Molecular least-squares superposition

Molecular structures may be described and compared in terms of external or internal coordinates. The question of which is to be preferred depends on the type of problem that is to be solved. For example, one problem that is much easier to solve in a Cartesian system is that of finding the principal inertial axes of a molecule indeed, if only internal coordinates are given then, in general, the first step is to convert them to Cartesian ones and then proceed as described in Section 1.2.4. Similarly, the optimal superposition of two or more similar molecules or molecular fragments, i.e. with the condition of least-squared sums of distances between all pairs of corresponding atoms, is best done in a Cartesian system. On the other hand, systematic trends in a collection of molecular structures and correlations among their structural parameters are more readily detectable in internal coordinates. 

In this chapter only QSAR methods which use physicochemical or structural features of molecules will be discussed, while in Chapter 25 3D-QSAR approaches will be presented. These so-called 3D-QSAR techniques, e.g. CoMFA, use the basic statistical principles, such as partial least squares (PLS), of QSAR methods, but in addition use the three-dimensional characteristics of a molecule specifically related to electronic, steric and lipophilic field effects. In these methods the molecular superposition believed relevant to binding to the target is crucial. 

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