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 Schrödinger equations describing the
interaction of the fluorine and chlorine (in the 2P state) and oxygen and sulfur (in the 3P 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.