<p>Accurate double-hybrid density functional theory and isodesmic-type reaction schemes are utilized to report accurate estimates of the heats of formation (Δ_f<i>H</i>) for all 24 isolated-pentagon-rule isomers of the third most abundant fullerene, C₈₄. Kinetic stabilities of these C₈₄ isomers are also considered via C-C bond cleavage rates (<i>P</i>_cleav) calculated using density functional theory. Our results show that the relative abundance of C₈₄ fullerene isomers observed in arc discharge synthesis is the result of both thermochemical and kinetic factors. This provides timely insight regarding the characterization of several C₈₄ isomers that have been obtained experimentally to date. For instance, the established assignments of C₈₄ isomers of (using the Fowler-Manolopoulos numbering scheme) 22 [<i>D</i>₂(IV)], 23 [<i>D</i>_2<i>d</i>(II)], 19 [<i>D</i>_3<i>d</i>], 24 [<i>D</i>_6<i>h</i>], 11 [<i>C</i>₂(IV)], and 4 [<i>D</i>_2<i>d</i>(I)] are consistent with the relative Δ_f<i>H</i> and <i>P</i>_cleav values for these structures. However, our thermochemical and kinetic stabilities of <i>C</i>_<i>s</i> isomers 14, 15, and 16 indicate that the two experimentally isolated <i>C</i>_<i>s</i> isomers are 15 and 16, contrary to some previous assignments. Of the remaining isolated isomers of symmetry <i>C</i>₂ and <i>D</i>₂, definitive assignment was not possible with consideration of only Δ_f<i>H</i> and <i>P</i>_cleav.</p>