Substitution data set

Let s be any of a number of rigid mass point sets, s = 1, A/, which all have the same (relative) geometry but differ in the mass ma(s) of one or of some of the mass points a=, Na. The points are described by their masses ma(s) and their positions ra with respect to an arbitrary Cartesian reference coordinate system. This ensemble of mass point sets is the model for a number of isotopomers of a molecule, often called the substitution data set (SDS). This SDS is required for the determination of the molecular structure (the relative geometry) by any of the current methods. The total mass M(s) and the position of the center of mass rcm are then given by ... 

If the moments / of more than one species are required to determine the molecular structure, this averaging is no longer feasible. The -structure must then be obtained by direct calculation (or by a least-squares fit, if possible) using a substitution data set composed in a completely balanced manner of complementary sets of isotopomers. The linear XYZ molecule, e.g., is a problem which must be treated in this way. This restructure is still expected to approximate the restructure better than the restructure does. 

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