  In this paper, we study the exact physical quantities in the thermodynamic
limit of the one-dimensional Hubbard model with unparallel boundary magnetic
fields based on the off-diagonal Bethe ansatz solution. At the half-filling, we
obtain the different patterns of Bethe roots of the reduced Bethe ansatz
equations for the different boundary parameters. According to them, we obtain
the densities of states, ground state energy density and surface energy. Our
results show that the system has the stable boundary bound states when the
boundary magnetic fields satisfy some constraints.
