  Accurate ro-vibrational energies, eigenfunctions, radial densities,
expectation values are presented for the exponential-type Manning-Rosen (MR)
potential. Bound states accurate up to ten significant figure are obtained by
employing a simple, reliable generalized pseudospectral method. \emph{All} 55
eigenstates with $n \leq 10$ are treated for arbitrary values of potential
parameters, covering a wide range of interaction, through a \emph{non-uniform,
optimal} spatial radial discretization. A detailed investigation has been made
on energy changes with respect to \emph{screening and other} potential
parameters. A systematic estimation of \emph{critical} screening parameters are
given for these eigenstates. Special emphasis has been given to \emph{higher}
states and in the vicinity of \emph{critical screening} region. A thorough
comparison with literature results is made wherever possible. This
\emph{surpasses} the accuracy of \emph{all} other existing methods currently
available. Several \emph{new} states are reported for the first time. In short,
a simple, efficient scheme for accurate calculation of this and other molecular
potentials is offered.
