Accuate double-hybrid density functional theory and isodesmic-type reaction schemes are utilized to report at estimates esmic-type reaction schemes are utilized to repot estimates of the heats of formation (Delta H-f) for all 24 isolated-pent-rule isomers of the third most abndant fullerene, C-84. Kinetic stabilities ers are also considered via C-C bond cleavage rates (P-cleav) calculated using density functional theory. Our results show that the C-84 fullerene isomers observed in arc discharge synthesis i both thermochemical and kinetic factors. This provides timight regarding the characterization of several C-84 isomers thaeen obtained experimentally to date. For instance, the established assinments of C-84 2g(K) [D-2(IV))] 234 [D-2d(II)], 19 [D-3d], 24 [D-6h], 11 [C-2(IV)], and 4 [D-2d(I)] are consistent with the relative Delta H-f and P-cleav values for these structures. However, our thermochemical and kinetic stabilities of C-s isomers 14, 15, and 16 indicate that the two experimentally isolated C-s isomers are 15 and 16, contrary to some previous assignments. Of the remaining isolated isomers of symmetry C-2 and D(2,)definitive assignment was not possible with consideration of only Delta H and P-cleav.