Advances in materials science and molecular biology followed rapidly from the ability to characterize atomic structure using single crystals^{1, 2, 3, 4}. Structure determination is more difficult if single crystals are not available⁵. Many complex inorganic materials that are of interest in nanotechnology have no periodic long-range order and so their structures cannot be solved using crystallographic methods⁶. Here we demonstrate that ab initio structure solution of these nanostructured materials is feasible using diffraction data in combination with distance geometry methods. Precise, sub-ångström resolution distance data are experimentally available from the atomic pair distribution function (PDF)^{6, 7}. Current PDF analysis consists of structure refinement from reasonable initial structure guesses^{6, 7} and it is not clear, a priori, that sufficient information exists in the PDF to obtain a unique structural solution. Here we present and validate two algorithms for structure reconstruction from precise unassigned interatomic distances for a range of clusters. We then apply the algorithms to find a unique, ab initio, structural solution for C₆₀ from PDF data alone. This opens the door to sub-ångström resolution structure solution of nanomaterials, even when crystallographic methods fail.

1. Department of Physics and Astronomy,
   
2. Department of Computer Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA

Correspondence to: S. J. L. Billinge¹ Correspondence and requests for materials should be addressed to S.J.L.B. (Email: billinge@pa.msu.edu).