The adsorption of H or F species on B vs N atoms on the h-BN (001) surface has been investigated theoretically within the DFT method, using a cluster approach. Only the boron atoms were subjected to a local transformation from hexagonal to cubic phase. It occurred either upon the adsorption of F species or the adsorption of H species. For the latter situation, a neighboring surface B atom was substituted by a C atom and, hence, the number of electrons in the system was increased. The nitrogen atoms did not undergo, with one exception, any phase transformation. The adsorption of H species resulted in a local transformation from sp(2) to sp(3) hybridization with a hereby connected negative adsorption energy (-55 kJ/mol). This adsorption process is therefore highly unlikely to occur in a CVD synthesis.