  We examine effects of encapsulated metal atoms inside a C$_{60}$ molecule on
the activation energy barrier to the Stone-Wales transformation using {\it ab
initio} calculations. The encapsulated metal atoms we study are K, Ca and La
which nominally donate one, two and three electrons to the C$_{60}$ cage,
respectively. We find that isomerization of the endohedral metallofullerene via
the Stone-Wales transformation can occur more easily than that of the empty
fullerene owing to the charge transfer. When K, Ca and La atoms are
encapsulated inside the fullerene, the activation energy barriers are lowered
by 0.30, 0.55 and 0.80 eV, respectively compared with that of the empty
C$_{60}$ (7.16 eV). The lower activation energy barrier of the Stone-Wales
transformation implies the higher probability of isomerization and coalescence
of metallofullerenes, which require a series of Stone-Wales transformations.
