Local spin and charge densities on a two-dimensional honeycomb lattice are calculated by the Landauer-Keldysh formalism (LKF). Through the empirical tight-binding method, we show how the realistic band structure can be brought into the LKF. Taking the Bi(111) surface, on which strong surface states and Rashba spin-orbit coupling are present [Phys. Rev. Lett. 93, 046403 (2004)], as a numeric example, we show typical intrinsic spin-Hall accumulation (ISHA) patterns thereon. The Fermi-energy-dependence of the spin and charge transport in two-terminal nanostructure samples is subsequently analyzed. By changing EF, we show that the ISHA pattern is nearly isotropic (free-electron-like) only when EF is close to the band bottom, and is sensitive/insensitive to EF for the low/high bias regime with such EF. With EF far from the band bottom, band structure effects thus enter the ISHA patterns and the transport direction becomes significant.