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A Linear Scaling Ab Initio Electronic Structure Technique for Nanotechnology

D.R.Bowler* and M.J.Gillan

Department of Physics and Astronomy, University College London

This is an abstract for a presentation given at the
Seventh Foresight Conference on Molecular Nanotechnology.
Additional material, a full version of the paper, and more information on the CONQUEST technique can be found at


Over the last fifteen years, accurate, ab initio electronic structure calculations and nanotechnology have been converging towards a common scale in terms of system sizes which can be addressed: electronic structure from below, and nanotechnology from above. The advantage of using electronic structure calculations in conjunction with experiments is that they allow details of the system which are not accessible to experiment to be found; increasingly, calculations are being used predictively. Ab initio techniques have the dual advantages of giving details of the electronic structure, and of good transferability - a quality typically missing from more empirical schemes.

However, there is a bottleneck associated with traditional methods: the scaling of computational effort and memory with the number of atoms. These scale with the square of the number of atoms, and the effort scales asymptotically with the cube of the number of atoms. This means both that there is an effective limit of a few hundred atoms (even on the most powerful computers), and that increases in computing power are not used efficiently.

In recent years, there has been a tremendous amount of effort in development of techniques which scale linearly with the number of atoms: these are often called O(N) techniques. They all rely on the locality of bonding within condensed matter to achieve this. Our technique, CONQUEST, has been designed from the beginning to work on massively parallel platforms, as a result of which we hope to report ab initio calculations on up to 50,000 atoms (one to two orders of magnitude higher than previously possible) soon. With this many atoms, a reasonable sized biological molecule or an area of semiconductor surface of side length between 25 and 40 nm (sufficient for modelling self-assembled quantum dots) could be addressed.

*Corresponding Address:
David Bowler
Dept. of Physics and Astronomy, University College London
Gower Street, London WC1E 6BT UK
Phone: +44 171 419 3500; Fax: +44 171 391 1360
Email:; Web:


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