  We investigate the thermodynamic limit and exact surface energy of the
isotropic spin-1 Heisenberg chain with integrable generic open boundary
conditions by a novel Bethe ansatz method. We obtain the homogeneous Bethe
ansatz equations for the zero roots of the transfer matrix. Based on the
patterns of the zero roots, we analytical calculate the densities of zero roots
and the surface energies of the model in all regimes of the boundary
parameters.
