  Rotational spectroscopy is the most accurate method for determining
structures of molecules in the gas phase. It is often assumed that a rotational
spectrum is a unique "fingerprint" of a molecule. The availability of large
molecular databases and the development of artificial intelligence methods for
spectroscopy makes the testing of this assumption timely. In this paper, we
pose the determination of molecular structures from rotational spectra as an
inverse problem. Within this framework, we adopt a funnel-based approach to
search for molecular twins, which are two or more molecules, which have similar
rotational spectra but distinctly different molecular structures. We
demonstrate that there are twins within standard levels of computational
accuracy by generating rotational constants for many molecules from several
large molecular databases, indicating the inverse problem is ill-posed.
However, some twins can be distinguished by increasing the accuracy of the
theoretical methods or by performing additional experiments.
