  The rotational constant parametrizes the relative spacing between a
molecule's rotational energy levels. It depends on the molecule's classical
moments of inertia, which, in all studies, are expressed by treating the
constituent nuclei as point masses separated by the bond length. We point out
that treating the finite nuclear size leads to a correction to the rotational
constant at the Hz level, which is resolvable with recently developed
ultra-high-resolution molecular spectrometers. Nuclear-model-independent
measurements of nuclear matter radii can thus be envisioned in the future using
such apparatuses, advancing beyond the existing hadronic scattering experiments
and further developing the intersection of nuclear and molecular physics. In
the present time, it appears that the computational ability of ab initio
quantum chemistry might be the limiting factor to the technical readiness of
the approach. To test the premises of the proposed method, we call for
benchmark experiments using HD+ that are feasible with state-of-the-art
experiment and theory.
