Angular spectroscopy - rapid visualization of 3-dimensional substructure dissimilarity using valence angle or torsional descriptors

A simple method, termed ''angular spectroscopy'', is developed for the rapid visual assessment of 3D shape diversity (conformations, metal coordination geometries) that is exhibited by a specific chemical substructure as observed in a number of different crystal structures. If there are q = 1 --> N-s instances of the substructure in 3D and each conformation is defined by i = 1 --> N-t torsion angles, then we can calculate a set of dissimilarity coefficients D-pq(n) that relate each of the q instances to some fixed reference conformation p. The Minkowski metric, adapted to take account of permutational isomerism and enantiomorphic inversions, is used to calculate city-block (n = 1) or Euclidean (n = 2) dissimilarities. The N-s values of D-pq(n) provide a unidimensional representation of the multivariate parameter space and can be plotted as a simple histogram. Multiple peaks in the histogram, or torsional spectrum, indicate the presence of multiple conformations in the dataset. Dissimilarity calculations based on valence angle descriptors can be used to assess the different coordination geometries that may exist around; a metal of fixed ligancy. The reduction in dimensionality of the representation, i.e., from N-t to unity, can lead to information loss and to the accidental overlap of peaks due to different conformations. To combat this problem, two simple modifications of the Minkowski metric have been investigated which generate multiplicative (M(pq)(n) and cumulative (C-pq(n)) dissimilarities, respectively. When all three types of coefficient are applied to a variety of example substructures, then the known conformational or configurational diversity in these datasets is clearly revealed. It is found that the multiplicative coefficient, M(pq)(n) is generally effective in minimizing peak overlap.