The first-order post-adiabatic representations in the sense of Klar and Fano (Klar, H.; Fano, U. Phys. Rev. Lett. 1976, 37, 1132-1134) are obtained for two-channel stationary Schrodinger equations describing the interaction of the fluorine and chlorine (in the P-2 state) and oxygen and sulfur (in the P-3 state) atoms with a number of closed-shell particles, in particular, with rare gases, hydrogen, deuterium, and methane. Information on the adiabatic potentials and the nonadiabatic coupling comes mostly from scattering experiments, although some input from ab initio quantum mechanical calculations is also exploited. Various trends in the behavior of the first-order post-adiabatic coupling are analyzed, and the optimal ways to estimate the smallness of this coupling are discussed. The best measure of the strength of the post-adiabatic coupling of order s is found to be the differences between the respective post-adiabatic potentials of orders s and s + 1. A rigorous proof is given of the fact that post-adiabatic representations exist only in the important case of a single "slow" degree of freedom.