Two-Dimensional Descriptors Distance Maps and Related Descriptions

Two-Dimensional Descriptors Distance Maps and Related Descriptions 

A radial distribution says nothing about the actual spatial positions of short- and long-distance atomic contacts. A 2D descriptor in the form of a matrix derived from distances is the natural extension. The 2D description of a OD model is a topic thoroughly discussed in the literature. For completeness, a brief review of the key notions is included here. 

Two related matrix descriptors are a distance matrix d and the metric matrix G. i Let us denote with X the matrix containing the Cartesian coordinates for all the nuclei in an -atom molecule (X is a member of the space 

The information contained in the matrix d can be displayed in contact maps. Several alternatives have been proposed with applications in structural analysis and pattern recognition. For instance, the maps can be displayed as contour levels of distance d,y, where the indices i and / (1 i,j n) are the axes of a 2D diagram. 

Usually, the contact maps are displayed in its simplest form, where a point is indicated whenever i and j have a contact. This information can be stored in a family of integer contact matrices (8), defined in terms of a scalar 8. The parameter 8 is the distance cutoff so = 1, if 8 (a contact ) and %i = 0, if dij 8 (no contact). 

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