Geometric properties of nucleic acids with potential for autobuilding

Algorithms and geometrical properties are described for the automated building of nucleic acids in experimental electron density.

Ab initio reconstruction of difference densities by charge flipping

The charge-flipping algorithm in its `band-flipping' variant is used to reconstruct density difference between a superstructure and average structure from superstructure reflections only. This technique can be used for the structure solution of superstructures, some types of twins and intergrowths of polytypes as well as for the solution of modulated structures and superstructures of quasicrystals.

Practical applications of averages and differences of Friedel opposites

The practical use of Friedel-difference intensities for space-group determination, least-squares refinement and structure validation is described.

Coincidence lattices in the hyperbolic plane

Expressions for coincidence indices and bases for coincidence lattices in the hyperbolic plane are obtained using Clifford algebra.

Generation of (3 + d)-dimensional superspace groups for describing the symmetry of modulated crystalline structures

A complete table of (3 + 1)D, (3 + 2)D and (3 + 3)D superspace groups has been enumerated that corrects omissions and duplicate entries in previous tables of superspace groups and Bravais classes. A new online data repository provides detailed information about each superspace group.

PVMR: assembling small helix fragments as structural solutions for molecular replacement

A new real-space implementation of the molecular-replacement method is described, in which the search model vectors are directly matched with the Patterson self and cross vectors. This method enables the searching for small helix fragments in the target crystal and is able to produce fragment-assembled solutions that are structurally homologous to the target structure.

Patterson-function direct methods for structure determination of organic compounds from powder diffraction data. XVI

A new type of direct methods are presented that directly explore the Patterson instead of the modulus function. Since they work with the experimental intensities, they are particularly well suited for handling powder diffraction data of organic compounds.

Euclidian embeddings of periodic nets: definition of a topologically induced complete set of geometric descriptors for crystal structures

Given the topology, the lattice together with the set of distance vectors from each atom to the centre of gravity of its neighbours determine the geometry of a crystal structure. A special construction provides the lattice type.

Isomorphism of lattices of subgroups of the layer and rod groups with sublattices of subgroups of the space groups

It is shown that lattices of subgroups of reducible space groups contain copies of lattices of subgroups of layer and rod groups as sublattices.

On the allowed values for the triclinic unit-cell angles

The possible range of angles for a triclinic unit cell are explored in detail.

Report of the Executive Committee for 2009

Notes for authors 2011