Using a single-configuration formulation, analytical expressions are derived for the (X (2)Pi(g)) ns sigma(g), np pi(u), and np sigma(u) Rydberg-valence interaction matrix elements in O-2. In addition, new results from diabatic, coupled-channel deperturbations of experimental data dependent on these interactions are reported for n=3 and 4. Using these results, the large differences in magnitude between the Rydberg-valence couplings for the constituent states of the np pi(u) Rydberg complex that are predicted by the analytical expressions are verified experimentally. Effective values for several two-electron integrals are obtained semiempirically through comparison between analytical expressions and deperturbed experimental values for the Rydberg-state energies and Rydberg-valence couplings, allowing predictions to be made for the spectroscopy of the np pi(u) (1)Sigma(u)(-) Rydberg states which have yet to be observed.