  The extended carrier lifetime in hybrid halide perovskites was attributed to
a quasi-indirect band gap that arises due to Rashba splitting in both
conduction and valence band edges. In this paper, we present results for an
effective relativistic band structure of (CH3NH3)PbI3 with the focus on the
dispersion of electronic states near the band edges of (CH3NH3)PbI3 affected by
thermal structural fluctuations. We establish a relation between the magnitude
of Rashba splitting and a deviation of Pb-atom from its centrosymmetric site
position in the PbI6 octahedron. For the splitting energy to reach the thermal
energy kT~26 meV (room temperature), the displacement should be of the order
0.3 Ang, which is far above the static displacements of Pb-atoms in the
tetragonal phase of (CH3NH3)PbI3. The significant dynamic enhancement of the
Rashba splitting observed at earlier simulation times (less than 2 ps) later
weakens and becomes less than the thermal energy despite the average
displacement of Pb-atoms remaining large (0.37 Ang). It is randomization of
Pb-displacement vectors and associated cancelation of the net effective
magnetic field acting on electrons at the conduction band edge is responsible
for reduction of the Rashba splitting. The lattice dynamics also leads to
deterioration of Bloch character for states in the valence band leading to
subsequent localization of holes, which affects bipolar mobility of charge
carriers in (CH3NH3)PbI3. These results call into question the quasi-indirect
band gap as a reason for the long carrier lifetime observed in (CH3NH3)PbI3 at
room temperature. An alternative mechanism involves dynamic localization of
holes and their reduced overlap with electrons in reciprocal space.
