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