  e have calculated the spin-orbit (SO) splitting $\Delta_{SO}=\epsilon
(\Gamma_{8v}) - \epsilon (\Gamma_{7v})$ for all diamond-like group IV and
zinc-blende group III-V, II-VI, and I-VII semiconductors using the full
potential linearized augmented plane wave method within the local density
approximation. The SO coupling is included using the second variation
procedure, including the $p_{1/2}$ local orbitals. The calculated SO splittings
are in very good agreement with available experimental data. The corrections
due to the inclusion of the $p_{1/2}$ local orbital are negligible for lighter
atoms, but can be as large as $\sim$250 meV for 6$p$ anions. We find that (i)
the SO splittings increase monotonically when anion atomic number increases;
(ii) the SO splittings increase with the cation atomic number when the compound
is more covalent such as in most III-V compounds; (iii) the SO splittings
decrease with the cation atomic number when the compound is more ionic, such as
in II-VI and the III-nitride compounds; (iv) the common-anion rule, which
states that the variation of $\Delta_{SO}$ is small for common-anion systems,
is usually obeyed, especially for ionic systems, but can break down if the
compounds contain second-row elements such as BSb;(v) for IB-VII compounds, the
$\Delta_{SO}$ is small and in many cases negative and it does not follow the
rules discussed above. These trends are explained in terms of atomic SO
splitting, volume deformation-induced charge renormalization, and cation-anion
$p$--$d$ couplings.
