  We study the thermodynamic limit of the anisotropic XYZ spin chain with
non-diagonal integrable open boundary conditions. Although the $U(1)$-symmetry
is broken, by using the new parametrization scheme, we exactly obtain the
surface energy and the excitation energy of the system, which has solved the
difficulty in the inhomogeneous $T-Q$ relation. With the boundary parameters in
the regions making the Hamiltonian Hermitian, we have obtained the distribution
patterns of the zero roots of the eigenvalue of the transfer matrix for the
ground state and the excited ones. We find that the surface and excitation
energies depend on the parities of sites number $N$, due to the long-range Neel
order in the bulk. The spontaneous magnetization and easy-axis for all the
regions of boundary parameters are studied. We also obtain the physical
quantities in the thermodynamic limit of boundary XXZ model by taking the
triangular limit.
