  We have performed first principles study for bismuth crystal structure at
pressure from 0~14 GPa based on structure search and quasi-harmonic
approximation. A new stable phase with Pbcm symmetry is predicted by structure
search method. We find that the most stable structures of bismuth at 0 K are
R-3m(0 ~ 3.29 GPa), Pbcm (3.29 GPa ~ 4.91 GPa), Cmce (4.91 GPa ~ 10.57 GPa) and
Im-3m ( > 10.57 GPa), respectively. By quasi-harmonic approximation, we
predicted the phase diagram of bismuth from first principles calculations. We
found that the phase transition pressure reduces with increasing temperature.
Our calculation agrees with the trend of experimental phase diagram. The P4/ncc
model structure for the incommensurate Bi-III phase is not a stable phase in
our calculation. A better model for the Bi-III phase is still needed. We also
note that the spin-orbital interaction is very important for phase-diagram
simulation of bismuth. By using first principle based structure search method,
we successfully determine the low temperature high pressure phase diagram of
bismuth, showing that the structure search method can effectively find the most
stable structure of given material at high pressure even with high Z elements.
