Linear scaling methods for electronic structure calculations and quantum molecular dynamics simulations

In the past five years, notable advances in the field of electronic structure calculations have been made, by the development of linear scaling methods for total energy calculations and quantum molecular dynamics simulations. These are methods implying a computational workload which grows linearly with the system-size, in contrast to standard algorithms where the workload scales as the cube of the system-size. Therefore the use of linear scaling methods can considerably widen the class of systems and type of problems being tackled with quantum simulations. At present, linear scaling methods using semi-empirical Hamiltonians allow one to perform simulations involving up to a thousand atoms on small workstations, and up to ten thousand atoms for tens of picoseconds when using supercomputers. This has made it possible to study problems such as large organic molecules in water, thin film growth on a surface and extended defects in semiconductors. Although the implementation of first-principles linear scaling methods is less advanced than that of semi-empirical methods, promising results regarding organic molecules and metal-alloys have already appeared in the literature.