Volume 1 Chapter 7 Geometric Objects

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7.5 Composite Geometrical Parameters

In some cases, even this range of geometrical parameters is not adequate to describe the structural characteristics that we seek to compare or use as search terms. It may be that we wish to compare, for example, the geometry of three-membered rings in terms of the mean bond length in the ring, and then to select rings for which this mean lies within certain limits.

The calculation of this mean involves the further transformation of three basic parameters (the ring bond lengths) to generate the desired mean value:

In practice, a variety of parameter transformations have been found useful: sums, means, differences, absolute values, trigonometric functions of angles, etc. All of these transformations can encapsulate 3D structural knowledge in a form that is often more useful than the individual parameters from which they are derived.

The transformation of parameters is also illustrated by the morphine example:

SETUP  X1  7  8  9  10  11  12
SETUP  P1  7  8  9  10  11  12
SETUP  P2  1  2  3  4  5  6
DEFINE  NANG  1  6  5
DEFINE  N - C1  1  6
DEFINE  N - C2  5  6
DEFINE  DIST  X1  6
DEFINE  ?ANG  P1  P2
TRANSFORM  ?SIN = SIN  ?ANG
TRANSFORM  PANG = ASIN  ?SIN

The initial calculation of the interplanar angle ?ANG between P1 and P2 may result in an angle of x degrees in one fragment, but in a value close to its supplement (180-x) degrees in another. This is a result of the fact that we cannot prescribe the vector direction of the plane normals.

If we wish to calculate a systematic value for inter-fragment comparison and searching, then we might choose to obtain the acute value in all cases. This can be done by:

By convention the symbol ? indicates that the defined parameter is to be considered as an intermediate parameter.


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Volume 1 Chapter 7 Numerical Limits for the 3D Search.