Volume 1 Chapter 7 The Geometric Basis of 3D Searching

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7.4 Geometric Objects

In describing 3D molecular structures, it is natural to think in terms of the standard geometrical parameters, viz. bond lengths, valence angles and torsion angles, ie. parameters which are calculated directly from the coordinates of 2, 3 or 4 bonded atoms.

However, in describing the spatial arrangements of more general patterns of atoms, we can extend these descriptors to include general distances, angles and torsions derived from the coordinates of 2, 3 or 4 atoms which may not be bonded.

In these cases, the atom is the key geometric object from which the parameters are calculated.

For many years, structural chemists (and crystallographers in particular) have used many non-standard geometrical parameters to describe specific structural features. Calculation of these parameters often requires the use of geometric objects which are more complex than the individual atom positions.

Examples, illustrated below, are:


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Volume 1 Chapter 7 Composite Geometric Parameters.