Abstract

Multidimensional scaling (MDS) is a collection of data analytic techniques for constructing configurations of points from information about interpoint distances. Such constructions arise in computational chemistry when one endeavors to infer the conformation (3dimensional structure) of a molecule from information about its interatomic distances. For a number of reasons, this application of MDS poses computational challenges not encountered in more traditional applications. In this report we sketch the mathematical formulation of MDS for molecular conformation problems and describe two approaches that can be employed for their solution. 1 Molecular Conformation Consider a molecule with n atoms. We can represent its conformation, or 3-dimensional structure, by specifying the coordinates of each atom with respect to a Euclidean coordinate system for ! 3 . We store these coordinates in an n \Theta 3 configuration matrix X. Given X, we can easily compute the matrix of interatomic distan...

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