Accurate calculations have been performed for the addition reaction between methane and the second-row transition-metal atoms rhodium and niobium. The most interesting result obtained is that for the rhodium insertion there is nearly no barrier on the low-spin potential energy surface, which contains the MHCH3 complex. A remarkable similarity in reaction energetics between the low-spin state of the rhodium atom (2D) and the recently studied rhodium complexes RhCl(PH3)2 and RhCp(L) (L = CO, PH3) is noted. In particular, CH4-Rh sigma-complexes are formed as precursors in all the reactions, which is of key importance for a low barrier. The electronic mechanism responsible for the low barrier is an efficient mixing between the 4d9- and the 4d8s1-states which are both low-lying states of the rhodium atom. The results for the niobium atom, on the contrary, show a rather high barrier for the insertion with results similar to those of the previously studied nickel atom insertion.