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Three-Dimensional Pattern Recognition from Molecular Distance Minimization

A procedure optimizing the alignment of two three-dimensional molecules is presented. It uses atomic numbers, positions and radii, and optionally computed atomic charges. Neither bonds nor connectivities are required. The dissimilarity between two molecules is measured with a molecular distance, which is minimized under all rotations and translations with a Newton-like algorithm. This molecular distance is the usual norm of a two-components vector. One of the components is the electronic molecular distance, and the other is the protonic molecular distance. Both the electronic and the protonic component are computed with the same algorithm, which assumes a homogeneous spheres model. The resulting minimized norm is shown to be an intrinsic molecular distance. When a family of more than two compounds is involved, the intrinsic molecular distances matrix of the family is built. Various applications are presented, including comparisons of X-ray crystallographic data compounds, maximal common 3D-substructure se...