Letters to Nature

Nature 400, 644-647 (12 August 1999) | doi:10.1038/23210; Received 18 May 1999; Accepted 28 June 1999

Systematic enumeration of crystalline networks

Olaf Delgado Friedrichs1, Andreas W. M. Dress1,2, Daniel H. Huson3, Jacek Klinowski4 & Alan L. Mackay5

  1. FSP Mathematisierung-Strukturbildungsprozesse, Universitt Bielefeld, D-33501 Bielefeld, Germany
  2. Department of Chemical Engineering, City College, CUNY, Convent Avenue at 140th Street, New York, New York 10031, USA
  3. Department of Mathematics, Princeton University, Princeton, New Jersey 08544-1000, USA
  4. Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
  5. Department of Crystallography, Birkbeck College (University of London), Malet Street, London WC1E 7HX, UK

Correspondence to: Jacek Klinowski4 Correspondence and requests for materials should be addressed to J.K. (e-mail: Email: jk18@cam.ac.uk).

The systematic enumeration of all possible networks of atoms ininorganic structures is of considerable interest. Of particular importance are the 4-connected networks (those in which each atom is connected to exactly four neighbours), which are relevant to a wide range of systems — crystalline elements, hydrates, covalently bonded crystals, silicates and many synthetic compounds. Systematic enumeration is especially desirable in the study of zeolites and related materials, of which there are now 121 recognized structural types1, with several new types being identified every year. But as the number of possible 4-connected three-dimensional networks is infinite, and as there exists no systematic procedure for their derivation, the prediction of new structural types has hitherto relied on empirical methods (see, for example, refs 2–4). Here we report a partial solution to this problem, basedon recent advances in mathematical tiling theory5, 6, 7, 8. We establish that there are exactly 9, 117 and 926 topological types of, respectively, 4-connected uninodal, binodal and trinodal networks, derived from simple tilings based on tetrahedra. (Here nodality refers to the number of topologically distinct vertices from which the network is composed.) We also show that there are at least 145 more distinct uninodal networks based on a more complex tiling unit. Of the total number of networks that we have derived, only two contain neither three- nor four-membered rings, and most of the binodal and trinodal networks are new.