Carbene stabilization by aryl substituents. Is bigger better?

The geometries and relative stabilities of the singlet and triplet states of phenyl- (C_s), diphenyl-(C₂), 1-naphthyl- (C _s), di(l-naphthyl)- (C₂), and 9-anthryl-substituted (C_s) carbenes were investigated at the B3LYP/6-311+G(d,p) + ZPVE level of density functional theory. The singlet-triplet energy separations (ΔE_ST), 2.7, 2.9, 3.4, 3.7, and 5.7 kcal/mol, respectively, after including an empirical correction (2.8 kcal/ mol) based on the error in the computed singlet-triplet gap for methylene versus experiment, are in good agreement with available experimental values. Consistent with literature reports, triplet di(9-anthryl)carbene has a linear, D_2d symmetrical, allene structure with 1.336 Å C=C bond lengths and considerable biradical character. B3LYP favors such cumulene biradical structures and triplet spin states and predicts a large (>15 kcal/mol) "di(9-anthryl)carbene" singlet-triplet (biradical) energy gap. The resonance stabilization of both singlet and triplet carbenes increases modestly with the size of the arene substituent and overall, (di)arylcarbenes, both singlet and triplet, are better stabilized by bigger substituents. For example, methylene is stabilized more by a naphthyl than a phenyl group (singlets, 26.6 versus 24.4; and triplets, 20.9 versus 18.1 kcal/mol, respectively). The carbene geometries are affected by both steric effects and arene-carbene orbital interactions (σ-p and p-π). For instance, the central angles at the carbene are widened by a second arene group, which leads to increased s-character and shorter carbene bond lengths (i.e., C̈-C, C̈-H). In general, the aromaticity of the substituted rings in triplet carbenes is most affected by the presence of the unpaired electrons.