  Ruddelsden-Popper halide perovskites are highly versatile
quasi-two-dimensional energy materials with a wide range of tunable
optoelectronic properties. Here we use the all-inorganic
Cs$_{n+1}$Pb$_n$X$_{3n+1}$ Ruddelsden-Popper perovskites with X=I, Br, and Cl
to systematically model the effect of octahedral tilting distortions on the
energy landscape, band gaps, macroscopic polarization, and the emergence of
Rashba-/Dresselhaus splitting in these materials. We construct all unique $n=1$
and $n=2$ structures following from octahedral tilts and use first-principles
density functional theory to calculate total energies, polarizations and band
structures, backed up by band gap calculations using the $GW$ approach. Our
results provide design rules for tailoring structural distortions and
band-structure properties in all-inorganic Ruddelsden-Popper perovskites
through the interplay of the amplitude, direction, and chemical character of
the antiferrodistortive distortion modes contributing to each octahedral tilt
pattern. Our work emphasizes that, in contrast to 3D perovskites, polar
structures may arise from a combination of octahedral tilts, and
Rashba-/Dresselhaus splitting in this class of materials is determined by the
direction and Pb-I orbital contribution of the polar distortion mode.
