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www.tandfonline.com/doi/abs/10.1080/08893110211936  

Crystallography Reviews

Volume 8, Issue 1, 2002

Investigation of Hydrogen Bond Patterns A Review of MathematicalTools For the Graph Set Approach

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DOI: 

10.1080/08893110211936

Juliana Grella, Joel Bernsteina &  Gottfried Tinhofera 

pages 1-56

Available online: 17 Sep 2010

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In this paper we review a graph-theoretical reformulation of the elements of graph set analysis for describing

hydrogen bond patterns in crystal structures. We first collect a number of mathematical tools which are convenient for

this purpose such as crystal structure graph , H-bond graph , G-labeling , significant labeling , walks , paths and

periodic paths , qualitative descriptors for walks in a labeled graph , graph sets , and show how to use these tools for

graph set analysis. We demonstrate by mathematical reasoning that traditional graph sets, namely selfs, rings, chains

and discretes, are sufficient to describe H-bond patterns completely and we show that qualitative descriptors

characterize graph sets uniquely up to crystallographic equivalence. The second part of the paper is restricted to the

consideration of crystal structures in which all molecules are crystallographically equivalent and in a general position.

For this particular case, it is demonstrated how one can determine algorithmically whether a given descriptor

characterizes a graph set. With the aid of a particular example (the crystal structure of L-alanine) it is shown that the

H-bond graph is determined by the symmetry operations corresponding to the different types of H-bonds observed in

the crystal structure and by a finite set of rings. Further, we conclude that the H-bond graph is a Cayley graph, or may

be found starting with a Cayley graph and replacing edges by multiple edges.

  Download full text Keywords

  Crystal Structure Graph, 

  Hydrogen Bond,   Graph Sets, 

  H-bond Graph, 

  Paths Conditions, 

  Presentation Of Space Groups, 

  L-alanine, 

  Cayley Grap 

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Acta crystallographica Section B Structural crystallography and crystal chemistry(2000)

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Volume: 56 ( Pt 5), Pages: 857-871

  PubMed: 11006562 

Available from  journals.iucr.org 

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 Abstract 

The hydrogen-bond networks and crystal packing of 81 unique secondary di- and polyamides in the Cambridge

Structural Database are investigated. Graph-set analysis, as implemented in the RPluto program, is used to

classify network motifs. These have been rationalized in terms of the relative dispositions of the amide groups.

Peptide and retropeptides exhibit significant conformational flexibility, which permits alternative hydrogen-bonding

patterns. In peptides, dihedral angles of -psi approximately varphi approximately 105 degrees allow an

antiparallel ladder arrangement, containing rings of either the same or alternating sizes. For retropeptides, and

diamides with an odd number of CH(2) spacers, this conformation leads to a parallel ladder with rings of equal

size. If varphi approaches -60 degrees and psi 180 degrees, ladders adopt a helical twist, and if the conformation

is distorted further, a three-dimensional network is usually adopted. Diamides with aromatic or an even number of

CH(2) spacers generally form either antiparallel ladders or sheets, although some exhibit both polymorphs.

Symmetry relationships within and between hydrogen-bonded chains, ladders and sheets in the crystal packing

have also been analysed. Polyamides form considerably more complex networks, although many of the structural

motifs present in the diamides occur as components of these networks.