  The hydrogen molecule can be used for determination of physical constants and
for improved tests of the hypothetical long range force between hadrons, which
requires a sufficiently accurate knowledge of the molecular levels. For this
reason, we have undertaken a project of significant improvements in theoretical
predictions of H$_2$ and perform the first step, which is the solution of the
nonrelativistic Schr\"odinger equation to the unprecedented accuracy of
$10^{-12}$. This will inspire, we hope, a parallel progress in the spectroscopy
of the molecular hydrogen.
