Cross sections and rate coefficient calculations are reported for the Hornbeck-Molnar process in argon: Ar** + Ar(S-1(0)) --> Ar-2(+) e(-) where Ar** is a highly excited (Rydberg) argon atom. The semiclassical description adopted here is based on calculations of potential energy curves of Ar-2(+) taking into account the spin-orbit coupling. This approach brings to light the minor contribution of the atoms for which the core quantum number is j(c) = 1/2 and two possible channels for the reaction. The calculated rate coefficients are presented in the form of fitted expressions of practical interest for modelling studies as a function of the heavy particles temperature TA and the equivalent principal quantum number n* of the Rydberg atom. The results obtained are close to the experimental ones.