The addition of atoms to linear molecules forming linear or nonlinear adducts is treated using standardized valence potentials. The dynamics is analyzed with a combination of classical trajectory (CT) and statistical adiabatic channel (SACM) calculations. For classical adiabatic conditions, the two approaches coincide. The transition from adiabatic to nonadiabatic dynamics is investigated using CT calculations. The low-temperature adiabatic quantum range is studied by SACM. Thermal capture rate constants are represented in analytical form. Thermal rigidity factors are expressed in terms of molecular parameters such as the frequencies of transitional bending modes, the bond dissociation energy, the rotational constant of the linear fragment, and the ratio of the looseness and Morse parameters alpha/beta of the potential-energy surface. The final rate expressions are of simple form suitable for direct practical applications.