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A new multi-dimensional search approach, incorporating packing criteria with R-factor calculations for low-resolution X-ray data, proved to be extremely efficient for the solution of large molecular structures. A computer program, ULTIMA, based on this approach solved ab initio the structure of a double-helical DNA octamer and also reproduced the correct solutions of a double-helical DNA dodecamer and of a tRNA molecule (322, 486 and 1652 non-hydrogen atoms, respectively). The efficiency of the procedure is enhanced by using group scatterers in lieu of individual atoms. The method allows, for more complex structures, the separation of parameters in the multi-dimensional space, either by using one-dimensional reflection data or by approximating the entire molecule to a 'super-atom' scatterer.

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