity inherently scale linearly with the number of atoms. The project will implement and test a new algorithm which holds the promise of providing a computational scheme of comparable accuracy, but which scales only linearly with system size. This scheme is built implicitly on the physical localization of the one-particle density matrix. This same localizational property makes such an algorithm highly appropriate for implementation on a massively parallel computer architecture.
