  A large-scale configuration-interaction (CI) calculation is reported for the
hyperfine splitting of the 2^2S and 3^2S states of ^7Li and ^9Be^+. The CI
calculation based on the Dirac-Coulomb-Breit Hamiltonian is supplemented with a
separate treatment of the QED, nuclear-size, nuclear-magnetization
distribution, and recoil corrections. The nonrelativistic limit of the CI
results is in excellent agreement with variational calculations. The
theoretical values obtained for the hyperfine splitting are complete to the
relative order of \alpha^2 and improve upon results of previous studies.
