Parametrized density functional and ab initio based methods have been used to study the important model reaction where the C-H bond of methane is activated by transition metal atoms. All atoms from the three transition rows have been investigated. For the third transition row, spin-orbit effects are found to be quite important. These effects were obtained using two different simple schemes. In most cases good agreement between the methods and also with the sparse experimental information is obtained. Only the platinum and rhodium atoms are found to activate the C-H bond and of these only platinum can continue to form a carbene that is required for observing the reaction experimentally. The low barrier for the platinum reaction is a result of a low-energy crossing between different spin surfaces. The trends of the results are analyzed in terms of promotion energies, exchange energies, polarity of the bonds, and in terms of the relative size of the metal d orbitals. The main failure of the ab initio based computational scheme occurring for the nickel reaction is analyzed in detail. (C) 1997 American Institute of Physics.