Title: Can we geometrically sense the shape of a molecule?
Abstract: Can we hear the shape of a drum? This question was negatively answered decades ago by many authors including Gordon, Webb, Wolpert, who constructed non-isometric planar shapes that have the identical eigenvalues of the Laplace operator (Bull. AMS, v.27 (1992), p.134-138). The more general question: can we sense the shape of a rigid object such as a cloud of atomic centers representing a molecule?