  Using ab-initio methods for correlated electrons in solids, we investigate
the metal-insulator transition across the Ruddlesden-Popper (RP) series of
iridates and explore the robustness of the J_eff=1/2 state against band effects
due to itineracy, tetragonal distortion, octahedral rotation and Coulomb
interaction. We predict the effects of epitaxial strain on the optical
conductivity, magnetic moments, and J_eff=1/2 ground-state wave functions in
the RP series. To describe the solution of the many-body problem in an
intuitive picture, we introduce a concept of energy-dependent atomic states,
which strongly resemble the atomic J_eff=1/2 states but with coefficients that
are energy/time-dependent. We demonstrate that the deviation from the ideal
J_eff=1/2 state is negligible at short time scales for both single- and
double-layer iridates, while it becomes quite significant for Sr3Ir2O7 at long
times and low energy. Interestingly, Sr2IrO4 is positioned very close to the
SU(2) limit, with only 3% deviation from the ideal J_eff=1/2 situation.
