The magnetic hyperfine splitting constants, aJ, from theoretical calculations on the 32S, 22P, 32P, and 32D excited states of the Li atom are reported. The wave functions were calculated using the author's GF method, which corresponds to optimizing the orbitals of a Slater determinant after spin projection. Thus the wave functions include core polarization, but no appreciable correlation. For the 22P state we calculate a12=0.2206 a.u. (45.74 Mc/sec for 7Li) which is in good agreement with the experimental value, 0.2227 +/- 0.0017 a.u. (46.17 +/- 0.35 Mc/sec for 7Li), and the value from configuration interaction calculations, 0.2206. Thus for the Li atom core polarization accounts for most of the error in the Hartree-Fock values of aJ. These calculations yield <1r3> and spin density, Q(0), in agreement with other accurate theoretical calculations, and in disagreement with the values found using level crossing experiments, indicating that the interpretation of the level crossing experiments in terms of <1r3> and Q(0) may not be correct. It is found that for both the unrestricted Hartree-Fock and GF methods the use of a different Hamiltonian for each electron leads to virtual orbitals which are good approximations to the actual orbitals of excited states.