  Highly accurate results from frequency measurements on neutral hydrogen
molecules H_2, HD and D_2 as well as the HD^+ ion can be interpreted in terms
of constraints on possible fifth-force interactions. Where the hydrogen atom is
a probe for yet unknown lepton-hadron interactions, and the helium atom is
sensitive for lepton-lepton interactions, molecules open the domain to search
for additional long-range hadron-hadron forces. First principles calculations
in the framework of quantum electrodynamics have now advanced to the level that
hydrogen molecules and hydrogen molecular ions have become calculable systems,
making them a search-ground for fifth forces. Following a phenomenological
treatment of unknown hadron-hadron interactions written in terms of a Yukawa
potential of the form V_5(r)=\beta exp(-r/\lambda)/r current precision
measurements on hydrogenic molecules yield a constraint \beta < 1 \times
10^{-7} eV\AA for long-range hadron-hadron interactions at typical force ranges
commensurate with separations of a chemical bond, i.e. \lambda ~1 \AA and
beyond.
