  Spin-orbit splitting of surface states is analyzed within and beyond the
Rashba model using as examples the (111) surfaces of noble metals, Ag2Bi
surface alloy, and topological insulator Bi2Se3. The ab initio analysis of
relativistic velocity proves the Rashba model to be fundamentally inapplicable
to real crystals. The splitting is found to be primarily due to a spin-orbit
induced in-plane modification of the wave function, namely to its effect on the
nonrelativistic Hamiltonian. The usual Rashba splitting -- given by charge
distribution asymmetry -- is an order of magnitude smaller.
