M-M bond-stretching energy landscapes for M ₂(dimen) ₄ ²⁺ (M = Rh, Ir; Dimen = 1,8-diisocyanomenthane) complexes

Isomers of Ir ₂(dimen) ₄ ²⁺ (dimen = 1,8-diisocyanomenthane) exhibit different Ir-Ir bond distances in a 2:1 MTHF/EtCN solution (MTHF = 2-methyltetrahydrofuran). Variable-temperature absorption data suggest that the isomer with the shorter Ir-Ir distance is favored at room temperature [K = ∼8; δH° = -0.8 kcal/mol; δS° = 1.44 cal mol ^-1 K ^-1]. We report calculations that shed light on M ₂(dimen) ₄ ²⁺ (M = Rh, Ir) structural differences: (1) metal-metal interaction favors short distances; (2) ligand deformational-strain energy favors long distances; (3) out-of-plane (A _2u) distortion promotes twisting of the ligand backbone at short metal-metal separations. Calculated potential-energy surfaces reveal a double minimum for Ir ₂(dimen) ₄ ²⁺ (∼4.1 Å Ir-Ir with 0° twist angle and ∼3.6 Å Ir-Ir with ±12° twist angle) but not for the rhodium analogue (∼4.5 Å Rh-Rh with no twisting). Because both the ligand strain and A _2u distortional energy are virtually identical for the two complexes, the strength of the metal-metal interaction is the determining factor. On the basis of the magnitude of this interaction, we obtain the following results: (1) a single-minimum (along the Ir-Ir coordinate), harmonic potential-energy surface for the triplet electronic excited state of Ir ₂(dimen) ₄ ²⁺ (R _e,Ir-Ir = 2.87 Å; F _Ir-Ir = 0.99 mdyn Å ^-1); (2) a single-minimum, anharmonic surface for the ground state of Rh ₂(dimen) ₄ ²⁺ (R _e,Rh-Rh = 3.23 Å; F _Rh-Rh = 0.09 mdyn Å ^-1); (3) a double-minimum (along the Ir-Ir coordinate) surface for the ground state of Ir ₂(dimen) ₄ ²⁺ (R _e,Ir-Ir = 3.23 Å; F _Ir-Ir = 0.16 mdyn Å ^-1).