Electronic-structure calculations for the self-association of phenalenyl radical (P-center dot) predict the formation of dimeric species (sigma-P-2) in which both moieties are connected by a sigma-bond with r(P-P) similar to 1.59 angstrom and bond dissociation enthalpy of Delta H-D similar to 16 kcal mol(-1). Such an unusually weak sigma-bond is related to the loss of aromatic stabilization energy of similar to 34 kcal mol(-1) per phenalenyl moiety, largely owing to rehybridization. Ab initio calculations also reveal that the corresponding (one-electron) bond between phenalenyl radical and its closed-shell cation in sigma-P-2(+center dot) is unstable relative to dissociation. Time-dependent DFT computations indicate the absence of any (strongly allowed) electronic transition in the visible region of the absorption spectrum of phenalenyl sigma-dimer. Such theoretical predictions are supported by experimental (ESR and UV-NIR) spectroscopic studies, in which the availability of a series of sterically hindered phenalenyl radicals allows definitive separations of the sigma-dimerization process from interference by pi-dimerization. As such, the thermodynamic parameters (determined from the temperature dependence of the ESR signals) with Delta H-D = 14 kcal mol(-1) and Delta S-D = 52 e.u. can be assigned to the formation of the colorless sigma-dimer. Similar results are obtained for all phenalenyl derivatives (provided their substitution patterns allow a-bond formation) to confirm the energetic preference of sigma-dimerization over pi-dimerization.