Workshop report. Linear-Scaling Ab Initio Calculations: Applications and Future Directions

Abstract

The study of properties and of processes in materials, frequently hinges upon understanding phenomena which originate at the atomic level. In such cases the accurate description of the interactions between large numbers of atoms is critical and in turn requires the accurate description of the electrons which play a crucial role in the bonding of atoms into molecules, surfaces and solids. This can only be achieved by solving the equations of quantum mechanics. These equations are too complicated to solve exactly; however their solutions can be approximated by computational techniques. The most accurate ? but also most computationally demanding ? are the “ab initio” techniques which do not use any empirical adjustable parameters. Amongst them, the Density Functional Theory (DFT) formulation of quantum mechanics stands out as an excellent compromise between accuracy and computational efficiency. However, the applicability of ab initio techniques is severely limited by poor scaling: the computational effort needed to perform an ab initio calculation increases with (at least) the third power of the number of atoms, N. This cubic-scaling bottleneck limits the number of atoms we can study to a few hundred at most, even on parallel supercomputers. To overcome this length-scale limitation, a number of researchers worldwide have been pioneering the development of a novel class of ab initio methods with linear-scaling or “Order N” (O(N)) computational cost which nevertheless retain the same high level of accuracy as the conventional approaches. While physically motivated, such methods have proved particularly hard to develop as they introduce highly non-trivial localisation constraints. Nevertheless, many major obstacles have been overcome and a number of O(N) methods (SIESTA, CONQUEST, ONETEP, etc.) for ground state DFT calculations on systems with a gap (e.g. molecules, semiconductors and insulators) are now available and have reached a state of maturity that allows them to be used to study ”real” materials. The particular focus of this workshop is therefore to look forward to what can be achieved in the next few years. Our aim is twofold: (1) As O(N) methods are currently extending the applicability of DFT calculations to problems involving biomolecules and nanostructures they are leading to completely new levels of understanding of these systems. This CECAM meeting will give us the opportunity to make an appraisal of such large-scale simulations and their potential to connect more directly to experiments. (2) We also want to examine the options for extending linear-scaling to problems that cannot be treated by ground-state DFT but require other, more complex approaches. These include methods for treating metallic systems, excited states and wavefunction-based theories for including electronic correlation. Finding ways to transform these methods to linear-scaling cost, and hence extent their applicability to the nano-scale, is the next big challenge that the community of developers of large-scale electronic structure methods is beginning to face. We hope that this workshop will stimulate these major new O(N) methodological developments by bringing together the leading groups in the development of O(N) DFT methods with the leading groups in the development of metal and excited-state or wavefunction-based methods. Strong emphasis during the workshop will be given to discussion in order to promote the exchange of ideas between different communities (Physics, Chemistry, Materials Science, Biochemistry) which are all interested in large-scale applications with ab initio accuracy but are approaching them from different perspectives