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We have developed an extended distance matrix approach to study the moleculargeometric configuration through spectral decomposition. It is shown that thepositions of all atoms in the eigen-space can be specified precisely by theireigen-coordinates, while the refined atomic eigen-subspace projection arrayadopted in our approach is demonstrated to be a competent invariant instructure comparison. Furthermore, a visual eigen-subspace projection function(EPF) is derived to characterize the surrounding configuration of an atomnaturally. A complete set of atomic EPFs constitute an intrinsic representationof molecular conformation, based on which the interatomic EPF distance andintermolecular EPF distance in the eigen-space can be reasonably defined.Exemplified with a few cases, the intermolecular EPF distance shows exceptionalrationality and efficiency in structure recognition and comparison.

Geometrical Eigen-subspace Framework Based Molecular Conformation Representation for Efficient Structure Recognition and Comparison