  To explain recent experiment showing the role of odd fullerenes in formation
of abundant fullerene isomers a reactive molecular dynamics (MD) study has been
performed. Three types of bond rearrangement reactions are found by MD
simulations at 3000 K in odd fullerenes which contain an extra sp atom among
all other sp$^2$ atoms. The first type is sto-chastic sp-defect migration
analogous to exchange mechanism of adatom migration on a surface. The second
type cor-responds to changes in the ring configuration of the sp$^2$-structure
assisted by the sp atom which can lead to annealing of seven-membered rings or
separation of five-membered rings. The third type is formation of short-living
one-coordinated atoms or two additional sp atoms. Annihilation of a pair of sp
defects has been also observed in the MD simulations. It is shown that the
frequency of sp-defect migration at a lower temperature, as estimated from
performed density functional theory calculations of the barriers of sp-defect
migration events, is sufficient to deliver the sp atom to defects of sp$^2$
structure during the fullerene formation time. Based on these results, we
propose to supplement the self-organization paradigm of fullerene formation by
the following four-stage atomistic mechanism of formation of abundant isomers
of fullerenes: 1) attachment of single carbon atoms, 2) sp-defect migration to
sp$^2$-structure defects, 3) sp$^2$-defect annealing assisted by the sp atom
and 4) subsequent annihilation of pairs of sp defects.
