General-gradient approximation (PBE) and hybrid Hartree-Fock density functional theories (B3LYP) in conjunction with basis sets of up to polarized triple-zeta quality have been applied to study the Stone-Wales transformation of buckminsterfullerene (BF) to yield a C-60 isomer of C-2v symmetry with two adjacent pentagons (#1809). In agreement with earlier investigations, two different transition states and reaction pathways could be identified for the rearrangement from BF to C-60-C-2v on the C-60 potential energy surface (PES). One has C molecular point group symmetry with the two migrating carbon atoms remaining close to the fullerene surface. The other one has a high-energy carbene-like (sp(3)) structure where a single carbon atom is significantly moved away from the C60 surface. The carbene intermediate and the second transition state along the stepwise reaction path characterized previously at lower levels of theory do not exist as stationary points with the density functionals utilized here. The classical barriers of both mechanisms are essentially identical, 6.9 eV using PBE and 7.3 eV with B3LYP.