  We investigate the free-Fermion point of a boundary sine-Gordon model with
nondiagonal boundary interactions for the ground state using auxiliary
functions, obtained from T-Q equations of a corresponding inhomogeneous open
spin-1/2 XXZ chain with nondiagonal boundary terms. In particular, we obtain
the Casimir energy. Our result for the Casimir energy is shown to agree with
the result from the TBA approach. The analytical result for the effective
central charge in the ultraviolet (UV) limit is also verified from the plots of
effective central charge for intermediate values of volume.
